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Modelling and control of neuromuscular blockade Gilhuly, Terence J. 2007

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Modelling and Control of Neuromuscular Blockade  Terence J. Gilhuly B.A.Sc, The University of Waterloo, 1995 M.A.Sc, The University of British Columbia, 1998  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in T H E FACULTY OF GRADUATE STUDIES (Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA July 2007 © Terence J. Gilhuly, 2007  Abstract Standard administration of neuromuscular blockade drugs is in the form of large doses when required. This administration results in repeated overdosing, and creates problems for the surgery and for the patient, including loss of fine control and inability to intervene intra-operatively, and increased recovery time, curarization and reduced function post-operatively. By application of modelling and control to NMB, the problems of standard administration could be remedied by controlling and adjusting the dosing to the patient's needs. Prior work has had some success but with limitations: controllers were conservative; setpoints tended towards irreversibility; computer control was instituted after induction; monitoring with single twitch required delays at the start to tune the sensor; the systems were not tested in blinded, randomized, controlled, clinical trials. The goals of this thesis were to produce a system overcoming the mentioned limitations, and to prove its efficacy in a prospective, blinded, randomized, controlled, clinical trial. Many novelties were enacted, including: • Monitoring techniques for improved modeling and sensing • Inter-conversion of neuromuscular stimuli protocols • Description of NMB through relaxation and pseudo-occupancy • Linearization of the neuromuscular junction • Modelling techniques for nonlinear systems in noisy environments • Model adaptation schemes • Simulation of intrapatient variance The result was an adaptive control computer program, the Neuromuscular Blockade Advisory System (NMBAS). The NMB AS suggests rocuronium dosage and administration time based on a patient model and the history of the patient's response, to avoid the problems associated with conventional NMB drug administration. The NMBAS was compared to standard care in a prospective, randomized, controlled, clinical trial (N — 60). The NMBAS group experienced fewer peri-operative adverse events, and had reduced danger of inadequate reversal. Drug use and the incidence of postoperative adverse events were not different. Other items investigated included: using body mass index (BMI) to reduce overparalysis; stimulation current according to patient weight and BMI; and intrapatient variance due to anesthetic, blood loss and tissue loss.  ii  Contents Abstract  ii  Table of Contents  iii  List of Tables  vi  List of Figures  vii  Acronyms and Shortforms  ix  Symbols  xi  Acknowledgements  xiii  1 Introduction and Overview 1.1 Neuromuscular Blocking Agents 1.1.1 Rocuronium in Humans 1.2 Physiological Monitoring 1.3 Problems with Serial Overdosing 1.4 Past Effort in Control for Medical Applications 1.4.1 Bang-bang Control 1.4.2 Proportional-Integral-Derivative Control 1.4.3 Fuzzy Logic 1.4.4 Predictive Control 1.4.5 Adaptive Control 1.4.6 Control using ST and/or T l monitoring '. 1.5 Modelling and Identification in Pharmacological Applications 1.5.1 Pharmacokinetic Modeling 1.5.2 Pharmacodynamic Modeling Target Controlled Infusion 1.6 Variability as a Difficulty for Control 1.6.1 Drug Interactions 1.6.2 Age Related Differences 1.6.3 Health Related Differences 1.7 Summary and Contributions 1.7.1 Contributions 1.8 Research Ethics  iii  1 2 2 3 6 8 8 8 10 10 10 11 11 13 14 15 16 17 17 18 18 19 21  2  Neuromuscular Monitoring and Modelling  22  2.1  22 23 24 26 30 32 33 37 38 38 39 41 42 44 44 44  2.2 2.3 2.4 2.5  2.6  2.7 3  Controller Development, Simulation and Testing  46  3.1  46 47 52 53 54 56 59 63 63 63 66 67 68 69  3.2 3.3 3.4 3.5 3.6 3.7  3.8 4  Initial Data Collection Experiments for Model Building 2.1.1 Results of the Initial Data Collection The Enhanced-To4 and Relaxation Response Nonlinearities and Pseudo-occupancy Nonlinear Modelling Model Identification 2.5.1 Laguerre models Stability and Robustness of Laguerre Models and Controller . . . . 2.5.2 Model Structure Selection Optimal Model Structure Selection and Parameter Variation . . . . 2.5.3 Comments on the Initial Model Building Results Conversion of Standard Stimuli to To4 2.6.1 P T C to To4 2.6.2 DBS to To4 2.6.3 Interconversion of non-To4 Measurements Summary of Neuromuscular Monitoring and Modelling Controller Development 3.1.1 PID Controller Design and Tuning 3.1.2 The Laguerre Controller Preliminary Details of the Simulations Controller Testing eTo4 Testing in Simulation N M J Margin of Safety Testing in Simulation P T C Testing Model Adaptation 3.7.1 Model Swapping 3.7.2 Model Adaptation Through Recursive Estimation 3.7.3 Stability 3.7.4 Model Swapping Results in Simulation Summary of Controller Development, Simulation and Testing  Closed-Loop Control  71  4.1 4.2  71 74 77 78 79 80 83 85 86 88 89 90 90  4.3  Equipment Development In Vivo Controller Testing and Selection 4.2.1 Continued Testing of the Laguerre Controller 4.2.2 Comments on the In Vivo Testing 4.2.3 Optimizing the Forgetting Factor and Horizon Investigation of Modelling for Instability Investigation of the Horizon for Instability Model Size Verification 4.2.4 Handling Oscillation Simulating Intra-patient Variance 4.3.1 Inhalational Anesthetics 4.3.2 Irreversible Antagonists: a-Bungarotoxin 4.3.3 Reversible Antagonists: Pancuronium iv  4.4 4.5 5  -  Advisory Control and Human Clinical Studies  5.1 5.2  5.3  5.4 5.5  5.6 5.7 5.8  5.9 6  Rabbits versus Humans Summary of Closed-loop Control  The NMBAS in Detail 5.1.1 Prediction of Levels of Response and Doses Prostate Brachytherapy Patient Study 5.2.1 Prostate Brachytherapy Patient Study Methods 5.2.2 Prostate Brachytherapy Patient Study Results . 5.2.3 Observations from the Prostate Brachytherapy Patient Study The NMBAS Full Clinical Trial 5.3.1 Methods 5.3.2 Results Primary Outcome Secondary Outcomes 5.3.3 Discussion of the NMBAS Clinical Trial Results 5.3.4 Adverse Events 5.3.5 Noncompliance by Anesthesiologist with the NMBAS 5.3.6 Problems Encountered in the Clinical Study Pilot Study of the NMBAS for Infusions 5.4.1 Modelset Development Rocuronium Dosing by BMI 5.5.1 BMI Dosing Methods 5.5.2 BMI Dosing Results 5.5.3 Discussion of Dosing By BMI Stimulation Current by BMI Clinical Validation of the eTo4 Intrapatient variance seen in the NMBAS trial 5.8.1 Intrapatient Variance due to Anesthetic 5.8.2 Intrapatient Variance due to Blood Loss 5.8.3 Intrapatient Variance due to Tissue Loss Summary of Advisory Control and Human Clinical Studies  92 92 93  93 95 96 96 98 102 105 105 107 109 110 113 116 119 120 123 125 126 127 128 128 129 130 130 130 132 133 134  Conclusions and Overall Discussion  136  6.1  138  Future Directions  Bibliography  139  Appendices  146  A Animal Care and Ethics Committee Certificates of Approval  146  B  International Union of Pharmacology ( I U P H A R ) 2002 Conference Abstract . 149  C I E E E Engineering in Medicine and Biology Society 2005 Conference Paper . . 150 D  Canadian Anesthesiologist's Society 2006 Meeting Abstract  v  155  List of Tables 1.1 1.2 1.3  Representative control efforts for automated drug delivery Pharmacokinetic parameters of rocuronium for various patient groups Time of onset, maximum block and clinical duration of rocuronium with varied anesthesia and patient populations  12 17  25  2.3 2.4  T1/T0 vs. To4 measurements The relationship between NMB measurements, their physical manifestation and corresponding relaxation and pseudo-occupancy measures Comparison of the optimal model structures Stages in a typical procedure and stimulation used  29 39 42  3.1 3.2 3.3  Controller performance in simulation testing Results from testing bounds on acceptability of data for RLSE procedure Results of threshold simulation testing  55 58 60  5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10  Quantization of NMB error. Patient demographics for the standard care and NMBAS groups Time course of operations in the NMBAS clinical trial Clinical event incidence in the NMBAS clinical trial Intra-operative NMB-related drug use in the NMBAS clinical trial Intra-operative drug use in the NMBAS clinical trial Intra-operative anesthetic use in the NMBAS clinical trial Changes in the modelset throughout the NMBAS clinical trials Comparison of dosing by weight and BMI in the NMBAS clinical trial Patient demographics for the 70m^4 and other neuromuscular stimulation current groups in the NMBAS clinical trial  2.1 2.2  vi  18  107 109 109 110 110 Ill 112 126 128 129  List of Figures 1.1 1.2 1.3 1.4  Chemical formulae for pancuronium and rocuronium Ulnar nerve and innervated muscle anatomy. Commercially available stimulation techniques The pharmacokinetic multi-compartmental model  2 4 5 13  2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10  Relationship between blood concentration of a drug and response over time Relationship between NMB agent and response through a typical procedure Measurements and modeled results from the rabbit studies Estimated rocuronium responses for the human procedures Discrete time linear Laguerre model Discrete time nonlinear Laguerre model Laguerre modelling for a rocuronium impulse response Bode plots for the rabbit models Bode plot of the rabbit data Bode plot of the human data  26 29 32 32 34 35 36 39 40 40  3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18  Average model step response for the Ziegler-Nichols Step Response method Ziegler-Nichols Step Response method for average, low and high responding models. A block diagram for a plant with relay feedback Ziegler-Nichols Closed-Loop method for PID controller design Ziegler-Nichols Closed-Loop method for average, low and high responding models. . Anesthesiologist, PID and Laguerre control simulation results for a high responder. . Anesthesiologist, PID and Laguerre control simulation results for a low responder. . Simulated results when data included for RLSE are —0.5 < y < maxEffect Simulated results when data included for RLSE are —0.5 < y < 1. Simulation results for a low responder with NMJ margin of safety of 70% Simulation results for a low responder with NMJ margin of safety of 50.1% Simulation results for a high responder with NMJ margin of safety of 70% Simulation results for a high responder with NMJ margin of safety of 50.1% The modelling procedure with subgroups The modelling procedure viewed schematically Stability analysis of the remodelling procedure Simulation results for a low responder without model swapping Simulation results for a high responder without model swapping  47 49 50 50 51 56 57 58 59 61 61 62 62 65 67 68 69 70  4.1 4.2 4.3  Block diagram of the closed-loop control experimental setup Accelerometer assembly for control experiments Computer interfaced neuromuscular stimulator  72 72 73  vii  4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23  Experimental setup for closed-loop control experiments Accelerometry measurement with To4 stimulus Anesthesiologist, PID and Laguerre linear control in vivo comparison Closed-loop control with Laguerre linear controller on a rabbit Closed-loop control with Laguerre linear controller on a rabbit, part 2 Closed-loop control with Laguerre linear controller on a second rabbit Closed-loop control with Laguerre linear controller on a second rabbit, part 2 Closed-loop control with improvements Closed-loop control with instability Adaptation covariance matrix trace values under varied E F R A parameters Laguerre C under varied E F R A parameters Control inputs under varied E F R A parameters Control of NMB with 3 constraint, adaptive forgetting and a varying horizon between six and twenty timesteps Control of NMB with 3 constraint, adaptive forgetting and a varying horizon between six and ten timesteps Error and model parameters for various model sizes in infusion testing Closed-loop control with Smith prediction Application of disturbance rejection in closed-loop control Pancuronium impulse response measured immediately after recovery from rocuronium.  73 74 76 77 78 79 80 81 82 83 84 85  Block diagram of the NMBAS Connection of the NMT module to the patient for the mechanosensor Connection of the NMT module to the patient for the E M G sensor The NMBAS user interface Measured E M G response and modeled drug response for a low responder in the prostate brachytherapy patient study Measured E M G response 'and modeled drug response for a high responder in the prostate brachytherapy patient study Early prediction efforts in the prostate brachytherapy patient study. Prediction at the end of the prostate brachytherapy patient study Representative cases for the standard care and NMBAS treatments Inhalational anesthetic and rocuronium use to demonstrate normal usage of anesthetic and intervals for M A C mean calculations Case study of H57, a control group patient with adverse events Case study of H17, a control group patient with adverse events Case study of H29, a control group patient with adverse events Case study of H57, an NMBAS group patient with adverse events Case study of H32, an NMBAS group patient with adverse events. Case study of H23 demonstrating noncompliance. NMBAS infusion testing: output vs. setpoint, model parameters and drug input. . Modelset progression throughout the human clinical trials Time to return to 0.1 relaxation vs. eTo4 Case study of patient for testing intra-patient variance due to anesthetic Post-hoc analysis of H47 for anesthetic effect Response, modelling, anesthetic use and input for H51 A case study of intrapatient variance due to tissue loss  94 97 98 99  viii  86 87 87 88 89 91  100 101 102 103 108 112 117 118 119 120 121 122 . 125 126 131 132 133 134 135  Acronyms and Shortforms AC  Adaptive control  ACh  Acetylcholine  AChR  Acetylcholine receptor  ADC  Analog to digital converter / conversion  AIC  Akaike's informative theoretic criterion  Approx  Approximate  ARX  Auto-regressive exogenous  AUC  Area under the curve  Ave  average  BMI  Body mass index  BP  Blood pressure  BSA  Basal surface area  BSO  Bilateral salpingo-oophrectomy  CABG  Coronary artery bypass graft  DB, DBS  Double burst stimulation  ECG  Electrocardiogram  ECx  Effective concentration in X% of subjects  EDx  Effective dose in X% of subjects  EFRA  Exponential forgetting and resetting algorithm  Est  Estimate  eTo4  Enhanced train-of-four  FPE  Final prediction error  GPC  Generalized predictive control  HR  Heart rate  ICU  Intensive care unit  IEEE  Institute of Electronic and Electrical Engineers  Iso  Isoflurane  IV  Intra-venous  L B M , L B W Lean body mass; lean body weight LSE  Least squares estimation  MAC  Minimum alveolar concentration  MAP  Mean arterial (blood) pressure  ix  MAPE MCI MIS MPE MRT MSE NLE NMB NMBAS NMJ NMT OR PAR PC PD PK PORC PRBS PTB PTC RLSE RMS Roc SNP ST TAH TO Tl T4 TCI To4  Median absolute performance error Manually controlled infusion Minimally invasive surgical/surgery Median performance error Mean residence time Mean square(d) error Nonlinear estimation Neuromuscular blockade Neuromuscular blockade advisory system Neuromuscular junction Neuromuscular transmission / transmitter Operating room Post-anesthesia recovery (room) Predictive control Pharmacodynamic Pharmacokinetic Post-operative residual curarization Pseudo-random binary signal Post-tetanic burst Post-tetanic count Recursive least squares estimation Root mean square Rocuronium Sodium nitroprusside Single twitch Total abdominal hysterectomy Control (baseline) value for T l and ST measurements First twitch of the To4 magnitude, either the raw measurement value or magnitude in comparison to the value of the control (baseline) twitch, depending on context Fourth twitch of the To4 Target controlled infusion Train of four  x  Symbols a (3 e 7 A ii 7r r a A b B c(t) C C d D ECx EDx H I IR k K K Kss K L P Pjv x  c  u  E F R A gain E F R A tuning parameters; extended horizon controller equation denominator and input modifier Small amount E F R A tuning parameters; Hill slope coefficient E F R A forgetting factor Average P K disposition constant for the first compartment Time interval; timestep Laguerre pole; P K disposition constant for the second compartment P K parameter for second compartment volume; state space matrix P K disposition constant for the third compartment P K parameter for third compartment volume; state space input gains vector Concentration of drug at time t , State space state gains vector Concentration of drug in compartment x Number of timesteps in horizon for extended horizon controller Matrix of gains for nonlinear terms in nonlinear Laguerre controller Effective concentration in X% of subjects Effective dose in X% of subjects Unmodelled dynamics model Identity matrix, first person pronoun (unused as this is a technical report) Impulse response P K constant for mass transfer Controller model Gain for PID control law Process static gain Ultimate gain Laguerre state vector P K parameter for first compartment volume; plant model Nominal plant model  xi  Td Ti T u v Vd Vx y UN ysp u  Derivative time constant for PID control law Integrative time constant for PID control law Ultimate period Input P K volume of distribution scaling constant Volume of distribution Volume of distribution for compartment X Output Output from the nominal plant Output setpoint  xii  Acknowledgements "The service of others is the highest act." - Kurosawa Sensei What you are holding is the product of more than five years of research for myself, and many more for others contributing to the field. This Herculean task (or Sisyphean, depending upon your outlook) was aided by the following people and to the following degree: Alex Bouzane donated his research time to data collection in the OR and chart searching for the NMBAS clinical trial; Simon Hutchings provided surgical expertise; Christian Caritey helped in various repairs and the odd project, and allowed use of his beloved machine shop; Lui "Chicilino" Franciosi talked me into this; Mitrul Isbacescu entered data from the initial experiments; Jason Chiang wrote the initial pump driver software; Dennis Bhui made a serial port interface to the PI Dual Stim DX Peripheral Nerve Stimulator; Andrew Pursell made the initial software user interface to the same; Christopher Guppy soldered the accelerometers; Simon DiMaio helped with LaTex for the proposal; Sunny Chan helped in the initial experiments; Bernard MacLeod supervised the clinical aspects of the project and provided insight into the processes of anesthesia, doctors and clinical trials; Guy "in the end it doesn't matter how much money you make, its how much fun you have" Dumont supervised the electrical engineering and control side; Stephan Schwarz assisted with the trial at St. Paul's Hospital; anesthetists, nurses and hospital staff of St. Paul's Hospital and B C Cancer provided interest, enthusiasm, accommodation and patience; anonymous subjects of the trials participated in the scientific process and made this project possible; my esteemed reviewers reviewed - I sincerely hope that it was an enjoyable task as "what is written with effort can be read with pleasure", to rephrase Samuel Johnson; and James Gilhuly, my father, provided some final editing, proofreading and instruction on grammar. On a more administrative level, this work was supported by the Jean Hugill-Templeton Chair in Anaesthesia Research Fund, the research fund of the Department of Anesthesiology, St. Paul's Hospital, Vancouver, B C , Canada and the National Sciences and Engineering Research Council Discovery Grant, "Tools for Advanced Process Control". Special thanks to those fine organizations. Last, not least, and hopefully neither too typically nor too seemingly obligatory, very special thanks and love a ma famille for all their hypo- and hypertensive effects, and possible inspiration, being highly nonlinear and variable in their own right. You've made it clear that some things do not need to be under control. Thanks to all. As repayment, I hope that if you should need it this research will be of benefit to you and society as a whole.  xiii  Chapter 1  Introduction and Overview This work is an exploration of the application of process modelling and control techniques to the administration of drugs and in particular, to the administration of neuromuscular blocking agents. The hypothesis of this work was that by using these techniques, patient care is improved. The objective of this work was to test that hypothesis in a clinical setting. Computer controlled - or automatic - drug delivery is the process of administering a therapeutic regime to a patient with the assistance of some form of numerical processing. The patient may be under chronic or acute care, in an operating room or ambulatory care setting. While drug therapy is relatively successful when done manually, there are many reasons why computer control can improve drug therapy. Computer control could reduce drug usage and costs, permit the health care staff to work more efficiently and provide better standard of care, and allow the safe use of drugs that are difficult to administer. Computer control allows delivery of drug to match the dose to the patient's need. The drugs can be given when needed in the dose required, and not in a blanketing or prophylactic fashion. Furthermore, humans are prone to error and non-compliance with drug protocol. In the operating room (OR), anesthesiologists cannot continuously concentrate on one particular measurement as they have many other duties and distractions. They must rely on experience, intuition and sometimes guesswork to determine how the patient is progressing. In contrast, computers perform many tasks simultaneously, repetitively and with little chance of error. The computer can regularly and consistently monitor the patient, and rapidly perform calculations to determine objectively how therapy is progressing. Thus, computer control serves to increase the accuracy of drug delivery, extending the ability of the person determining the drug, therapy. In the study of Cosgrove [1], computerizing intensive care units (ICUs) improved the performance of the ICU nurses. The nurses were relieved of mundane tasks, and allowed more time for care giving, taking measurements and filling out patient charts. In computerized ICUs with auto-arrhythmia detection, the number of arrhythmias detected increased 37% while non-computerized ICUs had three times more arrhythmia related deaths and a 50% higher mortality rate. Similarly, computers can extend the abilities of the anesthesiologist by freeing them from routine monitoring and thereby allow them to work on more difficult cases. Computer control of drug therapy can increase the therapeutic window of drugs used through the tighter control provided. Tighter control permits improved use of many drugs for current indications, extended application of useful drugs to new therapeutic situations, and may convert compounds not currently used because of short durations and difficult manual control into valuable therapeutic agents.  1  1.1  Neuromuscular Blocking Agents  Neuromuscular blocking drugs produce paralysis. Paralysis permits surgeons to make smaller incisions, provides access to deep structures otherwise hindered by unconscious muscle action and allows intubation of the trachea. Occasionally patients require paralysis to permit effective controlled ventilation. Neuromuscular blocking drugs prevent muscle function by interfering with the post-synaptic action of the neurotransmitter, acetylcholine (ACh). One of two mechanisms is used: persistent depolarization or non-depolarizing competitive inhibition at the endplate channel receptors on the muscle cell in the neuromuscular junction (NMJ). A third mechanism of action is to block the release of ACh, but drugs with this capability are not used clinically (Rang [2]). Neuromuscular blocking drugs were chosen as the starting point for our work in automated drug delivery because of the absence of toxicity, other than that associated with its desired effect, paralysis. In toxicity testing, rocuronium (a commonly used neuromuscular blocker and the drug of this research) produced no appreciable local or systemic effect at doses almost three orders of magnitude above the effective dose for 90% of the population (EDgo) (Organon [3]). Provided that respiratory equipment is available, the patient is intubated (or in the process of being intubated) to permit continued respiration despite diaphragm paralysis and constant monitoring occurs, these are very safe drugs. 1.1.1  Rocuronium in Humans  The neuromuscular blocking agent used for this work is rocuronium. Rocuronium was selected as it is the most commonly used neuromuscular drug and the drug used at the hospitals involved in the studies. A faster acting drug - one with shorter overall duration of action, such as mivacurium would have been easier to control as an infusion. However, administration and monitoring of faster drugs requires more effort and attention on the part of the anesthesiologist, at least when given as bolii. 0  O  H ROCURONIUM  PANCURONIUM  Figure 1.1: C H E M I C A L F O R M U L A E FOR T H E NEUROMUSCULAR BLOCKING DRUGS PANCURONIUM ( L E F T ) AND ROCURONIUM (RIGHT).  Rocuronium is administered as rocuronium bromide, C^H^BrNzOi (Organon [3]). Rocuronium is a non-depolarizing neuromuscular blocking drug, achieving its effect through competitive inhibition of nicotinic ACh receptors. Rocuronium's chemical formula is shown with pancuronium's, 2  another neuromuscular blocking drug with similar mechanisms of action but longer duration, in Figure 1.1. Pancuronium will be further discussed in Section 4.3. Compared to other neuromuscular blockers, rocuronium has a rapid to intermediate onset depending on dose administered and has intermediate duration (Organon [3]). Time of onset is between one to two minutes. Clinical duration is between thirty and sixty minutes. After a single bolus administration, rocuronium displays a concentration time course with three exponential phases. Normal adults have a mean elimination half-life of 73 ± 7 minutes, a volume of distribution of 203 ± 10.5mL • kg* (14.2 ± 0.7L for a 70kg person), and a plasma clearance of 3.7 ± 0.2mL • kg* • min (Organon [3]). Protein binding is 25% (Atherton [4]). Clearance is reduced in the geriatric, and those with hepatic and renal failure. In ICU patients without multiple organ failure, volume of distribution was increased causing the elimination half-life and mean residence time to increase. In those with multiple organ failure, clearance decreased and the half-life, volume of distribution and mean residence time increased (Organon [3]). The manufacturer's recommended intubation dose for a healthy adult and the bolus dose for human clinical trials is 0.6mg/kg (2 x EDg$) (Atherton [4]). This allows for intubation within one minute and surgical paralysis in two. Clinical duration of this bolus is between thirty and forty minutes, with a total duration (time until return of 90% To4) of approximately fifty minutes. Recovery from 25% to 75% To4 takes approximately fourteen minutes. Recovery is increased when using inhalational anesthetics, e.g. isoflurane, by approximately twenty minutes, as rocuronium is potentiated by inhalational anesthetics. Excretion is primarily through the urine. Half of the drug is excreted in the parent form and half excreted as metabolite. Metabolites are inactive. The few complications associated with rocuronium are due to its effect on blood pressure and histamine release, and its interaction with inhalational anesthetics. Three percent of patients have some change in blood pressure and heart rate and those experiencing histamine release can also have histamine mediated complications such as asthma and bronchospasm, and extended neuromuscular blockade (NMB). 1  1  1.2  -1  Physiological Monitoring  In advising on and control of administration of drugs it is essential to know how the patient is reacting to the treatment in order to correctly titrate to effect. To determine how the patient is reacting, sensors are used. For measurement of neuromuscular response a neurostimulator is used to stimulate a nerve to evoke contraction of the muscle innervated by that nerve. The muscle's contraction can then be measured and quantified by electromyographic response, force, acceleration, deflection or another means. The nerve stimulated in the human clinical studies of this work was the ulnar nerve, whose stimulation produces contraction in the adductor pollicis muscle of the hand. The ulnar nerve runs on the medial inferior side of the arm from its origin in the brachial plexus nerves C8 and T l to its termination in the skin and muscles of the hand, including the adductor pollicis which is located at the base of the thumb. The relative locations of the nerve and muscle are shown in a drawing of the anatomy of the human arm in Figure 1.2. Placement of electrodes on the patient is as shown in Figures 5.2 and 5.3 of Chapter 5. Different stimulation patterns are available to the anesthesiologist via the commercially produced stimulators. These patterns include train-of-four (To4), double burst (DBS), tetanus and single twitch (ST) stimulation. These techniques are described in this section and are represented in Figure 1.3.  3  flexor dtgitorum prvfandus.  Adductor pollicis  •Palmahs brews .  Abductor. "Flexor  ^  ^'5rdc4th tumbricals Palmare dorsal mterossei Figure 1.2: THE  THE  ulnar  N E R V E A N D MUSCLES INNERVATED B Y IT ( A D A P T E D F R O M H A Y M A K E R  ulnar N E R V E R U N S T H E L E N G T H O F T H E M E D I A L A S P E C T O F T H E F O R E A R M .  M U S C L E O F C O N C E R N F O R THIS R E S E A R C H ,  adductor pollicis,  [5]).  T H E MAIN  IS A T T H E B A S E O F T H E T H U M B .  The most commonly used neuromuscular sensing modality is the To4. The To4 is used because of its clinical utility; because known values predict clinically significant markers such as ability to move and to breath spontaneously, and when reversal agents (drugs reversing the blockade) will be effective; and because of its comparative performance against the other stimulus modalities. The To4 is composed of four brief (between 100 and 300^s) current pulses (maximum of 70m^4) at 2Hz, repeated every 10 to 20s as electro-stimulation. Contractions produced by the first (Tl) and last (T4) pulses are compared and their ratio (specifically, To4 = T4/T1) provides an estimate of the level of neuromuscular blockade. As neuromuscular blockade increases, the twitches decrease in magnitude relative to their time of occurrence, i.e. later twitches decrease faster than earlier twitches. This leads to a decrease in the ratio with progressive blockade. When the last twitch is unreadable compared to the background noise, the To4 ratio is considered to be zero. Four pulses are used and not five as during partial non-depolarized block the fourth response exhibits maximal depression. Prior pulses show progressive decay from the first, and subsequent 4  ST To4 Tetanus PTC DBS Figure 1.3: PICTORIAL REPRESENTATION OF C O M M E R C I A L L Y AVAILABLE STIMULATION T E C H NIQUES WITH VERTICAL LINES INDICATING STRENGTH M E A S U R E D . F R O M L E F T : SINGLE T W I T C H , TRAIN-OF-FOUR, TETANUS, POST-TETANIC COUNT AND DOUBLE BURST STIMULATION. INITIAL STIMULATION IS UNDER F U L L STRENGTH CONDITIONS; FOLLOWING STIMULI A R E AT REDUCED S T R E N G T H . O N L Y ONE STIMULATION MEASUREMENT IS PRESENTED FOR T H E P T C .  pulses either level off or increase. Stimulation is at 2Hz because 1Hz is the maximum frequency at which muscle responds to multiple stimuli with individual peaks and it is the frequency at which the maximum decline between the first and fourth peaks is obtainable. Stimuli series are spaced by ten or more seconds (generally 20s is used to provide a margin of safety) to provide a rest period for full restoration of steady state conditions. Faster stimulation results in smaller evoked responses (Lee [6]). Being a ratio, the To4 has no need of a pre-recorded control value for comparison, and it has immunity to changing baseline measurements (Ali [7]). To4 is the recommended stimulus for use in onset, normal block, judging reversibility and recovery conditions. However, because of lack of response, To4 is not used for intense blockade. The ST stimulation consists of a single electrical pulse between ten and 70m^4 and duration of between 100 and 300/zs, repeated at intervals greater than or equal to one second. At least four seconds are needed between stimuli to prevent upregulation and alteration of the true muscle response. The ST is a ratio of the response evoked by the single electrical pulse to the response generated when the stimulation regime is first started. This later response is thecontrol response, labeled TO. To be specific, ST = TcurrentlTb.  Although the ST can provide data more frequently than the To4, the data provided is not as reliable. The ST does not account for changing conditions as its control measurement TO is taken before the case starts. After TO is taken, pH and temperature levels may change, and many drugs having an effect on the neuromuscular response may be given, all of which impact NMB sensing. As an example of the fragility of the measurement, twitch strength is decreased 6% for each degree Celsius drop in the temperature of the muscle being monitored (Kervin [8]). Furthermore, the ST measurement is more susceptible to noise than the To4 as it has no internal control twitch for comparison to under the current surgical and patient circumstances. The lack of a contemporary control twitch results in noisy signals and signals with electrocautery artifacts that must be accepted at face value, and cannot so easily be rejected as can To4 measurements for which the measurements do not fall into the pattern of decreasing magnitude from first to last. Lastly, a major limitation of the clinical utility of the ST measurement is its requirement for thirty minutes or so of stimulation prior to NMB drug administration, in order to stabilize and provide an unbiased control measurement (Stadler [9]). Tetanic stimulation is used in deep blockade as a means of evoking a large burst of ACh in order to overwhelm temporarily the N M B . It is a five second long 50 or 100Hz stimulation. The  5  degree of blockade can be qualified according to how the muscle can sustain a response throughout the stimulation. Tetanus is very uncomfortable and can only be repeated once every five or more minutes without influencing the measurement. Post-tetanic count (PTC) is a more quantified measurement used under similar circumstances. It consists of a tetanus at 50Hz for five seconds followed by a three second resting period and then a chain of up to thirty ST impulses at 1Hz. The number of impulses that can be measured inversely related to the degree of blockade. Tetanic and P T C stimulation release a great deal of ACh and thereby have the disadvantage of requiring time until the stimulation can again be considered normal. For example, mean (and measured range) recovery times for ST stimulation after 50 and 100Hz tetanus are 34 (3 to 60s) and 58s (13 to 104s), respectively. For To4 stimulation, these values are 34 (15 to 74) and 64s (23 to 104) (Brull [10], Saitoh [11]). Post-tetanic burst (PTB) is a method of stimulation similar to P T C . The difference is that bursts of three pulses at 50Hz are substituted for the train of ST pulses of P T C . Again the measurement is judged by successful muscle twitches. P T B was introduced in Saitoh [12] and further tested in Saitoh [13]. In a test using vecuronium O.lmg • kg , P T B return more quickly than P T C but without statistic significance. The mean time from administration to return was 23.7 ± 7.9 minutes for P T B and 30.7±7.0 minutes for P T C . Despite demonstrated advantage, to the author's knowledge, P T B is not provided as a stimulation option in commercial neurostimulators. The double-burst stimulation (DBS) technique is a mix of the P T C and To4 measurements. The patient is stimulated with two brief pulses (the "bursts") of 50Hz tetanic-like stimuli which are compared in a ratio to see effect. Although there is some variation in the time between pulses and the number of twitches inside each burst, the standard DBS consists of two trains of three pulses at 50Hz, spaced by 750ms. DBS is comparable in recovery to To4 and has some use in deep block. A problem for control of NMB is the infrequency of data due to the long time intervals between stimulation. As mentioned, these intervals exist because consecutive stimulations affect one another when the time between the stimuli is not long enough. Should the stimuli be too close together, upregulation can occur in the short term for some types of stimuli (such as trains of stimuli greater than four pulses at 2Hz). For longer term over-stimulation, as with tetani administered continuously and as with closely spaced ST trains longer than eight or so, there can be a reduction of the immediately available stores of ACh, resulting in a decrease in ACh released, and thereby a decrease in muscle contractility. Thus, each type of stimulation has a frequency response. The following amount of time is generally accepted as being required for separation (non-influence of the next stimulation) for the various commonly used stimuli: ST, between three and 4s; To4, 12.5s; DBS, 10s; and tetanus or P T C , between thirty and 60s (Ali [7]). Comparing the commonly available stimulation methods, To4 is less sensitive than tetanus, but more sensitive than DBS and ST. DBS can be used in normal block and judging reversibility, but To4 is superior. Tetanus has some use in onset, normal block and deep block conditions. P T C and P T B are best at, and should only be used for, deep block conditions due to their lack of information at other times and their limitations in frequency of application (Torda [14]). -1  1.3  Problems with Serial Overdosing  As NMB drugs have high therapeutic indices in hospital settings, they are often used in excess of minimal effective requirements. A strategy for administration is to provide an overdose to prolong paralysis, monitor for returning muscle function and, overdose again once it returns. A standard  6  technique is to provide a bolus and then 33% of the initial bolus when required (MacLeod [15]). The large dose delivers a rapid onset of paralysis, quick arrival at excellent surgical conditions, and avoids the need for titrating to a precise anesthetic dose (Miller [16]). This approach of giving large doses when required is a repeated overdosing that creates problems for the surgery and for the patient. These problems include loss of fine control (large oscillations in the measured response) during the procedure; increased recovery time, curarization and reduced function post-operatively; and inability to intervene (remove the paralysis) should surgical conditions change. The elimination of fine control due to the oscillatory on/off rough control associated with serial bolus dosing can be dangerous. Patient movement during neurologic procedures can lead to hemorrhage and stroke because of unintended patient contact with surgical tools. Injury can also result from patient movement during opthalmologic procedures, where blindness and debilitation can result. Patient bucking can also cause the contents of the eye to be forced out. Deep and even NMB aids neuorosurgery and opthalmological surgeries by preventing small motions that could be critical to the outcome of the surgery. Deep and even NMB allows the surgeons to concentrate better on their tasks. Increased recovery time due to too much NMB drug present at a crucial juncture in the case or at the end of the case can put the patient at risk. For example, in rod insertion for reshaping the spine, the surgeon assesses nerve impingement by the patient's ability to respond physically. Testing can be performed only after the return of muscle function. Additionally, after neurosurgery the patient needs to be awake as quickly as possible to learn of blockages due to thrombosis. Rapid treatment will prevent and/or reduce brain damage. At the end of the case, removal of the endotracheal tube and transfer to a recovery area is only safe when the patient's paralysis has disappeared. Depending on when the last dose was administered, the disappearance of paralysis may take some time. The result is higher costs due to longer recovery and supervisory time, greater risk of side effects due to overdosing, greater drug cost and increased use of reversing agents. Furthermore, if the NMB drug remaining at the end of the case is excessive it is impossible to reverse with drugs and paralysis will remain postoperatively. This may create a wait until the patient can be extubated, or the patient may be extubated prematurely. Post-operative residual curarization due to premature extubation is a matter of concern. The lesser the neuromuscular response of the unprotected airway, the greater will be the patient's muscle weakness, impaired hypoxic ventilatory response, pharyngeal dysfunction and risk of aspiration, hypoxemia and delays of emergence from anesthesia. Dysfunction of the pharynx and the striated muscles of the upper esophagus, which leads to risk of aspiration, are associated with a To4 ratio of 0.9 or less at the adductor pollicis (Eriksson [17]). A To4 ratio of 0.7 or less is associated with an impaired hypoxic ventilatory response, due to the residual NMB impairing normal chemosensitivity of the carotid bodies by an interaction with the cholinergic transmission of the chemoreceptor in the glomus caroticum (Eriksson [18]). In a blinded test for post-operative residual curarization in forty patients, forty clinical events of impaired neuromuscular function were found in nineteen patients. These events included ptosis, diplopia (blurred vision), failed sustained head lift, uncoordinated movements, oxygen desaturation and upper airway obstruction. Eighteen of these nineteen patients had a To4 of less than 70% at extubation (McCaul [19]). The overdosing strategy is also a source of inconvenience should complications arise and the surgical conditions change. An example of this was seen in the study used to collect data for the NMBAS starting model (Gilhuly [20], included in Appendix C). After paralysis and induction had taken place, examination of the patient revealed extensive invasive carcinoma. The procedure was cancelled, and the anesthesiologist and attending nurses had to monitor the patient until the drug 7  wore off enough that the patient could be reversed. The problems associated with bolus delivery could be remedied by controlling an infusion automatically and adjusting it to the patient's needs. For cases requiring breaks to test function, automatic control could keep the patient minimally paralysed until a test is required, reduce drug administration to allow function to return, and then re-paralyse for continued work with minimal waiting time by the surgical staff. Automatic drug delivery could improve drug therapy by allowing more efficient delivery, reducing drug usage and costs; by permitting health care staff to work more efficiently, providing better care; and by allowing the safe use of drugs that are difficult to administer manually because of low therapeutic indices. Furthermore, computer control of NMB would relieve anesthesiologists from the distraction of having to monitor muscle response, prevent loss of reversibility at procedure's end due to over-paralysis, and give anesthesiologists fine control of muscle tone.  1.4  Past Effort in Control for Medical Applications  Computer controlled NMB has been applied through many different control methodologies. These include bang-bang control, PID control, fuzzy logic, predictive control and adaptive control. These controllers and their application are discussed here and some relevant efforts from the literature are summarized in Table 1.1. Prior work has had some success but with limitations: controllers were conservative; setpoints tended towards irreversibility; computer control was instituted after induction; monitoring with single twitch required delays at the start to find a control twitch; and the systems - although they may have been tested in a clinical setting - were not tested in clinical trials with the appropriate accepted measured of blinding, randomization and a control group to test the treatment against. In some cases, the results shown in the table need to be taken with a grain of salt. Results show controllers that are somewhat effective although slow and sometimes unstable. Periods of statistical analysis were often started only once the controller was stable. And as mentioned, control was often guided by ST stimulation which requires a substantial control period at the start of case, making application of the controller feasible only in research settings and impractical in the OR. 1.4.1  Bang-bang Control  Bang-bang control is a method of control whereby a measured variable turns on and off a constant rate actuator according to whether or not it is within set bounds. Bang-bang control extremely simple to implement, yet inaccurate and unstable as the on/off nature of the controller causes oscillation of the process variable between its bounds. In Wait [21] bang-bang control was implemented to control a syringe pump through a relay triggered by error in the muscle response. The output was bounded, but oscillated between +6 and —3% of the setpoint in the period of analysis. 1.4.2  Proportional-Integral-Derivative Control  Proportional-Integral-Derivative (PID) controllers control by producing an input that is a function of the proportional, integrative and derivative gains of past error signals. PID is the first welldeveloped control technique and has become a workhorse for industry. The extension of this technique to drug control is natural. A major problem with PID is its non-adaptive nature cannot handle large parameter variability. PID cannot adjust for variability in patient response to the N M B agents, changes in sensitivity with time, differences in patient latency of responses and changing levels of surgical stimulation 8  Monk [22]. The rigid structure is particularly bad for drug control as variability present in biological systems is great. In two separate studies, a three-fold variation in response with 36 patients over the same dose range to atracurium and a ten-fold difference within twenty patients given vecuronium was seen (MacLeod [15]). As well, drug inputs are constrained to be positive semi-definite (the drug cannot be removed; it only flows in), which leads to oscillation for controllers that cannot counteract delay. The PID controller of Rametti [23] is illustrative of these problems. It produced oscillation in response and its performance was judged unsatisfactory. As the PID was tuned to an average patient it had greater problems with patients of high and low tolerance. The situation was improved by adding self-tuning of gain and delay compensation with information garnered from a state estimator. A more recent work on the control of NMB is that of Mendonca [24]. Using digital PID controllers based on Ziegler-Nichols step response methods and models for atracurium with varied parameters, control was maintained with some error. However, a bolus dose at the start and a training period to learn the patient and select the controllers were required. Models for response to atracurium (an NMB drug with a similar duration to rocuronium, but double the onset: two to four minutes) based on pharmacokinetic models in the literature were synthesized. PID controllers were built using Ziegler-Nichols step response calculations with varied parameters to control ST response to 10%. Patients were first stimulated (presumably they were anesthetized) for approximately thirty minutes to get the baseline for measurement. The patients were given a paralyzing bolus dose and then observed for ten minutes, at which point proportional control was begun and then continued for 20 minutes. Based on the response seen to the bolus, an appropriate patient model and PID controller were selected, and then, at thirty minutes, PID control was started. The mean response at steady state was 9.7±0.3% with a range of 8.7 to 10% for a setpoint of 10%, 3% error on average for this time period. Error performance was measured after thirty minutes, once the PID controller was started and no statistics were made or presented for performance in the first thirty minutes. In further work, the same group improved robustness by eliminating model-controller pairs that failed to guarantee stability of the chosen model in simulation [25] and improved performance by detecting and eliminating sensor faults [26]. The authors reported their mean time to 50% response after the bolus was three minutes, as compared to approximately one minute for other groups reported in the literature. This indicates a small bolus was used, undoubtedly to allow the system to observe the patient response for longer, but at the expense of the patient and OR staff who must wait the extra time until they can intubate and get the patient oxygen. Most likely this was to accommodate the information requirements of a slow and non-adaptive controller. Another NMB control effort of note for its recent publication of results is the work of Stadler [9] and Schumacher [27]. The controller used was not strictly a PID controller but was similar in spirit, being an observer based state feedback controller with additional integral action (essentially a PI controller). A mivacurium infusion was controlled to a T l level of roughly 5%. Mivacurium has approximately double the onset time (between two and four minutes) and one-third the clinical duration (between twelve and eighteen minutes) of rocuronium. Good results for both of these research groups were obtained in the sense that the control objective was met. The measured response was close to the desired setpoint through the period of comparison. However, there are three issues begging criticism here: the period of comparison, the desired setpoint, and the delay prior to intubation associated with ST stimulation (and T l monitoring) and control (discussed above). The period of comparison was chosen to be favorable to the controller, generally not until after it had been established and the patient was stable. In Mendonca [24], error performance was measured after thirty minutes, once the PID controller was started and no statistics were made or presented for performance in the first thirty minutes. In 9  Schumacher [27], "setpoint precision" was not evaluated until ten minutes after the controller was activated or the setpoint changed, whichever was the most recent. The desired setpoint was a low T I level which was convenient for the controller for producing a relatively easy to control plant, but not convenient to the patient and staff as the patient was overly paralysed. This will be discussed in detail in Section 1.4.6. Other reported problems typical to PID include, overshoot [28], offset due to P-type control and inconsistent performance due to patient variation (Asbury [29]), and slowness to reach target and stability (Assef [30]).  1.4.3  Fuzzy Logic  Fuzzy logic refers to modeling and control of complex systems with a finite number of rules relating combinations of categorized inputs to a discrete set of outputs. It is known as "fuzzy" because the grouping of inputs is a non-definite means of handling the system. Fuzzy models the imprecise modes of human reasoning and decision making needed for situations of uncertainty and imprecision (Linkens [31]). An improvement on fuzzy logic is self-organizing fuzzy logic control. Self-organizing fuzzy logic control is an attempt at making fuzzy logic controllers more adaptive. This was necessitated as patient variability made the fixed fuzzy logic controllers unusable. Fuzzy logic's strength is that a limited amount of knowledge is all that is required to create the rule sets, allowing quick, simple control. Its weakness is that it is influenced by the quality of information that is used to create the rules used. These are guided by expert opinion, which is rare, subjective, biased, expensive and can be questionable in its quality. Another problem with fuzzy logic is that similar to the change from on to off and vice versa in bang-bang control, there can be sharp transitions from one rule to another leading to instability.  1.4.4  Predictive Control  Predictive control (PC) uses information gained from observation of a system's performance to correct for delays and to improve performance. In PC, control inputs are decided according to past values of control inputs and/or outputs, and predictions of future outputs. Process outputs are predicted through a long-range time horizon according to a mathematical model of the process, and the best control action is taken to guide the output to where it is desired to be in the future. This prediction process is updated and repeated at every time interval. The advantages of PC over other self-tuning controllers include: it is robust to variable and unknown delay; it provides an over parameterization of the system models; and it builds in good disturbance rejection [32]. PC like all linear controllers has problems dealing with nonlinearity and is sensitive to mismatched parameters (Linkens [33]), including estimates of delay. A comprehensive description of methods of PC is presented in Clarke [34].  1.4.5  Adaptive Control  Adaptive control (AC) refers to a broad selection of control techniques whereby a model constructed from a priori estimates and a controller are adjusted over time to counteract erroneous modeling and/or changes that may occur during the course of the control action. Adjustment is generally through a least squares estimation (LSE) algorithm. A C includes gain scheduling, multiple model adaptive control, model reference adaptive systems, self-tuning regulators and others. AC is particularly useful in medical application as it can compensate for variability and allows for greater safety, as changes in system dynamics, instrumentation defects and actuator faults can be 10  detected. Adaptive control's roots begin in the 1950s with the development of the autopilot for high-performance aircraft. Since then there has been much theoretical development and application. A n in-depth review of this field appears in Astrom [35]. An example of an adaptive control technique that has been used not just in chemical batch processes but in clinical application as well is Generalized Predictive Control (GPC) (Clarke [34] and [36]), a general-purpose adaptive control method. This method was used in the operating room in control of NMB as described in Mahfouf [32]. A more recent application of adaptive GPC to NMB control was described in the abstract Janda [37]. There, twenty-two healthy (ASA I or II) adults undergoing intra-abdominal or trauma surgery had both hypnosis depth and NMB level controlled. The NMB drug used was mivacurium and it was controlled to a T1/T0 height of 10%. 1.4.6  Control using ST and/or T l monitoring  For many of the control efforts, the control objective was to maintain an ST measurement (or equivalently to monitor the T l of the To4) at between five and 10%. At this level the patient is highly saturated with neuromuscular blocking agent and becomes an easier to control plant. Variability is much reduced as the receptors are mostly blocked, and the setpoint is in a very flat and linear section of the sigmoidal response curve. Because of the simplification of the problem, the control objective can be met with many simple controllers. This was done for simplicity and as a best effort to overcome nonlinear pharmacodynamics. However, control to this level is heavyhanded as it puts the patient in a position of potential irreversibility. This level of blockade is not desirable at the end of the case when the patient needs to be awakened, and not desirable in cases where NMB should be at lighter levels. Control with ST or T l monitoring also has the disadvantage of requiring a calibration period. There is a long delay at the start of the case before NMB can be imposed - thus the patient is being stimulated in an awake state - possibly with analgesics but not intubated. Depending on the anesthetic given, this could be uncomfortable and/or painful for the patient. As well, patients are at risk in this time period due to their airway being unprotected. The extra time can be detrimental to patients who are of borderline health (ASA classes IV and above) and need to be on anesthetic for as little time as possible, and thus will limit application of closed-loop control to them. In a case presented in Schumacher [27], the figure shows that the initial bolus of NMB drug was not until fifty minutes into the case. The paper by Mendonca [24] also mentioned that the anesthetist has to hand-bag the patient during this time - an avoidable inconvenience for the anesthetist.  1.5  Modelling and Identification in Pharmacological Applications  Model based control involves incorporation of plant parameters into a model as a mathematical representation and application of inputs based on calculations through controllers. Accurate modelbased control requires detailed and precise knowledge of the system to be controlled in order to produce a reliable model. Detailed and precise knowledge is particularly important for open-loop control (such as with target controlled infusion (TCI), discussed below). For closed-loop control, the feedback provided by closing the loop allows for some correction of the remaining uncertainty. For control in medicine, the system is the patient and it is characterized by how the patient reacts to the treatment being given. To predict the patient response, pharmacologists traditionally rely on pharmacokinetic - pharmacodynamic (PKPD) models. Pharmacokinetic (PK) modeling predicts the concentration of drug in the tissue where the effect will be noted. It indicates what the body does to the drug. Pharmaco-  11  Table 1.1: R E P R E S E N T A T I V E CONTROL EFFORTS FOR AUTOMATED DRUG DELIVERY. Source  Controller method  Patients  Results  Wait [21]  Bang-bang: atracurium NMB  11 humans  Oscillatory: ST setpt +6,-3%. Duration: 82.9 ± 59.2min. Infusion: 0.5 ± 0.l3mg kg' hr' . Recovery: 25.5 ± 7.95 min 1  1  Schils [38] Brown [28]  Bang-bang: halothane control of EEG, MAP.  Dogs  Bang-bang used to desensitize, stabilize PID controller  PI: pancuronium NMB  10 humans  Overshoot due to windup. Setpt(ST=20%): 25.9 ± 4.3%. Time to setpt 9.4mm  Linkens [39] Webster [40]  P: atracurium NMB  10 humans  PID: atracurium NMB  20 humans  MacLeod [15]  PID: atracurium NMB  36 humans  Setpt(20%): 26%. Time to setpt: 9.4mm. Rate was less than conventional. Oscillation, long settling times, variable response time within same case. Setpt(ST=10%): 8.90 ± 0.47% 2 unsatisfactory, 1 unstable. Setpt(ST=20%): 18.7 ± 1.3%. Time to stable: 11 ± 9.1mm  Asbury [29] Assef [30] Meier [41] Mason [42]  P: pancuronium NMB  40 humans  P: pancuronium, vecuronium NMB Fuzzy logic PI, M A P  36 humans  Self-organizing fuzzy: atracurium NMB  10 humans  Stable surgical conditions. Setpt(ST=10%): -0.28% ± -0.39% Drug used: 81.9mg control vs. 107.5m<7 manual  11 humans  fuzzy:  Offset, performance variation. Setpt(ST=20%): 27.1 ± 3.13% Adequate paralysis. Oscillation; overshoot; slow to target& stability Superior performance to manual control  Linkens [31]  Self-organizing NMB  Mahfouf [32]  GPC, PI: atracurium NMB  10 humans  Setpt(ST=20%): 19.74 ±1.39%  Linkens [33] Linkens [33]  Smith Predictor/PID: NMB Self-tuning/poleassigning/PID: NMB  10 humans  Sensitive to mismatched parameters in the model  10 humans  Infusion initiated with PID  Uys [43]  Self-tuning: atracurium NMB  11 humans  Induction 7.8 ± 4.7mm, Setpt (ST=10%): 2.47 ± 0.95mm, overshoot: 22.77 ± 11.26mm  12  dynamic (PD) modeling predicts what response will be seen for a given concentration. It indicates what the drug does to the body. 1.5.1  Pharmacokinetic M o d e l i n g  As the flow of drug throughout the body cannot be measured continuously and often not at all at the areas of interest, pharmacokinetic models have been developed. Pharmacokinetic models approximate drug distribution, metabolism and excretion by considering the body to be made up of distinct groupings of tissues, called compartments. Compartmental groupings are made according to similar drug absorption and distribution characteristics. In a very complicated form, a compartmental model would have compartments for each organ and blood vessel. A relatively complicated version would include as compartments, the blood, the vessel rich group (brain, heart and kidney), the vessel poor group (other organs), muscles and adipose tissue. A three-compartment model representing plasma, and highly and poorly perfused tissues is used in this research, as is the most representative model for the pharmacokinetics of rocuronium (Organon [3], vanMiert [44]). Compartmental modeling generally assumes that the size of the compartment remains constant, distribution throughout the compartment occurs instantaneously, and transfer between compartments is a linear, first-order process proportional to drug concentrations (Ingram [45]).  Drug in  Absorption Compartment  k  a  k10/  ki2  Compartment One he  k2i  Compartment Two  \ ^13  \  elimination Effect Compartment  Compartment Three  ho  Compartment n Figure 1.4: T H E PHARMACOKINETIC MULTI-COMPARTMENTAL MODEL. T H E E F F E C T COMPARTMENT (DOTTED BOX) HAS BEEN INCLUDED TO SHOW T H E RELATIONSHIP OF T H E P H A R M A C O K I N ETIC MODEL WITH T H E PHARMACODYNAMIC M O D E L .  A compartmental model is depicted in Figure 1.4, where multiple compartments are presented including compartments for the tissue classifications; for absorption of drug to plasma; and for effect. The absorption compartment is a simple delay to account for differences in routes of administration. Intravenous delivery does not require it; subcutaneous delivery does. Although not strictly part of the pharmacokinetics, the effect compartment has also been drawn to show its relationship to the P K model. It has been drawn as a dotted-line box to show this. The effect compartment is described in Section 1.5.2.  13  Mathematically, the drug time course is described by a set of n differential equations: dc%  1  = ~°i Y  -jJ  V  k  y. 1 Y  +  j=l  i = l  0 3H  C  V  ()  k  L1  where n is the number of compartments, Q is the drug concentration in and Vi is the volume of distribution for compartment i, and kij is the rate coefficient for transfer of drug from compartment i to compartment j. Rocuronium distribution follows the equations: dt ^  • = -C2it)k  •  •  V i  +  ^C {t)V k  = -csWfcai +  ^^Kifcis  2l  l  l  l2  (1.2)  and its plasma concentration versus time curve can be described: Cpiasma(t) = ci(t) - P e " ^ + ,4e- + Be~ ai  pt  (1.3)  where IT > a > 3 are time constants for the various phases of elimination, and redistribution to the slow and fast compartments, and are derived from tangents to the concentration/response-time curve. Coefficients P , A and B are intercepts for the same tangents with the t = 0 axis. The curve is generated from the analysis of blood concentration levels taken throughout the administration and elimination of a bolus. Once these coefficients are known the rate constants of Equation 1.2 can be determined through regression analysis. 1.5.2  Pharmacodynamic Modeling  To model drug pharmacodynamics, an "effect compartment" is added to the P K model. The effect compartment is a conceptual compartment, not represented in the body, but implemented to translate drug concentration to effect. In the P K P D model, the effect compartment is connected to the compartment from which effect derives. Being that the N M J is perfused with blood at a greater rate than muscle as a whole and there is minimal resistance to transfer of muscle relaxants from plasma to the N M J , the effect model is attached to the central compartment (Miller [16]). The effect compartment has a negligible (Scheiner [46]) volume of distribution and thereby effectively receives no drug. Thus, the transfer rate constant is much smaller than the next largest rate constant and the exponential representing transfer of drug to the effect compartment does not enter into the pharmacokinetic model of Equation 1.3. The effect compartment corrects for the plasma concentration underestimating response during infusion and overestimating response following infusion. It can be viewed as a time delay to explain the lag in response to plasma concentration and can be used to model other nonlinearities such as tolerance and sensitization, and the lag that appears in NMB due to redundant receptors (Weatherley [47]). From Sheiner [46], the advantages of the effect compartment are: it separates the temporal and sensitivity components of pharmacodynamics; it uses the initial distribution phase to characterize a complete dose-response curve; and it models extremes of response. The effect compartment's limitations are: it is unable to separately assess the various factors contributing to pharmacokinetics (e.g. perfusion, diffusion, partition, post-receptor events); it assumes that no tolerance and no 14  sensitization to drug effects develops; it requires plasma concentration be measured; and it cannot describe complex pharmacokinetics. The equation for effect with the effect compartment in place is the Hill equation: Cp  ss  E  =  E  m  a  x  Cjfi'i  7  + Cp ^ 8  (  L  4  )  where Cp = k oZ/v\ and Z is an equation describing the drug flow in the system in terms of sums of decaying exponentials, such as Equation 1.3. This equation is the result of a century of research starting with Langmuir's model for the adsorption of gases to substrates. The parallel to drugs and receptors was seen by Clark. Clark's work was expanded to account for potency, efficacy and curve slope. ss  e Target Controlled Infusion One commercial instantiation of P K P D modelling is the Diprifusor Target Controlled Infusion (TCI) system (Astra-Zeneca Inc., UK) developed for the open loop administration of propofol, a hypnotic drug. TCI refers to the administration of a drug by infusion with rate set according to prediction by a P K P D model to produce a theoretical concentration at the site of clinical interest. The pharmacokinetic model is usually of third order with population mean values for the pharmacokinetic parameters (Gepts [48]). The process is completely open-loop, without regard for a measurable value or effect. The inputs to the system are patient weight and desired concentration in the central compartment. To accommodate patient variation from the population norm, titration of the target concentration is required, "in the same manner as an anesthetic vaporizer is adjusted to obtain a specific pharmacodynamic effect" (Glen [49]). TCI is a form of "more intelligent titration". The first published results from a study using TCI was Schuttler [50]. In that study, twenty patients of ASA class I-III, weight 52 to 85kg and age 18 to 52 years, received propofol and alfentanil by TCI. In most cases the procedure was acceptable and the measured versus predicted concentration ratio was found to be 0.88 ± 0.22 and 1.01 ± 0.28 for propofoland alfentanil, respectively. There were no controls for this study. A subsequent study is described in HuntSmith [51], where TCI was compared to manually controlled infusion (MCI) of propofol in 123 patients, 18 years in age or older with an average age of 51 for the TCI group and 47 for the MCI group. The patients were undergoing elective surgery and were of ASA score I, II or III. Exclusions from the study were those patients that were at greater than 120% of their ideal weight, pregnant, receiving drugs influencing anesthesia, and those with incapacitating illness, organ dysfunction or allergies to the constituents of propofol. No significant difference in performance was seen for recovery times (the time from discontinuing the pump until eye-open and until orientation of the person is had). The time to induction was longer for TCI but was obtained using a lower rate and with less drug. This could be predicted based on first order kinetics: with a slower delivery, there is less drug to metabolize, so less drug is used and it takes longer to achieve the desired effect. Overall drug use between the two groups was seen to be similar. This study implies that TCI use was not advantageous. The Diprifusor was approved for use in Europe after submission of compiled clinical data for 428 patients in eight clinical investigations. These studies defined concentration settings to induce and maintain anesthesia with TCI propofol in the adult, elderly and cardiac surgery patient; examined the influence of pre-medications and the system's predictive performance; and compared the performance versus manual controlled infusion. TCI has not yet been approved for use in North America. The reasons given for not adopting TCI and, by extension, other computer controlled drug therapies are: health implications; signifi15  cant incremental risk of anesthetic controllers; concerns that high level languages, general purpose computers and complex operating systems result in products too elaborate for complete verification; hesitation to accept the literature supporting clinical use on the basis that there is a publication bias towards positive outcomes (Egan [52]); and of the novelty of drug-device combinations and thereby the lack of regulatory precedent (Glen [49]). Another potential reason why the Diprifusor system is not accepted in North America is cost. Propofol based anesthesia is more expensive than inhalationals. In a comparison of isoflurane and total intravenous anesthesia by propofol patient groups, it was found that after fourteen days, general health scores showed no differences between patients. As well, a cost identification analysis focusing on overall cost differences given equivalent clinical outcome revealed an additional cost per surgical session for the infusion group was $28.98 for inpatients and $14.87 for outpatients (Visser [53]). In another study comparing propofol infusion to sevoflurane, desflurane and isoflurane inhalational anesthesia, intra- and postoperative costs were significantly higher in the propofol group by $30.73 per patient. Average cost for the propofol group was $0.24 per minute of anesthesia. The costs among the inhalational groups did not differ significantly, and were $0.15 per minute of anesthesia (Boldt [54]). There may have slightly higher costs for propofol as it was on-patent at the time and thereby more expensive to obtain. However, sevoflurane and desflurane were also on-patent at that time and they showed similar costs to isoflurane, which was off-patent.  1.6  Variability as a Difficulty for Control  The great inter- and intra-patient variability that is present in biological systems is problematic for NMB control. Drug interactions, and demographic and health differences affect how rocuronium is metabolized and how the model parameters will be represented. Table 1.2 shows a summary of the clinical trials compiled in Organon [3]. There, differences in P K parameters are seen due to anesthetic use, age and organ function. As it is desired to bring automated control to more than just the healthy adult, these sources of variation must be quantified and accounted for in the patient model. Although identification of differences in metabolic differences due to age and organ pathology are quantifiable as shown in Table 1.2, a more pessimistic view of the use of this information appears in Gepts [48]. There the authors when discussing application of TCI with propofol state, "it is unlikely that this variability (in individual P K parameters) can be reduced below a minimum level, even when using population kinetics and introducing multiple factors that might influence drug disposition such as weight, height, sex, age and quantified renal, hepatic or cardiac function." As some evidence for this, a study was run on 46 patients of relatively consistent characteristics, excepting age. In post-hoc analysis the patient results were split into age groups of 18 to 40 (ten patients), 41 to 55 (fifteen patients) and 56 to 80 (twenty-one patients) years old. No significant difference was seen for median performance error (subgroup means of 13.8, 17.7 and 16.2% with an overall of 16.2%) or median absolute performance error (subgroup means of 22.6, 25.0 and 24.2% with an overall of 24.1%) (Swinhoe [55]). Gepts [48] also felt that PD variability may be several times greater than P K variability in the individual, further complicating this mess. Expected variations in population pharmacokinetic model parameters are ±20 to 30% with a maximum between ±50 and 60% (Coetzee [56]). These are clinically acceptable and any greater accuracy is unlikely according to the authors. This section will briefly introduce and describe some sources of variability to give an idea of the magnitude of the problem for control. Drug interaction, age and health differences will be discussed.  16  Table 1.2: P H A R M A C O K I N E T I C PARAMETERS OF ROCURONIUM FOR VARIOUS PATIENT GROUPS (FROM [3]). f OPIOID/NITROUS O X I D E / O X Y G E N , I ISOFLURANE, * HALOTHANE ANESTHESIA. CI = C L E A R A N C E , VI = V O L U M E OF DISTRIBUTION AT STEADY STATE, T j /?=ELIMINATION HALF LIFE, M R T = M E A N RESIDENCE TIME s  X  Parameter  fAdults  fGeriatric  tAdults  C7(L/kg/hr) Vi (L/kg) 2 i / 3 (hr) MRT (min)  0.25 ± 0.08 0.25 ± 0.04 1.4 ± 0 . 4  0.21 ± 0.06 0.22 ± 0.03 1.5 ±0.04  0.16 ±0.05 0.26 ±0.03 2.4 ± 0 . 8 {44... 68}  s  2  1.6.1  i. Renal Transplant 0.13 ± 0.04 0.34 ±0.11 2.4 ± 1.1 {80...100}  2  ^Hepatic Disease 0.13 ±0.06 0.53 ±0.14 4.3 ± 2 . 6 {80...100}  *Pediatric 0.44 0.30 0.8 31  Drug Interactions  Rocuronium and other curare derivatives are known to have increased effect in the presence of halogenated volatile anesthetics. It is believed potentiation occurs because of desensitization of the motor end-plate to ACh at a site beyond the cholinergic receptor by the anesthetic (Fisher [57]) and through alteration of muscle blood flow (Ali [7]. From Table 1.2, comparing the results for adults reveals a decrease in clearance and an increase in the time for elimination associated with isoflurane anesthesia, indicating potentiation occurs. Furthermore, different inhalationals are known to produce different effects. For example, forane (discontinued in North America) anesthesia required one-third the amount of d-tubocurarine for paralysis as did halothane (Miller [58]). Increased effect is also seen in the presence of other drugs: succinylcholine; aminoglycoside and polypeptide antibiotics, acylamino-penicillin, tetracycline and high doses of metronidazole; diuretics, thiamine, monoamine oxidase inhibiting agents, quinidine and protamine; and alpha adrenergic blocking agents, magnesium salts, calcium channel blocking agents and lithium salts (Organon [3]). Rocuronium has a decreased effect in the presence of neostigmine, edrophonum, pyridostigmine and aminopyridine derivates; prior chronic administration of corticosteroids, pheytoine and carbamazepine; and noradrenaline, azathioprine, theophylline, calcium chloride and potassium chloride (Organon [3]).  1.6.2  Age Related Differences  Rocuronium PKs are influenced by age with effects seen in differences between the elderly, children, infants and non-elderly adults. Several studies showing this are summarized in Table 1.2. Although elderly patients show the same onset and volume of distribution pharmacokinetics as controls (see Tables 1.2 and 1.3), elimination of the drug is decreased. The onset and volume of distribution effects were attributed to a lack of change in cardiac output, while the decrease in elimination was attributed to slower metabolic processes due to a reduction in hepatic cell mass, liver size and splenic blood flow (Matteo [59]). As total body water and extracellular fluid are a larger percentage of total body weight in children and because of the age related metabolic differences, children require and tolerate larger weight adjusted doses. As well, the lean body mass per surface area decreases with age from twenty-one to eighty-one years old in healthy people. This decreases the volume of distribution (Vd) in the elderly. Finally, drug elimination is impaired in newborns due to their immature enzyme 17  systems. As for organ pathologies, renal disease affects excretion and drug binding, hepatic disease affects drug metabolism and cardiac disease affects drug transport to eliminating organs and can also influence the rate of distribution and redistribution. In children of four to eleven years old the clearance varies inversely with body weight and younger children typically have greater clearance than older. The post synaptic nicotinic receptors of infants are more sensitive, the values for volume of distribution at steady state are greater (a relatively larger head means an increased V2), and the clearance of NMB drugs differs, producing greater variability in the time course of these drugs. In a study comparing children and infants, it was shown that NMB in infants has a longer duration (Wierda [60]). See Table 1.3. Table 1.3: T I M E O F ONSET, M A X I M U M B L O C K A N D CLINICAL DURATION IN MINUTES, F O L L O W I N G 2 x EDg (0.Qmg/kg) 5  DOSE R O C U R O N I U M ADMINISTERED O V E R 5S, DURING OPIOID/NITROUS O X -  I D E / O X Y G E N ANESTHESIA (ADULTS, GERIATRICS), A N D H A L O T H A N E ANESTHESIA INFANTS) ( F R O M STUDIES C O M P I L E D IN O R G A N O N  Group Infant (3mo-lyr) Pediatric (l-12yr) Adults (18-64yr) Geriatric (>65yr)  1.6.3  Time to > 80% Block 0.8 (0.4-2.0) 1.0 (0.4-6.0) 2.3 (1.0-8.3)  (PAEDIATRIC,  [3]).  Time to M a x i m u m Block 0.8 (0.3-3.0) 1.0 (0.5-3.3) 1.8 (0.6-13.0) 3.7(1.3-11.3)  Clinical Duration 41 (24-68) 26 (17-39) 31 (15-85) 46 (22-73)  Health Related Differences  Diseases and physiological changes alter the rate at which muscle relaxants are distributed to tissues by the circulatory system, the rate at which they are eliminated from the body and may also alter the sensitivity of the neuromuscular junction to relaxants (Miller [16]). As can be seen from the data compiled in Table 1.2, renal and hepatic dysfunction both affect metabolism. For rocuronium, clearance is slightly decreased and the volume of distribution is increased with renal disease. These effects are larger with hepatic dysfunction, and the elimination half-life is nearly doubled. In a study of 21 healthy and 17 people with sclerotherapy of esophageal varices and hepatic cirrhosis, NMB was affected. In the non-healthy group plasma clearance was decreased, the slow redistribution half-life was increased, the elimination half-life was increased, the volume of the rapid equilibrating peripheral compartment increased, and the exit rate constant for the effect compartment k o was increased (van Miert [44]). The parameters CPIQ and 7 were unchanged indicating that there was no difference between the two groups at the neuromuscular junction, and further validation that effect is derived from the plasma concentration. e  1.7  Summary and Contributions  Control of drugs and NMB drugs is described in the literature. Yet, beyond the Diprifusor, there are no commercial products. Reasons for this include the resistance to change of both anesthetists and of regulatory bodies, the difficulty of the problem due to patient variability, and the difficulty of the problem in specific to N M B due to often scarce sensor data due to saturation effects and restrictions on the frequency of use. 18  Prior work has been moderately successful under the conditions the research environment allowed. However, the prior control algorithms also had many failings. These failings include: a conservative nature producing slow rise to setpoints; setpoints selected to tend towards over-dosing and irreversibility; institution of computer control only after the patient was induced requiring separate actions by the anesthetist to administer an initial bolus and then wait for the computer to learn how the patient reacts; and the problems associated with use of ST and T l monitoring. These failings are not compatible with the demanding environment of the OR. It is the belief of this research that the lack of availability of automated NMB is because of the lack of a system that meets the needs of the OR environment, the needs of the patient and the needs of the anesthesiologist. Following this belief, the objective of this research was to develop a system that would eliminate the worry and effort involved in ensuring proper NMB from the anesthetist, allowing the anesthesiologist to work on more complicated cases and concentrate more on their patient, and to extend the capability of the anesthesiologist in this fashion without increasing their workload or the time length of the case. For the most part, previous control efforts have been research driven projects and have held onto that philosophy through their implementation. These projects have focused on the "is it possible?" aspects of the problem and not on "is it useful and usable?" aspects. Results were assessed using advantageous periods of comparison, and control was done under conditions convenient to the controller and neither for the patient nor for the anesthesiologist with overly-deep NMB and large delays at the start of the case to tune the sensor. The clinical goal of this work was to provide automated control of NMB to produce surgically useful and easily reversible levels of paralysis, at all times and for any and all patients. Prior clinical work from the literature can claim to have met the objective of providing surgically useful levels of control. However, in most cases, this was control to levels of a ST measurement of 10%. At this point the second twitch has vanished and all that remains is the first twitch. This state is not pharmacologically reversible. This was acknowledged by Schumacher [27], as the controller of that study was not used if the T l required more than 30 minutes to recover after the intubation dose. 1.7.1  Contributions  The overall contribution of this research is the creation of a system demonstrating computer control of NMB within the constraints of the OR. This system demonstrates that computer control of drugs is feasible, and more efficacious than manual administration, using controlled administration of NMB drugs as a proxy. To the best of the author's knowledge, this is the first work to demonstrate automated administration of NMB drugs in the clinical setting in a prospective, blinded, randomized, controlled, clinical trial. As mentioned above, there have been many tests done in the clinical setting, however they have generally lacked one or more of blinding, randomization and a control (i.e. standard care) group to test the treatment group against. The detailed contributions of this thesis include: • Monitoring techniques and modeling to extend the range of NMB sensing and to increase data available to the modeling procedures: 1. The enhanced-To4, a means of quantifying To4 measurements with less than four twitches. 2. Quantitative translation of P T C to To4 measurements as continuous, non-categorical data. 3. Interconversion of neuromuscular stimuli protocols to allow their use with models developed for other stimulus protocols. 19  • The concept of relaxation to describe more intuitively NMB and to correlate the up to now distinct stimulus modalities • Novel handling of nonlinearities at the neuromuscular junction: 1. Quantifying the concentration-effect curve at the N M J with regards to the To4 measurement 2. The concept of pseudo-occupancy, linearized occupancy to account for greater than effective amounts of NMB drug in terms of multiples of a standard dose • A novel approach to building models for noisy, nonlinear systems combining nonlinear estimation of process equation parameters and then linear estimation to produce a linear model. • A novel model adaptation scheme to handle substantial inter- and intra-process variation present. This scheme adapts in two ways: 1. To the individual through a gross and then fine tuning of the patient model. Gross tuning involves model replacement with a more representative model from a population modelset once sufficient data is learned. Recursive estimation is used to fine-tune the model. 2. To the patient population by building up subpopulation modelsets of patient models clustered according to health and demographic information. With enough models in the subpopulation modelset, it can be used to replace the whole population modelset, providing a more representative initial model and more representative models for the gross tuning described above. • Methods for simulating intrapatient variance for more robust testing of in vivo closed-loop control, including inhalational anesthetics, irreversible antagonists and reversible antagonists. • Clinical application of the research in a prospective, randomized, controlled, clinical trial • Retrospective study of: 1. Using body mass index to calculate intubation doses to reduce overparalysis 2. Stimulation current according to patient weight and body mass index 3. Intrapatient variance due to anesthetic, blood loss and tissue loss The efforts required to produce these novelties will be discussed in the ensuing chapters. Chapter 2 discusses the novelties in monitoring and modeling developed. Chapter 3 discusses simulation and testing of these novelties and development of controllers to use them. Clinical testing of this research is described afterwards. Chapter 4 details the application and further development of the research conducted in the prior chapters in closed-loop control experiments. Chapter 5 describes testing of the thesis work in a prospective randomized, blinded, controlled, clinical trial of an advisory system, meant to be a surrogate for and a stepping-stone towards full-closed loop control in humans. A discussion of the findings of the thesis and future directions concludes the manuscript.  20  1.8  Research Ethics  Animal procedures were conducted under ethics approval by the University of British Columbia (UBC) Animal Care Committee. For the human measurements, informed consent was obtained from all subjects and the protocol was approved by the UBC/Providence Health Care Research Ethics Board. Copies of the Animal Care Committee and Research Ethics Board approval certificates can be found in Appendix A.  21  Chapter 2  Neuromuscular Monitoring and Modelling In the preceding chapter, control and modelling efforts from the literature were briefly summarized. These efforts were seen to be either experimental animal trials only, non-optimal in the clinical setting, or functional in a small population group. As the main goal of this work was development of controllers with broad applicability, new approaches had to be considered. The presence of large inter- and intra-patient variance hinted that adaptive schemes for modelling and control were required in order to manage the variation. This in turn steered the modelling of the patient towards structures to which adaptive control techniques could be efficiently applied. Experiments were conducted to collect subject data, confirm magnitudes of variation and to develop and test modeling techniques and control schemes. This chapter begins with a discussion of the initial experiments to gather data for developing the models. Then, a novel sensor developed to improve data collection and modeling is described. A description of the handling of nonlinearities follows. Then, the levels of variation found, model structures tested and the selection process to pick a best model structure are discussed.  2.1  Initial Data Collection Experiments for Model Building  To estimate levels of drug in patients and corresponding response at the present and in the future, a mathematical description of the patients and how they react to the drug is required. This description is termed the patient model. As it is neither safe nor ethical to test initially on humans, models were built from data obtained in experiments testing rocuronium response in rabbits. The initial experiments were part of a dose testing survey of conotoxins as novel NMB drugs (Gilhuly [61], included as Appendix B). The original protocol called for bolus testing with response measured by To4. This provided the impulse response data used to build the first models. An estimation of the ED50 based on literature values was used as a starting point and the drug was administered in a cumulative and increasing fashion, with additional doses given after reaching maximal effect. The cumulative dosing strategy was: 0.5 x ED50 then 0.5 x ED50 then 1 x ED50 then 2 x ED50 (running total of 4 x ED^Q) and then progressively doubling the dose. The EDg$ dose was 50p:g • kg* . To gather impulse response data, neuromuscular function was monitored in the presence of rocuronium administered as a 2 x ED95 bolus. Five rabbits were anaesthetized with isoflurane 5% for induction and maintained with isoflurane 2.5% for surgical interventions. The interventions 1  22  included: performing a tracheotomy for respiration, carotid artery isolation for monitoring blood pressure, jugular vein isolation for drug delivery and blood sampling, ear vein cannulation for delivery of saline and thiopental for anesthesia, placement of needle electrodes for sciatic nerve stimulation, and capture of the anterior tibialis and extensor longus digitorum muscle tendons for  force measurement. Because of isoflurane's potentiation of NMB, isoflurane was discontinued after the surgical interventions in favour of thiopental (2.5% solution). The infusion rate was varied to maintain a mean arterial pressure around 75mmHg. Blood pressure, ECG, CO2, O2, M A C , isoflurane concentration, respiratory rate (Datex-Ohmeda Capnomac Ultima), respiratory pressure (pressure gauge) and rectal temperature (thermometer) were monitored to assess and maintain the health of the subject. To4 stimulation of the sciatic nerve was used and monitored by a force transducer (Grass Instruments, USA) connected to the anterior tibialis and extensor longus digitorum muscle tendons to assess NMB. Measurements were recorded to tape. Once the rabbit was stable, the experiment began. Muscle function was monitored to obtain full strength data to act as a control point. The 2 x EDg$ (lOOpig/kg) dose was then given. Muscle function decreased as measured by the To4 until paralysis, and the time to 95% relaxation and the time to 75% of the muscle function return were timed and recorded. Muscle function was allowed to return to 100% of the control value and shortly thereafter the experiment was discontinued. As a comparison to the initial models in rabbits similar work to confirm the variation and model selection process was repeated in a pilot study of human rocuronium responses. This will be explored more fully in Section 5.2. For the human measurements, patients underwent their scheduled procedure without interference. A n anesthesia monitor was present in the operating room, from which physiological data was recorded. After the patient was anesthetized, rocuronium was administered according to the attending anesthesiologist's judgement and at or below the manufacturer's recommended dosage of 0.6mg • kg , 2 x ED95 for humans. To reconstruct the patient impulse response, To4 data was included from the time of first injection until the next drug affecting NMB was given, either a second dose of rocuronium or a reversant. -1  2.1.1  Results of the Initial Data Collection  All procedures went without complication. Physiological parameters were maintained within physiological norms. Muscle function response data was adjusted for noise and baseline, and To4 ratios were calculated. The data was time aligned according to when the drug was administered and converted to relaxation (a measure of paralysis opposite to contraction, described below). For linear model estimation to take place, a complete (one valid datapoint at every timestep) curve of datapoints was required. However, the measured response data had periods of sensor saturation in which the To4 ratio was zero. As well, there were periods of no measurable effect at the start of the case and in the recovery period, where drug was present but not detectable because of the nonlinear behavior of NMB drugs. A method to gauge drug levels from response, and to account for the nonlinearities of delay to response and presence of drug at the receptors at clinically non-detectable levels was needed. To solve these problems two approaches were taken. A method of converting saturated To4 counts with some (but less than four) viable twitches remaining to valid measurements was developed to increase useful data and visibility into saturation. Also, a method of linearizing the nonlinearities was developed.  23  2.2  The Enhanced-To4 and Relaxation  As the concentration of NMB drug increases at the NMJ, the ability for the muscle to function is decreased and the sensor measurement will reflect this. For the To4, this manifests as a reduction in response to the twitches with decay in order from the fourth twitch to the first and with the later twitches decaying faster relative to the earlier twitches. Decay of the twitches will proceed to the point where the fourth twitch (the twitches decay in order from fourth to first) is no longer distinguishable from the background noise, causing the sensor to report an error message or a To4 of zero. A To4 measurement of zero indicates that the fourth twitch is unreadable, yet the first, second and third twitches may still be viable. A novel contribution to NMB monitoring was the conversion of these partial To4 measurements to objective data useful for modelling and control. The concept of a single scale combining different NMB sensing modalities is not novel - a scale including To4, partial count To4 as a twitch count and P T C was proposed in Duckert [62]. However, the invention of Duckert [62] was a categorical scale lumping ranges of the three measurements onto a scale of zero to ten, that could not be used for modelling or control because of the error introduced through its lack of precision. The novelty to be described in this section (and later for the P T C and other stimulus modalities) is the conversion of these twitch counts into objective, validated values that can be used in adaptive modelling and control algorithms. The number of twitches remaining in the partial To4 can see into the level of muscle function beyond the saturation level of the To4 sensor and aid in modeling response and control. To uncover this hidden data, a linear relationship was established between the unsaturated To4 and accompanying T l (the first twitch of the To4) measurements. The results of Lee [6] and Ali [7] show that the fourth, third, second and first twitch disappear once the ratio of T l to its value in a control period (the TO measurement, so this ratio is T1/T0 which is the equivalent to the ST) when there is no NMB drug present, has reached 25, 20, 10 and 0%. A linear fit using least squares estimation of this data revealed the relationship: To4 = 1.22(T1/T0) - 31.2%  (2.1)  with an RMS error of 4.46%. The relationship was extrapolated into the saturated To4 region by calculating To4 values at three, two, one and zero twitch counts (T1/T0 equal to 25, 20, 10 and 0%) revealing the respective To4 estimates -0.7, -6.8, -19.0 and —31.2%. Details are listed in Table 2.1. Second and higher order linear fits, as well as exponential fits were made but found unsatisfactory compared to the first order least squares estimation. This was due mostly to poor performance in the region where the To4 approximation becomes negative. The relationship between T1/T0 and To4 was also mapped using a sigmoidal relationship. Sigmoidal relationships are more complicated than linear relationships such as Equation 2.1, but better capture the dynamic of drug binding at the neuromuscular junction because the general action of drugs at receptors is sigmoidal in nature. The sigmoidal equation takes the form: (Tl/T0r  where 7 is the Hill constant defining the rate of rise of the curve and £ 5 0 is the T1/T0 ratio corresponding to To4 = 50%. In an iterative process, nonlinear estimation was used to determine the coefficients of the equation. The datapoints used to construct Equation 2.1 were used as fitting points. As well to force a zero solution, a somewhat arbitrary point was added for zero effect (due to singularity at the logarithm of zero, the value 1 0 was substituted) at 1.5 relaxation. - 1 3  24  Table 2.1: T l / T O vs. To4 MEASUREMENTS, *REPORTED IN A L I [7] (HUMANS, N=34, TO  70  AND  AGES 10  Y E A R S O L D ) , AND E X T R A P O L A T I O N S BASED ON A LINEAR RELATIONSHIP B E T W E E N  Tl/TO  To4. # of Twitches  4  4  3  2  1  0  95  25  20  10  0  T l / T O [%]t  100  To4 [%]t  100  75  0  0  0  0  To4 [%] extrapolated  90.8  84.7  -0.7  -6.8  -19.0  -31.2  The parameters of Equation 2.2 - 7 and E50 - were found to be 3.75 and 0.12. The extrapolated To4 responses for the disappearance of the fourth, third, second and first twitch were —1.28%, —5.72%, —21.8% and —34.7%, respectively. These values were considered close enough to the linearized values that despite their intuitive appeal, the linear values were used in the simulations. Testing was done using these values as well in.rabbits but showed no obvious difference. To fully understand any effect that might be present, a full clinical trial would have to be done. As negative values for estimated responses of partially saturated To4s are not intuitive, because response can be proportionally correlated to the dose and blood concentrations of the drug, and for desire of simpler mathematics, effect can instead be described in terms of relaxation. Relaxation is a fractional measure of paralysis ranging from 0 to 1 for the range of 100% to 0% To4, and with values greater than one reflecting increasing block and/or concentration of NMB drug in the bloodstream beyond this level. To4 measurements are converted from percent to fractions and then subtracted from one: relaxation = 1- To4/100% (2.3) Some examples are: a 10% To4 measurement is translated to a fraction of 0.1 and then to a 0.9 relaxation measurement; a To4 of 100% indicating full strength becomes a relaxation measurement of zero; full relaxation in the To4 sense (a To4 of zero) is represented on the relaxation scale as a one. Saturated To4 measurements become greater than one in relaxation terms, e.g. a twitch count of two is 1.068 in relaxation units. With the relationship between the number of observable twitches and the level of relaxation established, control can be extended into the saturated region of To4 and the advantages of To4 can still be had. That is to say, mathematical algorithms can be used and linear controllers applied over a greater range of patient paralysis. Should deeper levels of paralysis be required, a means of delving deeper into saturation is now available and this will permit greater application of predictive control. It must be noted that in the above, T l / T O is equivalent to ST stimulation. In practice there is a difference in that the ST can be used more frequently than the To4, from which the T I measurement derives. The use of partial and full count To4 measurements together becomes a new extrapolated sensor, herein called the enhanced-To4 (eTo4). How the eTo4 improves models and thereby control is discussed in Section 3.4 where the results of simulations performed to prove the eTo4 are presented. Validation of the eTo4 is presented by analysis of clinical testing results, to be described in Section 5.7.  25  2.3  Response Nonlinearities and Pseudo-occupancy  When drugs are administered, measurements can experience nonlinearities in the form of delay to action and saturation of response. These nonlinearities are related to the pharmacological terms of potency and efficacy. Delay exists because it may be necessary to agonize (antagonize, for blocking drugs) a proportion of receptors before response is seen. This apparently non-operational proportion is known as the "receptor reserve" or "safety factor". Saturation occurs because the maximum response has been met either by agonizing all the receptors or a large enough percentage of the receptors to achieve that response. Mathematically, these nonlinearities can be seen at low and high concentrations when effect as a function of drug concentration is defined by the sigmoidally shaped Hill equation: E  ^  = -arl%cJ  -  E  (2 0  4)  where E is effect, E is the maximum effect possible, C is the concentration of the agent at the NMJ, 7 is the Hill coefficient corresponding to the slope of the curve, and EC50 is the effective concentration producing a 50% response. max  Figure 2.1: R E L A T I O N S H I P B E T W E E N B L O O D C O N C E N T R A T I O N OF A D R U G (SOLID LINE A N D A X E S ) A N D RESPONSE  (DASHED LINE A N D A X E S ) O V E R T I M E .  G R A P H S A R E O V E R L A P P E D TO SHOW  THAT RESPONSE IS NOT OBSERVABLE UNTIL A CERTAIN THRESHOLD ( B E T H A T C O N C E N T R A T I O N OR O C C U P A N C Y ) HAS B E E N R E A C H E D A N D B E C O M E S S A T U R A T E D A B O V E A CERTAIN L E V E L .  These nonlinearities can be seen in Figure 2.1, where concentration (solid line and axes) and effect (dashed line and axes) are overlaid to show contrast. As drug is added, it distributes throughout the patient and the concentration at the region of interest rises. At first effect is zero. After the drug has enjoined enough receptors, a threshold is reached and effect is seen. Effect increases with concentration to the point of saturation of the response (and/or sensor) after which effect plateaus. Concentration can continue to rise but without increase in effect. On examination of the primary action of the drug and neglecting side effects, concentrations above this level produce no  26  greater effect but instead just extend the time in saturation. Function returns with elimination of the excess drug. A curve for drug occupancy of receptors (drug binding to receptors) is a mix of concentration and effect curves. Although effect is not evident until the threshold of necessary receptors agonized (or antagonized for blocking drugs) is reached, receptor occupancy follows the concentration up to the point of saturation. At saturation, receptors have all or mostly been agonized and the receptor occupancy profile will saturate as does effect. The NMJ is an example of a system with receptor reserve. At the NMJ there are extra receptors to increase the probability of contraction on stimulation and decrease the likelihood of blockade. This serves to create a threshold to response. The NMJ also has a saturation level in that an infinite amount of force cannot be generated, and with regards to administration of NMB drugs, after a certain percentage of the receptors are blocked no contraction can be had. To describe the receptor reserve, in Paton [63], isolated cat anterior tibialis and sartorius muscles were stimulated in the presence of tubocurarine and other NMB drugs at known concentrations. The threshold to a decrease in contractility (the limit of the receptor reserve) was found by increasing the concentration of NMB drug until contraction achieved by application of a normal transmitter output was below a control value. The proportion of receptors blocked was determined by finding the ratio in which the dose of a stimulant must be increased in the presence of an antagonist (the NMB drug, e.g. tubocurarine) in order to match a control (without NMB drug applied) response. The authors labeled this ratio the "dose ratio". As ACh was too rapidly metabolized for stable measurements, contraction was obtained by direct application of succinylcholine, decamethonium or octamethonium. Occupancy was calculated as a simplified version of the Hill equation: occupancy =  dose ratio ; 1 — dose ratio  (2.5)  It was estimated that 76 ± 5% of the receptors had to be blocked by the antagonist before block was noticeable, and 92 ± 16% of the receptors had to be blocked for near complete blockade. Results for receptor reserve were obtained for humans in Quastel [64] and Pennefather [65]. To quantify the proportion of receptors necessary to be blocked to diminish ST (equivalent to the T1/T0 response) stimulation, end plate potentials at human intercostal muscle NMJs were measured. Reduction in response for the ST started at approximately 60% blockade with a 50% decay occurring at approximately 80% occupancy. In Waud [66], the experiments were repeated in vitro with guinea pig muscle preparations. The work was redone to obtain results within more controlled environments. Similar results were found, with 75 to 80% and 90 to 95% of receptors having to be blocked before the twitch began to fall and before complete abolishment was had. A nonlinear curve fitting of data from Quastel [64] and Pennefather [65] to the Equation 2.4 for response to ST stimulation at the NMJ according to the proportion of receptors free of drug was found to be: 3.73  FR  response(FR)  =  p  R  3  7 3  +  ( Q  ^  7 3  (2.6)  where FR is the proportion of free receptors, the Hill slope 7 was found to be 3.73, and the 50% response was found with 20% of the receptors being free. The response is proportional, hence the maximum response can be considered to be unitary and is thus not included in Equation 2.6. The curve of Equation 2.6 was linearized by retaining its slope and 50% response datapoint of 20% receptors free. Extending this new curve revealed an intersection with 0% effect (no relaxation) at a free receptor ratio of 0.3, indicating that 70% of the receptors would be blocked at the point where the ST response started to decay. 27  The linear relationship made between T l / T O (or ST for the above discussion) and To4 established in Section 2.2 defined a range of effect for To4 based on the translated value of less than four twitch counts. Considering T I (and ST) decay to begin at a To4 of 90.1% and 60% receptor blockage (linearized version of Quastel [64] and Pennefather [65]), extrapolation was made until the To4 curve reached 100%. This extrapolation revealed an occupancy of 50.1% as the point at which the To4 first begins to decay. Varying the threshold when response is first seen produces models for subjects with varying levels of resistance to NMB drugs. Raising the threshold produces models for subjects who are relatively non-responsive. Lowering the level produces models for subjects who are sensitive. In the extreme case of a threshold at 0%, the model becomes representative of a patient with a neuromuscular condition, such as myasthenia gravis, where there is a severe reduction in the normal redundancy of ACh receptors and any amount of NMB drug present reduces muscle strength. The maximum effect is more straightforward; it is seen when no more measurements can occur. To find the maximum effect with linearized To4, the T l / T O value in Equation 2.1 was set to 0. This results in a To4 in terms of contraction of —31.2%. To encompass the nonlinearities into a linear model so that linear adaptive modeling techniques could be applied, a linear relationship of response and receptor occupancy was developed, called "pseudo-occupancy". Pseudo-occupancy is a linearized version of true receptor occupancy and is analogous to the drug concentration at the effector site, the NMJ in the case of NMB drugs. This linearized model of occupancy includes levels greater than 100% (with a range of 0... oo) allowing for excessive doses larger than what is necessary to bind to all of the receptors, and accounting for the excess drug and how it is metabolized. Pseudo-occupancy is a total of how many multiples of the quantity of drug required to bind all of the receptors are present at the effector site. The receptor full level representing when effect is maximal was set to 100% occupancy. As this scale assesses response and not true physiology, this level will have different meanings in terms of occupancy depending on the form of stimulation being used. For example, To4 stimulation is more demanding in terms of available ACh and thereby decays faster than ST stimulation, as shown by decay to response first being seen at 50.1 and 70% receptor occupancy respectively. Relaxation data points are converted to pseudo-occupancy using the equation: r. , • P — relaxation =  =  P range , x —— h thresh ejfeet range , 1 — thresh relaxation x ——— \- thresh maxEf feet — 0  (1 - To4/100%) x  1  ~ °'  5 0 1  + 0.501  (2.7)  r . o i  where P is pseudo-occupancy, and the values found for maximum effect (maxEffeet) and the threshold in occupancy before response is seen (thresh), and Equation 2.3 have been substituted into the last line. As an example conversion, a To4 measurement of 10% converts to 0.9 relaxation which converts to a pseudo-occupancy of 0.83. Examples of pseudo-occupancy as compared to NMB measurements, clinical manifestations and relaxation can be seen in Table 2.2. In the table it will be seen that as blockade is increased the measurement is switched from To4 to P T C once the To4 becomes saturated. The maximum effect for relaxation is reached and then exceeded. For the last measurement, the relaxation is approximated at a level of 1.5 based on the techniques interrelating stimuli types to be described in Section 2.6 and the pseudo-occupancy is approximated at a level greater than one to indicate that there is more drug than required to block all the receptors.  28  Table 2.2:  T H E RELATIONSHIP B E T W E E N N M B M E A S U R E M E N T S , T H E I R P H Y S I C A L MANIFESTA-  TION A N D C O R R E S P O N D I N G R E L A X A T I O N A N D P S E U D O - O C C U P A N C Y M E A S U R E S .  Measurement To4= 100% To4= 30% To4= 0% To4= 1 twitch To4=0 twitch PTC < 7  Description / Manifestation full strength cannot hold head paralyzed paralyzed paralyzed deep block  Relaxation 0 0.7 1 1.19 1.31 ss 1.5  Pseudo Occupancy 0 0.77 0.88  0.95 1.0 « 1.1  PTC  • Measurement  Figure 2.2: CEDURE.  Stages of the Procedure •  R E L A T I O N S H I P B E T W E E N N M B A G E N T A N D RESPONSE T H R O U G H A T Y P I C A L P R O -  G R A P H S A R E O V E R L A P P E D T O SHOW THAT RESPONSE IS N O T O B S E R V A B L E UNTIL A  CERTAIN T H R E S H O L D ( B E THAT C O N C E N T R A T I O N OR P S E U D O - O C C U P A N C Y ) HAS B E E N R E A C H E D . C O N C E N T R A T I O N O F N M B A N D P S E U D O - O C C U P A N C Y A R E T H E DASHED LINE. T H E SOLID L I N E IS T H E N M T M E A S U R E M E N T M E A S U R A B L E D I R E C T L Y WITH T H E S T A N D A R D T o 4 .  29  Figure 2.2 shows NMB monitoring with respect to relaxation and pseudo-occupancy according to the stages of a typical case. Prior to administration measurements (PTC and To4) are at full strength, there is no relaxation and no occupancy. In the induction pre-threshold phase, drug is administered and starts binding to receptors and pseudo-occupancy rises without any change in measurements or relaxation. Then the threshold is reached, and the post-threshold induction phase shows an increase in relaxation as well, while the measurements of contractility decrease. In this particular case the patient is either a high responder (one who reacts relatively more to the treatment than the average case) or was intentionally overdosed, and saturation of the To4 measurement (it returns 0% contractility) occurs. Relaxation at this point is greater than the maximum effect visible by the To4, but there is still some contractility detectable by the P T C . This is now the deep block phase. As the maintenance period continues, the drug is metabolized, pseudo-occupancy (and true occupancy) fall and response returns to the To4 measurement. A perfect infusion is started and a good level of paralysis is maintained throughout the rest of this period, then reduced and maintained in the wrap-up period. Finally, the pump is stopped and NMB is allowed to come off completely in the reversal period. As the reversal period continues there is a return to full response as witnessed by the return of the To4 to 100%. Drug is still present and so pseudo-occupancy is greater than zero, but decreasing.  2.4  Nonlinear Modelling  With the use of the methods for handling data with partial To4 twitch counts and for linearizing the NMJ described above in Section 2.3, the response data was improved but still had some gaps due to fully saturated sensor measurements. As the ED^ dose achieves paralysis for 95% of the population, the 2 x EDg^ dose results in full paralysis for almost all patients. At this point the eTo4 sensor is saturated and the data cannot be used for impulse response modelling as the true value is not known. In addition, linear techniques for estimation of patient response requiring a non-interrupted vector of output data to match input data cannot be used. To overcome this and permit full identification with linear models, nonlinear modelling of the measured and extrapolated data was performed to obtain uninterrupted curves of regularly spaced points. Uninterrupted curves were arrived at through a nonlinear curve fitting estimation of the nonsaturated response points correlated to the time since the initial dose was administered. The shape of the curve is known from pharmacokinetic/pharmacodynamic studies to be a third order exponentially decaying pharmacokinetic profile (Organon [3]) with the pharmacodynamics being measured after an effect compartment: (t) = - ( j^-(e-^  C  V \K — 7T  - e~ ) + -r^-(eK— a kt  at  - e~ ) + T - ^ e " ^ - e' )\ k — (3 J kt  kt  (2.8)  where c(t) is the drug concentration; k is the coefficient of drug transfer for the effect compartment, v is the volume of distribution for the effect compartment; P, A, and B, and ir, a and 3 are the parameters describing drug flow in the various compartments; and t is the timestep. Initial estimates of the parameters required by the nonlinear estimation (NLE) routine were arrived at after experimenting with values published in vanMiert [44]. Solution of the NLE is sensitive to these initial estimates - they must be reasonably close to the true values to have a valid solution. For each subject, a dataset of matched output and time datapoints was assembled. Into it were placed all valid points - those with unsaturated response - and points were added at the end to force the estimation to return to zero in a reasonable time frame as would happen once the drug is completely eliminated. 30  Using the dataset, the parameters were iteratively calculated through recursive nonlinear estimation on a Taylor expansion of Equation 2.8. This was continued until the improved parameters produced an estimate of the dataset with error that was below a suitable threshold. This threshold was started at a root-mean-square (RMS) error of 0.001 and increased if a solution could not be found. A solution was considered to be unobtainable after 200 iterations. Parameter change was determined by the Jacobian matrix, J , a matrix of stacked rows of partial derivatives of the parameters to be estimated: dy dy dy  dy  dy dy dy dy  (2.9)  passed through a LSE type calculation scaling it by the current error vector, AV", at each iteration: ^parameter  = (J'J + 0.1 x diag(J'J))  -1  J'AV'  (2.10)  where y represents the concentration - c(t) of Equation 2.8 above - and diagQ represents the main diagonal elements of a matrix. J contains one row of Equation 2.9 for each datapoint used in the estimation. Equation 2.10 is the Marquandt version of the Levenberg-Marquandt compromise used to prevent singularity occurring in the calculations due to the inversion of very small numbers (Bates [67]). Prevention of singularity is achieved through the addition of the scaled diagonal matrix term, diag(J'J). Individual parameter updates were constrained in that excessively large and negative parameter values were not allowed, and thereby changes producing them were not implemented. Nonlinear estimation of the parameters is a computationally intensive and time-consuming process. It is temperamental and unpredictable in the sense that the result is influenced by the initial conditions as stated and can often result in an unworkable fit. As a result, this method of producing a model should not be used in an online real-time setting. Instead, the time constraint imposed and the demands on extraneous intelligence proved an impetus for use of a simpler modeling technique on-line and this nonlinear estimation was used offline to come up with complete models to be used for generating the linear models. With the parameter estimates, full time-courses for the drug according to the P K equation, Equation 2.8, were generated. For each subject, the subject's estimated parameters were inserted into the equation and calculations made for drug concentration for up to 300 timesteps (100 minutes at 20 seconds per timestep) for the rabbits and 1000 timesteps (5 hours, 33 minutes and 20 seconds at 20 seconds per timestep) for the humans. This concentration profile was considered to be the impulse response for the subject, the impulse being the 2 x ED95 dose. The number of timesteps used reflected that number of timesteps required before the calculated pseudo-concentration and relaxation for all subjects had fallen to zero (or close enough for practical purposes). Rabbit response data can be seen for the rabbits in the top graph of Figure 2.3. Note the periods of saturation in which the To4 is zero. Models of pseudo-occupancy were composed from this data. These are shown in the middle figure. The bottom chart of Figure 2.3 shows the modeled pseudo-occupancy for the average case. Estimated responses for the human cases of the prostate brachytherapy study appear in the top graph of Figure 2.4. The bottom graph shows the average response for the human dataset. The bottom two graphs show the length of the pseudo-occupancy response is much longer than that for the To4 measurement. This reflects the redundancy of receptors and the presence of drug lasting beyond the measurable effect. At this point, the data was ready for testing of model structure.  31  Rocuonium response tor rabbits: raw data(top), estimates (mid), average (bot)  0  Figure 2.3:  50  100  150  200  250  300  To4 DATA OBSERVED IN T H E RABBIT EXPERIMENTS EXPRESSED AS F R A C T I O N A L  RELAXATION: RAW DATA ( T O P ) , ESTIMATES O F INDIVIDUAL RESPONSES FOR P S E U D O - O C C U P A N C Y (MIDDLE) AND A V E R A G E P S E U D O - O C C U P A N C Y RESPONSE ( B O T T O M ) . T H E ABSCISSA REPRESENTS T I M E IN TIMESTEPS O F 20s. Estimated rocuronium responses (or humans: individual (top), ave. (bot.)  0  0  Figure 2.4:  l  0  100  200  1 1 1  100  200  300  400 500 600 Time (timesteps of 20s)  1 1r400 500 600 Time (timesteps of 20s)  - 700  j _  700  800  900  1000  1 1  800  900  1 1000  E S T I M A T E D ROCURONIUM RESPONSES F O R T H E HUMAN PROCEDURES:  PATIENTS ( T O P ) , A V E R A G E RESPONSE  2.5  300  INDIVIDUAL  (BOTTOM).  Model Identification  Once complete response curves were established, the average model was created by modeling the average of all responses and the process of model identification commenced. Optimal polynomial, ARX (auto-regressive exogenous) and Laguerre models were developed and compared. Calculations for the Laguerre models were aided by use of the Laguerre toolbox (Fu [68]) for Matlab (The MathWorks, Inc.).  32  Polynomial models were of the form: y(k) = a x  + an-iX™'  n  +  1  n  h a x + aix + a  (2.11)  2  2  0  where y is the response, ai are the defining terms, n is the order of the polynomial and x is the timestep. This model structure is not practical for application of adaptive modelling and control techniques but was included for comparison with the other structures. A R X models were defined by: . • . y(fc + l ) = b u(k) + biu(k - 1) H  h 6 _iu(fe - n + 1) —aoy(k — d) — a\y(k — d — 1) — • • • — a -\y{k n  0  n  —  (2.12)  d — n + 1)  where y is the output, u is the input, a and b are scaling parameters, k is the timestep and d is the delay. Optimal parameters for the polynomial and A R X models (the and bi terms) were found using LSE methods. These model structures are rudimentary to algebra and control and their description will be left to textbooks of those subjects. Laguerre models are not as commonly known as the above models, and will thus be discussed now in more detail. 2.5.1  Laguerre models  A Laguerre model is an orthonormal series representation of a plant's dynamics. It is used for its convenient network realization, transient signal similarity (important for responsive process control), and similarity to Pade approximation useful for identifying time delays. Laguerre models have simple representation and flexible structure, allowing for easy adaptation. The first filter block is a first order long-pass filter, the remainder are all-pass filters. Laguerre models were desired for their simplicity and ease of use in control and adaptation of the model. A good reference on Laguerre models is Zervos [69]. Laguerre models are based on Volterra equations. Volterra equations describe initial value problems related to dynamic systems. They are used for many reasons: as models, they are qualitatively well behaved; practical techniques exist for investigating their behaviour; and because model based control system design procedures are available. Volterra methods are attributed to Vito Volterra, who first used them to solve the nonlinear ordinary differential equation: ^  = F(x, y) , where y(x ) = y 0  (2.13)  0  as a series of functionals representing multiple convolutions of the stimulus, u(t): °°  poo  y(t) = Y~] / Jo n=0  fOO  ••• / Jo  Kin,  T )u(t - r i ) . . . u(t - T )dTi ...dr n  n  n  (2.14)  Volterra/Laguerre identification solves the above equation using the Laguerre series of orthonormal functions. These cascaded convolutions become the sum of a series of weighted, progressive multiplications of filter banks in the frequency domain, as shown in Figure 2.5. In discrete time, the basis functions take the form (Marmarelis [71]):  33  u  Vl-a  2  h  h  1—az  1-az  z—a  z—a  IN  z—a  Network Parameters  Figure  2.5: D I S C R E T E T I M E L I N E A R L A G U E R R E M O D E L ( F R O M D U M O N T [70]), W H E R E N IS T H E  N U M B E R OF FILTERS, A T H E L A G U E R R E P O L E , Z T H E DISCRETE T I M E FORWARD O P E R A T O R , K T H E L A G U E R R E V E C T O R COEFFICIENTS A N D C* T H E L A G U E R R E GAINS.  where a = { 0 . . . 1} is the Laguerre time-scale parameter determining asymptotic exponential decay behaviour. The progressive products are: M  v (t) j  = TY bj(r)u(t-T)  (2.16)  t  r=0  Here bj and Vj correspond to the filter blocks and k terms of Figure 2.5. A linear Laguerre model is defined by the state space representation: L(k + l)  =  AL(k)  y(k)  =  CL(k)  + Bu(k)  (2.17) (2.18)  where u is the input - the amount of drug given in multiples of a standardized dose (e.g. 2 x ED95), y is the output, k is the timestep and L is the patient state vector representing flow of input (drug) through the patient and composed of terms l\, l and IN of Figure 2.5, A and B are the state space matrix and vector representation monitoring flow of drug through the system, and C is the Laguerre model coefficient, vector, a vector of gains to weight the components of the state vector defined by a least squares-estimation on these equations and composed of terms c\, c and c/v of Figure 2.5. A and B are dimensioned by the number of filters and defined by the Laguerre filter pole p as: 2  2  {  P  \  (1-P )(-PT- 0 2  B(i)  =  J  1  y/T^i'-py-i  ,if<  i=j  i>3 y otherwise (2.19)  The Laguerre filter pole and C vector parameters are individual to each patient (and for average models). 34  Laguerre Network  l—az  VT-  Constant, I * order terms: [1, li,l , I3, • • • 2 order terms: hh,... l\,... /|,...] 3 order terms: [if, l\l , . . . Jf . . . /f ...] s  2  ci  nd  RD  2  Memoryless Nonlinearity  C2  C3  Figure 2.6: D I S C R E T E T I M E NONLINEAR L A G U E R R E M O D E L ( F R O M D U M O N T [70]) The Laguerre filtering concept can be used to create nonlinear system models by creating a linear equation of nonlinear terms. This can be seen in Figure 2.6 where multiplied combinations of the linear terms, h, l and £3, are scaled by their own gain constants, c and up, and summed to build the final model. Having obtained a linearized model of the nonlinear plant, standard prediction and control methods can be used. Using the calculated concentration data, the optimal Laguerre pole for each response was found. The optimal pole was found via an iterative search over the full range of possible poles. At each iteration, the available range was divided up into a set number of sections, the endpoints of which were tested as potential optimal poles. Each candidate pole was used to construct Laguerre matrices which were then applied to the above equations for state and output (Equation 2.17 and 2.18), to generate the response as it would be over the length of the test according to the input vector supplied. The difference between the generated response and the actual was the error. The pole generating the least error was selected as the best pole of the iteration and the process was repeated using the range between its nearest neighbors. The process was complete once the error fell below a threshold. The optimal pole for the rabbits varied between approximately 0.70 and 0.85. The human poles were slightly greater, as a result of greater response, ranging between approximately 0.80 and 0.95. Then, modelling of the filter gains for each model was done. This process was a least squares estimation of the parameters (the filter gains vector, C) of Equation 2.17, as: 2  2  C = (LL LL )~ T  T  1  Lr  (2.20)  y  where L is a matrix of the Laguerre vectors L , calculated using A and B matrices defined by the optimal pole as in Equation 2.19 and compiled as L = LQ : L\ : . . . LJV and y =[y y Q  l  ... y ] N  a vector of measured responses. The complete process of modelling a patient using Laguerre modelling is demonstrated in Figure 2.7. The process occurs sequentially from top to bottom in the figure. First the response data 35  0  20  40  60  80  100  120  Figure 2.7: L A G U E R R E M O D E L L I N G F O R A R O C U R O N I U M I M P U L S E RESPONSE: N M T RESPONSE DATA ( T O P ) , P S E U D O - O C C U P A N C Y CONVERSION (SECOND), P K RESPONSE (THIRD), L A G U E R R E MODEL PARAMETERS (BOTTOM).  is recorded in terms of relaxation. In the second chart, the non-saturated response data have been converted to pseudo-occupancy. The pseudo-occupancy data is modeled with non-linear estimation and a curve is generated for the patient's rocuronium pharmacokinetic response, as displayed in the third from top graph. Finally, the pharmacokinetic profile is remodeled as a linear Laguerre model, the parameter values of which are displayed in the bottom graph.  36  Stability and Robustness of Laguerre Models and Controller  To represent a system perfectly with a Laguerre model an infinite number of Laguerre filters are required. However, the math being inconvenient at that level, the series is truncated, introducing error due to the unmodelled dynamics. Provided an appropriately large enough number of filters is chosen to represent the system, control will be robust to the unmodelled dynamics as will be shown. The complete plant is actually described as: JV  M  (2.21)  P = PJV + H = J ^ C i i i + i=l  i=N+l  where PN is the nominal, modelled plant, H is the unmodelled dynamics, N is the number of filters in the model, and M is the total number of filters needed to completely describe the process. Stability to these unmodelled dynamics is obtained if the unmodelled dynamics have finite and minimal power in the bandwidth of the nominal plant in closed loop. This occurs if: PN(Z)F(Z)  m*)\ 1 +  (2.22)  < 1  P {z)F{z) N  where F is the transfer function for the controller. From the controller development described in Section 3.1.2, the extended horizon controller of this research is described as in Equation 3.7. Rearranging this, a transfer function for the controller relating the error signal (setpoint minus feedback) to the input to the plant is found: y -y(t)-C  (A -i)  T  T  ( d-X  C  0U  A  L(t)  d  R  u(t)  +  d-2  A  +  + I)B  e-k L{q- )u u 1 e p + kTL-iq- ) T  F  l  (2.23)  1  where [3 = C (A ~ + A ~ ... + I)B is the sum of the first d Markov parameters of the system and represents the predicted change in output due to the inputs to be given, e is error, q is the discrete time forward operator andfcjare terms of the vector K — C (A — I) . K x L is the predicted change in output due to state progression over time d. A, B and C are defined in Equations 2.17 and 2.18. Substituting the formulae for Pjv, H and K into Equation 2.22, T  d  l  d  2  T  d  M  i=N+l  1 J  2Zi=\ ih  (2.24)  < 1  c  As discussed in the more detailed explanation of this proof found in Dumont [72], Equation 2.22 reduces to M  < 1  (2.25)  i=N+l  Thus, stability and robustness in control are achieved with increased timeline d (which increases /3) and increased number of filters. Both increase the denominator and thereby decrease the overall gain of the unmodelled dynamics. Similarly increasing the number of filters N, decreases the number of terms and energy in the unmodelled dynamics which also decreases the gain. 37  2.5.2  Model Structure Selection  The various model types - A R X , Laguerre and polynomial - were assessed for accuracy and simplicity according to Akaike's Informative theoretic Criterion (AIC) and Final Prediction Error (FPE), mean squared error (MSE) and by the number of parameters required for estimation. AIC and F P E are defined: AIC  =  log[V(l + 2n/N)]  (2.26) (2.27)  where V is the variance of the residuals, N is the length of the data series and n is the number of parameters to be estimated. The lower the AIC and FPE, the better the model is judged to be. From Equations 2.26 and 2.27, AIC and F P E are both increased with increased variance in the residuals, corresponding to a worsening fit of the data by the model. The model is penalized according to its complexity by the increase in the F P E value seen with increasing number of parameters, because the denominator term approaches zero as the number of model parameters, ro, approaches the number of datapoints, N. As an example, consider a process being modeled with N = 100 measurements. A fit of the data with n — 10 parameters yielding a variance in the residuals of 0.1, will have AIC and F P E of -2.12 and 0.12, respectively. A second, worse fit having a variance of 0.5 and the same number of model parameters will have increased AIC and F P E of -0.51 and 0.61. A similar fit to the first with variance of 0.1, but requiring double the parameters (ro = 20) will have increased AIC and F P E of-1.97 and 0.15. Laguerre and A R X models were calculated up to maximum complexities as determined by the number of available terms in the data, forty-two. Forty-one was the maximum number of Laguerre filters; the maximum input and output parameter vectors were forty-one elements long for the A R X models. Delay of up to six timesteps was modeled for the A R X models. All subjects showed response by this point. Polynomial models were calculated up to order thirty, beyond which the models became very unrepresentative of the data. Models of the individual responses using the optimal model structure were constructed and parameter variation was measured to get an understanding of the requirements to be placed on the future controller.  Optimal Model Structure Selection and Parameter Variation  In testing for the best model structure, the sixth order Laguerre model was optimal. Although the optimal A R X model was best for the AIC, F P E and MSE criteria, it was not chosen as its complexity of thirty-five parameters was too large to be practical for adaptation. Near equivalent error performance and much reduced complexity were found with Laguerre models of between six and fifteen parameters. In total, forty-six A R X models had better error performance than the sixth order Laguerre model but the minimum number of parameters at twenty-seven was considered too high. Results of the measures are summarized in Table 2.3. Figure 2.8 shows the Bode plot for the average case using six and fifteen order Laguerre models. The plots are virtually identical indicating equivalence for control. As a demonstration of variation, rabbit data models had MSE ranging from 0.031 to 0.13, with a mean of 0.090±0.13. Laguerre optimal poles ranged from 0.89 to 0.95 with a mean of 0.91±0.026. Impulse response static gain values ranged from 17.6 to 57.9 with a mean of 33.4 ± 15.2. For the human data, error between the measured data and the estimated responses varied from 0.048 to 38  Table 2.3: T H E O P T I M A L MODELS F O U N D FOR T H E A R X , P O L Y N O M I A L A N D L A G U E R R E 15  th  6  th  AND  O R D E R STRUCTURES. M O D E L T Y P E S A R E IN T H E FIRST C O L U M N .  Polynomial ARX Laguerre l5 order Laguerre 6 order th  th  AIC  Complexity  FPE  MSE  -7.24 -8.86 -8.85 -8.61  19 35 15 6  7.80e-4 4.75e-4 8.44e-4 1.05e-3  4.8e-2 1.8e-2 2.3e-2 3.22e-2  0.14 with a mean of 0.085 ± 0.032. Laguerre optimal poles ranged from 0.96 to 0.99, with a mean of 0.97 ± 8.9 x I O . Static gain ranged from 85.9 to 564, with a mean of 301 ± 138. To investigate frequency response and controllability of these models, Bode plots were compiled. The rabbit data Bode plots are shown in Figure 2.9. The human Bode plots appear in Figure 2.10. Variance in gain for the rabbit has a maximum at O.OOOlrad • s of approximately !2dB, ranging from 24 to 36dB. This range narrows between I O and 10~ rad • s but remains near 6dB on average. The range in phase is less than or equal to 45° throughout. Phase margin is adequate throughout the range of measure and is far from the unstable point of —180° well past the —3dB points for all models. The human data was similar in terms of phase margin and stability but larger in terms of variation. The range of human gains was approximately 15dB throughout. The phase had a maximum range of about 75°. -3  _ 1  - 3  2.5.3  2  _ 1  Comments on the Initial Model Building Results  This section presented data collection and methods for the selection of a model class for automated control of neuromuscular blocking drug administration. Although valuable data were collected, it 39  Nyquist plol lor rabbit models (dashed) and average (solid)  Frequency (rad/sec)  Figure 2.9: B O D E PLOT OF T H E RABBIT DATA: INDIVIDUALS (DASH-DOT) AND AVERAGE (SOLID). Bo do plot for human models (dashed) and average (solid)  Frequency (rad/sec)  Figure 2.10: B O D E PLOT OF T H E HUMAN DATA: INDIVIDUALS (DOTTED) AND A V E R A G E (SOLID). must be noted that the population sizes were not large and this may affect the results. As well, human data was taken strictly from elderly males to better ensure homogeneity of results at the start, making the average response less representative of society as a whole. Laguerre modeling was pursued despite there being A R X models with better AIC results. This was for reasons of complexity and ability to work in control. The A R X models were accurate and many had better mean squared error and F P E results. However, this was always at the price of much higher parameter counts. Large numbers of parameters are particularly hazardous for A R X models. The higher order can cause pole-zero cancellation to take place, which leads to moving poles and zeros with continued estimation. These modelled but non-existing dynamics prevent solving of the Diophantine equation and are a disaster for control. As well, the A R X model used 35 filters to model a 42 point dataset to  40  the equivalent detail of the 15 order Laguerre model. A ratio of 1.4 datapoints to every parameter is overkill, not realistic, and vulnerable to error in the identification process later on. Laguerre modeling is known for its usefulness in control. Laguerre models are adept at handling process delay, even if it is of great magnitude relative to the sampling time (Dumont [73]). Laguerre functions are orthogonal and thus can be scaled independently of each other for better flexibility in modeling, approximations can be truncated to smaller order, and unlike A R X , Laguerre models do not have pole-zero cancellation. Laguerre methods are linear and can be implemented with least squares estimation (LSE) techniques. Importantly, these models can be updated easily with recursive-LSE to allow their application in adaptive control schemes. Because of the great variability seen, adaptive control methods are required. The standard deviation of the average estimate static gain was 45.4 and 45.8% of the mean for the rabbit and human models respectively. The ranges of static gains were 121 and 159% of the mean for the rabbit and human datasets. The Bode plots also displayed substantial variation amongst both groups. Although a robust controller could handle perturbations of that magnitude, it would likely be quite conservative and hence of little practical use.  2.6  Conversion of Standard Stimuli to To4  To4 stimulation is advantageous compared to the other stimulation modalities but is not optimal under all circumstances. Other stimulation techniques are used as a matter of preference and because each has different sensitivities to the level of NMB. For example, when the patient is completely paralysed as attested to by To4 and ST stimulation, tetanus, P T C and DBS may still show some function. As such, under these circumstances other stimuli can provide useful data regarding patient state if converted to and interpreted in terms of the defining method, e.g. converted to To4 ratios when the patient response model is defined in terms of the To4. (The defining method refers to the stimulation means used to collect the data used to build the response model. The model describing the patient response is dependent upon the method used to garner that response.) Another contribution of this research is the interconversion of the various sensing modes. The use of different techniques increases the amount of useful data and range of operation for control of NMB. Interconversion of this data allows the many stimuli modalities to be used as mathematical equivalents, allowing the application of control and modelling techniques well beyond the range of a single modality. The importance of this can be seen in an illustration of a typical case in which more than one sensing modality is used, shown in Table 2.4. The To4 is the preferable sensing method at the start and through most of the case. It is used at induction and until the block becomes deep with partial To4 responses converted to eTo4 measurements as described in Section 2.2. Since this occurs prior to complete NMJ ACh receptor occupancy, there is still the possibility of some response. Response is revealed by using a more ACh liberating method of stimulation such as P T C . If the deep block is unintended the P T C could be used to monitor and adapt the sensor while in saturation. If deep block is desired, it will be necessary to solely use PTC. Once the drug has worn off to allow at least a partial To4 measurement, To4 stimulation can be resumed for the maintenance, wrap-up and reversal portions of the case. This scheme was used in the experiments and clinical trial of this thesis. All measurements were converted to relaxation. Relationships between To4 and ST (or TI) have been discussed in Section 2.2. Some other commonly used stimuli modalities and their means of conversion to To4 are now described.  41  Table 2.4:  STAGES IN A T Y P I C A L P R O C E D U R E AND STIMULATION USED (TIMEWISE IN ORDER OF  A P P E A R A N C E AND NOT TO S C A L E ) .  To4  Induction JJ.  Deepening block  To4 with less than four measurable twitches, translated to eTo4  Deep block  PTC translated to T 4 0  (overshoot or by demand)  2.6.1  Maintenance  To4  Wrap-up  To4  Reversal  To4  P T C to To4  To enable the scheme of Table 2.4, a method for converting P T C measurements to To4 was developed for this work. Although there are conditions when it is impossible to get any response, the PTC may be able to evoke response when To4 and ST twitches cannot. The response evoked by the P T C indicates when the To4 will return. In Schultz [74], 108 patients of health status ASA class I or II undergoing earnose-throat surgery and using rocuronium as the NMB agent, were monitored to find a correlation of P T C to time to return of the first twitch of the To4. The relationship learned was: (2.28)  r = 18.8 - 6.46v PTC /  where r is the number of minutes until return and PTC is the number of measurable post-tetanic twitches. For example, if a P T C of 1 is measured, the To4 will return in 12.34 minutes. This measurement is not an eTo4 measurement but it is information that can be used to obtain one. Based on Equation 2.28 the PTC will indicate the amount of time until a To4 with one twitch, or a relaxation of 1.19 (from an equivalent To4 of —19% for a ST, Section 2.2) or a pseudo-occupancy of 0.95, arrives. The amount of time is converted to timesteps and the model for occupancy is used to arrive at what the present patient state is. Using a Laguerre state space model, drug flow through the patient can be described by Equations 2.17 and 2.18. Typically B and C of these equations are vectors, but could also be scalars for one-dimensional or matrices for multi-variable systems. C is referenced to time as in an adaptive system it would be modified to reflect the changing patient or to allow adaptation to patients not identical to the initial model. Assuming that the C matrix describing the patient is constant for the next r timesteps, then the current patient state can be calculated from: L(t + T) = C{t)- y(t 1  + T) = C{t)  C(t)T (t) C  42  (2.29)  The equation is calculated taking care for whether or not C is a scalar, vector or matrix. If C is a non-zero scalar or a matrix as for multiple input, multiple output systems, Equation 2.29 may be solvable. If it is not or if C is a vector and thereby not invertible, the subsequent method is used. Assuming that there will be no inputs (PTC is only used when the patient is relaxed beyond producing useful To4 measurements, and therefore additional drug will not be given), from Equation 2.17: L(t+1)  =  L(t + 2)  =  AL(t + 1) =  L(t + r)  =  A L(t)  L(t)  AL(t) A L(t) 2  and  T  = A~ L[t + T) T  (2.30)  The pseudo-occupancy estimate for current amount of drug at the NMJ is found by substitution into Equation 2.18: y(t) = A~ L(t T  + r)C(t)  (2.31)  since Equation 2.17 for L(t + 1) becomes L(t + 1) = A L(t) in times of zero input. Another method of converting P T C to To4 starts by advancing the L matrix the r steps into the future determined by Equation 2.28: L(t + T)= A L(t)  (2.32)  T  (again, no input is assumed because of the saturation condition present to predicate the use of the PTC stimulus). A n estimate of y at this future point is: y t(t + T) = C(t)L(t + r) es  (2.33)  Since the system is assumed to be linear, the ratio of y(t + r) to the y that should be seen when the To4 first begins to return (at full relaxation) will indicate the appropriateness of the model (the accuracy of A, B and C) and can be used to scale the L matrix: ^approx —  L(t + r) — — — (2.34) where 0.95 is the pseudo-occupancy - an estimate of the receptor occupancy and thereby the amount of drug at the NMJ - when the To4 returns. This information can be used to construct an estimate of what the current occupancy must be: y(t) = C(t) L ppr a  0X  (2.35)  albeit most likely greater than 100% - which is legal in this linearized view. Finally this value is converted to an estimate of what the equivalent To4 measurement would be - undoubtedly negative in strength, greater than 1.32 in relaxation. It needs to be noted that this approach has some potential inaccuracies: C is assumed to be true; L and y estimates are artificial as they are based on other estimates; and results of Equation 2.28 are for a population (the patients of that study) average that will not always be representative. This correlation between the P T C and the time of return of the To4 has been determined for various NMB agents, including pancuronium, attracurium and rocuronium. For illustration the rocuronium results are displayed here. Should a different drug be used, the parameters of Equation 2.28 need to be adjusted. 43  2.6.2  D B S to To4  DBS and To4 are similar in their range of utility, and conversion can be made between the two using a relationship found in Engbaek [75]. Using the standard DBS consisting of two trains of three pulses at 50Hz, spaced by 750ms, To4 and DBS can be interconverted as: DBS = 1.07 To4 - 3.2 or To4 =  D  B  ^ *  3  2  (2-36)  where DBS and To4 are both in percent units. Then, when DBS stimulation is indicated, the measurement is converted to To4 for use by the modelling and control algorithms. Some non-traditional DBS techniques were also characterized for relationship to To4. In percent, the relation between DBS and To4 found for other twitch, frequency and delay between bursts parameters are (Nielson [76]): =  DBS3@SOHZ,O.5S,2@50HZ DBS  ,. @  3MOHZ 0 75ST2  2.6.3  =  50HZ  0.76 To4 — 1.8 0.78 To4 + 3.8  (2.37) (2.38)  Interconversion of non-To4 Measurements  As the To4 measurement was judged to be the best of the commercially available modalities, the models used in this research were built from To4 measurements and to this point other modalities have been related back and interpreted as To4 equivalents (but in terms of relaxation). However, for various reasons it might be required to use and work in terms of another, non-To4 modality. As different stimuli types (e.g. ST or DBS) would show different response, a modeling system revolving about a different base type with conversions to that based type is possible. For example, if DBS was the preferred stimulation, To4 measures could be converted to DBS using Equation 2.36 and, based on P T C could be converted to DBS (Nielson [76]) as follows: DBS3@50Hz,0.5s,2@50Hz = DBS z,o.75s,2®40Hz  =  3moH  DBS3@80Hz,0.75s,3@50Hz —  1-2  PTC  0.85 1-2  PTC  PTC  — 2.3  (2.39)  - 0.39  (2.40)  2.3  (2-41)  —  The authors found that a PTC of 6 indicated the reappearance of DBS. Finally, multiple conversions could be used to get from one type to another and back to the base type if needed, e.g. DBS converted to To4 to ST. Of course, error can be introduced by approximation and variance of parameters at each step.  2.7  Summary of Neuromuscular Monitoring and Modelling  This concludes the chapter concerning neuromuscular monitoring and modeling. This chapter concentrated on the novel neuromuscular monitoring techniques and modelling developed in this research. The initial experiments to collect data for model building were described. The responses gathered were highly nonlinear with delay to response, sensor saturation and substantial periods of time during which drug was present but not decreasing response. To manage these nonlinearities, novel monitoring techniques and modeling were developed. These techniques extend the range of sensing, increase data available to the modeling procedures and circumvent the nonlinearities at the N M J to produce full impulse responses. Use of the novel monitoring and modeling techniques 44  facilitated nonlinear estimation of concentration profile of NMB drug producing the effect, which could then be sampled to create full impulse responses, and which allowed the development of linear models to describe them. Model identification was undertaken to find an optimal model structure permitting application of adaptive control techniques. Several model structures were compared and the Laguerre model structure was found to be best for the purposes of this investigation. With the model structure selected, the development of the controller and associated adaptation schemes could begin. These topics are discussed in the following chapter, Chapter 3.  45  Chapter 3  Controller Development, Simulation and Testing In the previous chapter the outline of the selection process for modelling was developed and details of the initial experiments in order to build those models were discussed. With those models at hand, simulations could be performed to test controllers, test model adaptation and develop the advisory system and closed-loop control system for application in the clinic. This chapter will start with a discussion of the details of the controllers implemented, the computer simulation to test them with, and the controller selection process and results. The chapter will continue with discussion of the testing of the eTo4, nonlinearity linearization, adaptation and PTC to To4 conversion. Finally, development and testing of a novel adaptive modeling scheme to handle the large patient variation is discussed.  3.1  Controller Development  Several controllers were tested and developed for experimental and then clinical application. These controllers included bang-bang control, controllers implementing statistical process control (SPC), GPC, a method of control replicating the actions of the anesthesiologist's serial bolus approach, PID controllers, and linear and nonlinear extended horizon predictive controllers for the Laguerre models. The bang-bang controller was implemented as described in Section 1.4.1. Controllers implementing SPC were similar to the bang-bang controllers in concept but with input rate adjusted based on the standard deviation of the error signal relative to the expected noise level. GPC was mentioned in Section 1.4.5. The GPC controller was implemented as described in Clarke [34]. The anesthesiologist controller gave an initial dose at 1.5 x the 2 x ED95 dose and then subsequent doses at 2 x ED95 when function returned to the setpoint. The initial dose is one recommended for rapid onset. The following doses were slightly larger than they would be under normal conditions but representative of an anesthesiologist who wants to ensure blockade. The remaining controllers - PID and Laguerre methods - were seen to be more successful and more likely to succeed in the clinic, as compared to the others. As such, these controllers were developed further and will be described in greater detail next.  46  3.1.1  PID Controller Design and Tuning  The PID control law can be described as: e(t) + — J e(t)dt +  Tj d  (3-1)  t  where u is the input, e is the error signal and the control law parameters are K is the proportional gain, Ti is the integral time constant and Td is the derivative time constant. An accepted industry standard method of tuning PID controllers to determine the control law parameters is the open-loop Step Response Method of Ziegler-Nichols (described in Astrom [77]). The Ziegler Nichols Step Response method drives a system with a step input and deduces the PID controller parameters based on the measured output according to: c  K  c  Tj T  d  =  1.2/a  =  2L  =  (3.2)  L/2  where L is the delay, and a is the intercept on the (negative) ordinate axis with a tangent to the point at 0.63 of the final magnitude. Average model step r e s p o n s e (top) and derivative (bottom)  0  1  1  1  5  10  15  i  i 10  15  1  1  1  20  25  30  I  i  i  20  25  30  35  i  1  35  40  40  Figure 3.1: Z I E G L E R - N I C H O L S S T E P R E S P O N S E M E T H O D F O R PID C O N T R O L L E R DESIGN. A V E R A G E M O D E L S T E P RESPONSE ( T O P ) A N D DERIVATIVE ( B O T T O M ) . U N I T S O F T H E ABSCISSA A R E 20s TIMESTEPS.  Applying the step input to the average response produces the curve of the top graph of Figure 3.1. In the same figure is a graph of the derivative of the step response to determine the slope of the tangent to the response. From the graph of step response, it will be seen that time until the response reaches 0.63 of the maximum rise occurs at timestep 13 when response is a pseudo-occupancy 47  of 6.69. At this point the derivative of the step response is 0.51 pseudo-occupancy/timestep. Using the derivative as the slope of the tangent, the intercept is found from the equation for the slope of the line with intercept point (0,a) and tangent intersection point (13,6.69): m  0.51 a  =  Vi ~ V2 X\ - X2  6.69 - a 13-0 0.51 x 13 - 6.69 = -0.06 = =  (3.3)  Delay, L, was found to be 3. Equations 3.2 then produce the PID parameters: Kc — 1.2/0.06 = 20, Ti = 2L = 2 x 3 = 6, T = L/2 = 3/2. By empirical testing, it is known that these rules apply only for systems for which 0.1 < L/T < 0.6 (Astrom [77])). This holds true here, as L/T = 3/(13 - 3) = 0.3. This design was tested in simulation for performance with the average model, and with high (reacting relatively more to the treatment than the average case) and low (reacting relatively less than the average case) responders. The results have been charted in Figure 3.2. Performance was good for the average case, although there was overshoot at the start that saturated the sensor. The low responder showed better performance remaining legible to the eTo4 and having continuous infusion throughout the case. The performance for the high responder, however, was abysmal. The initial input caused a large overshoot, a very long recovery and a pump that could not turn back on. This malfunction is most likely a result of the accumulated error being sufficient to swamp the integral action, with little way to relieve it. Beyond the problems seen in the above, the open-loop method has the problem of great sensitivity to disturbances, being that it is made with open-loop methods. Another method, the Ziegler-Nichols Closed-Loop Step Response method (described in Astrom [77]), was used to tune the PID controller. This approach uses relay-based feedback to produce a square wave input that will drive the system into a state of limit cycle oscillation. The relay appears relative to the plant as shown in Figure 3.3. The relay provides an input of one when the output is below the setpoint (in this case zero), and an input of negative one when the output is above the setpoint. When the system is in oscillation, the fundamental gain (K ) and frequency (the "ultimate" period - T encompasses this) parameters can be determined. These in turn can be used to determine the PID parameters as: d  u  K  =  C  u  0.6K  U  Ti  = 0.5T  T  = 0.12T„  d  U  (3.4)  A simulation was conducted applying relay input to the average response and the output, input and error signal are shown from top to bottom in Figure 3.4. From these charts, the ultimate period was T = 17.1 timesteps and the ultimate gain, K = 0.223. These values were put into Equations 3.4 and the parameters were: Kc = 0.134, Ti = 8.5 and T^ = 2.05. It must be recognized that this was a mathematical exercise in simulation (and only possible in simulation), and not a biologically sound procedure, for the reasons that negative drug cannot be given for this class of drugs, negative response cannot be measured, and the actions could not be implemented ethically. A controller with the calculated values was implemented in simulation and tested for performance with average, low and high responders. The results are shown in Figure 3.5. Performance was much improved over the open-loop tuning with reduced overshoot in the average and low u  u  48  1.5 1 0.5 0  \ i -  1  — » - - \ ,  i  • \y  • „•  • i  0.2  J  j  . J  1  j  i  L  J  <_  J  ZieglerNichols Open-loop method:  !  Average model  i  !  r^^i  • i ,  i ,  i ,  :  :  !  >  i  I  i  i  i  0.1 0 1 0.5  \  n  _/\.... * • # *  1  I  i  i  Low Responder  0.2  High Responder  Figure 3.2: APPLYING T H E ZIEGLER-NICHOLS STEP RESPONSE METHOD TO AVERAGE (TOP TWO CHARTS), LOW (MIDDLE TWO CHARTS) AND HIGH (BOTTOM TWO CHARTS) RESPONDING MODELS. CHARTS ARE IN PAIRS WITH T H E TOP CHART IN EACH PAIR SHOWING RESPONSE (DOTTED LINE) AND SETPOINT (SOLID LINE) AND THE BOTTOM CHART SHOWING INPUT. UNITS OF T H E ABSCISSA ARE 20s TIMESTEPS.  49  system/plant  relay  y  h+1 -1  Figure 3.3:  ZIEGLER-NICHOLS  C L O S E D - L O O P S T E P R E S P O N S E M E T H O D : CLOSED LOOP C O N T R O L  OF A P L A N T WITH R E L A Y F E E D B A C K . .  Figure 3.4: Z l E G L E R - N l C H O L S C L O S E D - L O O P METHOD FOR P I D C O N T R O L L E R DESIGN: STIMULATED RESPONSE IN R E L A X A T I O N ( T O P ) , INPUT IN N U M B E R OF 2 X EDg DOSES (MID) AND ERROR SIGNAL IN R E L A X A T I O N ( B O T T O M ) . UNITS OF T H E ABSCISSA A R E 20s TIMESTEPS. 5  50  ZieglerNichols Closed-loop method:  1 0.5 0 0.4  Average model  0.2 0 1 0.5  i  * •  ;  i  i ;  ;  1  r ;  ;  Low Responder  1  ;  *  i  0 0.4  i  i  i  i  i  i  0.2 0 1.5 1 0.5 0 0.4  [  i  i ,  i T  i  i  r  1  i  L High Responder  r  J *  •  i  i  i  I  i  100  150  200  250  300  i _  0.2  0  Figure 3.5:  {  50  350  APPLYING T H E ZIEGLER-NICHOLS C L O S E D L O O P METHOD TO AVERAGE (TOP TWO  C H A R T S ) , LOW (MIDDLE T W O CHARTS) AND HIGH ( B O T T O M T W O CHARTS) RESPONDING MODELS. C H A R T S A R E IN PAIRS WITH T H E T O P CHART IN E A C H PAIR SHOWING RESPONSE ( D O T T E D LINE) A N D SETPOINT (SOLID LINE) AND T H E B O T T O M CHART SHOWING INPUT. UNITS O F T H E ABSCISSA A R E 20s  TIMESTEPS.  51  responders, and decreased undershoot and a return to good control with the high responder. However, the undershoot seen would be detrimental to surgery by allowing the level of blockade to fall to a point where the patient could regain some muscle function. In an attempt at improving performance with high responders, setpoint weighting (see Astrom [78] for details) was implemented. This modified the control law from Equation 3.1 to the following:  u = K (e c  + Y Jedt  p  +  i  T ^jfj  (3.5)  d  where u is the input, e = y — y is the error signal as before, e = by — y is the error signal weighted for the proportional case and e = cy — y is the error signal weighted for the derivative case, and b and c are constants ranging between zero and one. For the standard case as before, they have a value of one. Manipulating b and c worsened performance of the controller by increasing delay and overshoot. As a result, it was decided to leave the PID controller as it was without setpoint weighting. 3.1.2 The Laguerre Controller sp  p  d  sp  sp  The Laguerre controller was an extended horizon controller (an algorithm using a state-space model to calculate inputs based on predicted response at a defined length of time into the future). The controller uses the model to predict future response levels as affected by the predicted elimination of the drug. These levels are then used to make predictions on what drug would be required to arrive at the chosen setpoint of a To4 measurement of 10% in 20 minutes and at the end of the case. This setpoint was chosen as it is at the most responsive end of the range of surgically useful and easily reversible levels of NMB. Starting from the initial state equation, assuming a constant input and extrapolating for a horizon of d timesteps into the future, the Laguerre state and output equations (Equation 2.17 and 2.18) representing the process become: L(t + 1)  = A L{t) + B u(t)  L(t + 2)  = AL(t + l)+Bu{t =  L(t + d)  + l) = A(AL(t)  + Bu(t))  + Bu(t + l)  A L(t) + (ABu(t) + B)u(t) 2  (3.6)  = A L(t) + {A*' + A ~ + • • • + I)Bu d  1  d  2  The second equation was arrived at by substituting the first equation for L(t + 1). The future response will be yu = C L(t + d) and the current response is y(t) = C L(t). Then, the input required to get from the present to the future can be found by subtracting the future and current response and then solving for u: T  y -y{t)  = C (L(t  +  =  L(t) + (A ~ + A ~ + ••• + I)Bu(t) - L(t))  T  R  u(t) H  T  )  -  ~  C (A T  V  d  R  d  T  l  d  2  ~ ~° ^ ~ (A ~ + A ~ + ... + I) B V { t )  C  d)-L(t))  d  T  l  {  d  I  ]  L  (  t  (3 7)  )  2  {  '  For bolus-style, discrete inputs, there are no other inputs between this input, u(t), and the next predicted dose and Equation 3.7 reduces to: u  (  t  )  _  V  R  - ,  M  - c ^ - i  52  )  m  (  3  8  )  Controllers were made nonlinear by modifying the output equation as mentioned in Section 2.5.1 and shown in Figure 2.6. Nonlinear controllers included controllers for Laguerre models with an extra term for the nonlinearity: y= C L+L D L (3.9) T  T  where D is a gains matrix configured to incorporate either combination terms: L{Lj where i ^ j, or square terms: LiLj where i = j, or both combination and square terms.  3.2  Preliminary Details of the Simulations  Software simulating the closed loop control of rocuronium administration with both bolus and infusion administration was developed for rabbit and human subjects. The goals of the simulation were to provide a means of testing and selecting optimal controller structure, and of experimental verification of modelling and control schemes, including the eTo4, the proposed methods of handling nonlinearities at the NMJ, the use of non-To4 stimuli and the adaptation scheme of model swapping and recursive estimation. Software for the simulation and control programs was coded using Labview (National Instruments Corporation, Texas, USA) with Matlab (The MathWorks, Incorporated, Massachusetts, USA) functions embedded, including some from the Laguerre toolbox (Fu [68]). The number of timesteps for each simulation run was 360, which, at 20s per timestep, corresponds to a two hour case. This duration was felt to be an appropriate size, as two hours is a typical anesthetic time for a medium length case - a case in which multiple doses of neuromuscular blocking drug would be required. This duration was comparable to the gynecological cases seen in the clinical testing (Chapter 5). For the closed-loop control simulations, either six or eleven models were available to test with, depending on whether or not model swapping (a model adaptation scheme requiring a modelset of known patients, it is disclosed in Section 3.7.1) was implemented. When model swapping was implemented, five known models and an average made up the known modelset and the other models were used as validation data. When there was no model swapping, only the average model was known to the computer. To test robustness, in some experiments Gaussian distributed noise was added to the measurement with three standard deviations being defined as 20% of the measurement range. This value was chosen to mimic results seen in the literature and laboratory testing. Evaluation of the results was done using MSE, performance error (PE), median performance error (MPE), median absolute performance error (MAPE), wobble, time to setpoint, time to minimal surgical conditions and time spent within 5% of the setpoint. Whereas MSE is familiar to engineering, the other measurements are not as well known. As developed in Sheiner [79] and Varvel [80], they will be briefly discussed here. P E is a ratio measure of error comparing the measurement and desired setpoint: PEi =  V m i  ~  (3.10)  Vpi  where y i and y i are the measurement and setpoint values at time i. Results presented in this thesis for P E are mean P E for the length of the case. M P E is the median measure of PE. It provides an assessment of the accuracy of the infusion. M A P E is the median value of the absolute value of the P E values for the case: m  p  MAPE  = median{\PEi\,i  53  = 1... AT}  (3.11)  M A P E provides an idea of the power in the error signal, somewhat analogously to MSE. Wobble assesses the variability in the measurement. It is a calculation of the median absolute deviation of P E from MAPE: wobble = median{\MAPE - PEi\,i = 1... TV} (3.12) A larger magnitude wobble indicates greater oscillation in the output. The simulation was judged to be producing "close enough" results when the output was within ± 5 % of the setpoint, where the setpoint was 0.9 relaxation (a To4 of 10%). This setpoint was chosen to reflect a compromise between obtaining good surgical conditions and an easily reversible state. Good surgical conditions are found considered to be had at To4 measurements of 20% or less (relaxation of 0.8 or higher) As stated in Stoelting [81], "In an adequately anesthetized patient, twitch height of less than 10% or a To4 of less than 20% should provide adequate surgical relations. If the response is less than this, difficulties with antagonism may develop." Difficulties arise with antagonism, a.k.a. reversibility, because of the mechanism of action of the reversants used. Reversal agents block acetylcholinesterase, the enzyme that breaks down ACh, the neurotransmitter used at the neuromuscular junction. Reversants thus permit more ACh to accumulate, increasing transmission and muscle function. However, as rocuronium is a competitive antagonist of the ACh receptor (AChR), if there is too much rocuronium, the ACh cannot access the AChR, and the patient cannot be reversed. Reversibility becomes possible once enough of the NMB drug has been metabolized to permit a To4 measurement having two twitches.  3.3  Controller Testing  Simulations for controller selection took place in two separate runs. The first run was a quick trial aimed to test and eliminate most of the controllers, resulting in a small group of controllers able to adequately control the average model. The controllers tested included all those mentioned in Section 3.1. As could be predicted by the results seen in Wait [21], the bang-bang control was inaccurate and unstable because of the on/off nature of the controller causing oscillation of the process variable between its bounds. Because of the oscillation, the use of the bang-bang controller was discontinued. The SPC controller was similar to the bang-bang controller, but to a lesser degree. Its tuning of the input rate based on error reduced the oscillation over time, but was never able to eliminate it. It was decided not to use it in experimental testing as it took too long to settle to be clinically useful. The Laguerre nonlinear controllers were also eliminated. The parameter gains on the nonlinear terms were large, causing the controllers to rapidly destabilize. The best of the control schemes and the controllers that underwent further testing were the linear Laguerre, PID, and GPC controllers. The anesthesiologist controller underwent further testing to provide a benchmark to current clinical practice, despite its poor performance. In the testing, the rank of the controllers was PID, Laguerre, GPC and then anesthesiologist. The PID controller demonstrated lower error as seen by the mean MSE, MPE, M A P E and wobble values calculated. PID demonstrated better performance in terms of spending the most time at or near the setpoint. PID also had quicker times to setpoint and minimal surgical conditions than Laguerre and GPC, but was slower than the anesthesiologist approach. Results found are displayed in Table 3.1. Graphs comparing measured response and setpoint, with corresponding inputs for the two best controllers and standard care are shown in Figures 3.6 and 3.7. In Figure 3.6, the subject being simulated is a high responder. The standard care approach (top two charts, labeled Anesth.) produces a series of large overdoses showing little time where the patient can be reversed. The PID controller (middle two charts) produces overshoot at first, then 54  Table 3.1:  C O N T R O L L E R P E R F O R M A N C E IN SIMULATION T E S T I N G .  N U M B E R O F T H E TIMESTEPS T O R E A C H T H E SETPOINT. OF  " T I M E T O S E T P T " IS T H E  " T l M E T O M I N S U R G " IS T H E N U M B E R  T I M E S T E P S TO R E A C H M I N I M U M SURGICAL CONDITIONS.  "TlME  AT S E T P T ± 5 % " IS T H E  N U M B E R O F TIMESTEPS S P E N T WITHIN 5% O F T H E SETPOINT.  Controller  Laguerre PID GPC Anesthesiologist Controller  Laguerre PID GPC Anesthesiologist  MSE  0.41 0.27 0.46 1.39  ± 0.14 ± 0.14 ± 0.17 ± 0.12  MPE  -0.23 ± 0.14 0.02 ± 0.06 -0.27 ± 0.17 -1.02 ± 0.15  MAPE  0.25 0.11 0.30 1.02  ± 0.14 ± 0.13 ± 0.16 ± 0.14  Time to  Time to  Time at  setpt  min. surg.  setpt ± 5 %  10.6 ± 1.2 7.9 ± 1.0 10.3 ± 1.1 3.6 ± 0.5  9.5 7.2 9.1 3.2  ± 0.8 ± 0.6 ± 0.5 ± 0.4  Wobble  0.49 0.11 0.57 2.04  ± ± ± ±  0.27 0.12 0.32 0.29  103 db 32.0 289 ± 140 108 ± 42.9 26.2 ± 0.71  decay below the setpoint while the controller unwinds and deals with the less than zero constraint (negative drug cannot exist and to handle this all negative inputs are zeroed). This deficiency is eventually corrected and the response is brought to and maintained at the setpoint. The Laguerre controller (bottom two charts) shows improvement as the case goes on and the model is adapted. Throughout the case, the patient is basically saturated - not as badly as for standard care, but badly enough that some time might be required to reach reversible conditions again. The PID controller was best overall based on the performance calculations. However, it can be seen to be dangerous. After the initial overshoot, an unacceptable level of response occurs and lasts for some time (for more than fifteen minutes between timesteps 75 and 125). During this time the patient could breathe and move. In Figure 3.7, the subject being simulated is a relatively low responder. For the anesthesiologist approach (top two charts, labeled Anesth.), the patient condition necessitates drug being given more frequently and there is again the series of overdoses, but not quite so large as with the high responder case. The PID controller (middle two charts) shows good control, having a brief overshoot before coming to and remaining close to the setpoint. The Laguerre controller (bottom two charts) provides functional control but is not perfect. There are a series of overshoots at first as the patient model is learned. These eventually disappear and the response is held at setpoint towards the end of the case. The decreased error for the PID controller was a surprise as it was expected to have difficulties accommodating patient variance. However, it was the better controller suggesting either that it was the superior approach, or that the PID controller just happened to be well tuned for the subjects of the validation dataset. The final test of this was in in vivo testing where imperfect sensors, varied patients and other sources of error would be seen. The PID and Laguerre linear controllers were tested against themselves to learn the importance of adaptation, and against standard care to have a baseline for reference. This will be discussed in Chapter 4.  55  Setpt. response and input for model 6  0  Figure 3.6:  50  100  150  200  ANESTHESIOLOGIST ( T O P T W O C H A R T S ) ,  PID  250  300  (MIDDLE T W O CHARTS) A N D L A G U E R R E  LINEAR ( B O T T O M T W O CHARTS) C O N T R O L SIMULATION RESULTS FOR A HIGH RESPONDER.  IN  E A C H PAIR T H E T O P G R A P H SHOWS T H E M E A S U R E D RESPONSE (THICK D O T T E D LINE) A N D S E T POINT (THIN SOLID LINE) IN R E L A X A T I O N , A N D T H E B O T T O M G R A P H SHOWS T H E DRUG INPUTS GIVEN IN UNITS O F  3.4  2  X  EDg  5  DOSES. UNITS OF T H E ABSCISSA A R E  20s  TIMESTEPS.  eTo4 T e s t i n g i n S i m u l a t i o n  The utility of the eTo4 (see Section 2.2) as an aid to modelling and control was tested by simulation. In noisy and noise-free conditions, simulations were conducted where the data deemed valid and useful for updating the model fell into three categories: • measurements with at least one twitch: —0.5 <y< • all measurements: —0.5 < y <  maxEffect  maxEffect  • valid To4 measurements: — 0.5 < y < 1 where the response, y, is measured in relaxation units and maxEffect is the relaxation measurement when there are no twitches available. maxEf feet was 1.312 relaxation as found by the eTo4 with zero twitches. The stimulation modality was To4 only. The results are presented in Table 3.2. In the table, "max" represents the maximum value that can be measured by the N M T measurement being used. Onset timing was similar for all three groups. Time to reach 0.7 relaxation for minimal surgical conditions was between nine and ten 56  Figure 3.7: ANESTHESIOLOGIST ( T O P T W O C H A R T S ) , P I D ( M I D D L E T W O CHARTS) A N D L A G U E R R E L I N E A R ( B O T T O M T W O CHARTS) C O N T R O L SIMULATION RESULTS F O R A L O W R E S P O N DER.  I N E A C H PAIR T H E T O P G R A P H SHOWS T H E M E A S U R E D RESPONSE (THICK D O T T E D LINE)  A N D S E T P O I N T (THIN SOLID LINE) IN R E L A X A T I O N , A N D T H E B O T T O M G R A P H SHOWS T H E D R U G INPUTS G I V E N IN UNITS OF 2 X EDg  5  DOSES. UNITS OF T H E ABSCISSA A R E 20s  TIMESTEPS.  timesteps (three to 3.3 minutes); time to reach 0.9 relaxation for minimal surgical conditions was approximately eleven timesteps (3.67 minutes). The first and third categories were compared using a Student-t test to assess the null hypothesis that they would have similar results in testing. Statistically significant results (at p < 0.05) were obtained for MSE, MPE, M A P E , wobble and for time at and near the setpoint demonstrating difference and showing substantial improvement by including the converted one, two and three twitch To4 measurements. Results were similar for comparisons between the second and third categories. Comparison between the first and second categories found no detectable difference. The difference between the first and third categories can be seen graphically in Figures 3.8 and 3.9 for a typical case with a relatively high responder. The top graph of each of the figures shows the simulated measurements (dotted curves), the modeled response (dashed curves) and the setpoint of 0.9 relaxation (thin solid line). The input traces are displayed in the middle charts of the figures. The bottom chart of the three figures shows the model parameters and how they adjust throughout the case.  57  Table 3.2: "max"  RESULTS FROM TESTING BOUNDS ON A C C E P T A B I L I T Y OF DATA FOR  R L S E PROCEDURE,  REFERS T O MAXIMUM E F F E C T , C O M P L E T E SATURATION OF T H E SENSOR,  p V A L U E IS  C A L C U L A T E D USING A S T U D E N T - T T E S T COMPARING T H E FIRST AND THIRD CATEGORIES.  "TlME  WITHIN 5%" IS T H E NUMBER OF TIMESTEPS SPENT WITHIN 5% OF T H E SETPOINT.  RLSE  MSE  MPE  MAPE  Wobble  category  Time within 5%  -0.5 < y < max  0.41 ± 0.12  -0.23 ± 0.13  0.25 ± 0.12  0.49 ± 0.24  103 ± 28.7  -0.5 < y < max  0.42 ± 0.15  -0.23 ± 0.14  0.26 ± 0.14  0.50 ± 0.28  101 ± 34.9  -0.5 < y < 1  0.67 ± 0.18  -0.52 ± 0.16  0.53 ± 0.16  1.05 ± 0.31  31.4 ± 6.38  0.037  0.032  0.026  0.026  0.017  p value  The case begins with the controller believing the system to be the average model. As such, drug is given to paralyze a patient of average response and our patient, being a higher responder, is rapidly overdosed. The model believes it will just reach the setpoint but actually overshoots it. With the overshoot occurring the response is much higher than required so the controller turns off the pump and waits for recovery. The measurement data that is considered valid and can be used by the controller is used to update the model. The cycle repeats and the resulting measured response looks likes a series of overdoses caused by the infusion pump being turned on and off. This continues until the model is adequately representative of the patient, a continuous infusion can be given, and error between measurement and setpoint eventually reduced to zero.  A, _ 3 f  Figure 3.8:  ^Sltft^^i  S I M U L A T E D RESULTS W H E N DATA I N C L U D E D F O R  R L S E A R E - 0 . 5 < y < maxEffect.  T H E T O P CHART SHOWS R E S P O N S E ( T H I C K , D O T T E D C U R V E ) , E S T I M A T E D R E S P O N S E (DASHED C U R V E ) A N D S E T P O I N T (THIN, SOLID L I N E ) .  T H E M I D D L E C H A R T SHOWS T H E INFUSION G I V E N .  T H E B O T T O M CHART SHOWS T H E C PATIENT M O D E L P A R A M E T E R S . M S E is 0.38.  The first two categories (represented by Figure 3.8 for the first category) using the eTo4 measurements are fairly similar. There are a series of overdoses (seen in the top chart of response) but by-and-by adaptation occurs (as shown by the gradual rise in the model parameters shown in the bottom chart) and the measured response moves to the setpoint. For category three, in Figure 3.9, 58  in which only full count To4 measurements were used for RLSE of the model parameters, little data is available to update the model because of the serial overdosing. Adaptation is very limited as can be seen in the bottom chart where the C parameters maintain their levels for long periods of time, and the infusion (the middle chart) is a series of short bursts throughout the case. Some improvement can be seen by the trend towards larger magnitude model parameters and the change in shape of the infusion pulses to shorter, longer bursts. However, the setpoint is not maintained in the procedure. The MSE for these cases was 0.38 for those using the eTo4 (the first two categories) and 0.69 for the case in which only To4 (the third category) data was used.  Figure 3.9: SIMULATED RESULTS WHEN DATA INCLUDED FOR R L S E A R E —0.5 < y < 1. T H E TOP CHART SHOWS RESPONSE (THICK, DOTTED C U R V E ) , ESTIMATED RESPONSE (DASHED CURVE) AND SETPOINT (THIN, SOLID LINE). T H E MIDDLE CHART SHOWS T H E INFUSION GIVEN. T H E B O T T O M CHART SHOWS T H E C PATIENT MODEL P A R A M E T E R S . M S E IS 0.69.  The addition of saturated measurements on the whole is not overly detrimental. There is a slight increase in error on average, but there is more variance added as well. The relative lack of effect due to the extra saturated datapoints may result, because the time spent at saturation was short, being that the rabbit responses (on which this simulation was run) have relatively small AUCs. In humans where the responses are longer more error would be introduced. Based on the results and this last fact, it was decided to use the eTo4 measurements but not those at maximum effect.  3.5  N M J M a r g i n o f Safety T e s t i n g i n S i m u l a t i o n  A concern of this work was the proper capturing of the nonlinearity for delay to response due to the threshold to effect arising from the redundancy of ACh receptors at the NMJ. The N M J margin of safety was discussed in Section 2.3. Separate studies were summarized in which the N M J was estimated to have a 76 ± 5% redundancy of receptors in one, and an approximately 60% redundancy in another. For this work the N M J was approximated to have a threshold of 50.1% with regards to stimulation by To4. Simulations were run using various values for the threshold around the stated values to find which would produce the best results in terms of error seen in the. modelling and control process. 59  The results for the testing at two values: 70%, a compromise value between the results of the mentioned in vivo ST stimulation studies and 50.1%, the receptor occupancy threshold for To4 effect determined here, are displayed in Table 3.3. The 50.1% threshold performed the best. A l l of the error measurements showed the groups were different and the 50.1% threshold better at the 20% significance level; MSE showed different and better performance at 10% significance; P E showed different and better performance at less than 1% significance. Time to minimum surgical conditions, setpoint and time at setpoint were not different. Table 3.3: R E S U L T S O F T H R E S H O L D E R R O R . M A P E IS M E D I A N A B S O L U T E  SIMULATION T E S T I N G .  M P E is  MEDIAN  PERFORMANCE  P E R F O R M A N C E E R R O R . " T l M E TO S E T P T " IS T H E N U M B E R  OF T H E TIMESTEPS TO R E A C H T H E SETPOINT. " T l M E T O M I N S U R G " IS T H E T I M E S T E P S T O R E A C H M I N I M U M SURGICAL CONDITIONS. " T l M E AT S E T P T ± 5 % " IS T H E N U M B E R O F T I M E S T E P S S P E N T WITHIN 5% OF T H E SETPOINT.  Threshold  70% 50.1% p value Threshold  70% 50.1% p value  MSE  PE  MPE  0.65 ± 0.27 0.70 ± 0.33 0.40 ± 0.13 -0.25 ± 0.20 0.081 0.0006  -0.41 ± 0.28 -0.23 ± 0.12 0,16  Time to  Time to  Time at  setpt  min. surg.  setpt ± 5 %  10.8 ± 1.36 11.2 ± 1.27 0.76  10 ± 1.05 9.75 ± 0.97 0.80  98.2 ± 48.9 105 ± 26.2 0.80  MAPE  Wobble  0.43 ± 0.27 0.85 ± 0.55 0.25 ± 0.12 0.49 ± 0.23 0.16 0.15  Examples of the application of the higher threshold can be seen in Figures 3.10 and 3.12. In these figures control of NMB is being applied to low and high responders with the threshold estimated as 70% receptor occupancy. The same test but for a threshold of 50.1% can be seen in Figures 3.11 and 3.13. The top graph of each of the three figures shows the simulated measurements (dotted curves), the modeled response (dashed curves) and the setpoint of 0.9 relaxation (thin solid line). The infusion rate is graphed in the middle charts. The bottom charts show the model parameters and how they change throughout the case. For the low responders (Figures 3.10 and 3.11), the infusion starts off too low and initially no relaxation is measurable. The modeled response shows a quick rise but it is ahead of itself, and is revised downwards as the model adapts to the zero response condition. After some time the model corrects to the point where the infusion rate is increased and an effect is seen. For both thresholds, effect is short-lived and there is a return to zero response and another lull before the model is corrected enough to drive the infusion rate to reach and maintain setpoint. In comparison it will be seen that the setpoint is reached and maintained for both thresholds; however, for the 70% threshold case there is a longer time to see any effect and more importantly a longer time to reach surgically useful conditions. For the 70% threshold it takes approximately 60 timesteps vs. 40 for the lower threshold. For the higher responders (Figures 3.12 and 3.13), the opposite occurs and response overshoots the setpoint quickly. There is a period of no input while the patient recovers and then the setpoint is reached and maintained. There is slightly less oscillation in the response for the lower threshold but beyond that little difference in performance. 60  i  1  ./.::: >r. / ft ;:  L*.  i  * *Jf  ;  x  —  Figure 3.10: O F 70%.  1  : 50  • • i  i  1  i i i  i r  i  i  • i I  i i  i  1  1  i  i  i  1  1  i i i i •  i i r i i  i I i i i  • I i i i  I i i i i  1  1  • Ii i  I  i  1  i  1  1  1  1  1  1  1  1  1  1  •  i  •  •  I  • i  • I  i i  i i  i i  i i  • •  i i  i i  I i  250  300  _ l , 150  100  i • •  i  1  1  0 0  iii i  1  1  :  • i• i  ,  1  200  -  1  350  SIMULATION RESULTS FOR A LOW R E S P O N D E R WITH N M J M A R G I N O F S A F E T Y  T H E T O P G R A P H SHOWS M E A S U R E D O U T P U T (THICK C U R V E ) , ESTIMATED O U T P U T  (DASHED LINE) A N D SETPOINT (THIN, SOLID LINE) IN R E L A X A T I O N UNITS. T H E MIDDLE C U R V E IS INFUSION R A T E IN UNITS OF 2 x ED . 95  T H E B O T T O M C U R V E SHOWS T H E PATIENT C V E C T O R  M O D E L P A R A M E T E R S . U N I T S O F ABSCISSA A R E IN 20S T I M E S T E P S . M S E is 0.37.  Figure 3.11:  S I M U L A T I O N RESULTS FOR A LOW R E S P O N D E R WITH N M J M A R G I N O F S A F E T Y  OF 50.1%. T H E T O P G R A P H SHOWS M E A S U R E D O U T P U T (THICK C U R V E ) , ESTIMATED O U T P U T (DASHED LINE) A N D SETPOINT (THIN, SOLID LINE) IN R E L A X A T I O N UNITS. T H E MIDDLE C U R V E IS INFUSION R A T E IN UNITS O F 2 X EDg^. T H E B O T T O M C U R V E SHOWS T H E PATIENT C V E C T O R M O D E L P A R A M E T E R S . U N I T S O F ABSCISSA A R E IN 20s T I M E S T E P S . M S E IS 0.28,  61  i  1 1 JIII^UMI  1 1  1i  i—  1 1  1 1  1 1  1 1  1 1  -  i i  1  1  =i 1  trr..\  0I 0  1i  i  I  V,  i  1  '  —  f  [  & —  i— 50  j  •trrm  i  T  i  iI  100  150  1i  1  1  1  1  i.  j. r  r i  ii  iI  -  i—,  i  1  1i  1  1  i  • i i  TTTtr. : i  ii  iI  i  ~ — )t— —  200  250  300  350  Figure 3.12: SIMULATION RESULTS FOR A HIGH RESPONDER WITH N M J MARGIN OF SAFETY OF 70%.  T H E TOP GRAPH SHOWS MEASURED OUTPUT (THICK CURVE), ESTIMATED OUTPUT  (DASHED LINE) AND SETPOINT (THIN, SOLID LINE) IN RELAXATION UNITS. T H E MIDDLE CURVE is INFUSION RATE IN UNITS OF 2 x ED . T H E BOTTOM CURVE SHOWS THE PATIENT C VECTOR MODEL PARAMETERS. UNITS OF ABSCISSA ARE IN 20s TIMESTEPS. M S E IS 0.28. 95  Figure 3.13: SIMULATION RESULTS FOR A HIGH RESPONDER WITH N M J MARGIN OF SAFETY OF 50.1%. T H E TOP GRAPH SHOWS MEASURED OUTPUT (THICK CURVE), ESTIMATED OUTPUT (DASHED LINE) AND SETPOINT (THIN, SOLID LINE) IN RELAXATION UNITS. T H E MIDDLE CURVE IS INFUSION RATE IN UNITS OF 2 X EDG . 5  T H E BOTTOM CURVE SHOWS THE PATIENT C VECTOR  MODEL PARAMETERS. UNITS OF ABSCISSA ARE IN 20S TIMESTEPS. M S E IS 0.23.  62  Because of the improved error and performance, it was felt that the estimated receptor reserve threshold of 50.1% was accurate and representative enough for use in the OR. This level of threshold to response was adopted.  3.6  P T C Testing  As mentioned in Section 2.6.1, a scheme was developed to convert P T C to eTo4 values such that useful data could be obtained when response could no longer be evoked with the To4. To this end, the algorithm described in Section 2.6.1 was coded and tested under simulation. To reflect the reality and in agreement with what was stated in Section 1.2, once P T C stimulation was used, To4 stimulation was not available to the software for one minute and P T C was unavailable for five minutes. As there was no direct computer control of the stimulator, P T C had to be initiated by the user. To aid this alarms were presented to the user after five minutes (if the patient muscle response was still saturated) to inform them that they could use P T C again. Simulation testing was done using the first seven patients and their average as the known model set. The remaining seven patients were used as validation models and advisory control of them was attempted. Simulations were then run for use and non-use of the P T C stimulation. When the P T C was not used the average MSE was 17.3 ±2.40. The MSE reduced to 12.3 ±3.21 when the P T C was used. Assuming a normal distribution of errors and testing this with a Student-t test revealed a 14% chance that these two groups were the same. While it could not be said that the two groups were different with reasonable statistical significance, use of the P T C potentially offers benefit. As such, P T C stimulation was used in the OR, with the measured results converted to eTo4 measurements in relaxation for modelling purposes.  3.7  Model Adaptation  Early test of adaptive control methods applied in simulation (simulation and efforts to be described in Section 3.2) were found to be too conservative and too slow to handle properly the variation present in the measured population. A modelling scheme was required that could handle a great deal of variation in patient parameters, and do so quickly. This task had to be done in real time and in a fashion useful for application in the OR. OR use demands the patient be paralysed quickly to allow rapid intubation to protect the patient's airway. As the patient is unknown to the computer on their first meeting, the model for the patient response to the drug being advised upon or controlled can only be guessed at. As a best estimate, the response is set to the population average response. Adaptation of the model is performed to reduce error due to mismatch between the model estimate and true patient. The system of this work improves upon the model in two steps: model swapping and then recursive estimation. 3.7.1  Model Swapping  Adaptation is only capable of handling patient model parameter variation of approximately 30%. Model swapping is a method of gross tuning to reduce the error in the model parameters to something manageable by adaptation. Model swapping refers to the substitution of a more representative model for the current model. This substitution can be done according to the current circumstances as in gain scheduling, or according to time with continuous or interval swapping. The initial model of the subject is an average of available historical data from a patient response database. The database consists of stored, measured impulse responses from previous cases gath-  63  ered in experiments and/or preclinical trial phases by. administering a bolus dose to the subjects, monitoring their responses, and modeling the response data. As the operation proceeds, data is gathered for the level of blockade seen (the output), drug given (the input) and the modeled patient occupancy level. After an appropriate number of iterations of patient stimulus, blockade measure and drug level adjustment, the current model is compared to the other models within the patient's subgroup (a grouping of subjects based on common features such as sex, relative age and/or health conditions) or in the overall population should the numbers of previously measured patients falling into the subgroup not be great enough. Calculations are made for what response would be had (what level of blockade would be seen) for the other patients based on the history of drug inputs. A best model is chosen based on least error and the current model (subgroup or population mean) is replaced by the best matching pre-recorded individual model based upon the closest matching calculated response. Should the initial model prove to be the most representative, no substitution is made. Typically, the remodelling occurred after gathering at least forty valid (non-noise, non-saturated) datapoints post-induction. This number of datapoints allowed approximately two datapoints per model (after classification by BMI or weight), which was judged sufficient to reduce mis-modelling but not so much data gathering as to cause delays to adequate performance. The slowness of the return of function in humans allowed enough time to gather these measurements. In the rabbit testing, remodeling took place after twenty datapoints were obtained, as the response returned much more rapidly (in approximately one quarter the time witnessed for humans). At this point, the rise has been developed and depending on the actual subject, the response will be saturated (for the high responders), heading back towards the limit of acceptable control or somewhere in-between. There is a slope to compare amongst the other models according to what their reaction would have been to a similar history of inputs. Model swapping could also be performed at the request of the user or automatically if conditions of under- or overdosing are detected. In these situations, the model is generally wrong, suggesting that the patient can move when saturated or that the patient is saturated when they are clearly responding to the NMT stimulus. When the computer can see that a series of datapoints are not in agreement with the model, it could change the model to move in the appropriate direction. To ensure the remodeling does not move the model to one that is less representative of the patient, the following steps were implemented: • remodeling only if needed: if the current model is within a certain range (e.g. model parameters are within 20%) of the model started with, do not remodel. • exclusion of potentially incorrect models from the database (or subgroup) of which the model might be changed to. For example, if adaptation demonstrates that the model is likely to be a high responder, do not test the adapted model against the low responder models, use only the high responders. A range might be desired around this, i.e. use the high responders and the next closest 25% of the low responders. and/or: • rejection of the model selected in the remodeling process if it is an obvious mistake, e.g. a model adapting towards a high responder should not be replaced with a low responding model. As the software is used with more patients and the patient responses to the drug measured, recorded and classified according to demographics (age, sex, height, weight, ethnicity, ...) and health conditions (grouping based on relevant health conditions, such as liver, kidney and heart 64  Start  Patient is classified into a subgroup based on demographic and health information input. Modelset is set to patient subgroup.  Select subgroup  Patient model is subgroup average  Collect Data  A decision is made: is there enough data to remodel the patient reliably?  Remodel  I Iterative RLSE adaptation of model  Patient model is best fit to individual in subgroup Patient model is adapted to account for variation from the selected subgroup individual for remainder of case.  Store and classify patient response by demographidhealth.  Figure 3.14:  T H E MODELLING PROCEDURE WITH SUBGROUPS.  B E F O R E THE MODEL  A N D A D A P T A T I O N T A K E P L A C E T H E R E IS T H E I N I T I A L S T E P O F P A T I E N T  SWAPPING  CLASSIFICATION A N D  ELIMINATION OF NON-RELEVANT MODELS FROM T H E MODELSET.  failure), the number of patients in subgroups (subpopulations) based on mutual patient characteristics of health and demographics will grow. As the number of patients in a subgroup becomes sizeable, a statistically meaningful average response can be calculated for the patients within that subgroup. This subgroup average model can then be used instead of the over all. population average response model as the initial model (the anesthetist would facilitate this by entering patient data prior to the procedure to classify the patient). This grouping is done to reduce possible variance between the initial model and the actual patient response by using a subgroup response that should bear more resemblance to the individual's response. The accumulation of responses and the development of the subgroups and subgroup models is a method of continual improvement of the system and method of reducing the variation in each of these groups. This process is flowcharted in Figure 3.14.  65  For patients that have been exposed to the system in previous operations, a record of their response to one or more drugs will exist. These historical responses can be recalled and used as the first estimate of their current response. As intrapatient variability does occur there is a chance that the patient's response may have changed and therefore adaptation from the original model may still be required. An example of patient change requiring continuing adaptation is the development and/or progression of kidney disease reducing drug clearance and thereby extending effect. Although it could be done frequently, for this work it was found that model swapping was only necessary once. The improvement of the model was sufficient enough to ensure stability and improve error performance to the point of acceptability. Also, it was judged to not be worth the additional computation time and effort, the loss of information gleamed through recursive least squares estimation (RLSE) to repeat the model swap process and the risk of instability (discussed in Section 3.7.3). It was judged that model swapping arrived close enough to the true model that the fine-tuning process of the next section could manage the remaining patient variation and complete a rapid movement towards representative model parameters. 3.7.2  Model Adaptation Through Recursive Estimation  Once the initial modeling is completed, RLSE is used to update the gain parameters (the C matrix) as new information in terms of output (level of patient blockade) and the patient state vector is received. RLSE is performed using the Exponential Forgetting and Resetting Algorithm (EFRA) as developed in Salgado [82]. The equations describing this algorithm are the following: e(t + l )  -  y(t + l)-L [t T  + l)C(t)  where these are equations for error, the new parameter update and for the error covariance matrix, respectively. The E F R A parameters can be modified as the case progresses to reflect a better understanding of the patient. The forgetting factor, A, can be increased from its starting value of 0.95 to 1.0, to retain more of the information which is now believed to be more reliable. As well, the parameters 3 and 7 can be reset to zero as they are not required once the forgetting is turned off (at A = 1.0). This update occurs when a certain number of doses have been given or when a certain number of measurements of response have been recorded. Also, the parameters could be modified according to factors known to affect response to the drug being advised upon, such as temperature and the presence of other drugs, to reduce the forgetting in times of greater certainty and increase the forgetting when these factors have a greater influence (in order to maintain fast adaptation), such as when there is sufficient volatile anesthetic to affect the NMB. RLSE is desirable at all times (even before the remodeling point at which models are switched and adaptation potentially lost) to avoid situations of under-dosing, which can happen if too little drug is given and then the system is unable to get data for remodeling, as can happen with low responders. The system can then be stuck waiting for the model to correct itself and eventually the User may have to take over. The overall process of adaptation presented here is depicted in Figure 3.15.  66  response for population/ subgroup  FIGURE 3.15:  separate modelsets based on demographic/ health parameter  most representative model from subset  further adaptation by RLSE  T H E M O D E L L I N G P R O C E D U R E V I E W E D S C H E M A T I C A L L Y . T H E C A S E BEGINS ON T H E  L E F T WITH T H E PATIENT BEING R E P R E S E N T E D  B Y T H E A V E R A G E O F T H E K N O W N MODELS. T H E  N E X T S T E P IS A R E P L A C E M E N T OF T H E O V E R A L L A V E R A G E M O D E L WITH T H E A V E R A G E C A S E F O R T H E SUBSET O F SIMILAR MODELS (PROVIDED T H E R E A R E E N O U G H MODELS IN THAT S U B S E T ) . A F T E R S O M E DATA IS C O L L E C T E D , A M O R E A P P R O P R I A T E  M O D E L IS S E L E C T E D .  T H I S M O D E L IS  T H E N F U R T H E R A D A P T E D WITH R L S E B A S E D ON T H E ONGOING C O L L E C T I O N O F DATA.  3.7.3  Stability  As the modelling scheme presented is novel, it is important to explore its stability. Figure 3.16 presents an argument for the stability of the model switching scheme. Drug concentrations and related drug responses in the metabolically active are bounded by decaying exponential functions and can thereby be considered asymptotically stable. Consider a modelset composed of two asymptotically stable state space systems of two states each, as shown in part A. The top diagram shows a plant, HQ, that is more reactive for the X\ state and the bottom diagram shows a plant, Hi, that is more reactive for the XQ state. Although in a P K state-space model the states represent drug concentrations in two compartments, for clarity of explanation, here the states will refer to as position or distance for XQ and velocity for xi. Part B of Figure 3.16 shows the results of scenarios in which a model-based controller is used for controlling a plant modeled by these two systems, and switching is performed between the two systems as the state trajectory moves from one quarter to the next to demonstrate the effects of continuous switching. On the left, the result is a stabilized system with an improved result in terms of getting the states to their final values. Starting from plant Hi in quadrant four (positive distance and negative velocity), the system switches to plant HQ for quadrant three (negative distance and negative velocity), and then the plant is Hi again for quadrant two (negative distance and positive velocity). The switching scheme is able to take advantage of each plant's quadrants of lower reactivity. On the right, the opposite effect is seen when the system becomes unstable as at each quadrant the change is to the plant which is most reactive in that quadrant resulting in an expanding state trajectory. Part C of Figure 3.16 shows what happens the worst-case scenario for the re-modelling scheme of this work. In this case there is only one instance (or a small and finite number of instances should the user desire to remodel at a later time) of switching plant models. In the diagram this happens as plant HQ is moving from quadrant four to quadrant three, resulting in an expanding trajectory. However, as this switching only happens once the switch is to a trajectory that, because the new plant model is also stable, is still contained and therefore stable. In this particular incidence a  67  switch to H1  Figure 3.16: S T A B I L I T Y ANALYSIS O F T H E R E M O D E L L I N G P R O C E D U R E (WITH S O M E INSPIRATION F R O M L I B E R Z O N [83]): A) S T A T E SPACE M A P S F O R TWO S T A B L E P L A N T S ; B) SWITCHING E V E R Y Q U A R T E R PRODUCING A A S Y M P T O T I C A L L Y S T A B L E S Y S T E M ( L E F T ) A N D A N U N S T A B L E S Y S T E M (RIGHT); C) W O R S T - C A S E SCENARIO F O R SWITCHING D U E T O R E M O D E L I N G  PROCEDURE.  mistake was made by switching to the wrong model (e.g. going to a high responder when the change should have been to a low responder); however, it is not a fatal mistake - more error is introduced but the system is not caused to go unstable.  3.7.4  Model Swapping Results i n Simulation  Simulation results revealed the model swapping procedure to be effective in reducing the modelling error rapidly. The case of a low responder without model swapping (relying on RLSE only to correct for modelling error) is shown in Figure 3.17. In the top graph of the figure, it can be seen that the output (the heavier curve) rises slowly to the setpoint level (thin, solid curve at 0.9) taking about 75% of the case to reach it, and even a period in which the infusion rate is not high enough to maintain the relaxation above the threshold. As well, the surgical conditions would not be sufficient until after timestep 200 (at approximately 67min). Note that the modeled output, as demonstrated by the dashed line, believes it is already close to the setpoint. The middle chart shows the infusion to have a high spike at the start for the induction and then a slow rise to its final value. The bottom chart shows the C vector model parameters throughout the case. These parameters decline gradually towards their final values. When model swapping is used with this subject, the case appears as in Figure 3.11 of Section 3.5. In the bottom chart of that figure, the C vector model parameters show immediate decay due to the RLSE and then an abrupt correction of the parameters when the model swap occurs near timestep forty. Some further adaptation occurs, but it is slight because of the similarity of the true model to the model swapped to in the modelset. In the middle graph, the abrupt change in the model  68  Figure 3.17:  SIMULATION RESULTS F O R A LOW RESPONDER WITHOUT M O D E L SWAPPING. T H E  T O P G R A P H SHOWS M E A S U R E D O U T P U T (THICK C U R V E ) , ESTIMATED O U T P U T (DASHED LINE) A N D SETPOINT (THIN, SOLID LINE) IN R E L A X A T I O N UNITS. T H E MIDDLE C U R V E IS INFUSION RATE IN UNITS O F 2 X EDG . 5  T H E B O T T O M CURVE SHOWS T H E PATIENT C V E C T O R M O D E L P A R A M E T E R S .  UNITS O F ABSCISSA A R E IN 20s TIMESTEPS. M S E is  0.39.  corresponds to an increase in the input rate as the system has realized that the responsiveness of the system was overestimated and corrects. The improved model and increased infusion rate corresponds to a better approach to the setpoint, and it is reached very rapidly after the model swap as shown in the top graph. From there until the end of the case, the error is slight. The top graph shows measured output (thick curve), estimated output (dashed line) and setpoint (thin, solid line) in relaxation units. The middle curve is infusion rate in units of 2 x EDg$. The bottom curve shows the patient C vector model parameters. For the high responder, the opposite problem of over-saturation occurs because of the model being thought of as an average case. In Figure 3.18, where there is no model swapping, the model parameters change slowly as adaptation is hamstrung by the lack of available data (RLSE occurred if there was at least one viable twitch). The lighter, lower curve charts the estimated output and shows that the simulation believes that the subject is not saturated. The contrasting case, where there is model swapping for a high responder, is shown in Figure 3.13 of Section 3.5. With model swapping, some saturation results from the high initial response but the problem of over-saturation is mostly corrected for by the model swap. The model swap occurs around timestep thirty when the parameters are disjointedly increased and then are adapted more continuously. Model swapping quickly corrects for most of the difference in error and the output reaches and remains at its setpoint. Similarly, the infusion quickly becomes level.  3.8  S u m m a r y of C o n t r o l l e r D e v e l o p m e n t , S i m u l a t i o n a n d T e s t i n g  In this chapter, controller development was described, starting with the development and testing of competing controller classes, and following with the reduction of these down to a few best, including PID and adaptive extended-horizon model-based control. Software simulations were developed for testing these controllers and other aspects of the model and research. Tested and validated were the eTo4, the N M J margin of safety, the conversion and use of PTC. 69  Figure 3.18: S I M U L A T I O N RESULTS FOR A HIGH R E S P O N D E R WITHOUT M O D E L SWAPPING. T H E T O P G R A P H SHOWS M E A S U R E D O U T P U T (THICK C U R V E ) , ESTIMATED O U T P U T (DASHED LINE) A N D SETPOINT (THIN, SOLID LINE) IN R E L A X A T I O N UNITS. T H E MIDDLE C U R V E IS INFUSION R A T E IN UNITS OF 2 X EDG . 5  T H E B O T T O M C U R V E SHOWS T H E PATIENT C V E C T O R M O D E L P A R A M E T E R S .  UNITS OF ABSCISSA A R E IN 20S TIMESTEPS. M S E is 0.31.  A novel model adaptation'scheme to handle the high variation in patients was put forth and tested in simulation. This procedure consisted of model swapping from a patient population representative model to an individual representative model after some data had been collected, and then performing recursive estimation for the remainder of the case as a means of fine-tuning. With the controller developed, it was now time to test it in vivo. Details of this testing follow with animal work described in Chapter 4 and the human clinical studies described in Chapter 5.  70  Chapter 4  Closed-Loop Control In anticipation of implementation of closed-loop NMB drug administration in humans, controller algorithms were tested in simulation and in animal trials using rabbits. The emphasis of the closed-loop control experiments was on experimentation - testing of ideas and controllers, and details relevant to them such that an application could be made in humans with little chance of failure. Control was to be done with the philosophies of real-time operation with an outlook towards meeting the anesthetist's needs, practical application of the device in an operating room, and with minimal intervention by the anesthetist. From the simulation work (see Section 3.1) two best controllers were determined, PID and Laguerre linear, and tuned for optimal performance with the average model. These controllers were tested along with a controller simulating the anesthesiologist serial overdosing procedure for comparison. This chapter begins with a description of the experimental setup and its development. Then the experiments for selection of the best controller are presented. Testing and development of the best controller are described. Finally, methods for creating intra-patient variability are presented as a means of creating more difficult patients and testing the controller for its limits.  4.1  Equipment Development  In the prior rabbit experiments, tendons were captured and force measurements made with transducers recording the measurements to tape for later transcribing. To reduce the surgical load and the time spent analyzing tape, it was decided to build a custom data acquisition system. The data acquisition system was composed of a computer (Panasonic CF-45 Toughbook, Pentium 2 processor, 64Mbytes of memory) running the control software (custom), a stimulator (PI Dual Stim DX Peripheral Nerve Stimulator) interfaced for computer input via a serial port, a twoaxis accelerometer (Analog Devices, ADXL311 with custom instrumentation to interface with the ADC board) to measure induced muscle motion, an analog-to-digital converting (ADC) board (custom designed) and a computer-interfacing infusion pump (IVAC Medical Systems P7000). These objects interacted with themselves and the patient as shown in the block diagram of Figure 4.1. Pictures of the accelerometer, the stimulator and the experimental setup can be seen in Figures 4.2, 4.3 and 4.4. The custom solution was built strictly for NMT monitoring; anesthetic monitors were used for monitoring blood pressure and capnography. The subcomponents required hardware interfacing to allow communication between them. The interface between the computer and the pump was an RS-232 link. A parallel port interface was developed to provide control signals to the stimulator and ADC from, and receive feedback back 71  infusion pump  NMB drug motion patient  nerve stimulator  &| accelerometer A2D converter  electrical stimulus  computer with software  measurement  Figure 4.1: B L O C K D I A G R A M O F T H E C L O S E D - L O O P C O N T R O L E X P E R I M E N T A L S E T U P . " A N A L O G T O DIGITAL" .  Figure 4.2: A C C E L E R O M E T E R A S S E M B L Y F O R CONTROL E X P E R I M E N T S .  72  A2D is  Figure 4 . 3 : THE  COMPUTER  TOP CENTER  COMPUTER  INTERFACED  OF THE FIGURE,  INTERFACING  UNIT.  L E F T SIDE A N D S T I M U L A T I O N  Figure 4 . 4 :  NEUROMUSCULAR STIMULATOR.  RESTING  UPON  T H E COMPUTER  T H E STIMULATOR  THE ANALOG-TO-DIGITAL INTERFACE  CONVERSION  TO THE STIMULATOR  73  CONTROL  AND  IS O N T H E  LEADS A R E ON T H E RIGHT.  EXPERIMENTAL SETUP FOR CLOSED-LOOP  IS A T  EXPERIMENTS.  from the ADC to the computer. Between the ADC and accelerometer, wiring and support circuitry were required to allow them to communicate appropriately and to provide noise rejection through a 50Hz low-pass filter (Analog Devices Corporation [84]). Software protocols were written to control and communicate with the equipment. This was done using Labview with some Matlab functions embedded. Simulation work was done using Matlab. Raw data for: 20060606151742amg.txt #channels=4 datapts/chan=404 1  h ! > 0.51 0.5  I  0  1  d : - c2 : ' ~' rY -•  i 200  400  600  i 800  1000  i 1200  1400  1600  i 1800 2000  acceleration derived from combined channels  0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time(ms); T1 0.452361 T2 0.287485 T3 0.151188 T4 0.127059; To4 0.280880  Figure 4.5:  A C C E L E R O M E T R Y MEASUREMENT WITH  T H E T O P CHART SHOWS M E A S U R E M E N T S  To4  STIMULUS REVEALING A  To4  OF  0.28.  FOR ACCELERATION ABOUT T H E X A N Dy AXES. T H E  B O T T O M G R A P H SHOWS T H E P R O C E S S E D DATA.  For each stimulation, the accelerometric measurements were quantified in real-time. The two channels were read iteratively. Means were calculated for each channel and then subtracted from the readings. The absolute value of the two channels were taken and then added together to arrive at the processed data. The value for each stimulus was calculated by binning the measurements in time. For example, for a To4 measurement, T I was a sum of the absolute value of the mean adjusted data between zero and 500ms, T2 was the sum between 500ms and 1000ms, T3 was the sum between 1000ms and 1500ms, and T4 was the sum between 1500ms and 2000ms. As always, the To4 was the ratio of T4 to T I . Sample raw data for the two channels can be seen in the top chart of Figure 4.5. The processed data for the corresponding measurement appears in the bottom chart. Calculations of the motion energy for each twitch appears in the text below the bottom chart.  4.2  In Vivo Controller Testing and Selection  The methods for the experimental setup were similar to those described in Section 2.1. The exceptions were the use of halothane instead of isoflurane, discontinuation of ear vein cannulation and replacement by jugular vein cannulation, replacement of anterior tibialis tendon capture for 74  force sensing with taping an accelerometer to the foot for accelerometry, and discontinuation of tape recording of muscle response in favour of individual files for each stimulation saved on the computer hard drive. The PID, Laguerre and anesthesiologist controllers found to be the best in simulation testing (see Section 3.3), were tested in vivo. The PID and Laguerre controllers were as described in Sections 3.1.1 and 3.1.2, with two versions of the Laguerre controller being implemented - one using only full-count To4s and one using eTo4. For the Laguerre controllers, the horizon was six timesteps and the forgetting factor 0.95 throughout the cases. The anesthesiologist controller was modified by reducing the level of the second and following doses to one-half 2 x EDg$. The setpoint was alternating between periods of light wrap-up conditions (To4 of 30%), maintenance (To4 of 10%) and ideal induction (To4 of two twitches only) for three consecutive simulated cases. Retrospectively, this was shown to have been an aggressive setpoint profile. One rabbit was used for each controller test. Total time of each case was two hours. The measured response compared to the desired setpoint and inputs given are shown in Figure 4.6. Results found in the clinical testing showed that neither the PID nor anesthesiologist means of providing control were acceptable. These controllers were unable to meet the objective of control to an easily reversible level. The anesthesiologist approach had no fine control. This deficiency is shown in the top two graphs of Figure 4.6. As was appreciated before the test, the anesthesiologist approach leads to long periods of saturated paralysis with no response, punctuated by brief periods of some function before re-overdosing. The test proved this view, as the response was either one or no twitches throughout most of the case. The bottom of the two top charts, illustrates the many incidents when doses were given in clusters, very close together. This clustering would not happen with a real anesthesiologist but happened here because the computer was fooled by noisy measurements. The anesthesiologist controller was a very heavy-handed approach and would only be useful by chance, if the end of the case occurred simultaneous to the return of function after a drug bolus. The PID controller, although it performed well in simulation, was disastrous in practice. It was very sensitive to noise and quickly became unstable, showing some oscillation and then entering a saturated state of paralysis. This defect is shown in the upper-middle two graphs of Figure 4.6. In the bottom of these two graphs, the infusion pump output was never continuous, but constantly turning on and off. The Laguerre controller provided better results. As shown in the bottom four graphs of Figure 4.6, the lower-middle two graphs show testing of a Laguerre controller using only full-count To4 measurements for adaptation and the bottom two charts showing the Laguerre controller using eTo4 sensing. For the To4-only case, the rise to setpoint was very slow at first, the model was swapped at about timestep 25 and then there was rapid saturation and the output remained at one or no twitches. The pseudo-occupancy (dashed line) fell to zero, where it remained because of the lack of input (the To4 produces less than four twitches) to the RLSE algorithm. Eventually usable data was produced, the model adapted and performance improved towards the end of the case. For the eTo4 case, output appeared quickly and then fell off - indicating the rabbit is most likely a low responding subject. Towards the end of the first third of the case, adaptation occurred and the output rose. The following two thirds of the case show some oscillation, possibly because of the choice of horizon and forgetting factor. Although control is never good, it appears that the extra data from using the less than four twitch To4 measurements does improve the modelling. In both cases, it will be seen that the pump was at least stabilized, being on continuously for periods of time with only gradual changes in output levels. As the Laguerre controller showed some promise, it was decided to continue with its development. Work with the PID and anesthesiologist controllers discontinued at this point. 75  1 0.5  5^  Anesth. M  .tf--  . -tf-V  -?- - i T F T V - ** * ^ - ~ - - - - - - 1  0  1.5  1  0.5  T i m i i I I I I T  0  PID. 1  0.5 *  0  *  fflitttiiihi  0.410.2  o  Laguerre (no eTo4)  ««*-*!-»*^tf'W  1 h-Vcid  •jt  J*ft- - -  •VtfT^Sfj.M.L  1  - • . ! . A L  Laguerre (eTo4)  i£V*--r0 0.4 h 0.2 0  F i g u r e 4.6:  l  —*100  50  150  200  250  300  350  ANESTHESIOLOGIST (TOP PAIR), P I D (SECOND PAIR F R O M T O P ) , L A G U E R R E LINEAR  C O N T R O L WITHOUT (THIRD PAIR) AND WITH A R E IN PAIRS OF T H E M E A S U R E D E M G  ETo4  ( B O T T O M PAIR) IN VIVO RESULTS.  (DASHED LINE) AND SETPOINT (SOLID LINE); AND DRUG INPUT IN REPRESENTS TIME IN TIMESTEPS OF  GRAPHS  RESPONSE IN R E L A X A T I O N (DOTS), M O D E L E D O C C U P A N C Y 20s.  76  2xEDg  5  DOSES. T H E ABSCISSA  4.2.1  Continued Testing of the Laguerre Controller  As the setpoint profile for testing the various controller types was aggressive and not representative of a true case, it was decided to test control under more realistic circumstances.  0 Figure 4.7:  50  100  150  200  250  300  C L O S E D - L O O P C O N T R O L WITH L A G U E R R E LINEAR C O N T R O L L E R ON A RABBIT. I N T H E  T O P G R A P H A R E DRAWN RESPONSE MEASUREMENTS ( D O T T E D ) , M O D E L E D O C C U P A N C Y (DASHD O T ) A N D SETPOINT (SOLID LINE). T H E MIDDLE G R A P H SHOWS T H E INFUSION INPUT IN  2 X EDg  5  DOSES. T H E B O T T O M G R A P H SHOWS T H E C M O D E L P A R A M E T E R S . T H E UNITS OF T H E ABSCISSA A R E TIMESTEPS O F  20s.  Figure 4.7 shows application of the Laguerre controller to a female, 4.7kg, approximately seven months old rabbit, for a setpoint (solid line in top chart) of 0.9 relaxation through the entire case. The horizon was six timesteps and the forgetting factor 0.95 throughout the case. As seen in the top chart, the case starts with the initial up and then down of response (dotted line) associated with low responders being overestimated by the average model. This up and down response repeats and then the setpoint is overshot. After a short time above setpoint, the response drops below and the controller being slow to react repeats this dampened oscillatory behaviour before reaching the setpoint. Shortly afterwards, the case is discontinued. The middle chart shows the input for the case. It is continuous and relatively smooth with ripples corresponding to the times of oscillation in the output. The bottom chart shows the adaptation of the Laguerre model C vector. The case starts with the average model. At timestep twenty, the model is swapped, but in the wrong direction (as judged by the direction of the later adaptation). Adaptation continues with the RLSE and the model parameters decrease throughout the case. After allowing recovery of function, control was attempted again with the same rabbit but with a slightly varied setpoint profile, as shown in Figure 4.8, where the setpoint is seen to be varied from relaxation of 0.9 to 0.5 to 1.0 (three twitches, To4 of 0) and then back to 0.9 over the period of two and a half hours. At timestep 425, a-Bungarotoxin (20p,g • kg~ ) was administered to see kinetics of effect and l  77  Figure 4.8: C L O S E D - L O O P C O N T R O L WITH L A G U E R R E L I N E A R C O N T R O L L E R ON T H E R A B B I T OF F I G U R E 4.7 R E P E A T E D WITH A SLIGHTLY VARIED SETPOINT, A N D WITH ADMINISTERED AT T I M E S T E P 425.  OJ-BUNGAROTOXIN  I N T H E T O P G R A P H A R E D R A W N RESPONSE  MEASUREMENTS  ( D O T T E D ) , M O D E L E D O C C U P A N C Y (DASH-DOT) A N D SETPOINT (SOLID LINE). T H E MIDDLE G R A P H SHOWS T H E INFUSION INPUT IN 2 X EDG  5  DOSES. T H E B O T T O M G R A P H SHOWS T H E C M O D E L  P A R A M E T E R S . T H E UNITS O F T H E ABSCISSA A R E TIMESTEPS O F 20S.  its possible usefulness as an inducer of intra-patient variance. This dose resulted in very quick termination of response contrary to the expected gradual rise. The case was discontinued. This toxin and its intended use will be detailed in Section 4.3.2. Similar experiments were run with another rabbit (female, 3.45fc<?, approximately six weeks old). In the first experiment closed-loop control was operated to a setpoint of 0.9 relaxation, then two twitches and then 0.7 relaxation. There was some control but with sensitivity to changes in setpoint. The results are shown in Figure 4.9. In a second test, the setpoint was maintained at 0.9 and then 0.7 relaxation for approximately five hours. To test pancuronium's usefulness as an inducer of intra-patient variance and the resulting impact on adaptation, at timestep 216, 0.5 x ED95 (0.09mL of 0.2mg • mL- ) pancuronium was given. As shown in Figure 4.10, the control was oscillatory and slow to reach setpoint. As well, the pancuronium had little effect. There seems to be a slight rise in measurements, but due to the noise in the measurements it is too difficult to know. 1  4.2.2  Comments on the In Vivo Testing  In the experiments to this point, control was noted to be inadequate with a slow rise to setpoint and oscillations on its way there. For the rabbits of the above section, a major reason for the poor control was a bug in the software. The mistake in the software was the use of the modeled occupancy data for the input to RLSE routine. Thus, instead of using measured data and converting it to pseudooccupancy and then doing the RLSE, it was the direct application of Upseudo—occupancy — C L. This T  78  Figure 4.9: BIT.  C L O S E D - L O O P C O N T R O L WITH L A G U E R R E LINEAR C O N T R O L L E R O N A SECOND R A B -  I N T H E T O P G R A P H A R E D R A W N RESPONSE M E A S U R E M E N T S ( D O T T E D ) , M O D E L E D O C C U -  P A N C Y (DASH-DOT) A N D S E T P O I N T (SOLID LINE). INPUT IN 2 X EDG  5  DOSES.  T H E M I D D L E G R A P H SHOWS T H E INFUSION  T H E B O T T O M G R A P H SHOWS T H E C M O D E L P A R A M E T E R S .  THE  UNITS O F T H E ABSCISSA A R E T I M E S T E P S O F 20S.  injects error into the estimation, as the controller believes what it thinks is happening is reality. This condition can be corrected but only very slowly. Other problems with these two rabbits were corrected for in later experiments. RLSE was not done until after model swapping occurred. The lack of RLSE can be seen in the figures by the absence of change in the model parameters for the first twenty timesteps. As well, there were no checks on the model swapping to prevent swapping to an inappropriate model. Checks could have helped the first case of the first rabbit and the second case of the second rabbit. Model swapping was done after twenty timesteps and not twenty good datapoints. Thus datapoints of no effect (those of strength To4=100%) and saturated datapoints (To4=0%) where nothing is revealed about the patient were entered into the calculation of best model. Finally, the number of datapoints used for judging the best model to swap to may have been too small. However, this number of datapoints may be the best that can be had, a compromise between getting the best answer and getting it as quickly as possible. Reduced error occurs with more information. However, accumulating that information takes time which delays surgery if the patient is not responding. For some rabbits, more than one experiment was performed. For these, the possibility exits of bias to the results as some drug may still be present. As well, the health of the animal and drug interactions may affect the measurement. The potential for these problems to occur increases with time. 4.2.3  Optimizing the Forgetting Factor and Horizon  Changes were made to the controller software to fix the problems mentioned at the end of the last section. The program was retested on a male rabbit, roughly eleven weeks old and of weight 4.1%. 79  0  Figure  100  200  300  400  500  4.10: C L O S E D - L O O P C O N T R O L WITH L A G U E R R E LINEAR C O N T R O L L E R ON T H E R A B B I T O F  F I G U R E 4 . 9 , WITH A VARIED S E T P O I N T T R A J E C T O R Y A N D P A N C U R O N I U M ADMINISTRATION AT T I M E S T E P 2 1 6 . I N T H E . T O P G R A P H A R E DRAWN RESPONSE M E A S U R E M E N T S ( D O T T E D ) , M O D E L E D O C C U P A N C Y (DASH-DOT) A N D S E T P O I N T (SOLID L I N E ) . T H E MIDDLE G R A P H SHOWS T H E INFUSION INPUT IN 2 X £ X >  9 5  DOSES. T H E B O T T O M G R A P H SHOWS T H E C M O D E L P A R A M E T E R S . T H E UNITS  OF T H E ABSCISSA A R E TIMESTEPS O F 20S.  The setpoint profile was chosen to represent a mini-case with control to 0.9 relaxation and with brief periods at two twitches and 0.7 relaxation. The horizon was six timesteps and the forgetting factor was 0.95. The results of this test are shown in Figure 4.11. The initial response and modelling were improved; however, there was still oscillation. Once the case was completed and the rabbit muscle function returned, another case was started, shown in Figure 4.12. This time the data was remodeled using subgrouping by weight. This rabbit was in the higher classification. Control was good at the start with the output reaching the setpoint approximately two minutes after the pump was started. However, N M B wore off and good control was not seen until about half way through the case. There was some oscillation about the setpoint. Then, at roughly forty minutes, the input jumped up to 3.0 (6 x EDg§). The cause of this surprising jump was possibly a combination of error introduced in modelling and instability due to small gains in the control law. In addition to these, the parameter structure was scrutinized for complicity.  Investigation of Modelling for Instability  In the top chart of Figure 4.11, the modeled pseudo-occupancy (dash-dot line in the top chart) falls near zero just before the massive increase in control input u. The C model parameters were stable, of low gain and non-negative; however, their order had become corrupted from what was usual with shorter cases. The order of the C parameters from largest to smallest became C 3 , Co, C2, C \ , C5, and then C 4 , showing a great reduction in the magnitude of the first normally two largest parameters and a large increase in C 3 normally a middle to small sized parameter. The  80  Figure 4.11: EMG  CLOSED-LOOP CONTROL WITH IMPROVEMENTS.  RESPONSE  (SOLID LINE).  T H E T O P G R A P H SHOWS M E A S U R E D  IN R E L A X A T I O N ( D O T S ) , M O D E L E D O C C U P A N C Y ( D A S H E D LINE) A N D S E T P O I N T  M I D D L E G R A P H IS T H E I N F U S I O N I N P U T I N  2 X EDg  5  DOSES. T H E B O T T O M G R A P H  SHOWS T H E M O D E L P A R A M E T E R S T H R O U G H T H E C A S E . T H E UNITS O F T H E ABSCISSA A R E T I M E IN  SECONDS.  time under anesthetic had been long up to this point, about seven hours. Therefore, despite the charged nature of rocuronium, this ample time allowed for accumulation in fat and other spaces in the body, perhaps causing the changes in the model. Although the problem may have been biological, the mathematics required exploration. • As stated in Section 3.7.2, post-remodelling adaptation was through use of an E F R A scheme (see Equations 3.13) with central variable A for forgetting and variables 3 and 7 to provide bounds on the eigenvalues of the error covariance matrix. At 0.95, A was chosen to provide fast adaptation through rapid forgetting. A A of 1.0 would provide no forgetting and would be more stable but would provide slow adaptation. The values for 3 and 7 were set to 0.005 to provide bounds of approximately 0.1 and 10 on the eigenvalues. It was theorized that, despite the 7 and 3 parameters used in the RLSE update having been chosen to limit growth of the error covariance matrix, P, the matrix was still growing throughout the case. To test this theory, traces were calculated for the P matrix throughout the case with the instability under varied conditions: normal forgetting (A = 0.95, 3 = 7 = 0.005); reduced forgetting (A = 0.98 3 = 7 = 0.005); a hybrid version where A was increased from 0.95 to 0.98 to 1.0 after forty, sixty and eighty valid datapoints were collected (multiples of the number of timesteps used for determining when to swap the model) and E F R A parameters 3 = 7 = 0.005 until A = 1.0 at which point they were reset to 0; and for the case of no forgetting (A = 1.0, 3 = 7 — 0). The update gain - a - was kept at unity throughout. As the covariance matrix was continually updated and changes not-recorded, the original trace data was not available and so had to be reconstructed. The resulting traces are shown in Figure 4.13. The traces for the normal (top) and reduced forgetting (second from top) cases increased and become large - 49.8 and 19.2, respectively, at  81  Setpt, y . , yOc -. vs. Time (top); u vs. Time (mid); C vs time (bot)  FIGURE 4 . 1 2 : C L O S E D - L O O P C O N T R O L O F A RABBIT WITH A P P E A R A N C E O F INSTABILITY. T H E T O P G R A P H SHOWS MEASURED E M G RESPONSE IN RELAXATION ( D O T S ) , M O D E L E D O C C U P A N C Y (DASHED LINE) A N D SETPOINT (SOLID L I N E ) . M I D D L E GRAPH IS T H E INFUSION INPUT IN  2XED  95  DOSES. T H E B O T T O M GRAPH SHOWS T H E M O D E L PARAMETERS T H R O U G H T H E CASE. T H E UNITS OF T H E ABSCISSA A R E TIME IN SECONDS. INSTABILITY OCCURS A T T H E E N D O F T H E CASE WHERE T H E INPUT IS SEEN GOING T O 3 . 0 .  the point where the original input became 3.0. Furthermore, at this point their trends were still upwards. This pattern indicates a propensity for large changes in the parameters being adapted, potentially producing the instability. The non-forgetting (third chart from top) version showed a decrease in value and came to rest at a trace of about 4.2 at this same point. The trace of the hybrid version (bottom) showed an initial increase, leveled off and then decreased down to 14.8 when the original input became 3.0. The trends for the last two methods were downwards indicating movement towards greater stability. In the same simulation, the model gain C and the input vector u were charted to see the changes in the model and for the control input due to the varied EFRA plans as well. In the chart of the model gain vectors, Figure 4.14, the C matrix parameters are well behaved for the non-forgetting and hybrid versions. However, for those with substantial forgetting throughout Cs (the dashed, heavy line) which is normally of middle magnitude compared to Co grows and switches positions with Co indicating a drastic change in the model to one with more energy mid response. In Figure 4.15, the large input considered to be unstable is seen in the top chart at timestep 199. The simulation shows fidelity by being able to reproduce this (but to a smaller magnitude) in the next lower chart. The following charts show that with decreased forgetting (A being closer to one), the large inputs are nullified and what would have been a large input at timestep 200 is instead a negative input, which would be filtered off without affecting the subject. That the input values were changed and made manageable, and that the C vector stabilized by the non-forgetting suggested that this was an improvement. However, the fact that the recalculated input was large for the hybrid forgetting indicates that that was not the final solution.  82  Figure 4.13: A D A P T A T I O N C O V A R I A N C E M A T R I X T R A C E VALUES U N D E R VARIED E F R A P A R A M E T E R S . F R O M T O P T O B O T T O M , N O R M A L F O R G E T T I N G A = 0.95, R E D U C E D F O R G E T T I N G A = 0.98, NON-FORGETTING ALLY BECOMING  A = 1.0, A N D A HYBRID STARTING WITH N O R M A L F O R G E T T I N G A N D G R A D U NON-FORGETTING.  Investigation of the Horizon for Instability  Investigation of instability continued by examining the role of the horizon. Another way for the input to (seemingly) spontaneously become large is through a short horizon on the extended horizon controller. In this scenario, the 3 parameter, 3 = C ( i 4 + A ~ + ... + I)B, of the controller in Equation 3.7 becomes very small. In Dumont [72] it was recommended that the horizon, d, be selected such that 3 as defined by Equation 4.1 is the same sign as the process static gain of Equation 4.2 and of sufficiently large amplitude: r  8 sign(C (I T  - A)~ B) l  3  =  C7 (^ - + A~  3  >  K  >  e\C (I - A)~ B\  T  D  1  d  2  = C (I-A)- B T  SS T  1  l  + ... + A + I)B  d _ 1  d  2  (4.1)  (4.2) (4.3)  where Kss is the process static gain, and e is the weighting for sufficient size. In this case e was set to 0.5 as "sufficiently large" was suggested to mean greater than 50% of the value (Dumont [72]). 8 was introduced in Section Equation 4.3 was implemented to create a horizon that expanded until the condition was met. As a result, the performance suffered in two ways. First, the constraint increased the conservative nature of the controller by decreasing response at the start of the case. As such, control of low responders was vastly delayed while the system adapted to the differences between the average model and individual subject. Second, the process was computationally intensive with mismatched models. The extra computation became prohibitive for implementation, particularly with the low 83  C: original, lambda .95 r e m a k e , lambda . 9 8 , lambda 1, hybrid  0  20  40  60  80  100  120  140  160  180  200  220  Figure 4.14: L A G U E R R E M O D E L C P A R A M E T E R S U N D E R VARIED E F R A P A R A M E T E R S . F R O M T O P TO B O T T O M , ORIGINAL DATA, R E C O N S T R U C T E D N O R M A L F O R G E T T I N G A = 0.95, G E T T I N G A = 0.98,  R E D U C E D FOR-  N O N - F O R G E T T I N G A = 1.0, A N D A HYBRID VERSION STARTING WITH N O R M A L  F O R G E T T I N G A N D G R A D U A L L Y B E C O M I N G N O N - F O R G E T T I N G AS T H E SIMULATION  PROCEEDS.  responding models where the true models have smaller gains than the average case (and thereby demanding more terms in Equation 4.1). A partial solution was to apply this gain only once the patient had been remodeled through the model swap procedure. Based on experience, problems with ft were unlikely to occur at the start of the case. Furthermore, constraints on the maximum horizon (e.g. 50 timesteps) were enacted to force the use of the input calculated at that maximum horizon should it be reached, subject to correction for negativity and violation of maximum constraints. To reduce the computational load, the horizon was given a maximum of 30 timesteps. (The previous experiments used four and six timesteps.) In another set of experiments, a male rabbit, approximately sixteen weeks old and weighing 3.8% was subject to computer controlled N M B with fixes for the constraint on ft, adaptive forgetting (the hybrid A) and a horizon allowed to vary between six and twenty timesteps. When response was seen to be slow, the maximum horizon was reduced to ten at timestep sixty-two. After this (or maybe coincident to this, as the model was improving steadily), the infusion rate immediately jumped and corrected towards the setpoint. The case was discontinued shortly after the decaying oscillatory rise seemed to settle about the setpoint, in order to try again with the new horizon range. The details of this experiment are shown in Figure 4.16. In a second experiment with the same rabbit, the horizon was allowed to range between six and 10 timesteps. The results appear in Figure 4.17. Rise to setpoint was slow and oscillatory, possibly because model swapping did not take place, and the computer was forced to rely solely on the RLSE scheme for adaptation. Towards the end of the experiment, it was decided to test control at two twitches. However, 84  U: original, lambda .95 remake, lambda .98, lambda 1, hybrid 3 2 1 0 5' 0 -5 -10 0 0  0.1 0.05 0 -0.05  1  i  i  i  ;  ]  !  !  !  20  40  60  20  i  JUW.I  0  l  I  I  140  160 I  180 I  200  220  40  60  J 80  I 100  I 120  J 140  L 160  J 180  L 200  220  1  1  1  1  1  1  1  1  I  :  j  :  i  i  J 20 J  L 40 L.  i 80  i 100 1  i 120 J  1 i  20  ..1  I  1,  ~ . :  :  140 L  i 160 J  A-  1-  i 180 1  1 200  i.  -J  i  ,  I  180  T 200  1  220  V  :  40  60  80  100  INPUTS U N D E R V A R I E D  120  EFRA  140  160  PARAMETERS.  O R I G I N A L D A T A , R E C O N S T R U C T E D N O R M A L F O R G E T T I N G A = 0.95, 0.98,  §.....  i  -i- —  0 -f^i -0.2 -0.4  CONTROL  I  !  L . .J 100 120  I  Figure 4.15:  j  1 80 I  i  -0.2 -0.4  1  220  FROM TOP TO BOTTOM,  REDUCED FORGETTING A =  N O N - F O R G E T T I N G A = 1.0, A N D A H Y B R I D V E R S I O N S T A R T I N G W I T H N O R M A L F O R G E T T I N G  AND G R A D U A L L Y BECOMING NON-FORGETTING AS T H E SIMULATION  PROCEEDS.  this was a fickle decision and quickly stopped, but not before causing saturation of the response. The experiment was halted and the neuromuscular response allowed to recover.  M o d e l Size Verification  It was postulated that the source of instability and possibly the oscillation seen, was unmodelled dynamics. As discussed in Section, stability and robustness in control is had with increased horizons and filter count. However, the optimal structure found in Section 2.5.2 was only sixth order. As well, the reason that control was not better may have just been because of a mismatch of models. It was decided to verify this use of a relatively smaller number of model parameters in the closed-loop control experiments. To test the optimality of the sixth order model, measurements collected from an experiment in which there was slow onset followed by decaying, oscillatory control were fit with Laguerre models of six, nine and twelve filters. The results of this experiment can be seen in Figure 4.18. As shown, there was a slightly better fit with the higher order models. This better fit was also expressed as a decrease in error from an MSE of 0.0263 for the sixth order to 0.0235 for the twelfth order. The price of this decrease was a large increase in the size of the model parameters (Co to C 5 are listed on the right side of the figure for each model) to magnitudes greater than three thousand for model parameters previously less than five. The increased magnitude of the parameters is countered by equally large increased parameters in the opposite sign suggesting that the additional filters are not adding detail but instead just counter-balancing. Similar fits and parameters were found for other experiments as well. This suggested that the 85  Figure 4.16:  C O N T R O L O F N M B WITH [3 CONSTRAINT,  ADAPTIVE FORGETTING  AND A VARY-  ING HORIZON B E T W E E N SIX A N D T W E N T Y , A N D T H E N SIX A N D T E N T I M E S T E P S .  IN THE TOP  G R A P H A R E D R A W N RESPONSE M E A S U R E M E N T S ( D O T T E D ) , M O D E L E D O C C U P A N C Y (DASH-DOT) A N D SETPOINT (SOLID LINE).  T H E MIDDLE G R A P H SHOWS T H E INFUSION  INPUT IN 2 X EDg  DOSES. T H E B O T T O M G R A P H SHOWS T H E C M O D E L P A R A M E T E R S . T H E UNITS O F T H E ABSCISSA A R E TIMESTEPS O F 20s.  relative size of the model was not the issue. 4.2.4  H a n d l i n g Oscillation  In the last experiment of Section and in some of the others, oscillation was seen in the response as it approached the setpoint. It was postulated that control could be improved by considering the oscillation due to mishandled delay and/or as a disturbance. In a simple experiment to counteract potential delay, a Smith predictor (a method of handling control loops with dead time, first proposed in Smith [85]) was implemented to approximate the delay seen and then feedforward the output accordingly. Delays based on prior experimental observations were applied to counteract various frequencies in the oscillating output response. A female rabbit, approximately twenty-six weeks old and weighing 4.1% was the subject for this experiment. As could be guessed, the estimate of the delay was crucial to the performance of the controller. Delays of twenty-six, eighty-six and 160 timesteps were tried. Smith prediction with the smaller delay of twenty-six timesteps failed, with the controller unable to reduce the response to the setpoint. It was quickly stopped. The delay of eighty-six timesteps was also unable to reach setpoint and instead rose and fell continuously back to a To4 of 100%. The best of the Smith predictors was the one with delay of 160 timesteps. Its results are shown in Figure 4.19. The response can be seen to be choppy with a long time to reach setpoint and then continued oscillation once there. In another experiment attempting to eliminate the oscillation in response, setpoint changes 86  5  Figure 4.17:  C O N T R O L O F N M B WITH (5 C O N S T R A I N T ,  HORIZON B E T W E E N SIX A N D T E N TIMESTEPS. SUREMENTS  ADAPTIVE FORGETTING A N D A VARYING  I N T H E T O P G R A P H A R E D R A W N RESPONSE  MEA-  ( D O T T E D ) , M O D E L E D O C C U P A N C Y ( D A S H - D O T ) A N D SETPOINT (SOLID L I N E ) . T H E  MIDDLE G R A P H SHOWS T H E INFUSION INPUT IN 2 X EDg5  DOSES. T H E B O T T O M G R A P H SHOWS  T H E C M O D E L P A R A M E T E R S . T H E UNITS O F T H E ABSCISSA A R E TIMESTEPS O F 20s.  #Filters=6 err= 0.0263 j _| p = 0.947 C = {2.72 4.02 2.78 1.38 0.053-0.491 } #Filters=9 err = 0.0238 p = 0.904 C = {2.61 4.18 2.98 1.05-1.82-2.88 ...} #Filters=12 err = 0.0235 -| p = 0.861 C = {2.11 -5.26-75.5 -408 -1380-3340...} 10 Figure 4.18:  20  30  40  50  60  70  80  90 100  E R R O R A N D M O D E L P A R A M E T E R S FOR VARIOUS M O D E L SIZES IN INFUSION  M E A S U R E M E N T DATA (SOLID LINES)  IN C L O S E D - L O O P  CONTROL  TESTING.  IS C O M P A R E D T O P O S T - H O C  M O D E L E D VERSIONS OF T H E M E A S U R E M E N T DATA ( B R O K E N LINES) WITH SIX (TOP G R A P H ) , NINE (MIDDLE)  AND TWELVE (BOTTOM)  FILTER L A G U E R R E M O D E L S .  A R E T I M E S T E P S O F 20s.  87  T H E UNITS O F T H E  ABSCISSA  1 _ ^ J N • i  i  i  '  *  :  i  i  i #  rl  1 1 1  V/  1 1 V 11 J • J1 l1 i T  V  r  J. 1  L  A  ft  i  I  .  1  T  i  i  i  i  i  "i  ft' ^  •  i  i i i I  •  i  i  *  20  i  i  it  *-v.  l  \  1  -^d^^T*  ^^^^^^^^hi  i  i i i i i  i  i i i t  i  1  1  1  >  i  L  -i  i • i i i  ---  r — ^ — ' •  ' 0  1  i  L  1  * 4J ^ ^ ^ ^ ' ' ^ ^ ^ r f L i  i  i i i  1 1  ^  :  i  J  i i i  i  1  lr i  ^  :  •  i i i  1  i  ' •  :<!  1 1 r.zf..I •i...7> 1  1  40  60  80  100  120  <  1  1  140  — i  160  180  Figure 4.19: C L O S E D - L O O P C O N T R O L WITH S M I T H PREDICTION. I N T H E T O P G R A P H A R E DRAWN RESPONSE M E A S U R E M E N T S ( D O T T E D ) , M O D E L E D O C C U P A N C Y (DASH-DOT) A N D SETPOINT LINE). T H E MIDDLE G R A P H SHOWS T H E INFUSION INPUT IN 2XEDQ  5  (SOLID  DOSES. T H E B O T T O M G R A P H  SHOWS T H E C M O D E L P A R A M E T E R S . T H E UNITS O F T H E ABSCISSA A R E TIMESTEPS O F 20S.  were considered to be disturbances and disturbance rejection implemented to counteract them. The counter-oscillation was described as a gain: F = -D/P  (4.4)  where D is the disturbance model, an exponentially decaying sinusoid, and P is the plant (the rabbit) model. The input to counteract the disturbance was calculated with a zero/pole model of F being driven by the derivative of the setpoint to react to the presumed disturbance of setpoint changes. The equation for the input disturbance was then: u ist{k) D  =  [ - 0 . 0 6 0.44 - 1.27 2.05 - 1.98 1.15 - 0.37 0.05] x setpoint{k...k - [ - 6 . 6 6 19.0 - 30.1 28.6 - 16.3 5.13 - 0.69] x u  {k  Dist  - l...k - 7}  -7}... (4.5)  Feedforward control had been designed and implemented based on providing an input signal of contrary oscillation to that seen in the response. As fate would have it, no oscillation was seen for this rabbit and as a result, disturbance rejection was not applied. Instead, the experiment appeared as is shown in Figure 4.20. The horizon was set at nine timesteps to eliminate one variable. The case was ended when a pump failure occurred at timestep 240.  4.3  Simulating Intra-patient Variance  As stated, intra-patient variance is a great concern for closed-loop control of drug therapies and a big reason why these therapies have failed in the past. Controllers must be flexible and robust 88  Figure 4.20:  A P P L I C A T I O N O F D I S T U R B A N C E R E J E C T I O N IN C L O S E D - L O O P C O N T R O L . I N T H E T O P  GRAPH A R E DRAWN RESPONSE MEASUREMENTS (DOTTED), MODELED OCCUPANCY A N D SETPOINT (SOLID LINE).  (DASH-DOT)  T H E MIDDLE G R A P H SHOWS T H E INFUSION INPUT IN  2  X  EDg  5  DOSES. T H E B O T T O M G R A P H SHOWS T H E C M O D E L P A R A M E T E R S . T H E UNITS O F T H E ABSCISSA A R E T I M E S T E P S O F 12s.  A P U M P FAILURE OCCURRED AT TIMESTEP  220.  enough to deal with a patient changing during the procedure. In order to test the ability of the controller to control a patient that is varying within the case and demonstrate safety while doing so, models and methods for instilling intra-patient variance were developed. Methods considered for producing artificial and repeatable intra-patient variance included administration of additional neuromuscular blocking agents; administration of inhalational anesthetics synergistic with NMB drugs; administration of sympathetic stimulants, such as a-adrenoceptor agonists to reduce kidney function; switching NMB drugs mid-procedure; and changing the NMB drug concentration during procedure with the extreme of replacing rocuronium with saline. The first two methods were investigated and will be elaborated upon here. The first method, administration of additional NMB drugs, will be expanded upon as administration of irreversible and reversible competitive antagonists to the ACh receptor. The other methods are mentioned as possibilities and were not investigated in this report. 4.3.1  Inhalational Anesthetics  Inhalational anesthetics are known to potentiate the effect of neuromuscular blockers by stabilizing the NMJ. In guinea pig nerve-lumbrical muscle preps, Waud and Waud (Waud [86]) showed that volatile anesthetics could depress ST stimulation. Depression of the twitch was seen at 3.5 to 5 MAC for halothane, mehtoxyflurane and isoflurane; 2 to 3.5 MAC for diethyl ether and fluroxene; and 1.5 to 2.5 MAC for enflurane. These levels are unrealistic clinically as they could not be sustained for any significant amount of time without killing the patient. Waud and Waud make the valuable observation that the presence of the volatile depresses membrane depolarization making it harder for muscles to function and easier for blockade to occur. 89  In a solo work by B.E. Waud, the author goes on to quantify this by measuring the shift in the dose response curve for tubocurarine in the presence of 1 M A C volatiles. It was learned that the ED50 dose decreases fractionally by 0.311 for methoxyflurane, 0.334 for halothane, 0.335 for isoflurane, 0.462 for diethylether, 0.58 for fluroxene and 0.697 for enflurane (Waud [87]). In more recent work, this procedure was done in humans in a study comparing rocuronium use under propofol, halothane and isoflurane anesthesia. The amount of rocuronium used was 636 ± 191, 496±107 and 384 ±127 fig-kg~ -hr for the propofol, halothane and isoflurane groups respectively (VanddenBroek [88]), indicating a roughly 40% decrease in need when using isoflurane. The NMBAS study (described fully in Chapter 5) was not specifically powered to detect effect due to the volatile anesthetic; however, some changes in patient modelling were noticed that might be attributable to the anesthetic. This will be discussed in greater depth in Section 5.8.1. l  4.3.2  -1  Irreversible Antagonists: a-Bungarotoxin  a-Bungarotoxin is a toxin produced by the bungaris multicinctus snake, also known as the Chinese krait. It has two forms being one of either sixty to sixty-two, or seventy to seventy-four amino acids with total weight ranging between 6000 and 8000 Dal tons (Mebs [89]). a-Bungarotoxin is a neuromuscular synapse, AChR blocker that is partly irreversible but with high affinity to the receptor due to a-BT covalent binding to the AChR. Once injected, muscle response shows a gradual decrease in ability as the drug slowly blocks more and more receptors. This decline goes on over a period of up to half an hour. Muscle function returns only after the creation of new receptors and/or new cells, a process taking as much as one month.. Although binding is permanent with respect to the short cases of this work, a-Bungarotoxin was thought to be a good inducer of intrapatient variance due to its reputed lengthy onset. This would allow great changes in the patient over long periods of time as the AChR were gradually blocked. The literature was searched to find appropriate doses to produce paralysis in a rabbit model. Two papers were found. In Takamori [90], 80/Up • kg administered intravenously was used to paralyse. It took 30 minutes for onset, and a peak effect was arrived at in between three and five hours. In Durant [91], doses were titrated to arrive at paralysis. The doses ranged from 39 to 50fig • kg with a mean of 42 ±2fi • gkg- . A third paper was found with toxicity results for the complete venom (containing a-, (5- and K-Bungarotoxins). It stated that the minimum lethal dose in the rabbit was produced with Q.2mg • kg~ with either subcutaneous or intravenous administration (Brown [92]). However, as was seen in the results of 4.2.1 in practice this onset can be quite fast. After administration of a-Bungarotoxin 20/xg • kg , the animal saw a very fast drop in response to one or no twitches. This rabbit may have been sensitive to the toxin, or it may just have been that the receptors were already blocked for the most part and there was no receptor reserve to be gradually taken up. The drawback of a-Bungarotoxin in the experimental setting is its permanence. There is no means of determining if the effect seen at the junction was because of the toxin or the surgery. For this reason, a-Bungarotoxin use was concluded, and an agent that could be eliminated and that allowed response to return within the duration of the experiment, was sought out. -1  -1  1  l  -1  4.3.3  Reversible Antagonists: Pancuronium  As a-Bungarotoxin is irreversible in the timescale of the experiments conducted there is no way of knowing whether or not the animal has recovered function after the experiment is over. It was postulated that NMB agents could be used if their pharmacokinetics are significantly different from  90  the primary NMB. In these experiments, shorter acting drugs such as mivacurium could be used to enact short term changes to the patient, e.g. acute and massive bleeding. Longer acting drugs such as pancuronium are ideal for their slow and long-lived kinetics. Comparing rocuronium and pancuronium, both drugs are members of the ammonio-steroid chemical class. The drugs have similar cores (the steroid) and small differences in their side chains (see Figure 1.1). Behaviorally, both drugs are known to be non-depolarizing, competitive antagonists of acetylcholine receptors (AChR). Rocuronium is metabolized in the liver primarily with some renal elimination; pancuronium is strictly eliminated through the kidneys. Pancuronium also has a longer delay to onset (four to six minutes, versus one to two for rocuronium at clinically useful doses). Pancuronium has the longer duration of action, between 120 and 180 minutes in humans at clinical doses; rocuronium's duration is between thirty and sixty minutes (Goodman [93]). Because of the similarities in their chemical structure and mechanism of action, it can be assumed that the two drugs will have an additive effect. However, this may be open to debate. In Waud [94] interaction among different NMB agents was tested. Additive, competitive action was seen with combinations of gallamine, metocurine, pancuronium and tubocurarine, except for the combinations of pancuronium with metocurine and metocurine with gallamine. For these last two there was seen potentiation beyond additivity: there were 41 and 21% further shifts in the dose-response curves than was expected for additive action alone. Again, the drugs that had the non-additive effect were chemically very different and this may be the reason for the apparent synergy. Similar testing would have to be done to know with certainty. For testing as a potential inducer of intra-patient variance, a first guess was made at the correct dose to see effect based on the literature. Rocuronium has a 2 x EDg$ dose of 0.6mg • kg' in humans (Organon [3]), and O.lmg • kg' in rabbits (Gilhuly [61]). A pancuronium dose of 0.06 to O.lmg • kg- has a duration of 90 to 100 minutes in humans (ACCM [95]). Scaling to approximate rabbit doses based on rocuronium result suggests 0.01 to 0.017 mg- kg' for similar effect. 1  1  1  1  150 i To4 [%]  50 10  15  20  25  _L 30  35  40  45  Time in timesteps of 20s  Figure 4.21: PANCURONIUM IMPULSE RESPONSE MEASURED IMMEDIATELY A F T E R RECOVERY F R O M ROCURONIUM.  A pancuronium test was made with a rabbit after function had returned. Rocuronium had been given in excess to fill up the margin of safety at the N M J . Function was allowed to return to approximately 100% to allow seeing the full effect of the pancuronium dose; arguably the receptor reserve had been taken up and the nonlinearity exhausted. Therefore any new drug input having similar action (i.e. non-depolarizing competitive blocking at the N M J ACh receptor) would produce an immediate observable effect. Pancuronium 0.005mg/kg was administered at timestep number 171 (timesteps are 20s long). The response to the To4 was seen to decrease starting at 0.97, falling to 0.11 and then gradually rising back to 0.84 at timestep 201 (10 minutes later). This particular rabbit had been showing a plateau of sorts at this level when recovering from the rocuronium preloading. Full response returned at timestep 215, showing a full effect of approximately fifteen 91  minutes. This response adjusted for time of injection is shown in Figure 4.21. As this effect only lasted for fifteen minutes, it was decided to double the dose to O.Olmg • kg . This dosage was justified because the initial test was conducted in a large rabbit. Pancuronium being a charged molecule was felt to be more responsive to lean muscle mass; thus, a similar dose in a lean rabbit was likely to have even less effect. -1  4.4  R a b b i t s versus H u m a n s  An important lesson learned in the in vivo studies is that rabbits do not make good research subjects for automated NMB. Rabbit impulse responses compared to humans were one-quarter the timelength and approximately one-tenth the size as judged by the area under the curve (AUC) measurement. These differences indicate a much quicker and more difficult response to control, particularly with the restrictions on the stimulation. Compared to humans, it is analogous to attempting closed-loop control with data only available every eighty to 200s. Beyond that, the lower EDg$ for rabbits (one sixth that of humans) and overall much smaller mass means more demanding requirements for the pump in terms of volume, precision and sensitivity to changes. Another complication was the anesthetic propofol. In Ypsilantes [96] it was noted that a tolerance to propofol's sedative effect occurred in mechanically ventilated rabbits, with significant difference noticeable after one to two hours. Propofol consumption in the rabbit experiments of this thesis varied during the case, and anecdotally the rate was noticed to increase throughout the case. Rates were varied from 50mg • hr (5mL • hr* of concentration Wmg • mL" ) to 190mg • hr" (19mL • hr* ), with brief periods of 380mg • hr* (38mL • hr ), all this depending on the weight of the rabbit, of course. Thus, the observed trend to increased drug administration with propofol may have been because of tolerance. Tolerance is a concern as the hypnotic effect expected may have been wearing off and to some extent this may have influenced measurements. On a positive note, in another recent paper, Yamamoto [97], in which xenon was being tested for effect on myopotentials, it was found that the effect of propofol on the N M J was substantially less than that of xenon and even further reduced as compared to isoflurane, a drug known to potentiate NMB. This result supports the "cleanness" of the experimental protocol. Because of the potential problems with the rabbit model, the differences in rabbit and human N M B drug metabolism, and the need to use this technology clinically, it was decided to conclude work with rabbits and proceed with clinical studies in humans. These studies are described in Chapter 5. -1  1  4.5  1  1  1  -1  S u m m a r y of C l o s e d - l o o p C o n t r o l  This chapter described the in vivo testing of the controllers developed in the previous chapters. It described the equipment developed to perform the testing. It described the testing of the controllers, selection of a best for human clinical work, and its further-tuning and development. This included optimizing of the RLSE and controller parameters, investigation for instability and managing oscillation. For further work and more robust testing of future controllers, simulation of intrapatient variance was discussed as well, with reference to inhalational anesthetics, irreversible antagonists and reversible antagonists. The rabbit studies were very informative. Best model structures and controllers were found. Control parameters were optimized. Methods of inducing intra-patient variance were explored. This was great experience that would benefit human application of the research. Human studies are described in the next chapter. 92  1  Chapter 5  Advisory Control and Human Clinical Studies In the previous chapters, controller algorithms were developed and tested in simulation and in animal trials in anticipation of implementation of closed-loop NMB drug administration in humans. The emphasis of the closed-loop control experiments was on experimentation - the testing of ideas and controllers, and details relevant to them, such that an application could be made in humans with little chance of failure. Although the control seen in the rabbit work was not perfect, a great deal was learned regarding control of NMB in general and in specific that the rabbit was not a great substitute for humans. As such, it was decided to apply control to human patients. As closed-loop control of drug administration was unproven for application in humans, an intermediate step was taken: an advisory system for NMB drug administration was developed, the Neuromuscular Blockade Advisory System (NMBAS). This advisory system presented dosing recommendations - how much and when - to the user based on measured patient response and an internal model of the patient. The initial dose was determined by manufacturer's recommendations or an appropriate dose for the patient's population subgroup. Subsequent doses were adjusted to adapt to the individual's response to the drug. The advisory system learned the response for each patient and was better able to predict the optimum dose required. At all times, the anesthesiologist was to have the final say on what was given. This supervision made the NMBAS safe to use in a clinical setting; all advice was questioned, and accepted or rejected based on medical experience. Clinical testing of the NMBAS was done in three stages. First, a study was conducted to develop a modelset for humans and test algorithms. This study is mentioned in scant detail in Section 2.1 with presentation of some of the results for comparison against rabbit models in Section 2.1.1. Then, a full clinical trial to test the safety and efficacy of the NMBAS against standard care was done. Finally, a pilot study to test feasibility of an infusion-based NMBAS was conducted. A l l of these will be elaborated upon in this chapter. The chapter begins with a discussion of the implementation of the NMBAS.  5.1  The N M B A S in Detail  The advisory system is composed of input handling to gather data on the patient and drug given from the user and sensor data from the patient monitoring equipment; a patient model; a database of other patient models obtained from prior patient testing (the modelset); algorithms for adaptation of the model to better suit the patient, for estimating current drug levels and response, prediction of future drug levels, responses and time to those levels and responses, and generation of advice; 93  and a means of presenting the advice to the user. A block diagram of an advisory system for administration of drugs appears in Figure 5.1, as it would be incorporated into a module retained inside a patient monitor. The patient monitor interacts with the patient, sending N M T stimuli to elicit response and receiving response data for processing and display to the user. The user gives drug to the patient, and information on drug administered, and patient and case details to the patient monitor.  drug  Patient  measured response  User  stimulation A n e t h e s i a Monitor Advisory S y s t e m drug given Input record | R e s p o n s e r e c o r d ^  Sensing modules: NMT ECG  Sp02... (with processing)!  patient model patient & c a s e parameters Estimation: current drug levels/response Prediction: future drug levels/response  Advice: d o s e / time  Databus  Display  Figure 5.1:  B L O C K DIAGRAM OF T H E N M B A S .  The advisory system receives data on drug given from the user and response data from the sensing module in the anesthesia monitor. The advisory system also receives data on the patient and case parameters to aid selection of an initial model of the patient response from the modelset and for use by the other procedures. Other procedures include algorithms for adaptation of the model to better suit the patient, for estimating current drug levels and response, prediction of future drug levels, responses and time to those levels and responses, and generation of advice. The user begins by informing the advisor as to the patient's demographic and health status characteristics. The advisor then selects a mathematical model of drug response - either an average model based on the entire dataset or one based on the information provided: demographics such as age and/or sex, and/or health conditions such as liver function or another characteristic can all be used. The advisor then suggests a starting dose to administer to bring the patient to a 94  certain indicated response at an indicated desired time. The user administers a dose and informs the advisor as to how much was given. The effects of the dose are monitored and predictions of when the patient will next need drug are made. As patients have large variation in their response to drugs, the dose given will most likely be sub-optimal to start, but with monitoring the advisor system will learn how the patient reacts and will adjust the model of the patient accordingly (using the adaptation schemes of Section 3.7). The NMBAS computes how much drug is left in the patient, the amount of time until the response reaches various levels, and how much drug the patient will need until the next time for dosing or until the drug is no longer required. This information is presented to the user. 5.1.1  Prediction of Levels of Response and Doses  The advisory system informs the user on the length of time until indicated response levels are reached. For the NMBAS, it was desirable to know when the response will recover to the setpoint, when the patient can breathe spontaneously (judged to be a To4 measurement of 30%), and when the patient can be considered reversed (a To4 measurement of 100%.) These times were determined by advancing the model in time until the level of drug falls enough that the response desired is reached. Calculations are performed for the model, as represented by Equations 2.17 and 2.18, modified for no-input conditions: L{t  + 1)  =  A L(t) + Bu = A L(t)  y(t)  =  C  (5.1)  L(t)  T  This calculation is performed iteratively while increasing time t until the desired level is reached or until the maximum time horizon of concern (to prevent infinite calculation) is exceeded. Prediction of the required dose to arrive at the future response is achieved in a similar fashion, also by advancing the Laguerre model into the future. At each timestep, recommendations are made for the amount of drug needed to reach the pre-determined length of case at the desired setpoint, and for the amount of drug required to be at the desired setpoint after the minimum amount of time desired between doses. The model is manipulated to take it from the current state to the future setpoint. Starting with the formula Equation 2.17 and assuming only one input at the current time, the equation defining the model d timesteps into the future is: y(t + d)  =  C{t + d) L{t + d)  (5.2)  L(t + d)  =  A L(t)  (5.3)  T  d  + A - Bu(t) d  l  where y(t+d) is the desired future setpoint, L(t + d) is the future state vector, and d is the horizon, the number of timesteps into the future we wish to look. Assuming that the model is known C(t + d), C(t) and C are equivalent. Substituting C and the equation for L(t + d), Equation 5.2 becomes: y(t + d) = C A L(t) T  d  -f- C B - u{t) T  d  l  (5.4)  Rearranging the resulting equation reveals that the input to administer now to arrive at the future desired state based on the current conditions is:  95  Including the current measurement information in this equation makes it similar to the extended horizon controller of Equation 3.7: «C> -  V  R  -  m  -  c  f  A  i f  B  -  I  )  L  {  t  )  (5-6)  Once the dose has been determined, the value is examined to ensure that it is not larger than the maximum size permitted and that it is positive. An estimate of the amount of input remaining is recalculated each timestep to keep up with impulse response changes due to model adaptation and the diminishing effects of the inputs as time proceeds. This estimate was a convolution of the impulse response with the input history vector over a recent period of time equivalent to the length of the impulse response. For example, a patient whose impulse response to the drug is predicted to last for 300 timesteps, and who has received drug at timestep 0 and 200, at timestep 350 will have no remaining drug due to the first dose and remaining drug due to the second dose proportional to the area under the curve of the impulse response between relative timestep 150 (from current timestep, 350, subtracting the timestep of administration, 200) and the end of the impulse response, timestep 300.  5.2  Prostate Brachytherapy Patient Study  A pilot study has been conducted to develop and test the NMBAS. The objectives of the pilot study were to gather human data to build the dataset for simulation testing, to aid development of the software and algorithms of the NMBAS to the point where the NMBAS could be evaluated in a clinical trial, to test and improve upon the case report forms and associated data collection for a clinical trial, to develop the patient model necessary for the clinical study, and to test on initial feasibility. Data collection was performed during prostate brachytherapy procedures. Prostate brachytherapy cases involve the placement of between five and 30 needles containing between 100 and 150 radioactive seeds into the patient's prostate. Needles are guided and positioned with a stereotactic frame fixed to the patient for location. The surgeon visualizes the seed placement with an ultrasound probe inserted into the patient's rectum and x-ray fluoroscopy. The surgery often requires muscle relaxation for intubation and prevention of patient motion that can disrupt placement of the seeds, injure the patient, and misalign the stereotactic frame and ultrasound probe. These procedures were chosen because the procedures are fairly common, relatively short and use N M B agents. Depending on the case, one or two doses are all that is normally required. The reduced number of doses makes the analysis of response to the drug simpler.  5.2.1  Prostate Brachytherapy Patient Study Methods  No particular hypotheses were being tested during this study. Being a pilot study, there was neither blinding nor separation into control and treatment groups with associated randomization. Patients were enrolled in the study until it was felt that sufficient numbers of patient models had been obtained, and that the NMBAS software was ready for deployment in a clinical trial. Obtaining many patient responses was advantageous as the more responses available to the NMBAS, the more responses were available for swapping to and more patient variability was captured. As a result, the better modelling and prediction became. The constraint was the time required to capture the models. Software readiness was determined by bug-free performance. The patient population for this trial consisted of patients undergoing prostate brachytherapy. This choice minimized variability in the measured responses by having a standardized patient 96  population, and provided short cases usually requiring only a single bolus dose of rocuronium. Patient eligibility was determined by examination of the patient charts and through a patient interview. Inclusion criteria were: • Males, aged 18 years or older • ASA physical status I-III • Scheduled for surgery under general anesthesia utilizing NMB • NMB agent to be used is rocuronium Exclusion criteria were: • History of hypersensitivity or allergy to rocuronium or any component of its formulation or other neuromuscular blocking agents • Liver failure • Renal failure • Severe obesity, BMI>35 • History of neuromuscular disease • Decreased/low neuromuscular response in forearm, low/non-responsive to N M T / E M G measurement (e.g. peripheral neuropathy, myasthenia) • Inability to communicate or provide informed consent • Receiving drugs interfering with neuromuscular transmission  Once the patient was anesthetized, To4 stimulation of the ulnar nerve was started at a rate of once every 20 seconds. Measurement was at the adductor pollicis muscle using either mechanomyography (MMG) mechanosensor (Datex-Ohmeda M-NMT Mechanosensor) or electromyography (EMG; Datex-Ohmeda M-NMT Electrosensor) via the sensors provided with the anesthesia monitor and stimulation module (Datex-Ohmeda S/5 and NMT module). These sensors and how they are connected to the patient are displayed in Figures 5.2 and 5.3. Rocuronium was administered according 97  FIGURE 5.3:  C O N N E C T I O N O F T H E N M T M O D U L E TO T H E PATIENT F O R T H E E M G SENSOR  (MODIFIED F R O M D A T E X - O H M E D A  [98]).  to the attending anesthesiologist's judgement and at or below the manufacturer's recommended dosage of 0.6mg kg- , the 2 x ED95 dose for humans. Patients underwent their scheduled procedure without influence by the computer and/or its operator. Physiological data was recorded from the anesthesia monitor. Recording was through custom software, running on a portable computer (IBM Pentium II PC) interfaced to the monitor via a serial port connection. For the purpose of constructing an average model of the patient rocuronium response to be used in the NMBAS clinical trial, individual patient models were constructed and averaged over time. To make the individual models, To4 data was recorded during the case, processed for noise and baseline, and correlated to the administration of the first bolus. Data was included from the time of the first injection until the next drug affecting NMB was given - either a second dose of rocuronium or a reversant. The impulse response was constructed from the measurements using the techniques discussed in Chapter 2. 1  5.2.2  Prostate Brachytherapy Patient Study Results  Thirty patients were evaluated. Thirteen were excluded because of various technical problems. Three were excluded as rocuronium was not used and served only for testing the computer interface to the anesthesia monitor. Fourteen patients were evaluated and used to construct the average patient model. Patients were male, of average age 61.9 ±8.3 years. Average weight and height were 80.1 ± 8 . 8 % and 173 ± 5.5cm, with an average body-mass-index of 26.7 ± 2.6. ASA scores were either I, II or III with a mode of II. All patients underwent prostate brachytherapy procedures of average case length 59.8 ± 12.6mm. The general anesthetic used was desfurane or sevoflurance with nitrous oxide. This was delivered at an average end-tidal average anesthetic concentration of 0.79 ±0.13 times the minimum alveolar concentration (MAC). Average rocuronium use was 41.2 ± 6.8mp. Generally there were only one or two doses of rocuronium administered. Doses subsequent to the first were administered if the case was going longer than expected or if the surgeon requested additional drug. After these 30 patients, the program was deemed workable for use in the clinical study, and data necessary and important for recording and study was known and case report forms were modified to capture this. The user interface as it was at the end of the trial is shown in Figure 5.4. Inputs are on the left hand side of the screen with patient data at the top, and event input at the bottom. Outputs are on the right hand side, with N M B measurement data at top (status variables, raw and 98  Patient Data/History NMT Outputs Use  Heath*''  STAR". . Cff*. Minu:e since intUb.uOSS  0,30 DceeP,em  €§»  M e d l  i/SUj<-ry^  ^  h 0  f  Haghtfcm] Wt.[kg] Locaton Procedu-e L60 60 SPM TAH disease is«a«e diseaie disease  A^i enprn;?  A j  BMI 0.00  remodel?  Time/srjrn[s]  Musing  InlCd? Me;  "JRS  • •  ijprdM cal'd  Coun:  Anesthetic 3.00 O.0C 0 NIMTMCde PuloeWidth Current PTCWo'd I emp(C) 0.00 0 0.00 NMT 2.0 0  Case T'>t raU'j(%)Allowabe i.o Lengthl" mini? clear eJ? #twidnes? 3.5  ?90  ;  rirreSetween ioso:<mn)? vj 20  TrAn<mir' Intervals]  , IO.O0"  J'""  MaxDose ,-, nrj F.oc.[rrg]? "  Event Input Event?  m  Oug, dose injected or ,-1 4  Notes tor other event  1  Occupancy yRebxation  ocConvertToPeUx 0 00  Overdose  EvertPeady? NO  no event  1 .U  Underdose  oUKIDO^Iiifuaon ~ n c (mh) to: (my) ug/rrin Desired .3To4 '. 0.00 0.00 0.00 0.C0 Cose(rrg) Rec  Irans. Kecer/e# u  Tl  i.s  n.r*'i  3  Age[vrs] Sex[m/f]  Count  U  Cl  c  o  1.0To4 O.OO I Dose (mo; Rec(EOC)  Figure 5.4: T H E N M B A S USER I N T E R F A C E . charted data below that); estimated drug level information charted below that; predictions until the response returns to the level of the user's indicated setpoint, the level of function returning and until reversal; and the charted inhaled anesthetic information in the bottom right hand corner as represented by multiples of MAC. The results of the modelling process for a low responding patient are shown in Figure 5.5. The E M G measurements recorded between the first dose given (at timestep eight), until the second dose was given (at timestep 52) is displayed in the top chart. In the bottom chart are the impulse responses calculated using the nonlinear estimation and generated through the Laguerre modelling processes. The curves overlap because of the fidelity of the Laguerre modeling to the pharmacokinetic model of Equation 2.8. This patient can be seen to exhibit rapid onset and relatively long duration of the drug in the patient, having a noticeable presence up to 600 timesteps (200 minutes). Similar data to that of Figure 5.5 but for a higher responder appear in Figure 5.6. In the top graph showing measurements made, the response is seen to saturate quickly and remain in a saturated state for a long time (approximately 30 minutes), as shown in the modeled drug response by the greater than one values and the longer duration. In comparison to the previous model of Figure 5.5, there appears to be circulating drug for at least another 200 timesteps (67 minutes). Gaps in the recorded data are because of rejection of noisy measurements. A sample of prediction occurring with one of the earlier patients is shown in Figure 5.7. The top graph shows input ("x"s, mostly at zero but with three greater than zero signifying the three doses of rocuronium given) and EMG signal (dots) together. The next three graphs show from top to bottom, the real-time prediction from in the OR (solid lines - if they were on the chart) juxtaposed with post-hoc calculated time (dashed lines) to the next dose required, return of ability to breathe and reversal of the patient (To4 measurements of 10, 30 and 100%). In the figure, the real-time 99  Figure 5.5:  T H E MEASURED  EMG  RESPONSE ( T O P ) IN TERMS O F R E L A X A T I O N AND M O D E L E D  DRUG RESPONSE ( B O T T O M ) FOR A LOW RESPONDING PATIENT IN T H E PROSTATE B R A C H Y T H E R A P Y PATIENT STUDY. T H E E M G DATA P R E S E N T E D W E R E R E C O R D E D B E T W E E N ADMINISTRATION OF T H E FIRST AND SECOND DOSES.  T H E UNITS O F T H E ABSCISSA A R E TIMESTEPS OF 20s.  predictions cannot be seen as during the procedure, the computer was convinced that the response was much smaller (on the scale of what a rabbit would experience) and thereby these events had already taken place, and therefore produced zero values throughout. The post-hoc calculations are the result of a simulation of what the timing would be with the same schedule of rocuronium dosing seen in the case being given to the model response composed using the measurements between the first and second dose. It is used to make comparison and assess performance of the modeling over time against what was reported in the OR. The time to the events in question was then predicted at each timestep based on the drug in the system, the drug metabolism and the effect seen on the E M G measurement. There will be some discrepancy between the post-hoc calculation and reality because of intrapatient variance, mainly via the effects of the volatile anesthetic used throughout the case. As mentioned in Sections 1.1.1 and 1.6.1, volatile anesthetics potentiate the neuromuscular junction, increasing the effect of the NMB agent. Both of the anesthetics used here, sevoflurane and desflurane, have this effect. The models of rocuronium response are formed with data from the start of the case, not taking into account the extra bias towards greater responsiveness added by the volatile anesthetic. These models can be viewed as an average response to the NMB and anesthetic between the first and second administrations of the NMB. As a result, there will be an apparent increase in the effectiveness of the rocuronium as the case wears on, and an increasing bias in the difference between actual and predicted time to next dose, breathing and reversal. Adaptation of the model will help this. It also must be noted that because of the extensive saturation of the measurement (as can be seen in the top charts of Figures 5.7 and 5.8), little adaptation results. Few non-saturated data 100  patient22 response as relative relaxation (raw data)  Figure 5.6:  T H E MEASURED  EMG  RESPONSE ( T O P ) IN T E R M S O F R E L A X A T I O N A N D M O D E L E D  D R U G RESPONSE ( B O T T O M ) F O R A HIGH RESPONDING PATIENT IN T H E P R O S T A T E B R A C H Y T H E R A P Y PATIENT S T U D Y . T H E E M G DATA P R E S E N T E D W E R E R E C O R D E D B E T W E E N ADMINISTRATION OF T H E FIRST A N D S E C O N D DOSES. T H E UNITS O F T H E ABSCISSA A R E T I M E S T E P S OF 20s.  points are available as a result of the serial overdosing approach used by the anesthesiologist, and thereby adaptation of the model is slow. The progress in the development effort can be seen through the improvement in the prediction as demonstrated with predictions for a patient at the late stages of the pilot study, in Figure 5.8. In this figure, the real-time calculations are available and non-zero. The two peaks will be due to model swapping taking place at roughly timestep 125, not because a second dose was given (there was not). After the model swapping, some agreement can be seen between the real-time and post-hoc calculations in the time to function chart (third graph from the top), but the time to next dose is overestimated and the time to function is underestimated, suggesting that the true model - as represented by the post-hoc calculation - has more weight in the tail section of its response than the model adapted to in real-time. With a longer case and more data available, this event may have been corrected for. Prediction improved because of the improvement in the modelsets used in the cases. At the start, the only patient models available were those found in the preliminary rabbit studies. These were not representative and thus prediction estimates were completely off. A much smaller response was expected and thereby much smaller times to return of setpoint, function and recovery, e.g. the early patient whose data is shown in Figure 5.7. The modelset for Figure 5.8, where the prediction was somewhat improved, contained fourteen models (thirteen models and one average), all of human origin. Because of the changing nature of the patient through the procedure (mostly, the anesthetic affects the NMJ), quantifying the performance of the prediction routines is difficult. Modelling and prediction improvement would be assessed by markers of performance in the clinical trial: error, 101  patient14 y,u; time to next dose, function, reversal: estimate (solid), calculation^-) *  MW  «r 20  «««»»»  40  —I  f f I  40  j  1  80 11  100 1 1  120 11  140 11  160 11—  60  80  100  120  140  160  120 i 1  140  160 1r—  i  20  40 r  -I J  Figure  »--  -^ ^  I • • —  0  •  1  r  l _i l  60  •  f 20 I  0  I  i  :  0  0  j  .4 I N M M M M  •  I  20  60 ... ...  iI  40  80  r™  — i  I  i  60  100 1  I  80  i  I  100  I  120  1 i  I  140  \ i  160  5.7: E A R L Y PREDICTION EFFORTS IN T H E PROSTATE B R A C H Y T H E R A P Y PATIENT S T U D Y .  T H E T O P CHART SHOWS M E A S U R E D RESPONSE ( D O T T E D LINE) A N D INPUTS ( " X " ) . T H E T H R E E G R A P H S F O L L O W I N G A R E T H E T I M E IN T I M E S T E P S UNTIL T H E N E X T DOSE IS REQUIRED, A N D UNTIL F U N C T I O N A N D R E V E R S A L O C C U R , B O T H F O R WHAT WAS C A L C U L A T E D DURING T H E C A S E (SOLID LINE) A N D P O S T - H O C BASED O N T H E M O D E L L I N G D O N E ( D A S H E D ) . T H E UNITS OF T H E ABSCISSA A R E T I M E S T E P S O F 20S.  timing, drug use and event occurrence. 5.2.3  Observations from the Prostate Brachytherapy Patient Study  Eleven patients were excluded because of technical difficulties arising while debugging the software. Battery failures and computer problems accounted for two of these. Two patients were excluded because of the anesthetist not using a stimulator. These patients were used for testing of the data acquisition instead. Another three were excluded when the anesthetist decided a propofol infusion alone would suffice for muscle relaxation and no rocuronium was given. These last five patients served to test the computer software and its interface to the anesthesia monitor. Many problems became evident during the trial that will have an impact upon the randomized, controlled clinical study. The sensor type was an issue at the beginning of the study when the M M G was used. The M M G had the advantage of being easier to setup: it required attachment of two electrodes versus five for the E M G . However, it was unreliable. Visible twitches were sometimes not measured by the monitor. In one case, a patient was showing a visual count of four twitches with the To4 but no measurement was produced on the monitor. Even though all four twitches existed (the arm was moving) there was nothing measured. In another case, the patient showed a P T C of zero twitches yet was still capable of breathing. It is possible these mis-measurements were because of a decreased sensitivity of the mechanical sensor or a raised threshold to sensing (as protection from noise) for 102  patient30 y,u; time to next dose, function, reversal: estimate (solid), calculation(~)  Figure 5.8:  P R E D I C T I O N AT T H E E N D O F T H E PROSTATE B R A C H Y T H E R A P Y P A T I E N T STUDY.  T H E T O P C H A R T SHOWS M E A S U R E D RESPONSE ( D O T T E D LINE) A N D INPUTS ( " X " ) . T H E T H R E E G R A P H S F O L L O W I N G A R E T H E T I M E IN T I M E S T E P S UNTIL T H E N E X T DOSE IS R E Q U I R E D , A N D UNTIL F U N C T I O N A N D R E V E R S A L O C C U R , B O T H F O R WHAT WAS C A L C U L A T E D D U R I N G T H E C A S E (SOLID LINE) A N D P O S T - H O C BASED O N T H E M O D E L L I N G D O N E ( D A S H E D ) .  T H E UNITS OF T H E  ABSCISSA A R E T I M E S T E P S O F 20S.  the M M G . The M M G was also sensitive to being compressed. The hand could not be wrapped and surgical staff could not lean against the hand since these activities prevent motion. This does not affect the E M G but definitely prevents the M M G from making an accurate measurement. Arthritis is a contra-indication for use of the M M G as the calcified joints of the hand may limit motion and thereby decrease sensitivity. The M M G was discontinued in favour of the E M G . Temperature affects on muscle contractility became obvious. Muscles need to be kept at a constant temperature and one appropriate for muscle function. This can be done with blankets or warmers. The operating rooms were typically at a cool temperature, 19°C. Anesthetics can have an effect on temperature, usually causing a decrease, due to altered reactions in the thalamus. The most commonly available neuromuscular stimulators were the handheld stimulators with two electrodes for stimulation and a reliance on the anesthetist to make the measurement by themselves, either visually or by tactile means. The reliance on the anesthetist to make the measurement is problematic due to their inaccuracy - humans cannot easily distinguish between To4 of 50% and 100% (Murphy [99]). As well, anesthetists tend to use the muscles of the face because they're more convenient (close by and out from under the surgical drapes). This choice introduces error as the facial muscles do not correlate to the adductor pollicis muscles of the hand, which more accurately reflect diaphragm function. As well, accurate placement is more difficult in that the exact nerve desired is difficulty to pinpoint, leading to stimulation of many muscle groups and often not the group desired. Care must be taken in placing the electrodes as the measurement is sensitive to positioning. 103  Inaccurate placement leads to increased neuromuscular stimulation currents and sometimes reduced sensitivity, as the inaccurate placement can increase resistance because of a larger separation of the electrodes than desirable or a misplacement of the electrodes relative to the nerve, for the stimulating electrodes, and/or the muscle, for the monitoring electrodes. In one patient, a slight adjustment in electrode positioning produced a change from a PTC with three twitches to a To4 of 85% in the span of two minutes. This change was unlikely due to time passing, as a transition of this magnitude would normally require much more than eighteen minutes (Howardy-Hansen [100]). As a caveat, this patient's stimulation was not calibrated and the supra-max current was not found, so the large proportion of this problem may have been due to user error and not the sensor. Repositioning electrodes leads to a decrease in their adhesion and a decrease in the amount of conductive gel at the point of contact. The former sometimes results in the electrode falling off, while the later can cause an increase in resistance and decrease in signal. These two events can prevent measurement and attempts at fixing the situation may be disruptive to surgery as intrusion into the sterile field is involved. If the electrode needs to be repositioned, it is best to replace it with a new one. Briefly, some other potential sources of error that may affect results in the full clinical study: • Accuracy in administration of doses, reporting of doses administered and recording of doses administered are all sources of error due to the user. Dosing administration and reporting error is an issue here as there was no pump and the advisory system had no direct feedback of the drug input, but instead the anesthesiologist told this information to the data recorder. • Timing of the dose: the anesthesiologist needed to relay the dosing information to the computer operator (they are not able to do both at the same time for legal/ethical/objectivity reasons). If this was done late or done and not mentioned, this was a source of error. • Entry port in the IV line: a standard distance of the injection port needs to be established to make constant the delay to entry of the drug into the patient. Delay to entry is also regulated by the height of the IV pole and by the rate of injection. It is best to minimize the distance. However, with a timestep of 20s due to the time between stimulations the extra time it takes for the drug to enter the patient may be of little consequence. • Accuracy of patient self assessment of demographic information such as weight can be a source of error. People tend to estimate and round-off. • Dose accuracy can be a source of error. The NMBAS recommends doses to fractions of mL. Anesthesiologists give at grosser levels typically. Rocuronium is distributed in concentrations of lOmg mL . To get the fractional doses dilution is required to obtain accuracy. -1  As mentioned, variability is a huge concern with biological systems. To reduce variability in this clinical setting and thereby better ascertain the NMBAS function, whether or not it was working appropriately, and any problems needing fixing, two actions were taken. A single anesthetist was dedicated to the project and a single type of patient - the prostate brachytherapy patients - was used. These actions were beneficial to the software development as competing issues could be eliminated. However, this reduced applicability of the NMBAS in the real world setting making its testing in the clinical trial potentially more difficult. This population was homogeneous in that it was male and typically elderly. This population has an increased likelihood of other diseases and conditions being present. As well, elderly patients may have slower clearance of rocuronium due to increased circulatory time. Use of this exclusive population will have specialized the advisory system to this population, as the modelset will consist solely of this type of patient. 104  In summary, the objectives of the pilot study were all met to some degree. The NMBAS was tested, debugged and improved. Case report forms evolved as data important to a clinical trial became evident and the forms were modified to capture: patient health conditions, drugs used to mitigate or extend the effects of NMB agents, timing of the case (arrival of the patient, intubation, surgical start, et cetera), clinically significant events (patient bucking and/or breathing on the ventilator, demands for more drug...) and assessment of error. The modelset was substantially improved by adding fourteen human models and removing the rabbit data. Improvement was seen in prediction and feasibility of the NMBAS was demonstrated. The NMBAS was now ready for application in a clinical trial.  5.3  The N M B A S Full Clinical Trial  With the pilot study completed, a working prototype NMBAS prepared and a positive result for feasibility, the clinical trial was started. This was a randomized, double-blinded clinical trial, the methods and results of which are presented here. 5.3.1  Methods  The objective of this study was to determine if the NMBAS improved patient care compared to standard practice. The incidence of the failure to provide adequate relaxation measured by clinical adverse events and the incidence of overdose was the primary endpoint. The deviation from a theoretical ideal To4 and the total dose of rocuronium, anesthetic agents, and reversal agents were measured as secondary indirect endpoints. The patient and data analyst were blinded to patient group assignment. For patient safety the anesthesiologist was aware of the treatment group. The sample size was calculated to be thirty patients in each group. A sample size of thirty patients per group was calculated in an interim analysis after ten patients without exclusions had been enrolled in each group (a = 5%, 3 = 20%, 25% difference in adverse events). Thirty patients under each treatment provided enough power to support a null hypothesis (to reject the false negative) for similar incidence of clinically significant, intra-operative adverse events. For patient safety an interim analysis was used to determine whether or not the NMBAS was safe and effective enough to warrant continuing, and the number of patients required to complete the study. Patient eligibility was determined by examination of the patient charts and through a patient interview. Inclusion criteria were similar to those of the pilot study as described in Section 5.2.1 with the following enhancements and additions: • Male or female, aged 18 years or older • Anesthesia predicted to last at least one and a half hours Exclusion criteria were also similar to those of the pilot study, with the following changes: • Pregnancy • Epidural anesthesia in the operating room During the patient interview patient demographic and health status details were obtained. Demographic data obtained included sex, age, weight, height and ASA Physical Status. BMI was calculated. Significant health conditions were polled for. These included: coronary artery disease,  105  heart failure, hypertension, liver disease, kidney disease, neuromuscular disease, respiratory disease, diabetes, abnormal lab results and smoking history. Medications currently used were recorded. Patients were randomly assigned to one of two groups, standard care and care with advice from NMBAS. This was done in groups of four patients; two each of standard and advisor care in a random sequence as the patients were admitted to the trial. Response data was captured for all patients. Calculations and administration advice were reported to the anesthesiologist for the NMBAS group only. All surgeries were conducted as normal. Anesthesiologists of the standard care group were instructed to conduct NMB according to their standard practice. All anesthesiologists administered bolus rocuronium based on clinical observation and measurements from a handheld neuromuscular stimulator (Fisher Paykel Healthcare, Auckland,). In the NMBAS group the anesthesiologist administered bolus rocuronium as recommended by NMBAS, subject to their clinical judgment. Neuromuscular stimulation was used to determine the drug effect throughout the procedure. Standard stimulation protocols available to the anesthesia monitors (Datex-Ohmeda S/5 with N M T module), train-of-four (To4) and Post-Tetanic Count (PTC), were used throughout the case and measurements were made with an electromyography (EMG) sensor. EMG measurements produced via the NMT module were not displayed to either group's anesthesiologists. A portable computer (IBM PC, Intel Pentium 3 processor) was interfaced to the anesthesia monitor for recording and analysis of the measured E M G response. The initial rocuronium dose was based on the manufacturer's recommended dose for intubation (O.Gmg • kg ). Recommendations for subsequent doses were based on the patient's response to the NMB drug and as a compromise between surgical needs and reversibility, with the aim of maintaining the To4 ratio below 0.2 and with at least two measurable twitches. The anesthesiologist had the choice of agreeing with, modifying or disregarding the advice of the NMBAS. Incidence of and reasons for anesthesiologist noncompliance with the NMBAS were recorded. All drugs administered intra-operatively were recorded. The timing of the following events was recorded: the patient entering the operating room, starting anesthetic induction, intubation of the patient, starting surgery, completion of surgery requiring NMB, extubation of the patient, and admission of the patient to the post-anesthesia care unit. Significant intra-operative clinical events were recorded including: patient motion, breathing against the ventilator, bucking/coughing on the ventilator and inadequate surgical relaxation as judged by surgeon requests for more relaxation. Post-operative events recorded included inadequate reversal. Patient motion included any non-stimulated motion by the patient. Breathing against the ventilator referred to the patient making attempts to breathe while ventilated. Breathing against the ventilator was assessed by irregular dips appearing in the C O 2 trace and changes in ventilation pressure. Bucking on the ventilator referred to the patient experiencing irregular, abdominal motions while ventilated. Inadequate surgical relaxation was generally because of tensing of the abdominal (or other) muscles to the point of impeding the surgical work. Post-operative actions included the recording of medications administered, and adverse events and corrective actions taken. Analysis was done for patient demographics and health conditions, drug use, timing of the procedure, intra- and post-anesthetic adverse clinical events (both incidence of and cumulative), and deviation from the desired setpoint or error. The patient demographics and health data were compared to test the equivalency of the two groups. The record of procedure events was used to test that the procedures in each group were comparable. Drug use, clinical event and error information were compared to judge benefit. Neuromuscular response was quantified to assess performance by measuring deviation from -1  106  the desired condition of reversibility with adequate relaxation for surgery. At each timestep of the procedure, error is assessed as a score based on the measured NMT response according to the scheme displayed in Table 5.1. This scheme penalized for under- and over-paralysis, with a range around the To4 measurement of 10% considered to be optimal. The overall performance measurement for the case is the sum of the error scores at each timestep, normalized for the length of the case. The range was set to this level as this provides a surgically useful while easily reversible level of blockade. As stated in Stoelting [81], "In an adequately anesthetized patient, twitch height of less than 10% or a To4 of less than 20% should provide adequate surgical relations. If the response is less than this, difficulties with antagonism may develop." Table 5.1:  QUANTIZATION OF N M B  ERROR.  N M T Measurement Range  Score  To4 > 50% To4 < 50% and To4 > 20% To4 < 20% and number of twitches = 2 or 3 Number of twitches = 1 Number .of twitches = 0  2 1 0 1 2  The two groups were also compared for incidence of the worst performances (scores of two) normalized by the length of the case to see if either of the methods was more likely to produce over- or under-paralysis. Data for each comparison was tested for normalcy by assessing kurtosis and symmetry. Normal data was evaluated with Student's t-test with a p value below 0.05 considered to be significant. Nonnormal data was tested with Mann-Whitney rank testing, with a Z value of scaled rank difference greater than 1.65 indicating significant difference. One exception to the statistical testing procedure was the handing of adverse event incidence. This comparison was tested as contingency data using the Fischer Exact test. Reversants were compared as a combined statistic. Since either neostigmine and edrophonium were used as per routine clinical practice, the doses of neostigmine and edropohium were normalized based on equipotency values derived from Stoelting et al [101] and Barash et al [102]. These values were: neostigmine O.OQmg • kg and edrophonium 0.45m<7 • kg . -1  5.3.2  -1  Results  Seventy-three patients provided informed consent to take part in the trial. Thirteen were excluded from data analysis because of sensor failures or protocol violations (the anesthesiologist became aware of response measurements). There were twenty-four women and six men in the standard care group and twenty-six women and four men in the NMBAS group. Surgeries were predominantly gynecological in nature, with twenty-eight total abdominal hysterectomies, six myomectomies, three ovarian cystectomies and two oophrectomies. The other cases were primarily bowel resection and repair, including ten anterior resections, seven cholycystectomies, five pelvic pouch constructions, four colon resections, two colectomy-ileostomies, two hemicholectomies, one abdominal tumor resection, one bowel polyp removal, one ventral hernia repair, and one colostomy closure. Representative cases demonstrating the data that was measured and the process undertaken 107  are shown in Figure 5.9. The standard care case on the top is for patient H34, a woman undergoing a hysterectomy. The NMBAS case on the bottom is for patient H32, a woman undergoing a cholecystectomy. Both cases started with large intubation doses (the manufacturer's recommended dose for intubation) to paralyse the patient and were followed by small maintenance doses. The standard care response fell to a relaxation of 0.5 before the first maintenance dose and then to a relaxation of 0.65 for the second. The first fall to 50% allowed the return of substantive muscle tone, triggering a complaint from the surgeon. Similarly, the second dose was administered after noticing the patient breathing against the ventilator. Response, pseudo-Occupancy, setpt; u; dose recommended: for the control group.  0  100  200  300  400  500  600  700  ... and for the NMBAS group 1  1  • •  i i  i i  i i  i i  : 0.5  /  1  0 i 1 0.5 JTi 0 2 1 0  -j"  i  i . i  i i  i i •  i i i  i  T  r1 - r  FIGURE 5.9:  i  1  1  1  1  1  1 1 1  1 1  1 1 1  1 1 1  1 1 1  i  i  !  !  i  i i  i i i  i i i  i i i  i  i  i  i  I  i  i i  1  i  n  •  1  i _  50  I 100 — 150 t  I  I  1  i ,  1  1 •  i  i  i - 250 200  iSj+ i  1  A  i  i. 300  i 350  i 400  1  I  1  , i  1  I  I  1  i"  i i  i  i i  i  i 450  J500  i i  i i  R E P R E S E N T A T I V E CASES FOR T H E S T A N D A R D C A R E ( T O P F I G U R E ) A N D N M B A S  ( B O T T O M FIGURE) T R E A T M E N T GROUPS. S E T P O I N T (SOLID L I N E ) , M E A S U R E D R E S P O N S E ( D O T T E D LINE) IN T E R M S O F R E L A X A T I O N , WITH M O D E L E D P S E U D O - O C C U P A N C Y ( T O P G R A P H ) ; A N D D R U G INPUTS ( M I D D L E ) A N D R E C O M M E N D E D DOSE ( B O T T O M ) IN T E R M S OF 2  95  DOSES. T H E  ABSCISSA AXIS IS T I M E IN UNITS O F 205 T I M E S T E P S .  The NMBAS response shows an initial decrease to approximately 0.65 relaxation. At this point there were two adverse events when the patient simultaneously moved and breathed. Drug was administered, blockade was restored and the procedure continued. The NMBAS then adapted to the patient's response and the muscle function recovery was limited to smaller and smaller levels, eventually maintaining the eTo4 above 0.8 relaxation, with short periods of saturation (approxi-  108  mately 15 minutes). Administrations became regular, occurring every 2 0 minutes, corresponding to the indicated minimum time between doses. The patient demographic parameters showed no statistical differences. This data is displayed in Table 5.2. Significant health conditions were few and distributed evenly in each group. In the standard care group, there were two cases of coronary artery disease, four cases of hypertensives, one case of kidney disease, one case of respiratory disease, two cases of with abnormal lab results, and one case with a defective thyroid. In the NMBAS group, there was one case of coronary artery disease, six cases of hypertensives, one case of respiratory disease, one case with abnormal lab results, and three patients with defective thyroids. Table  5.2: P A T I E N T D E M O G R A P H I C S F O R T H E S T A N D A R D C A R E A N D  Group Standard NMBAS  Sex f/m  Age yrs  Weight  24/6 26/4  NMBAS  kg  Height cm  A S A Class I/II/III  51±13  68±13  163±10  10/16/4  53±13  66±12  164±8  8/19/3  GROUPS.  No difference could be found between the cases in the timing of the cases. Numerical results for the timing of cases for the two groups is in Table 5.3. Table  5.3: T I M E C O U R S E O F O P E R A T I O N S I N M I N U T E S :  M E A N A N D STANDARD DEVIATION DATA  A D J U S T E D F O R T H E T I M E O F P A T I E N T E N T R Y INTO T H E O P E R A T I N G R O O M .  Event  Standard Care  NMBAS  P  Z  11.5 ± 6 . 5  10.9 ± 5 . 4  -  0.09  16.2 ± 6 . 5  16.6 ± 6 . 7  -  0.15  35.3 ± 9 . 2  34.5 ± 8 . 0  0.92  -  145 ± 4 3  142 ± 3 7  0.94  -  154 ± 4 5  154 ± 3 8  0.99  -  138±46  138±37  0.99  -  161 ± 4 2  164 ± 3 5  0.92  -  Induction start Patient intubated Surgical start Surgery requiring N M B complete Extubated Time between extubation, intubation Admission to PAR  P r i m a r y Outcome  NMBAS reduced the incidence of clinically significant adverse events from 48 to 15. The incidence of breathing against the ventilator and inadequate surgical relaxation were significantly reduced by NMBAS from 24 to 6 and from 14 to 3, respectively. The incidence of intra-operative motion and bucking were also reduced by NMBAS, but not with statistical significance. Neither group experienced inadequate reversal postoperatively. Details appear in Table 5.4. Nineteen patients in the standard care group and eight in the NMBAS group had an incidence of any adverse event. Thirteen patients in the standard care and five in the NMBAS group had at least one event. Both of these statistics had significant difference with p values of 0 . 0 0 8 9 and 0 . 0 4 7 respectively. 109  Table 5.4: C L I N I C A L E V E N T INCIDENCE: I N T R A - O P E R A T I V E MOTION, B R E A T H I N G AGAINST A N D B U C K I N G ON T H E V E N T I L A T O R , INADEQUATE SURGICAL R E L A X A T I O N A N D T O T A L N U M B E R O F EVENTS.  " P R E " INDICATES RESULTS T A K E N AT T H E I N T E R I M ANALYSIS POINT.  Motion  Group  Standard (pre) NMBAS (pre) Standard NMBAS Difference Z statistic  Breathing  Bucking  Inadequate  Total  against  on the  surgical  events  ventilator  ventilator  relaxation  9 5 24 6 yes 2.35  2 2 3 2 no 0.36  8 1 14 3 yes 1.79  5 4 7 4 no 0.27  24 12 48 15 yes 2.75  Secondary Outcomes  NMB at reversal and extubation was statistically different between the two groups. Prior to reversal To4 measurements were lower (Z = 8.34) for the standard care group at 5.6 ± 30% (recorded as eTo4 measurements of 0.94 ± 0.30 relaxation) versus 11.3 ± 35% (0.88 ± 0.35 relaxation) for the NMBAS group. At extubation To4 response was also lower (Z = 2.47) for the standard care group at 59 ± 27% (0.41±0.27 relaxation) versus 71 ± 23% (0.29±0.23 relaxation) for the NMBAS. The performance measure for quality of NMB, the total deviation from desired NMB levels normalized for time, was 1.21 ± 0.47 and 1.20 ± 0.49 for the standard care and NMBAS groups respectively. The incidence of the extremes of errors (scores of two) was 0.68 ±0.25 and 0.72 ±0.26. These differences were not significant. The amounts of drugs that affect NMB were not statistically significantly different between groups. Rocuronium use was not different for either total dosage or dosage normalized by weight and time. The combined reversant use statistic was normally distributed and revealed no significant difference between the groups. Numerical results for these comparisons can be found in Table 5.5. Details on the usage of the drugs separately can be found in Table 5.6 Table 5.5: I N T R A - O P E R A T I V E N M B - R E L A T E D D R U G USE: T O T A L A N D N O R M A L I Z E D F O R W E I G H T A N D T I M E ROCURONIUM USE, A N D COMBINED R E V E R S A N T U S E B Y R E C O M M E N D E D P E R kg DOSE.  Group  Rocuronium  Rocuronium  Combined  Normalized mg  Standard NMBAS p value Z statistic  60±26 54±17 1.00  mg kg"  1  Reversant  min  -1  (6.4 ± 2.4) x IO" (5.9 ± 1.7) x 10~ 0.81  3  3  0.86±0.73 0.91±0.37 0.89 -  Propofol and inhalational anesthetic (desflurane and/or sevoflurane) use was analysed to determine if NMB needs were being met by increasing anesthetic drug use. The inhalational anesthetics 110  T a b l e 5.6:  INTRA-OPERATIVE  DRUG  USE BY GROUP:  MEANS A N D STANDARD DEVIATIONS F O R  DRUGS ADMINISTERED.  Drug (units) Acetaminophen (mg) Atropine (mg) Bupivicaine (2.5%, mL) Cefazolin (g) Dexamethasone (mg) Dicloflenac (mg) Dolasetron (mg) Droperidol (mg) Edrophonium (mg) Ephedrine (mg) Fentanyl (ug) Glycopyrrolate (mg) Hydromorphone (mg) Ketamine (mg) Ketoralac (mg) Lidocaine (mg) Midazolam (mg) Metronidazole (mg) Morphine (mg) Neostigmine (mg) Pentaspan (mL) Phenylephrine (ug) Propofol (mg) Rocuronium (mg)  Standard  AT/30  NMBAS  AT/30  V  Z  867±336  6  794±287  9  0.70  0.81±0.33  13  0.72±0.38  10  13.3±5.2  6  10dz0  9  -  1.57±0.60  21  1.6±0.61  17  0.35  -  5.78±2.1  9  6±2  5  0.92  50±0  5  50±0  8  13.6±2.6  25  13.0±2.55  24  0.56±0.09  2  0.81±0.27  2  46±18.4  10  37±6.75  10  0.64 0.69  10±5.77  7  10dz0  7  -  258±98  30  279±135  28  0.99  -  0.41±0.073  10  0.41±0.13  21  2.41  1.07±0.67  6  2.2±0.4  4  40±30  7  22±8.4  5  30±0  11  30±0  4  39.1±28.8  10  40.4±23.7  16  1.28±0.45  8  1.39±0.63  14  500±0  11  500±0  8  8.75±4.99  12  6.97±3.72  18  3.4±1.21  12  3.19±1.04  20  500±0  2  500±0  2  140±54.8  5  200±141  4  186±77  27  163±53.4  27  59.6±25.5  30  53.5±17.1  30  -  1.49 1.02 0.04 0.24 0.05  0.15 0.72 2.86 1.35 1.56 2.29 0.55 2.63 0.07 0.19 3.56 1.00  were tested for mean levels throughout the case, maximum levels, mean levels between the second last and the last doses of rocuronium (first interval), mean levels between the last dose of rocuronium and the end of the case (second interval), and the difference between the mean levels for the first and second intervals. A view of a typical case with the first and second interval graphically defined is shown in 5.10. Here, the anesthetic concentration was reduced at the end of the case. Mean anesthetic use was not different: the average M A C was 0.94 ± 0.28 for the standard care group vs. 0.91 ±0.24 for the NMBAS group. The mean level during the first interval was statistically significantly greater for the standard care group (1.0±0.41 vs. 0.94±0.28). The difference between the intervals was found to be statistically different [Z = 5.45), with the NMBAS difference being greater at 0.15±0.20 vs. 0.076±0.19. Details appear in Table 5.7. Propofol use was also statistically different (Z = 3.56) with the standard care group using more: 192 ± 68.9 vs. 163 ± 53.4m<?. Opiate usage (fentanyl, morphine, hydromorphine, remifentanil, sufentanil) was common in both groups. No significant differences were detected with respect to these drugs.  Ill  Figure 5.10: INHALATIONAL A N E S T H E T I C USE ( T O P G R A P H , M A C ) A L I G N E D WITH R O C U R O N I U M USE ( B O T T O M ) TO D E M O N S T R A T E N O R M A L USAGE OF A N E S T H E T I C A N D INTERVALS F O R M A C M E A N C A L C U L A T I O N S . T H E ABSCISSA AXIS IS T I M E IN UNITS O F 20s TIMESTEPS.  Table 5.7: I N T R A - O P E R A T I V E A N E S T H E T I C USE. A V E R A G E INHALED ANESTHETIC USE: T H R O U G H O U T T H E C A S E ( M A C A L L ) , F O R T H E INTERVAL B E T W E E N T H E SECOND A N D L A S T DOSE O F R O C U R O N I U M ( M A C 1ST), F O R T H E INTERVAL B E T W E E N T H E L A S T DOSE OF ROCURONIUM A N D T H E E N D O F T H E CASE ( M A C 2ND), A N D T H E D I F F E R E N C E B E T W E E N T H E T W O INTERVALS (2 — I ); A N D PROPOFOL USE T H R O U G H O U T T H E C A S E . " D I F F E R E N C E " INDICATES W H E T H E R OR N O T T H E DATASETS A R E STATISTICALLY DIFFERENT. nd  st  Group  M A C all  MAC 1  st  MAC 2  n d  Interval diff: -^st 2 ^  Propofol 186±77 163±53 yes 3.56  n<  Standard NMBAS Difference p value Z statistic  0.94±0.28 0.91±0.24 no  1.00±0.41 0.94±0.28 yes  0.90±0.30 0.82±0.28 no  -  -  -  0.076±0.19 0.15 ±0.20 no 0.70  0.11  5.45  0.74  -  mg  -  Other drugs administered at least twice per group but without significant difference included: acetaminophen, bupivicaine, cefazolin, ciprofloxacin, clindamycin, dexamethasone, dicloflenac, dolasetron, droperidol, ephedrine, ketamine, lidocaine, midazolam, metronidazole, naloxone, pentaspan and phenylephrine. Their usage is summarized in Table 5.6. Drugs that were administered only once or twice in the trial have been excluded from Table 5.6. These include dimenhydrinate, gentamicin, hydralizine, hydrocortisone, labetolol, metoprolol, metoclopromide, perphenazine, sufentanil, sodium thiopental, remifentanil and vasopressin. Because of their low usage there was no calculation of statistical significance between the two groups. Post-operative administrations and incidents were similar for both groups. In twenty-six of the standard care and twenty-five of the NMBAS cases, post-operative drugs for pain (e.g. morphine) 112  and non-NMB related conditions were administered. In four cases for the standard care and in six cases for the NMBAS, nausea and vomiting were experienced. These incidents were remedied with administration of either dolasetron, dimenhydrinate, scopolamine or perphenazine. In one case for the standard care and two for the NMBAS, low blood pressure was experienced and rectified by administration of additional fluids (saline and/or pentaspan). Anesthesiologist non-compliance with the NMBAS recommendations occurred eleven times. Eight times the anesthesiologist refused to dose because of the proximity of the end of the case. Two non-compliances were recommendations of clinically insignificant amounts of drug. These were ignored until the dose became significant. The last noncompliance came when the anesthetist ignored a recommendation to dose because he felt the patient was adequately blocked. 5.3.3  Discussion of the N M B A S Clinical Trial Results  In this study, computer controlled drug therapy in the form of an advisory system for the NMB drug rocuronium provided improved care relative to standard practice. Because of the low incidence of morbidity or mortality associated with NMB, surrogate markers were used to demonstrate improved patient care. These surrogate markers showed a dramatic decrease in adverse events intraoperatively through use of the NMBAS. All intraoperative clinically significance adverse events showed some reduction, indicating improved care. Patients receiving treatment under guidance from NMBAS will move less, breath against the ventilator less and receive less propofol, and be extubated stronger. This indicates smoother surgery throughout and improved respiration at the end of the case. Significantly, surgeons in the OR with the NMBAS will have a better time of things with easier work and less need to call for more relaxant. As adverse events may happen simultaneously, and because adverse events are not necessarily equal, incidence of any adverse event was also investigated for difference as categorical data. The NMBAS group had significantly less incidence of any event further strengthening the prior result and confirming it as a safer method of administering NMB drugs. The To4 measurements taken at reversal and at extubation were higher for the NMBAS group, indicating that the level of blockade was better maintained and response was quicker to return for the NMBAS group. The neuromuscular response is a matter of concern because the lower the neuromuscular response is, the greater is the patient's muscle weakness, impaired hypoxic ventilatory response, pharyngeal dysfunction, and risk of aspiration, hypoxemia and delays of emergence from anesthesia. Problems start at To4 measurements between 70 and 90% (Murphy [103]). The larger responses of the NMBAS group demonstrate that the NMBAS is the safer treatment. It is important to re-emphasize that the measurement obtained from the E M G was not displayed to either group and that extubation was made based on the anesthetist's intuition, observation and measurement with the handheld neuromuscular stimulator (not the N M T module). The incidence of post-operative adverse events was not significantly different. The incidence of nausea and vomiting was not different but there is no direct relationship to NMB. Also there was no post-operative residual curarization (PORC) noted. According to (Eriksson [18]), incidence of PORC is between five and 10% for patients receiving intermediate-acting NMB drugs, such as rocuronium. This suggests that each group should have seen between one and three incidents. Events may have been missed due to lack of recording or simply because of good nursing care (e.g. pre-emptive administration of oxygen) preventing their occurrence. A weakness of this study is that post-operative events were measured through post-hoc analysis of the patient's chart and not through active observation. The weighted scale designed to quantify the overall quality of N M B did not reveal any significant difference deviations from the setpoint, despite difference being found in adverse events. The lack 113  of difference may be because of inadequate weighting of the scale for periods of poor relaxation, and may also have been because of the vast proportion of most cases being spent in a saturated state for which there was no To4 ratio. Any advantage seen by one treatment might not have had a large enough effect to overcome the time averaging that occurs in summing the error. To better capture a clinically relevant result, a better scheme would have been to impose higher penalties for higher To4 ratios intra-operatively to capture under-dosing and for lower To4 ratios at the end of the case, post-surgical completion, to capture over-dosing. The scale proposed was somewhat arbitrary based more on engineering judgment and not clinical expectation. It was postulated that a scale more reflective of what level of blockade was important to the surgery, as opposed to the arbitrary scale initially proposed, would be more representative. A simple scheme was tested whereby penalties were assessed according to the undershoot from the start of the case up until surgery was completed to catch the underdosing that could influence the procedure, and according to the overshoot at the end of the case when reversal was desired. The overall score was calculated as a sum of error at each timestep normalized for the length of the case, where the error at each timestep during the surgical period (prior to reversal and/or the end of the case) was: e(t) = 0.8  -  y(t)  (5.7)  if y(t), the measurement in relaxation, was less than 0.8, and: eit) = y(t) - 0.1  (5.8)  if y(t) was greater than 0.1 for timesteps from the reversal and/or end of the case until extubation. Relaxations of 0.8 and 0.1 were used as these were considered to be the minimal levels for surgical conditions and for safe extubation, respectively. Error according to this new scheme was found to be 0.15 ± 0.21 for the control group and 0.074 ± 0.055 for the NMBAS group. Comparing these statistics using Student's t-test revealed the probability of rejecting the null hypothesis of similarity to be p = 0.19 compared to p = 0.91 for the scale of the clinical protocol. Although results are not significant, the assessment is more realistic with regards to clinical outcome than the previous comparisons were. Overall neuromuscular related drug use was not different. As shown in Table 5.6, larger doses of reversants were given on average in the standard care group, but reversants were given more frequently for the NMBAS group. As the anesthesia monitor N M T module based measurements were not available to the anesthesiologist and they relied on visual assessment of the To4 (or no NMB monitoring), this may be an indication of prophylactic application of reversant in the NMBAS group. The patients of the NMBAS group did not need the reversant as much as those in the standard care group; however, the anesthesiologists were dealing with something unfamiliar and by giving reversants to all patients took extra precautions. The reduced need in the NMBAS group for reversant is attested to by the greater relaxation at reversal for the standard care group. The larger doses of reversant on average indicated that the standard care group patients were more likely to be visibly very weak. Propofol and inhalational anesthetic use were analysed to investigate their use as substitutes for NMB agents. Under standard care, the anesthesiologist might elect to use more anesthetic to dampen patient sensitivity and to avoid administering more NMB agent. Substitution may have happened in the trial, as there was increased propofol usage and anesthetic M A C was higher between the second and last doses of rocuronium for the standard care group; however, the mean M A C for the. whole case and the difference between the, first and second intervals were,not significantly different.  114  Opioids may be used to reduce bucking and breathing against the ventilator by depressing the respiratory drive. However, since no difference was found, either these drugs were not being used in this fashion, the study did not have enough power to pick up an effect or the drugs were being used in this way equally for each group. Despite the ability of non-NMB drugs to reduce the appearance of N M B requirements, the need for NMB will be the same. For example, fentanyl will reduce spontaneous breathing but won't help with bowel extrusion. The non-NMB drugs do not decrease muscle tension, and furthermore introduce side-effects that would not be seen with drugs as specific as NMBs. The use of non-NMB drugs to relieve the symptoms of NMB need are neither beneficial to the patient nor to the surgical team and serve only to make the anesthesiologist's job easier temporarily. One potential confounding factor in this study was the many anesthesiologists involved and the variation introduced because of the difference in their practice. A total of twenty-four anesthesiologists were involved. The number of cases (including exclusions) per anesthesiologist ranged between one and eight, with a mean of 3.0 and median of 2.5 cases. Due to the standardization of NMB drug administration provided by the NMBAS, multiple anesthesiologists would have a greater impact on the standard care group, increasing the variance of the dose of NMB related drugs. Other differences of importance concerning NMB practice include reversant and neurostimulator use. However the variation in practice is easier to extrapolate to clinical practice. Patients were selected for admission according to the specifics of their procedure and not according to the anesthesiologist in charge of their care. As anesthesiologists have many different ways of practicing care (e.g. preferences in analgesic use) that will indirectly influence NMB and other outcomes, it was very important that the NMBAS could work effectively with the many different anesthesia styles, which would be more reflective of the clinical reality. That it was able to do so and achieve a positive result shows that NMBAS can be an effective clinical tool. The low incidence of non-compliance with NMBAS is a further demonstration of applicability and utility. As stated non-compliance occurred eleven times in the thirty cases with only one event - a suggestion to dose when the patient was already well paralysed - having the potential for clinical consequence (the others concerned non-administration due to the proximity of the end of the case and recommendation of clinically insignificant doses). Of the twenty-four anesthesiologists in the study, seventeen were involved with NMBAS cases. It can be argued that the NMBAS must be truly useful to be accepted by such a diverse group. Two potential confounding factors that could have made the difference between the two groups less recognizable were electrocautery effects and patient repositioning. Electrocautery produces a great amount of electrical noise that can lead to corruption of E M G measurements. As electrocautery was involved in all of the clinical trial cases, its use will have corrupted measurements in all cases. The effect of the cautery was an introduction of electrical noise into the E M G measurement, with noise power exaggerated by proximity to the grounding plate. The noise decreases the accuracy of the measurements and increases the difficulty in controlling the level of NMB. Repositioning of the patient and/or the body part that the E M G is attached to can cause a shift in the relative position of the stimulation wires to the nerve being stimulated. This shift can lead to a decreased ability to stimulate the nerve and thereby a decreased measurable response. Repositioning can also lead to a shift in the position of the electrodes with respect to the muscle being sensed. The new position will result in a changed resistance, impacting the measurement being made. As the NMBAS group was more reliant upon the sensor for its decision making and prediction, it was more sensitive to the influence of electrocautery and patient movement. Despite this, NMBAS provided better care. Arguably, some of the benefit of the NMBAS could have been obtained with continuous objective 115  monitoring by the anesthesiologist. The anesthesiologist could have watched the sensor, seen when it was recovering and then make estimates of how to change the dose based on what the previous dose size was and the time length of its effect. Most of the intra-operative clinical events could be avoided, and if nothing else, post-operative outcomes could be improved by waiting until the To4 measurement was greater than 90% (the measurement considered necessary for proper function of the pharynx and the upper esophagus as found by Eriksson [17]) instead of the 59% that was found for the control group in the trial. However, monitoring like this is labour intensive for someone who - for the betterment of the patient - cannot solely devote himself to the N M T sensor. This limitation on attention is one reason why objective monitoring is not done continuously, but instead only at key points in the case, such as extubation, and/or not at all. Beyond this, if monitoring is done it is done at non-optimal muscles convenient to the procedure and to the anesthesiologist. Although they are less sensitive than adductor pollicis, the muscles of the face such as orbicularis occuli are commonly used. The result of non-use and mis-use of N M T monitoring is that a great many patients are extubated prematurely. Incidence of post-operative residual curarization (PORC) is between five and 10% for intermediate-acting compounds, such as rocuronium (Eriksson [18]), and between sixteen and 42% will have To4 ratios of less than 0.7 to 0.8 (Murphy [99]), which as mentioned in Chapter 1, can lead to impaired hypoxic ventilatory response and other complications. A great advantage of the NMBAS is that it provides the benefit of continuous monitoring without increasing the workload of the anesthesiologist. The anesthesiologist is freed from one distraction and can handle mundane cases better and complicated cases more easily. Thereby, patient safety is improved. It is important to re-emphasize that the measurement obtained from the E M G was not displayed to either group and that extubation was made based on the anesthetist's intuition, observation and measurement with the handheld neuromuscular stimulator (not the N M T module). As can be seen from Table 5.6, more reversants were given on average in the standard care group, but given more frequently for the NMBAS group. Edrophonium usage was 46 ± 18.4m<7 vs. 37 ± 6.75mg both in ten of thirty patients, and neostigmine usage was 3.4 ± \.2\mg in twelve of thirty and 3.19 ± 1.04mp in twenty of thirty patients for the standard care and NMBAS groups respectively. These comparisons were not different statistically. 5.3.4  Adverse Events  In the trial there were several patients with adverse events. Their cases are explored here briefly to explore the difference between the two methods of drug administration, and to demonstrate some of the issues in monitoring and control of NMB. Patient H57 (control group, male, 79 years old, 6lAkg, 163cm, BMI 23.1, ASA 3, minimally invasive surgical (MIS) anterior resection of the colon, neuromuscular stimulation current 35mA, history of coronary artery bypass graft (CABG) and arthritis) experienced two incidents of breathing on the ventilator. His results are shown in Figure 5.11. Despite showing a zero twitch To4 for most of the case the patient was still noted to be breathing, even after receiving almost lOOfig more fentanyl than the average patient (350/J.g versus the average 258/i#). This patient was of above roughly average weight and BMI, but above average age (50 years) for his group, possibly meaning that he would have required more fentanyl. As well, he received no morphine compared to the average of 3.6mg. In the figure, the modelling is seen to be roughly stable throughout the case because of the lack of available data. In the bottom curve, there is a steep change in the dose recommended at the point of model swapping. The patient is reversed around timestep 440 where it will be seen 116  Response: y, pseudo-Occupancy, setpt; model C; u; dose recommended 1.5 1  » -  - .  i  •  •  -t  » . . . L .  •  —  0 5 ri;  Sp  1DU  1£0  200  250  300  350  400  50  lTJO  150  200  2S0  300  350  400  J  1  1  '  _L  JL  50  1DQ  150  2QTJ  250  30TJ  j_ 50  100  150  200  250  300  450.  10  •  0 1  t»-  I  I  '  ^450.3  -X--.._.-.J..--_.._L._--_-J_.__--_L-.  0.5 0  0  Figure 5.11:  CASE STUDY OF  i  I  i  _L  350  400  450.  350  400  450  =fc  H57,  A CONTROL GROUP PATIENT WITH ADVERSE EVENTS.  RE-  SPONSE ( D O T S ) , S E T P O I N T (SOLID LINE) A N D P S E U D O - O C C U P A N C Y ( D A S H E D LINE) ( T O P ) ; M O D E L PARAMETERS (SECOND FROM TOP); NMB ( B O T T O M ) F O R H57.  INPUTS (THIRD); A N D DOSING  RECOMMENDATIONS  T I M I N G O F T H E R E V E R S A N T A D M I N I S T R A T I O N IS N O T E D B Y G A P S I N T H E  INPUT CURVE.  the response comes back to normal quickly and the modelling parameters and dose recommended become erratic. Patient H17 (control group, female, 36 years old, 55%, 149cm, 24.8, ASA 2, laparotomy and myomectomy, neuromuscular stimulation current 70mA) breathed once on the ventilator and had one incident of inadequate surgical relaxation. From Figure 5.12 it will be seen that her response was also quite saturated through the case. She received two doses of rocuronium: at the start of the case and around timestep 90 when the response was starting to return. Reversal occurred well before the end of the case at timestep 220, which may have resulted in the patient's breathing and increased muscle tension. The patient's reduced fentanyl use, about half the average at 175/ig, may have influenced the patient's breathing. However, this was a relatively short case, with extubation occurring at 111 minutes compared to the average of 152 minutes, meaning the smaller amounts may have been appropriate and comparable to normal care. In contrast, the cause of the adverse events for patient H29 (control group, female, 35 years old, 54.5%, 150cm, BMI 24.2, ASA 1, myomectomy - uterine fibroid removal, neuromuscular stimulation current 29mA) is not a mystery. This patient experienced motion once, breathing twice, bucking once and incidences of inadequate surgical relaxation twice in a case of average length (152 minutes vs. 152 minutes). The patient also only received one dose of rocuronium at the start. From Figure 5.13, it will be seen that the response had returned to a point at which breathing could occur around timestep 100, one-quarter of the way through the case. This patient did not require reversal agents. During the case non-NMB drugs were given when adverse events arose. The patient received approximately 780/xg of remifentanyl by infusion, lOOjig of fentanyl and 380m<7 of propofol. 117  Figure 5.12:  C A S E STUDY OF  H17,  A CONTROL GROUP PATIENT WITH ADVERSE EVENTS.  RE-  SPONSE ( D O T S ) , S E T P O I N T (SOLID LINE) A N D P S E U D O - O C C U P A N C Y ( D A S H E D LINE) ( T O P ) ; M O D E L P A R A M E T E R S (SECOND F R O M T O P ) ; N M B INPUTS ( B O T T O M ) F O R H17.  (THIRD); A N D DOSING  RECOMMENDATIONS  T I M I N G O F T H E R E V E R S A N T A D M I N I S T R A T I O N IS N O T E D B Y G A P S IN T H E  INPUT CURVE.  In the NMBAS group, adverse events did not occur as frequently as in the control group, and occurred even less frequently as the trial progressed because of improvements in the modelling (mostly because of a growing modelset). The most events in the NMBAS group for one patient were seen with patient H18 (NMBAS group using the prostate modelset, female, 51 years old, 65%, 162cm, BMI 24.8, ASA 2, subtotal hysterectomy and bilateral salpingo-oophrectomy (BSO), neuromuscular stimulation current 40m^4, hypertensive and a 10 pack year smoker) where there were three, one case each of bucking against the ventilator, breathing on the ventilator and intraoperative motion. As will be seen in Figure 5.14, this case was very similar to H17 in that the response was mainly saturated. As a result, modelling was flat until the modelswap at timestep 200 and then relatively flat until reversal. Patient H32 (NMBAS with a modelset of 38 patients (prostate plus initial NMBAS trial patients), female, 49 years old, 38.5%, 155cm, BMI 16, ASA 1, total abdominal hysterectomy (TAH) and BSO, neuromuscular stimulation current 23mA, latex allergy) had two events, one each of motion and breathing (see Figure 5.9). Despite the adverse events, this case shows the function of the NMBAS very well. In Figure 5.15, after the initial dose is given, several data points are collected and the model is remodeled as a higher responder than average around timestep 35. Corresponding to the remodeling there is a drastic decrease in dose recommended (bottom chart). The modelling from that point is by RLSE, which is accompanied by a gradual change is the model parameters and a slight reduction in the dose recommended and administered. The time between doses moves towards twenty minutes (sixty timesteps) reflecting the improving accuracy in the dose required. Saturation of the sensor is minimized; the case ends with the response close to the setpoint allowing 118  Response: y, pseudo-Occupancy, setpt; model C; u; dose recommended **  1 1  ...;  1 0.5 /  |  0  1 1  i  ^ST"  j  1 1  1  i  ^  ~!**—-i  j > ^  inn  I  i  1  '  ISO  ,  2Q0  250  300.  xin  ?^n  qnn  i ?nn  ! ?sn  3nn  Ann  10 5 0n  n  0  Figure 5.13:  ff  inn  i Rn  I mn  i  '  •  u... i  I  I  I  I  50  100  150  C A S E S T U D Y OF  H29,  I 200  i  '  r  i  ' I  250  •  I  300  i  Ann i  Ann i  I  I  350  400  A C O N T R O L G R O U P PATIENT WITH A D V E R S E E V E N T S . R E -  SPONSE ( D O T S ) , SETPOINT (SOLID LINE) A N D P S E U D O - O C C U P A N C Y (DASHED LINE) ( T O P ) ; M O D E L P A R A M E T E R S (SECOND F R O M T O P ) ; N M B ( B O T T O M ) F O R H29.  INPUTS ( T H I R D ) ; A N D DOSING  RECOMMENDATIONS  T I M I N G OF T H E R E V E R S A N T ADMINISTRATION IS N O T E D B Y G A P S IN T H E  INPUT C U R V E .  it to wear off without extra delay. 5.3.5  Noncompliance by Anesthesiologist with the N M B A S  A good example of mismodelling leading to anesthesiologist noncompliance is patient H23 (NMBAS group with the prostate modelset, male, 86 years old, 68%, 170cm, 23.5, ASA 2, MIS anterior resection, neuromuscular stimulation current 52mA). The noncompliance occurred in the following incidents: lOmg was recommended at sixty-eight minutes into the case and no NMB drug was given as the N M T was not producing any twitches; lOmg was given instead of 20m<? at ninetyseven minutes as the anesthetist felt the dose was too high; and 13m<7 recommended at 117 minutes was not given as it was too near the end of case. No other adverse events were encountered. In the top graph of Figure 5.16, the response (dotted line) can be seen to be at zero or one twitch throughout most of the case. However, the modeled pseudo-occupancy (dashed line) indicates the patient should have muscle function. Also note by comparing the setpoint (thin, solid line) and the response, the case ends approximately forty minutes before the patient is reversible. The patient was sensitive to rocuronium; the doses given were too large. These mistakes were a result of mismodelling of the patient during the model swap. Remodeling occurred in the wrong direction to a low responder instead of a higher responder. This mismodelling occurred because this patient was one of the earlier cases in the trial when the modelset still consisted only of prostate patients.  119  Response: y, pseudo-Occupancy, setpt; model C; u; dose recommended 1 1  1.5  *  1  1  1  1  1  1  1  1  1  •  *  0.5 __ J  J  '  0 _I 15<r  i  i  i  inn  150  _2QQ.  _2D0  1  i  M  250_  10 5 0 1 0.5 I0 0_  0  Figure 5.14:  inn  -5P-  _UYL  JL50_  50  100  150  CASE STUDY OF H18, AN  NMBAS  , ? 7  n  —i—'  i  200  250  •  ,  ^  GROUP PATIENT WITH A D V E R S E EVENTS.  RE-  SPONSE ( D O T S ) , S E T P O I N T (SOLID LINE) A N D P S E U D O - O C C U P A N C Y ( D A S H E D LINE) ( T O P ) ; M O D E L PARAMETERS  (SECOND FROM TOP); NMB  (BOTTOM) FOR H18.  INPUTS  (THIRD);  A N D DOSING  RECOMMENDATIONS  T I M I N G O F T H E R E V E R S A N T A D M I N I S T R A T I O N IS N O T E D B Y G A P S IN T H E  INPUT CURVE.  5.3.6  Problems Encountered in the Clinical Study.  In the discussion section (Section 5.2.3) of the pilot study, many problems encountered in monitoring NMB were discussed. Some time will be given here to further that discussion with new observations made. One major difference between the pilot study and this was the number of anesthesiologists involved. In the pilot, a single anesthesiologist participated; in the full clinical many participated. As a result, many different practices were introduced. NMB administration practice varied from those who administer rocuronium freely with many doses or one large, single dose for the entire case to keep the patient well paralysed; to those who administer only when (strongly) requested by the surgeon; to those who are reluctant to give any NMB drug past a certain point in the procedure and will instead use other drugs to mask the patient's need for relaxant. The non-NMB drug practice included use of hypnotics to prevent awareness (e.g. propofol); analgesics to dull pain sensation (e.g. desflurane); opiates (e.g. fentanyl) to decrease the responsiveness of the respiratory centre in the brain and inhibit breathing urges; and anti-anxiety drugs (e.g. midazolam) to relieve anxiety through their hyperpolarizing inhibitory effects on neurons. This might be an argument against the use of NMB drugs; however, as stated earlier, these non-NMB drugs do not decrease muscle tension and introduce side-effects that would not be seen with drugs as specific as NMBs. For elderly patients and those with heart problems, this approach of using non-NMB drugs to mask NMB effects cannot be used as the patient has to be run with a lighter anesthetic. The ability  120  Response: y, pseudo-Occupancy, setpt; model C; u; dose recommended  0.5 J  £p  L  1DQ  J  150  L  J_  200  250  300  350  400  450.  10 \~--r-  i  1n  r  5p. _. _ _inn.. _i c;n . . _?nn _ _ _  _ _ _ qnn _ _ _ w i . . . .ann ,..dsn  0.5  -JL. .^P. - - - -II!?- - - -1?!?- - - -? - . - - - ?5.. - - - .TJ? - - - .Tfl. - - -41"?- - 1  50  Figure  5.15: C A S E S T U D Y O F  100  H32,  n n  150  AN  200  n  250  NMBAS  300  J_ 350  .J 400  L 450  .. .fiP  500  G R O U P PATIENT WITH A D V E R S E E V E N T S . R E -  SPONSE ( D O T S ) , S E T P O I N T (SOLID LINE) A N D P S E U D O - O C C U P A N C Y (DASHED LINE) ( T O P ) ; M O D E L P A R A M E T E R S (SECOND F R O M T O P ) ; N M B INPUTS ( T H I R D ) ; A N D DOSING R E C O M M E N D A T I O N S ( B O T T O M ) F O R H32.  T I M I N G OF T H E R E V E R S A N T ADMINISTRATION IS N O T E D B Y G A P S IN T H E  INPUT C U R V E .  to give narcotics is decreased and better control of N M B is necessary. Neurostimulator practice also varied. Although some anesthesiologists never used a neurostimulator, most did. Application was to the facial nerve typically to view the function of the masseter and orbicularis occuli muscles. To prevent modification of care (even with the NMBAS group), although the To4 was stimulating every 20s at the adductor pollicis, the anesthesiologists were prevented from viewing the measured result unless they specifically requested. Similarly, reversant practice varies. Some anesthesiologists rarely if ever give reversants. They will instead rely on post-operative (in the OR and/or PAR) observations, and give based on patient comfort and attempts at breathing: if they see shoulder shrugs or other uncoordinated and/or weak muscle motion they may give the reversants post-operatively; if the patient can lift his head, cough and breathe, the anesthesiologist feels that the patient will be fine. Some always give reversants. One rationale for always giving reversants was that the finest clinical test was felt to be not good enough to pick up and prevent all residual blockade post-operatively. The need for the relaxant will change throughout the case. Most of the drug is required at the beginning of the case when intubation is desired, and difficult airways may require greater amounts of relaxant. Prevention of movement of the abdominal muscles requires a constant level of drug. Prevention of patient breathing requires more relaxant; the diaphragm is the most difficult of the muscles to paralyse (it is the most resistant to NMB agents). For patient 47, who was undergoing a minimally invasive colon resection, when the minimally invasive part of the case was completed and it was time for the section of colon to be removed, an incision was made and the section was brought out on top of the patient's abdomen. In order to prevent greater extrusion of the intestine, the 121  Response: y, pseudo-Occupancy, setpt; model C; u; dose recommended j j i  1.5 1 0.5  I  0 LE I  12 10 8 6 4 2  L  Sp  _L lip  200  250  300  350  400  450  500  =1=  1  1  5P_  0.5  inn ign ___?nn ___ pzr\___  _L_±  0 5 0  Figure  ISO  ^ 1"  0  50  5.16: C A S E S T U D Y O F  1  i  100  150  H23  J-J  L  250  300  qrjn___  _ _ _ jnn __ _  1 200  i  350  400  450  _ __ g j r j  i  500  DEMONSTRATING ANESTHESIOLOGIST N O N C O M P L I A N C E . R E -  SPONSE (DOTS), SETPOINT (SOLID LINE) A N D P S E U D O - O C C U P A N C Y (DASHED LINE) ( T O P ) ; M O D E L PARAMETERS (SECOND F R O M T O P ) ; N M B ( B O T T O M ) FOR H 2 3 .  INPUTS (THIRD); A N D DOSING RECOMMENDATIONS  T I M I N G O F T H E R E V E R S A N T ADMINISTRATION IS N O T E D B Y GAPS IN T H E  INPUT CURVE.  relaxant was increased beyond what was used in the case and to bring the patient into a saturated paralysis. The cases seen in the two studies were very different. The pilot study cases were all homogenous - strictly prostate brachytherapy procedures. The clinical trial involved no prostate procedures but instead gynecological and general surgery cases. Prostate brachytherapy involves no electrosurgery. Cautery was present in all of the clinical study cases. The effect of the cautery was an introduction of electrical noise into the E M G measurement, with noise power exaggerated by proximity to the grounding plate. Depending on when it takes place, this may appear as an orphan twitch amongst a fully paralysed To4, or could increase the twitch count by occurring immediately after a successful twitch. The software and hardware filtering provided by the manufacturer of the E M G for the most part was good at eliminating these measurements. However, by detecting them and then eliminating the measurement the data was lost and the patient state was unknown for a longer time to the N M B A S . In one case, the patient's arm was pinned, placing the hand and E M G electrodes adjacent to the cautery grounding pad on the patient's right thigh. As a result, the electrodes acted as electrical pickups, and produced many false triggers and non-existent twitches, excluding much of the data. After this was learned, where possible the E M G was connected to an untucked arm and on the opposite side of the body as to where the cautery ground connection was located. Moving the patient and/or just the arm that the N M B sensor is attached to can be problematic. This movement can increase electrical noise by increasing proximity to the grounding pad, and by raising the possibility of dislodging the electrodes. The movement leading to increased noise and 122  reduced signal is particularly problematic when the patient is fully paralysed; the change in sensors may be invisible to the patient monitor (neurostimulator). Generally, with properly attached electrodes this was not a problem for the E M G sensor. Furthermore, with arm tucking, mechanical sensors could be compressed and restrained, rendering them incapable of making a measurement. Repositioning of the patient and/or the body part that the E M G is attached to can shift the stimulation electrodes relative to the nerve. The new relative position can result in a changed resistance, changing the measurement being made. The ability to stimulate the nerve can decrease and thereby the measurable response also. Repositioning is complicated by fatty tissues that act as insulation between the electrodes, and the nerves and muscles. Patient H69 was an example. This patient had a normal induction with a clear To4 measurement using 40mA stimulation current, that proceeded to sensor saturation. While in saturation, the arm was tucked-in to accommodate the surgery. Because of the saturated sensor output, whether or not the repositioning had any effect on the sensor could not be determined. After some time, the measurement was still at zero twitches while four twitches were evoked at the face using a handheld stimulator, stimulating with 80mA. The stimulation current at the adductor pollicis was increased to 60mA and four twitches were evoked. Repositioning may have moved the electrodes attached to the skin relative to the nerve producing a different alignment, possibly with the electrodes separated from the nerve by a greater amount of tissue and/or fat than they were prior. Therefore, more current was required to obtain a measurement. The peri-operative adverse events recorded in the trial were not life-threatening in and of themselves. These events are instead surrogate markers for morbidity and mortality, as these events indicate a potential for things to go wrong. For example, at the end of the colon resection cases, sections of the intestine were brought out the abdominal cavity for examination. Spontaneous breathing or bucking at this time can cause unwanted expulsion of the intestine requiring more work to replace. Inadequate surgical relaxation prevents access and restricts work in minimally invasive surgeries. Motion can lead to tissue injury. Inadequate reversal leads to hypoxia, pharyngeal dysfunction and the other problems mentioned in Section 1.1. Excepting inadequate reversal, all of the peri-operative adverse events increase the difficulty for the surgeons causing them to work longer. This delay and extra work in turn interferes with the anesthetist's judgement of the progression of the case, changing the case and forcing them to replan their anesthetics. This affects the surgeons' work and the problems spiral.  5.4  P i l o t S t u d y o f the N M B A S for Infusions  The NMBAS was used to provide advice on infusion based administration of rocuronium as a proof of concept. Three patients were inducted into the pilot study as per the protocol of the NMBAS clinical trial. The procedure was identical to that used for the NMBAS trial, with these exceptions: an infusion pump for rocuronium was connected to the intravenous line; and after the bolus intubation dose, advice was given for administration by infusion. The modelset was the same for that used for patients H59 to H73: the prostate brachytherapy patient study and accumulated models from the trial with classification according to BMI. Calculations for the advised dosage were adjusted to accommodate infusion rates. The classic method for determining the infusion rate is through calculation of the replacement rate at steady state: infusion  rate = CI x C ss p  (5-9)  where CI is the expected clearance rate and C ss is the desired concentration in the plasma at steady state. This approach is not very useful outside of the average case, as it cannot tolerate variation p  123  in patient parameters. The pharmacokinetic terms have to be known exactly and specifically to the patient undergoing the procedure. Several methods were tested with the NMBAS. For the first, an extended horizon predictive controller was applied to derive the input repeated each timestep that will arrive at the desired setpoint at a desired time in the future (see Equation 3.7). As another method for calculating infusion rates, the rate was set to replace drug lost over the timestep. Drug removed can be found by calculating the drug remaining in the patient at the current time and subtracting what drug remains in the next timestep, which was achieved by subtracting time-shifted impulse response curves: oo  (5.10) r=0  where IR is the impulse response curve. Finally, infusion recommendations were made by calculating the repeated doses needed for horizons of increasing size up to the desired endpoint, and then averaging to get the final overall value recommended. The dose at each timestep is calculated according to Equation 3.7. It is mathematically possible to have negative values depending on the circumstances, such as if the current measurement is at a higher response than the desired future response. Therefore, another version of the average dosing approach is a constrained version in which only the positive values are included in the average. The patients were women undergoing gynecological surgery, of cases approximately two-and-ahalf hours long. The patients met the inclusion and exclusion criteria of the clinical study, gave consent and were enrolled. One patient was excluded from analysis as she did not require additional rocuronium beyond what was given for the intubating dose. A record of a case can be seen in Figure 5.17. In the top graph, the response can be seen to have been at one or two twitches through most of the case. The middle graph shows the change in the model parameters to have been mostly an increase in parameters C\, C and C gradually throughout the case. The input is shown in the bottom graph. The initial input appears as the solid bar at the left of the graph. It has a value of one and thus does not fit the chart. The infusion starts at timestep 157. It is increased at 166 the computer notices that the rate is not high enough to prevent emergence from NMB. At timestep 229 it is reduced on the recommendation of the NMBAS, as it is seen that the patient is not moving towards the setpoint as desired. Finally near timestep 290, the anesthesiologist halts the infusion because the case is coming to an end. The infusion rate was changed infrequently because in general the NMB was acceptable and therefore it was not necessary to further encumber the anesthesiologist. The time between recommendations for the infusion was five minutes normally. However, as in the example of Figure 5.17, the first change occurred after three minutes. This extra modification occurred because the recommended rate was seen to be increasing rapidly, indicating that the patient was a lower responder than average and that more drug was required soon. The extra modification is inconsequential; in closed-loop control the rate could be adjusted every timestep. Also, at the time the patient was stable and the anesthesiologist had the time to make the adjustment. In the case of Figure 5.17, the patient level of blockade was not perfect but was good for surgery and for reversal. The other two cases were similar. Control of the infusion rate in this fashion is difficult. Due to the nature of the extended horizon calculation, the level of blockade becomes a moving target constantly needing updating to reflect what is learned about the patient and their response. The wait to advice and correction of dosage becomes a long delay. Eventually once enough is learned, very little need exists for adjustment. 2  124  3  Setpt, y, yApprox; C, u 1 ..•/• —t  fc ' '!  !  0  !  ik \  50 1  i  100  150  1  I  200  (  5  --  0 -3 x 10 l n  4  1  -  50 ~l  100  250  !  •  i  i 300  >  350  400  1 1 ——r 1 -~—1—• !  10  0  ]1  1  t  0.5  ™" " •  "T"—  ,  zzz  ;  —1  150  1 200  j 250  1' 300  150  200  250  300  1  j  =====  1 350  400  350  400  r~  2 0  FIGURE 5.17:  N M B A S  50  100  INFUSION TESTING:  O U T P U T VS.  SETPOINT, M O D E L P A R A M E T E R S A N D  D R U G INPUT. UNITS O F ABSCISSA A R E 20S TIMESTEPS.  Thus, a longer case would have been interesting to see more adaptation and to see where the level would be maintained relative to the setpoint. In the three cases, one adverse event occurred when the first patient breathed against the ventilator. The event occurrence was most likely because of a modelling error, with the computer thinking the patient to be a higher responder than she was. The event occurred between the first dose and the start of the infusion. Basic feasibility of the NMBAS for infusion administration was shown. 5.4.1  Modelset Development  Throughout the clinical trial, collection of patient impulse response data took place. At different points in the trial, the modelset was updated to incorporate these changes and the dataset was analysed to determine whether or not better discrimination could be had between patients through classification in subgroups. In this way, a learning process went on whereby the NMBAS modelset grew and the NMBAS, through its use of model swapping, became better able to handle the interpatient variation. The initial modelset for the NMBAS clinical trial was composed of the fourteen valid models pulled from the prostate brachytherapy patient study. The first update took place after patient H29 when the modelset was increased to include the data obtained to that point in the trial. The second update occurred after patient H42 to incorporate the recent patients and to sort the modelset into two groups based on the difference found in impulse response for sex. A third update occurred after patient H58 when the modelset was resorted (but not increased in population size) to reflect difference found in impulse responses based on BMI. The overall change in modelset is depicted in Figure 5.18. The size of the modelset as the trial progressed has been tabulated in Table 5.8. Not 125  Rabbit models only at start until P16 N=5  Mixed rabbit/human modelset until P19  Prostate + trial models until H29 N=14  Human only modelset  Prostate+trial models H29 to H42 N=42  N=14 P20 to P30  JL  Prostate study  Prostate+trial models H43 to H58 classify by,sex fN=33+ave. mN=19+ave  Prostate+trial models H59 to H73 classify by BMI -N=27+ave. +N=25+ave  N M B A S Full Clinical study  Figure 5.18: M O D E L S E T PROGRESSION THROUGHOUT T H E H U M A N CLINICAL TRIALS. I N F O R M A TION PRESENTED R E F L E C T S T H E SOURCE OF T H E DATA, WHICH PATIENTS W E R E EXPOSED TO T H E PARTICULAR MODELSET, CLASSIFICATION CRITERIA IF IT EXISTED AND T H E N U M B E R OF PATIENTS IN T H E MODELSET OR SUBGROUPS T H E R E O F . C U R V E S A R E ILLUSTRATIVE ONLY AND NOT BASED ON REAL DATA.  mentioned but included in this figure and table are the details of the initial modelset used in the prostate brachytherapy patient study as well. Table 5.8: C H A N G E S IN T H E MODELSET THROUGHOUT T H E N M B A S CLINICAL TRIALS. Patient group  M o d e l source  Classification  N per group  HI to H28 H29 to H42  prostate prostate+trial  n/a sex  H43 to H58  prostate+trial  sex  H59 to H73  prostate+trial  BMI  14+average model female= 10+average male= 19+average female=33+average male= 19+average (BMI < it) =27+average (BMI > /x) =25+average  The small number of patients in the trial and in these subgroups of patients between updates complicates assessing the effect of the increased modelsets. However, as a casual observation a positive effect can be seen in Table 5.4, where the peri-operative clinical event data at the point of the interim analysis point is presented along with the full clinical trial results. The total number of events doubled for the standard care group and only increased by 25% for the NMBAS group. The numbers of included patients at the interim analysis were eleven in the standard care and thirteen in the NMBAS group, and thirty in each group for the final results. Operator learning may have confounded these findings.  5.5  Rocuronium Dosing by BMI  In the rabbit studies, it was noticed that smaller rabbits tended to have smaller impulse responses than the larger rabbits. This pattern was also noted with human patients, when, in the NMBAS 126  clinical trial, much more overshoot in response (more time spent fully paralysed) occurred for the more obese patients. The increased response may have been because rocuronium is a charged molecule and therefore not readily absorbed into adipose tissue. A more appropriate method of determining the dose for rocuronium administrations then may be to exclude fatty tissues and to dose by a measure such as lean body mass (LBM), or by body mass index (BMI) and not according to manufacturer's recommendations of dosing by weight. Dosing by L B M has been done before. In Wulfsohn [104], it was found that obese and lean individuals of equal weight required different doses of thiopentone per kg. The authors found a better correlation to the amount of drug needed until the elimination of the eyelid reflex for L B M than for basal surface area and weight. L B M was calculated as: LBM F  =  (100 - F) x weight  =  90 - 2(height - girth)  (5.11)  F is percent body fat, weight is in pounds, height in inches and girth is in inches measured at the umbilicus at end normal expiration. Thiopentone has a high fat solubility but only 18% remains in the fat after thirty minutes. Its initial distribution depends on blood flow - tissue mass ratio. Therefore the weight of the vessel rich group (brain, liver, heart and kidney) (75% of the cardiac output), and muscle mass and skin which get approximately 21% made the best indicator. Fat gets approximately 4% of the cardiac output. The obese person is more sensitive to the drug: they have a smaller L B M and thereby require less drug to fill the volume of distribution associated with it. In Wulfsohn [105], similar methods produced similar results for halothane dosing based on L B M . Finally, in Leslie [106], elderly patients were found to require less propofol based on total body mass, as explained because of the reduced clearance from the central compartment to the rapidly distributing compartment. The authors suggested that use of lean tissue mass to calculate doses eliminates effects of change in body morphology and previously observed differences in response between age groups and sexes, and that lean tissue mass accurately represents pharmacologically active mass for the patient. Dosing by lean body mass and/or by BMI was not found in the literature for rocuronium or other NMB agents. 5.5.1  B M I Dosing Methods  Because of patient sensitivities, girth measurements were not obtained in the NMBAS trial. However, height and weight information (and through calculation, BMI) were readily available through the pre-admission interview. Thereby it was decided that BMI might be a good way of assessing whether or not rocuronium could be better administered than it was by weight. This was assessed through two means: judging the probability of overdose for patients of higher BMI as judged by time spent with complete sensor saturation, and by comparison of impulse responses as calculated through the modelling process. The use of dosing by BMI was explored by asking the question, "using body weight as a dosage guide, is a patient of a higher BMI more likely to saturate the NMT sensor for a longer period of time than a lower BMI patient?" To determine this, the patient data from the prostate and NMBAS trials was searched and the length of time between the first and second doses was determined as a surrogate for time in saturation. The data for the patients of the prostate and NMBAS trials were examined. Patients without complete records (three were missing either weight or height information), patients only receiving one dose and those patients not receiving the manufacturer's recommended dose were excluded. 127  Those remaining were divided into two groups according to whether the patient was of above or below average BMI for this sample. Analysis was also done for grouping by above and below average weight. Comparisons were made of time in saturation and of strength of response. Time in saturation was judged as the time between the first and second doses, and was measured from the data records. Strength of response was measured by calculating the AUC for each patient. This was calculated by summing the impulse response data. The groups were compared using Wilcoxon rank sum testing. The null hypothesis tested was that there was no difference in time between the first and second dose for the two groups. Statistically significant difference was judged to occur at probability of accepting the null hypothesis values of less than 0.05. 5.5.2  B M I Dosing Results  Forty-five of eighty-nine patients were included in the data analysis. For the analysis by weight, there were twenty-one in the below and twenty-four in the above average weight groups. For the analysis by BMI, there were twenty-four in the below and twenty-one in the above average BMI groups. The average BMI was 25.3. The average patient weight was 68.8%. The Wilcoxon testing revealed statistically significant differences between above and below average BMI groups for both tests. The probability of the data being the same was 0.016 for the time between doses and 0.023 for the AUC tests. No difference was found between the groups when divided according to weight. Complete results including average and standard deviation data for the time and AUC calculations are compiled in Table 5.9. Table 5.9: C O M P A R I S O N O F DOSING B Y WEIGHT A N D B M I : T E S T I N G A B O V E ( > fi) A N D B E L O W (< fl) A V E R A G E WEIGHT A N D B M I PATIENT GROUPS FOR SIMILARITY IN T I M E B E T W E E N T H E FIRST A N D SECOND DOSE, A N D F O R A U C . T l M E IS M E A S U R E D IN TIMESTEPS OF 20s. Group  by weight by BMI  5.5.3  T i m e between  AUC  <fi  >/i  p value  163±98 139±77  162±72 190±86  0.387 0.0164  < A* 340±95 327±100  > fi  p value  374±121 395±112  0.255 0.0229  Discussion of Dosing B y B M I  Based on the results patients with higher BMI will experience longer duration of effect, when dosing is determined by body weight. Reducing the dose below manufacturer's recommendations for those in the higher BMI group, reduces time spent with a saturated N M T sensor. A proper dose finding may be required to determine the "per BMI" dose, but it may be possible to take a first guess by comparing the modeled responses. On average the dose given could be reduced by a multiple of: 395 A Dose = — = 1.21  (5.12)  where the numbers 395 and 327 are the mean AUCs from the modelling process (see Table 5.9 for the above average and below average BMI groups, respectively. The assumption made in applying 128  Equation 5.12 is that the linear modelling process is valid. Thus, the new recommended dose for those in the above average BMI group would be 0.496mgr • kg (realistically, 0.5mg • kg" ) as opposed to the recommendation of 0.6mg • kg" . A danger to this process is that a reduction of the dose below the manufacturer's recommended dose, could reduce the onset time in some patients and some patients might not get enough drug. However, the fast onset times seen in the NMBAS clinical trial and the relatively long delay to intubation of approximately five minutes post induction start (see Table 5.3), suggest that there will be plenty of drug. The prediction of adequate drug when dosing by BMI is reinforced by the 139 timesteps (46mm) between the first and second dose for the average patient in the below average BMI group. Instead, more patients will be ready for reversal at the end of surgery, and fewer will be irreversible. -1  1  1  5.6  Stimulation Current by B M I  Another point of concern in the trial, a testament to further inter-patient variation, and a learning experience for control in NMB applications was the observation that obese patients seemed to offer greater impedance to stimulation. This phenomenon was noted anecdotally in the trial and explored retrospectively. The question here was: "Is there a correlation of neuromuscular stimulation current and obesity as judged by BMI?" More specifically, "Are patients stimulated at the supramaximal level (70mA) more likely to be of above average BMI?" The NMBAS clinical study contained sixty patients with recorded neuromuscular stimulation currents. Of these, thirteen currents were supramaximal at 70mA. To test whether or not this population (the thirteen) varied from the others and to determine whether or not there was an increased chance of supramaximal currents based on physiology, the two populations were compared with two-tailed Student's t-tests testing for differences in age, weight, height and body mass index (BMI). It was found that weight and BMI were statistically significantly different, with p values of 0.014 and 0.005 respectively. Table 5.10 has the numerical details of the comparison. Table 5.10: P A T I E N T DEMOGRAPHICS FOR T H E 70mA A N D O T H E R N E U R O M U S C U L A R STIMULATION C U R R E N T GROUPS,  "P V A L U E " INDICATES T H E P R O B A B I L I T Y O F T H E T W O GROUPS BEING T H E  SAME.  Stim. Current  N  mA  /70mA 70mA p value  47 .13  Age  Weight  Height  yrs  kg  cm  50±13 55±18 0.31  66±13 79±16 0.014  164±9 164±11 0.80  BMI 24.5±3.9 29.0±4.5 0.005  This data can also be analysed using a binomial distribution to determine the likelihood of the number of patients with current 70mA being above average weight and of above average BMI. Of the thirteen patients in this group, eleven were above average weight and ten were of above average BMI. The probability of being either at 70mA or not was assumed to be 0.5. Then the probability of eleven people (those of above average weight) being in this group was calculated as: xp" 13  2  x (1 - p) = 0.0095 2  129  The probability for ten people (those of above average BMI) being in the group was found to be 0.035. Both of these numbers show significance and prove that it is not be chance One reason for the greater current requirement may be increased resistance due to the higher levels of adipose tissue. Adipose tissue may be a better electrical insulator than muscle. Another less complicated reason is that the extra adipose tissue may just create a larger distance between the stimulating electrodes and the nerve. The increased distance will have an increased resistance. To facilitate sensing in these more difficult patients, the stimulator could be modified to allow above 70mA stimulation. Within reasonable limits, increased stimulation should not be damaging and should not be more painful than stimulation at normal levels. The afferent and efferent nerves run in the same bundle (in the hand and extremities where this would most likely be used) and thereby an inability to evoke response should indicate the loss of sensation too, assuming that the patient does not have a neurodegenerative disorder.  5.7  Clinical Validation of the eTo4  To validate the model of the eTo4 (described first in Section 2.2), the relationship between time to return of function and eTo4 was explored to determine if the linear relationship proposed for the non-full count To4 measurements was realistic. Data from all participants in the clinical trial was used. For all unique measurements taken between the last dose of rocuronium and reversal and/or the end of the case, the time required until function returned to 0.1 relaxation (90% To4) was calculated. Curve fitting for time to return vs. eTo4 measurement was done for all values less than 1.0 relaxation. The times to return for less than four twitch count measurements was used for validation. The fit learned was: tToReturn = 81.05 x eToA + 11.9123 (5.13) where troRetum is the time to return in timesteps. This relationship is graphed along with original data in Figure 5.19. The data used to fit the curve had a mean squared error of 0.343 indicating that the data was somewhat noisy. The mean squared error for the validation data was comparable at 0.397.  5.8  Intrapatient variance seen in the N M B A S trial  Further to the work explained in Section 4.3.1, evidence of intrapatient variance was looked for in the results of the clinical trial. The caveat here is that the protocol was not powered to find this variance. This work was exploratory only.  5.8.1  Intrapatient Variance due to Anesthetic  As introduced in Section 4.3.1, inhalational anesthetics are known to affect N M B . This phenomenon was noticed for patient H47 ( N M B A S group subgrouped for remodeling by sex, male, 70 years old, 78.6%, 185cm, B M I 23.0, A S A 2, MIS colon resection, neuromuscular stimulation current 58mA, hypertensive) who appeared to have a decreasing slope in the return of his response measurement, when looked at as intervals between doses of rocuronium. His case was relatively long providing time to see many doses and to see an effect. The volatile anesthetic was desflurane administered at an average end-tidal concentration of 1.02 M A C .  130  Time to return to 0.1 relaxation vs. eTo4 measurement  Figure  5.19: E T O 4 V A L I D A T I O N : T I M E T O R E T U R N TO 0.1 R E L A X A T I O N VS. E T O 4 . T H E O P E N  BOXES ON T H E CHART R E P R E S E N T T H E A V E R A G E N U M B E R OF T I M E S T E P S T O R E T U R N TO 0.1 R E L A X A T I O N F O R T H E N O N - F U L L C O U N T To4  MEASUREMENTS.  From the second from top chart of Figure 5.20, the model parameters grew over time. If real, this change indicates a gradual shift to a higher responder, i.e. less N M B drug is required to see effect, a result in agreement with the effects of anesthetics. However, it was difficult to quantify the effect throughout the trial and would be difficult to produce a model for the effect. An attempt was made with in a post-hoc analysis represented by Figure 5.21. In the top chart, the effect due to the potential effect of the anesthetic on the modelling is seen in a comparison of modeled pseudo-occupancy gathered during the case and posthoc calculated pseudo-occupancy based on the rocuronium given and the patient model determined post-operatively. The modeled pseudo-occupancy was seen to start at a higher level and then drop below the post-hoc calculated level, suggesting the post-hoc modelling incorporated some anesthesia response as well. The bottom graph shows error in modelling the unexplained difference between the recorded occupancy and the post-hoc calculation of occupancy based on the convolution of the inputs given and the post-hoc model. The number of filters was varied from one to thirty and the pole from 0 to 0.95, by steps of 0.05. Because of the fact that the error cannot be reduced below 50% at thirty filters, it must be assumed that the error is inconsequential and will be represented through the model and/or adapted for as the case progresses. In a long enough case, a steady state will eventually be reached. Many more patients and a more specific protocol would be required to capture the dynamics of the effect and to quantify it for modelling.  131  it  Response: y, yApprox, setpt; model: C; MAC; u  1 hV0.5  10  Figure 5.20: THETIC.  0  50  100  _L 150  _L 200  250  300  350  400  450  5QQ_  0  50  100  150  200  250  300  350  400  450  500  ^j-  C A S E STUDY OF PATIENT FOR TESTING INTRA-PATIENT V A R I A N C E D U E TO ANES-  RESPONSE  (DOTS), SETPOINT  (SOLID LINE) A N D P S E U D O - O C C U P A N C Y (DASHED  LINE)  ( T O P ) ; M O D E L P A R A M E T E R S (SECOND F R O M T O P ) ; V O L A T I L E A N E S T H E T I C U S E IN M U L T I P L E S O F MAC  5.8.2  (THIRD); A N D NMB  INPUTS ( B O T T O M )  F O R H47.  Intrapatient Variance due to Blood Loss  Loss of blood can lead to a change in the patient. PK-wise the change would most likely manifest as a decrease in the central volume. For the sake of the modelling, this loss would be seen as a shift in the modelling parameters towards higher response - the same amount of drug is being diluted into a smaller volume and thereby a high effect is obtained. The cases in the trial were not emergency procedures nor were there any cases seen in which the case became an emergency. As such, drastic losses of blood were not seen. However in four cases blood expanders (starches such as pentaspan) were used during the case to compensate for blood losses. Patient H51 (NMBAS group subgrouped for remodeling by sex, female, 43 years old, 76kg, 163cm, BMI 28.6, neuromuscular stimulation current 46mA, receiving a TAH, ASA 2) had a great deal of bleeding throughout the case requiring blood expander administration. The bleeding occurred even when the vessels were tied off. It was suggested that the patient regularly took a great deal of Chinese herbs known to be blood thinners, which may have contributed. From Figure 5.22 it is seen that H51 remodels as a high responder, and that there is little change in the model parameters after the remodel despite having average inhaled anesthetic use of 0.9 M A C , and having plenty of data to perform RLSE with, suggesting blood loss produced no effect or was compensated for by the blood expander.  132  y A p p r o x = C L (dotted) a n d p o s t - h o c m o d e l l e d o c c u p a n c y v s . t i m e s t e p  100  200  300  400  500  600  error(filter, pole) for L a g u e r r e m o d e l of y C o n v U - y A p p r o x  1 0.9 0.8 0.7 0.6 -0 . 5 -100  200  300  400  500  600  #filters*20 + p o l e / 0 . 0 5  Figure 5.21:  POST-HOC  OCCUPANCY  DURING  ANALYSIS OF  T H E CASE  H47  (DOTTED  FOR ANESTHETIC CURVE)  EFFECT.  AND POST-HOC  MODELLED  PSEUDO-  CALCULATED  PSEUDO-  O C C U P A N C Y ( T H I N , S O L I D L I N E ) ( T O P ) , A N D E R R O R IN M O D E L L I N G T H E D I F F E R E N C E B E T W E E N T H E P S E U D O - O C C U P A N C I E S O F T H E T O P C H A R T B Y P O L E ( F R O M 0 T O 0.95) F I L T E R S ( T O A M A X I M U M O F 30)  5.8.3  A N D N U M B E R OF  (BOTTOM).  Intrapatient Variance due to Tissue Loss  Another situation in which intra-patient variance might be seen occurs with the removal of tissues, such as tumours and cysts. Changes from the perspective of drug administration are seen when the tissue no longer gets input - as when it is clamped off to be removed. A n example of this in the clinic was seen in patient H66 (a 44 year old, 50%, 160cm, BMI 19.5 woman, control group, neuromuscular stimulation current 40mA), where a large ovarian cyst was removed. This cyst was nearly 10% of the patient's weight, weighing approximately 4.9%. In Figure 5.23, some change was seen in the modelling parameters; however, it is impossible to say whether that was due to the cystectomy. A trend towards higher response exists as predicted; however, the anesthetic agent may have caused the drift. The level of anesthetic agent was not particularly high; however, there is sufficient time for accumulation and the depth and kinetics of effect have not been completely characterized. The average M A C through the case was 0.61. Fentanyl use was 300//g and propofol was 150m<7 at the start and a bolus of 7 5 ^ • kg" • min" throughout the case. The cyst was removed at timestep 175. However, effect would have been seen earlier when the cyst was clamped off. This time was not exactly recorded but occurred at approximately timestep 100. 1  133  1  Response: y, yApprox, setpt; model: C; MAC; u  ftl.. J . f f . . . . . ? ? . 1  20  j  9  n  -.- ? q  n  3  5  0  ^  4  5  0  10  1 0.5  r  fP. _ _ _ An?  0_  1  1^1?  ?Q .. n  7c:ri  q n n  ™  Ann  Atp cnn  _5p_  _L0D  X ISO  X 2QQ  X 250  300  X 350  X 400  450  50Q  50  100  X 150  X 200  250  300  X 350  X 400  450  500  0.5 0  Figure 5.22:  R E S P O N S E ( D O T S ) , S E T P O I N T (SOLID LINE) A N D P S E U D O - O C C U P A N C Y ( D A S H E D LINE)  ( T O P ) ; M O D E L P A R A M E T E R S ( S E C O N D F R O M T O P ) ; V O L A T I L E A N E S T H E T I C U S E IN M A C AND NMB  5.9  INPUTS ( B O T T O M ) FOR  (THIRD);  H51.  Summary of Advisory Control and Human Clinical Studies  In this chapter the monitoring techniques, and modelling and control methods developed for this thesis were implemented and tested in a clinical setting with humans. The chapter described the development of an advisory system - the NMBAS - as a stepping stone approach to full clinical control. Clinical development occurred in a prostate brachytherapy patient study. Full testing for bolus dosing occurred in the NMBAS prospective, randomized, controlled, clinical trial. A pilot study of the NMBAS for infusions was also done. Results of this testing were very positive. The NMBAS was found to reduce intra-anesthetic clinically relevant events, to reduce anesthetic use, and to increase patient strength at reversal and at extubation. Coming out of these trials were retrospective studies where rocuronium dosing by BMI, stimulation current by BMI, clinical validation of the eTo4 and intrapatient variance were all investigated. These studies found results that will be useful in future treatment and research. At the time of writing, the preliminary clinical results have been presented at the Sixth IFAC Symposium on Modelling and Control in Biomedical Systems (Gilhuly [107]) and the overall results at the 2006 Canadian Anesthesiologists' Society 62nd Annual Meeting (Gilhuly [108], included in Appendix D). Some technical aspects and a full manuscript describing the clinical trial have been submitted for journal publication.  134  Response: y, yApprox, setpt; model: C; MAC; u  Figure 5.23:  A  C A S E S T U D Y OF I N T R A P A T I E N T V A R I A N C E D U E TO TISSUE LOSS.  RESPONSE  (DOTS), SETPOINT (SOLID LINE) A N D P S E U D O - O C C U P A N C Y (DASHED LINE) ( T O P ) ; M O D E L P A R A M E T E R S (SECOND F R O M T O P ) ; INPUTS ( B O T T O M ) FOR  V O L A T I L E A N E S T H E T I C USE IN M A C  H66.  135  (THIRD);  AND  NMB  Chapter 6  Conclusions and Overall Discussion As mentioned before, this work follows the work of others who have been working on the problem of automated NMB with limited success. The success has been limited to tightly controlled environments and patient populations, under the compromises of well-dosed patients and non-optimal stimulus modalities. This is for good reason - control of NMB is a difficult problem. Modeling and control, which rely on plentiful data for performance, are hamstrung by the lack of data available with measurement of N M B . Sensors are slow and subject to noise and great nonlinearities. Control is made much more difficult by the variability present in biological systems. The patient is highly variable as they are subject to intraoperative changes such as fluid loss, sensitization and tolerance. The population is highly variable with differences in weight, BMI, sex, age and health conditions all having a role in determining the patient's response. In this thesis, work has been done towards the development of computer controlled drug therapies emphasizing NMB drugs, with the above problems in mind. Sensor limitations were improved upon and patient variation was managed. A system for monitoring and control of N M B that was developed and tested in a prospective, randomized, control, human clinical trial of a complete system. In this trial, the NMBAS was better at providing paralysis throughout, as there were fewer cases of underdosing as manifested by fewer adverse events. Also, the NMBAS demonstrated better ability to change the state from paralysed to non-paralysed, as witnessed by the greater muscle strengths found for those in the NMBAS group at extubation. There was a positive effect on patient outcomes as demonstrated by these surrogate measures showing reduced under- and over-dosing. Again, it is believed that this is the first work to demonstrate automated NMB drug administration in a prospective, blinded, randomized, controlled, clinical trial. To manage the problems of NMB and to reach this trial, a number of innovations were made. New sensing techniques were developed to extend the range of NMB sensing and to increase data available to the modeling procedures, including the enhanced-To4 which quantifies partial To4 measurements, translation of PTC measurements to eTo4 and the interconversion of neuromuscular stimuli protocols to allow their use with models developed for another stimulus protocol. To correlate these distinct stimulus modalities, a new sensing philosophy considering NMB in terms of relaxation and not contractile strength was put forward. Relaxation is more intuitive and provides a means of estimating blood concentrations of NMB drug. New methods of handling the nonlinearities at the N M J to allow the application of adaptive control techniques were engineered. The concentration-effect curve at the NMJ was quantified with regards to the To4 measurement. Pseudo-occupancy - linearized occupancy to account for greater than effective amounts of NMB drug in terms of multiples of a standard dose - was developed to describe drug present at the receptor at all times but particularly when the sensor was in saturation.  136  A novel form of model adaptation for control was introduced in this thesis. The combined model swap and RLSE adaptation scheme was seen to be effective at accommodating the extreme patient variance, with both adaptation to the patient as an individual and to the population. At the start of each case, patients were modeled with a population average model. The average model was replaced by one more representative of the patient after some response data was collected and correlated to estimated effect and drug levels. RLSE was used to further adapt the patient models, correcting any modelling errors and accommodating intra-patient variance. Post-procedure, the recorded patient response was added to the overall patient modelset and to subpopulation modelsets based on the patient's characteristics. As these subpopulation modelsets grew, they replaced the overall population modelset from which the average model and replacement models were drawn. In the clinical study, as more patients were enrolled and the NMBAS view of the population was increased, the NMBAS was better able to manage patient differences and improvement was seen as a decreased average number of clinical events per case. Classification was done first based on sex and then based on BMI to improve this modelling process even further. These two aspects of adaptation showed learning. The system was capable of adapting to the individual during the anesthetic and also capable of adapting to the population by increasing its modelset over time, as a growing database of patient responses. The result is improved patient care that continues to auto-improve. These innovations were all enacted in the NMBAS system, which was developed in rabbit and human studies and finally tested in a prospective, randomized, blinded, controlled clinical trial. On examination of the clinical results presented in Section 5.3.2, it will be seen that through the process control techniques applied, better control of NMB and better patient care resulted as compared to the standard care approach. The NMBAS improved care by reducing underdosing. Clinically, improvement was demonstrated by fewer episodes of patient breathing, bucking and movement, and reduced requests for more relaxation from the surgeons. These events are surrogate markers for morbidity during the procedure. These clinical surrogates were the clinical incidents that if left unattended would produce injury and/or death. A problem with poorly controlled NMB is its impact on the surgery. Should the muscles have sufficient strength to impede the surgery, it will take longer to complete the case. The change in case throws off the anesthesiologist's calculations for the other drugs being used, forcing the anesthesiologist to have to work harder and longer to accommodate these new changes. The anesthesiologist's adjustments in turn affect the surgeon's work causing them to work harder. A vicious circle is formed amongst the surgeon and the anesthesiologist with positive feedback resulting in an increasingly difficult case. The NMBAS also improved care by reducing overdosing. Objectively, improved care was seen as increased readiness for extubation, despite the anesthetist not knowing the value of the NMT measurement prior to extubation. The anesthesiologists in the NMBAS group were better prepared to reverse the patient. Studies were initiated to improve future NMB administration and monitoring. BMI was investigated as a better measure as compared to body weight for deciding intubation doses with the objective of reducing overparalysis. It was found that above average BMI patients tend to be fully paralysed with regards the To4 for much longer than those of below average BMI patients. A means was described to scale the intubation dose according to BMI such that this time spent in saturation is avoided. Stimulation current according to patient BMI was also explored. It was found that patients of above average weight and BMI require the maximal current for stimulation, suggesting that current levels may need to be increased for this patient population. To improve future control efforts, methods for simulating intrapatient variance for more robust testing of in vivo closed-loop control were developed. These included inhalational anesthetics, irreversible antagonists and reversible antagonists. As in-clinic estimates of intrapatient variance, blood loss and tissue loss were also explored. 137  6.1  Future Directions  The direction this research should take is towards clinical testing of the NMBAS - no longer as an advisory system - but as a system implementing full closed-loop control. Although closed loop control of anesthetics has been implemented under some circumstances, it has been mainly in research environments and not for a broad population. Consequently, closed-loop control has not achieved regulatory approval and is not commercially available. To this point, TCI is the closest thing to automated drug administration. Why has nothing else been implemented? As discussed in Section, TCI has met resistance in North America (but not in Europe) and it may be because the results presented were not earth-shattering. Compared to standard care, recovery time and drug use were similar and time to induction was longer for TCI (Hunt-Smith [51]). The lack of advantage may be because of TCI's open-loop nature and the variance seen in patients. A great detraction to open-loop control is its reliance on good models. When the true patient parameters vary, the infusion will be incorrect and then the anesthesiologist must use titration-to-effect as they would have done normally. Closed-loop control is less sensitive to the initial model as it benefits from the corrective effect of feedback. An advisory system was used in the clinical study of this thesis and not fully closed-loop control mostly as a way of managing risk. Now that the value of the NMBAS and its safety have been seen, it is time to move towards full control. Adaptation and testing of the NMBAS for infusions are the next steps. Instead of recommendations on bolii, recommendations are made on rate of infusion. The anesthesiologist would still intervene and implement and/or change the rate in accordance with their clinical judgment. This process was shown to be feasible in the brief pilot study of Section 5.4. This study should now be broadened. Following testing of the infusion advisory system, full closed-loop control can be implemented. The software has already been written and used in the rabbit study of Chapter 4. It is now time to get it into the clinic. Similar studies to the NMBAS clinical trial can be performed for both of these tests - advisory infusions and closed-loop control. Again, standard care can be compared to performance with the automated administration system. The primary outcome could be the incidence or overall prevalence of adverse events, and based on what was seen in the NMBAS clinical trial sample sizes can be calculated. Similar secondary outcomes would be tested for and similar patient and case data collected. The hypotheses of the studies would be, "will automated drug administration improve patient care?" Once full closed-loop control is proven in the clinic, application of closed-loop control to other drugs can be attempted. The general principles of the NMBAS can be applied directly to other NMBs besides rocuronium, to other drugs such as anti-arrhythmics and anti-hypertensives, to other diseases such as diabetes, and to computer controlled anesthesia as a whole. The patients will be treated more efficiently and with fewer side effects through the benefits of better monitoring, prediction of effect, and better control of dosage. As was the original intention, it is hoped that the NMBAS will act as a stepping-stone to application of closed-loop control of not just rocuronium and other neuromuscular blockers, but of many other drugs in the clinical setting as well. Patient care will be much improved.  138  Bibliography R.J. 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A Randomized, Controlled Clinical Trial of the Neuromuscular Blockade Advisory System (NMBAS). In 2006 Canadian Anesthesiologists'  Society 62nd Annual Meeting, Toronto, ON, Canada, June 2006.  145  Appendix A  Animal Care and Ethics Committee Certificates of Approval  146  Appendix B  International Union of Pharmacology (IUPHAR) 2002 Conference Abstract (Gilhuly [61]) Evaluation of the Dose Response and Pharmacokinetics of Conopeptide G I in the Rabbit Model T E R E N C E GILHULY, DR. CHAN, DR.  REZA  BERNARD MACLEOD,  L U I FRANCIOSI, N O A M B U T T E R F I E L D , SUNNY  TABRIZCHI  The a-conopeptides of the marine cone snails are known for their capacity for neuromuscular blockade. Conopeptide G I in particular, has been investigated for potential use as a clinical neuromuscular blocker in vitro and in-vivo using the cat and the rat as the principal species. In this study, the effects of this agent were investigated in the rabbit species with the clinical drugs rocuronium and rapacuronium used as standards for comparison. Rapacuronium was also compared because the controversy that surrounded it due to its occasional contractile effects on bronchial smooth muscle. The percent relaxation and the onset and recovery times of each agent were the primary measures as determined by train-of-four stimulation. Effects on haemodynamics and lung pressure were also assessed. The results were: • ED95 values for each agent: rocuronium, 50ug/kg; rapacuronium, lOOug/kg; and conopeptide G I , 25ug/kg. • Rocuronium and rapacuronium had the shortest onset and recovery: both were less than one minute while their offsets were six minutes and three minutes respectively. G I had an onset of 31 minutes and a recovery of 681 minutes. • Lung pressure increased in one case, following the administration of rapacuronium.  149  Appendix C  I E E E Engineering in Medicine and Biology Society 2005 Conference Paper (Gilhuly [20]) ©Copyright 2005 IEEE - All Rights Reserved.  150  Modelling for Computer Controlled Neuromuscular Blockade T.J. Gilhuly^, G . A . Dumontt, B . A . MacLeod* *Dept. Electrical & Computer Engineering *Dept. Pharmacology & Therapeutics University of British Columbia 2176 Health Sciences Mall, Vancouver, BC, V6T 1Z4, Canada  [terenceg@ece.ubc.ca )  Abstract—In this paper we present data collection and methods for the selection of a model class with the goal of automated neuromuscular blockade (NMB). Neuromuscular response was measured in the presence of rocuronium in rabbits (N=5) and humans (N=14). A n average response was formed and used to determine optimal A R X and Laguerre representations for a wide range of orders and parameters. A 6th order Laguerre model was selected based on its accuracy and simplicity. Models were identified for each subject. For each group, variation was measured by comparison to the average response. The standard deviation of the average impulse response static gain was 45.4 and 45.8% of the mean for the rabbit and human models, respectively. The range of static gain was 121 and 159% of the mean for the rabbit and human datasets. Frequency domain analysis showed differences in gain of 12 and 15dB, and phase of 45 and 75° for the rabbit and human models respectively. With this knowledge, design and development of appropriate controllers for N M B will proceed. I. INTRODUCTION  Automatic drug delivery can potentially improve drug therapy by allowing for more efficient delivery, reducing drug usage and costs; permitting health care staff to work more efficiently, providing better care; and allowing the safe use of drugs that are difficult to administer manually. It allows delivery of drug continuously while matching the dose to the patient's needs. This paper is concerned with the development of models for control of neuromuscular blockade (NMB). NMB drugs produce paralysis to prevent fighting of the surgical procedure by the unconscious body; paralysis permits tracheal intubation and allows access to deep structures with smaller incisions. As NMB drugs have high therapeutic indices in hospital settings, they are often used well in excess of minimal effective requirements. A strategy for administration is to provide a dose substantive enough that the duration of action is prolonged. The anesthesiologist monitors for returning muscle function and, once it returns, overdoses again [1]. A standard technique is to provide a large bolus and then 33% of the initial bolus when required [2]. The large dose delivers a more rapid onset of paralysis, quicker arrival at surgical conditions, and skirts the need for titrating to a precise anesthetic setpoint and regulating the level once there [3]. Unfortunately this approach eliminates fine control and increases the possibility of toxicity. Computer control of NMB would relieve anesthesiologists from the distraction of having to monitor muscle response,  prevent loss of reversibility at procedure's end due to overparalysis, and give anesthesiologists fine control of muscle tone. Fine control is crucial during surgeries where knowledge of the patient's state is important for safety. For example, in Harrington rod insertion for reshaping the spine, the surgeon assesses whether or not the rods have impinged nerves by the ability of the patient to respond physically. Testing can be performed only after the return of muscle function. Automatic control could keep the patient minimally paralysed until a test is required, reduce drug administration to allow function to return, and then re-paralyse for continued work with minimal waiting time by the surgical staff. Computer control of NMB has been attempted previously. Researchers have been able to deliver blockade at a nearconstant controlled, setable level compared to conventional practice, while using less drug [1], [2]. However, the controllers developed have not been stable or robust enough to handle the intra- and interpatient variability present for an entire case. Representative efforts include bang-bang [4], PID/Smith predictor [5] and fuzzy logic control [6]. This paper discusses model development for control of NMB agents. The methods used for the collection of data from rabbit and human subjects, and the shaping of this data into response models will be described. NMB response variability is quantified. Animal procedures were conducted under ethics approval by the University of British Columbia (UBC) Animal Care Committee. For the human measurements, informed consent was obtained and the protocol has been approved by the UBC/Providence Health Care Research Ethics Board. II. METHODS  Neuromuscular response and blockade observations were recorded from five New Zealand rabbits and fourteen human patients undergoing prostate brachytherapy procedures requiring general anesthesia. Human patients were male, with average age 61.9 years and ASA class of I, II or III. Rabbits were anesthetized with 5% isoflurane for induction and maintained with 2.5% isoflurane for the surgery. Surgery included: tracheotomy for maintaining respiration, carotid artery cannulation for monitoring blood pressure, jugular vein cannulation for drug delivery, placement of needle electrodes  151  for sciatic nerve stimulation, and capture of the anterior tib- Laguerre filter pole p as: ialis and extensor longus digitorum tendons for force measurement. Isoflurane was replaced by thiopental after the surgery -i-i to prevent N M B potentiation. The infusion rate was varied to maintain a mean arterial pressure of 75mmHg. Blood B(i) (- )'(3) pressure, E C G , C 0 2 , 0 2 , M A C , isoflurane concentration and respiratory rate were monitored via an anesthesia monitor Models were assessed for accuracy and simplicity according (Datex-Ohmeda AS-3). N M B was assessed by Train of Four to Akaike's informative theoretic criterion (AIC) and Final (ToF) stimulation of the sciatic nerve monitored by a force Prediction Error (FPE), mean squared error (MSE) and by the sensor (Grass Instruments; Electronics for Medicine monitor). number of parameters required for estimation. A I C and F P E Rectal temperature was measured by digital thermometer. are defined: Lung pressure was monitored using custom made equipment. AIC log[V(l + 2n/N)] (4) The experiment began once the rabbit was stable. The T O F 1 + n/N FPE x V (5) was recorded to use as a baseline for twitch comparison in 1-n/N the presence of the N M B A . Rocuronium O.lmg/kg, double where V is the variance of the residuals, N is the length of the the effective dose for 95% of patients (2 x ED^) value as data series and n is the number of parameters to be estimated determined by a pilot experiment [7]) was administered as a Laguerre and A R X models were calculated up to maximum single bolus and the response measured. Muscle function was complexities as determined by the number of available terms allowed to return to the control value. in the data, 42. The Laguerre optimal pole was used [8]. Delay of up to six samples was modeled for the A R X models. A l l For the human measurements, patients underwent their subjects showed response by this point. scheduled procedure without interference. A n anesthesia monModels of the individual responses using the optimal model itor was present in the operating room, from which physiostructure were constructed and parameter variation was mealogical data was recorded. After the patient was anesthetized, sured to get an understanding of the requirements to be placed rocuronium was administered according to the attending aneson the future controller. thesiologist's judgement and at or below the manufacturer's recommended dosage of Q.&mg/kg, 2 x ED^ for humans. III. R E S U L T S To4 data was included from the time of first injection until A l l procedures went without complication. Physiological the next drug affecting N M B was given, either a second dose parameters were maintained within physiological norms. of rocuronium or a reversant. Response data was collected and can be seen for the rabbits For both groups, response data was adjusted for noise, and in the top graph of Figure 1. This data was averaged to form baselines and T O F ratios were calculated. The response data the response (not shown) used for determining the best model was time aligned according to when the drug was administered structure. In testing for the best model structure, the sixth order and converted to relaxation by inverting. Laguerre model was found to be optimal. Although the A R X The rabbit data was used to form an average response, and model was best for all criteria, it was not chosen as its Laguerre and A R X (auto-regressive exogenous) models were complexity of 35 parameters was deemed impractical. Near estimated using Matlab (The MathWorks, Inc.) calculations equivalent error performance and much reduced complexity was found with Laguerre models of between six and fifteen and the Laguerre toolbox [8]. A R X models were defined by: parameters. Results of the measures are summarized in Table I. y(k + 1) = b u(k) + b u{k - 1) + b u{k - 2). Figure 2 shows the Bode plot for the average case using six and fifteen order Laguerre models. The plots are virtually identical —aoy(k — d) — a\y{k — d — 1) — (1) indicating equivalence for control. Forty-six A R X models were where y is the output, u is the input, a and b are scaling better than the sixth order Laguerre model but the minimum parameters, k is the timestep and d is the delay. Laguerre number of parameters at 27 was considered high. models were defined by the equations: Estimation was performed for the rabbit and human datasets using the 6 order Laguerre model. Estimated responses for AL(k) + Bu(k) L(k+1) the rabbit cases appear in the middle graph of Figure L CL{k) y{k) (2) Estimated responses for the human cases appear in the top where u is the input, y is the output, k is the timestep and L graph of Figure 3. In the bottom graph of both of these figures is the Laguerre state, A and B are the state space matrix and is the average response for the dataset. vector, and C is the Laguerre model coefficient vector defined Rabbit data models had mean square errors ranging from by a least squares estimation on these equations. A and B 0.031 to 0.13, with a mean of 0.090 ± 0 . 1 3 . Laguerre optimal are dimensioned by the number of filters and defined by the poles ranged from 0.89 to 0.95 with a mean of 0.91 ± 0.026. P  t /  0  x  2  th  152  TABLE I  Rocuonium response for rabbits: raw dala(top), estimates (mid), average (bot)  T H E O P T I M A L M O D E L S F O U N D . M O D E L T Y P E S A R E IN T H E FIRST C O L U M N . L A G 15 A N D L A G 6 R E F E R TO L A G U E R R E 15  th  AND G  th  ORDEI  MODEL CLASSES.  ARX Lag 15 Lag6  AIC -8.86 -8.85 -8.61  Complexity 35 15 6  FPE 4.75e-4 8.44e-4 1.05e-3  MSE 1.8e-2 2.3e-2 3.22e-2  Estimated rocuronium responses for humans: individual (top), ave. (bot.)  200  300  400 500 600 Time (timesteps of 20s)  200  300  400 500 600 Time (timesteps of 20s)  Fig. I. To4 data observed in the rabbit experiments expressed as fractional relaxation: raw data (top), individual responses (middle), average response (bottom).  700  800  900  1000  Bode plot lor average rabbit with 6tn (solid), 15th (dotted) erder Laguerre model  100  700  800  900  1000  Fig. 3. Estimated rocuronium responses for the human procedures: individual patients (top), average response (bottom).  than or equal to 45° throughout. Phase margin is adequate throughout the range of measure and is far from the unstable point of —180° well past the -MB points for all models. The human data is a similar in terms of phase margin and stability but is larger in terms of variation. The range of human gains is approximately 15dB throughout. The phase has a maximum range of about 75°.  Frequency (rad/sec)  Fig. 2. Bode plot for the average rabbit modelled by six (solid line) and 15"* (dots) order Laguerre models.  Impulse response static gain values ranged from 17.6 to 57.9 with a mean of 33.4 ± 15.2. For the human data, error between the measured data and the estimated responses varied from 0.048 to 0.14 with a mean of 0.085 ± 0 . 0 3 2 . Laguerre optimal poles ranged from 0.96 to 0.99, with a mean of 0.97 ± 8.9 x 1 0 ~ . Static gain ranged from 85.9 to 564, with a mean of 301 ± 138. To investigate frequency response and controllability of these models, Bode plots were compiled. The rabbit data Bode plots are shown in Figure 4. The human Bode plots appear in Figure 5. Variance in gain for the rabbit has a maximum at O.OOOlrod/s of approximately \2dB, ranging from 24 to 36dB. This range narrows between 1 0 ~ and I0~ rad/s but remains near QdB on average. The range in phase is less 3  3  2  IV.  DISCUSSION  Data collection and methods for the selection of a model class for automated control of N M B administration were presented in this paper. Although valuable data were collected, it must be noted that the population sizes were not large and this may affect the results. As well human data was taken strictly from elderly males to better ensure homogeneity of results at the start. As such, the average response may not be representative of society as a whole. Laguerre modeling was pursued despite there being A R X models with better A I C results. This was for reasons of complexity and ability to work in control. The A R X models were accurate and many had better mean squared error and FPE results. However, this was always at the price of much higher parameter counts. Large numbers of parameters are particularly hazardous for A R X models. The higher order can cause pole-zero cancel-  153  Nyquist plot lot rabbit models (dashed) and average (solid)  least square estimation ( L S E ) m o d e l s c a n be updated easily  techniques. Importantly, these with r e c u r s i v e - L S E to  allow  their a p p l i c a t i o n in adaptive c o n t r o l s c h e m e s . Due  to the great variability seen, adaptive c o n t r o l methods  are r e q u i r e d . T h e standard deviation o f the average estimate static gain was 4 5 . 4 and 4 5 . 8 % o f the m e a n for the rabbit and  h u m a n m o d e l s respectively. T h e ranges o f static gains  were 121 a n d 1 5 9 % o f the m e a n for the rabbit and h u m a n datasets. T h e B o d e plots also d i s p l a y e d substantial variation amongst  both  groups.  Although  a robust  controller  could  h a n d l e perturbations o f that m a g n i t u d e , it w o u l d l i k e l y be quite c o n s e r v a t i v e a n d hence o f little practical use. V.  CONCLUSIONS  M o d e l i n g o f r o c u r o n i u m response to the point where automated d r u g c o n t r o l can be attempted has been c o m p l e t e d . A n o p t i m a l structure has been d e t e r m i n e d and an understanding o f Fig. 4. (solid).  Bode plot for the rabbit data: individuals (dash-dot) and average  the variation that exists within its parameters has been learned. T h e d e v e l o p m e n t o f a control s c h e m e i m p l e m e n t i n g this m o d e l and  permitting automated d r u g d e l i v e r y o f N M B w i l l follow.  Bode ptot lor human modete (dashed) and average (solkj)  ACKNOWLEDGMENT T h e authors thank M i t r u l Isbascecu, Dr. L u i F r a n c i o s i and S u n n y C h a n f o r their aid in experiments, a n d the Jean H u g i l l T e m p l e t o n C h a i r in A n e s t h e s i a , the D e p a r t m e n t o f E l e c t r i c a l and  C o m p u t e r E n g i n e e r i n g , U B C and N S E R C , C a n a d a for  funding. REFERENCES [1]  D . A . Linkens, A . J . Asbury, S.J. Rimmer, and M tion and control of muscle-relaxant anaesthesia. 129(4): 136-141, 1982. [2] A . D . M a c L e o d , A . J . Asbury, W.M.Gray, and D . A . control of neuromuscular block with atracurium. Anaesthesia, 63:31-35, 1989. [3] R. Miller, C . Prys-RoberLs (editor), and C H u g  . Menad. IdentificaIEE Proceedings-D, Linkens. Automatic British Journal of Jr. (editor). "Phar-  macokinetics of Muscle Relaxants and their Antagonists". chapter 1I  [4] Fig. 5. Bode plot for the human data: individuals (dotted) and average (solid).  lation to take place, w h i c h leads to m o v i n g poles a n d zeros w i t h c o n t i n u e d estimation. T h e s e m o d e l l e d but  [5]  [6]  non-existing  d y n a m i c s prevent s o l v i n g o f the D i o p h a n t i n e equation and are a disaster for c o n t r o l . A s w e l l , the A R X m o d e l used 35 filters  [7]  XIV  to m o d e l a 4 2 point dataset to the equivalent detail o f the 15  th  order L a g u e r r e m o d e l . A ratio o f 1.4 datapoints to every [8]  parameter is o v e r k i l l a n d not realistic. L a g u e r r e m o d e l i n g is k n o w n f o r its usefulness in c o n t r o l .  [9]  L a g u e r r e models are adept at h a n d l i n g process delay, even i f it is o f great m a g n i t u d e relative to the s a m p l i n g time [9]. L a g u e r r e functions are o r t h o g o n a l  and thus can be scaled  i n d e p e n d e n t l y o f e a c h other for better flexibility in m o d e l i n g , a p p r o x i m a t i o n s can be truncated to s m a l l e r order, and unlike ARX,  of Pharmacokinetics of Anaesthesia. Blackwell Scientific Publications, 1984. C M . Wait, V . A . Goat, and C E . Blogg. Feedback control of neuromuscular blockade: A simple system for infusion of atracurium. Anaesthesia, 42:1212-1217, 1987. D . A . Linkens, M . Menad, and A . J . Asbury. Smith predictor and selftuning control of muscle-relaxant drug administration. IEE ProceedingsD, 132(5):212-2I8, 1985. D . G . Mason. J.J. Ross, N . D . Edwards, D . A . Linkens, and C S . Reilly. Self-Learning Fuzzy Control with Temporal Knowledge for Atracuriumlnduced Neuromuscular Block during Surgery. Computers and Biomedical Research, 32:187-197, 1999. T. Gilhuly, B . MacLeod, L. Franciosi, N . Butterfield, S. Chan, and R. Tabrizchi. Evaluation of the Dose Response and Pharmacokinetics th of Conopeptide G I in the Rabbit Model. In Proceedings of the World Congress of Pharmacology, San Francisco. C A , July 2002. Y. Fu and G . A . Dumont. A n optimum time scale for discrete Laguerre network. IEEE Transactions on Automatic Control. 38(6):934-8, 1993. G . A . Dumont and C . C . Zervos. Adaptive Controllers based on Orthonormal Series Representation. In Proceedings of the 2 IFAC Workshop on  L a g u e r r e m o d e l s d o not have p o l e - z e r o c a n c e l l a t i o n .  L a g u e r r e methods are linear a n d c a n be i m p l e m e n t e d with  154  nd  Adaptive Systems in Control and Signal Processing, Lund. Sweden, 1986.  lAppendix D  /Canadian Anesthesiologist's Society 2006 Meeting Abstract (Gilhuly [108]) A R A N D O M I Z E D , C O N T R O L L E D C L I N I C A L T R I A L OF T H E N E U R O M U S C U L A R B L O C K A D E A D V I S O R Y S Y S T E M (NMBAS) M A S c * t , A L E X B O U Z A N E M D * , S T E P H A N K . W . SCHWARZ M D P H D FRCPC*, BERNARD A. M A C L E O D M D FRCPC*, AND G U Y A. DUMONT P H D ! T E R E N C E J . GILHULY  * D E P A R T M E N T OF A N E S T H E S I O L O G Y , P H A R M A C O L O G Y T H E R A P E U T I C S A N D T D E P A R T M E N T OF E L E C T R I C A L C O M P U T E R E N G I N E E R I N G , T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A , 2176 H E A L T H SCIENCES M A L L , V A N C O U V E R , B . C . V 6 T 1Z4  INTRODUCTION: The traditional approach to neuromuscular blockade is one of sequential overdoses. Overdosing eliminates fine control crucial to procedures where neuromuscular function must be ascertained perioperatively; increases the risk of toxicity (see [1]); and result in delay should complications change the surgical conditions. We have developed a Neuromuscular Blockade Advisory System (NMBAS) advising anesthesiologists on rocuronium dose magnitude and timing for maintenance of NMB at surgically favourable, yet easily reversible levels. We conducted a prospective randomized, controlled clinical trial to investigate NMBAS safety and effectiveness, testing the hypotheses that NMBAS is at least as safe as, and provides better care as compared to standard practice. METHODS: With informed consent and approval of the trial protocol by the institutional Ethics Board, we enrolled 36 patients (11 control, 13 treatment, 12 withdrawals) undergoing surgeries of at least 1.5 hours and required to receive rocuronium throughout the case. Patients with rocuronium sensitivity, and health conditions affecting rocuronium metabolism and monitoring of NMB were excluded. Patients were randomized to standard care and care with NMBAS advice groups. Neuromuscular response data, drug use and physiological parameters were recorded. Safety was assessed by the incidence of intra- and post-anesthetic clinically relevant events. Quality of care was judged by deviation of neuromuscular response from a surgically useful and easily reversible level of blockade, requirements for NMB and anesthetic drugs, and timing of clinically significant events. Patients and data analysts were blind to group assignment. RESULTS: Patient demographics, procedures, drug use, and ability to maintain surgically favourable conditions with easy reversibility were equivalent between the two groups. The incidence of adverse events was half for NMBAS as compared to control. Of note, inadequate surgical relaxation occurred in one case versus eight, and breathing against the ventilator occurred in five cases versus nine for control. Train-of-4 ratios of the fourth to first twitch at reversal were 18 and 155  3 DISCUSSION: NMB administration guided by NMBAS was associated with a reduction in perioperative adverse events demonstrating increased safety. NMBAS showed improved neuromuscular function at reversal and extubation compared to standard practice, implying decreased risk of postoperative adverse events. NMBAS is an innovative technology with the potential to significantly improve patient safety in patients receiving NMB. REFERENCES: [1] Anesth Analg 2004 98:193-200.  156  


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