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Instrumentation and ultrasound imaging for epidural anesthesia Hor, King Wei 2007

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INSTRUMENTATION AND ULTRASOUND IMAGING FOR EPIDURAL ANESTHESIA by King Wei Hor B . A . S c , The University o f British Columbia, 2002  A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F THE REQUIREMENTS FOR THE DEGREE OF M A S T E R OF APPLIED SCIENCE  in T H E F A C U L T Y OF G R A D U A T E STUDIES (Electrical & Computer Engineering)  T H E UNIVERSITY OF BRITISH C O L U M B I A March 2007 © K i n g W e i Hor, 2007  ABSTRACT The loss-of-resistance technique in epidural anesthesia is the accepted standard for indicating the entry o f the needle into the epidural space. In conventional epidurals, it is also the only feedback mechanism to confirm needle entry. Unsuccessful epidurals due to the technical difficulties can result in mild to severe complications. These difficulties include correctly choosing the puncture site and needle trajectory, which are determined solely by palpation and the experience o f the anesthesiologist. Instrumentation o f the thumb's force on the plunger o f the syringe, displacement o f the plunger and fluid pressure is developed for laboratory and clinical trials to study the dynamics o f the lossof-resistance  technique.  Instrumentation  of  the  loss-of-resistance  technique  was  performed on culled domestic pigs using standard epidural procedures. A static and decay model, based on physical properties and empirical data, are used for estimating the pressure from the force and displacement values. The decay model is shown to be reasonably accurate and allows the omission o f the pressure sensor in clinical trials. Furthermore, the accuracy o f decay model is further improved for the "smooth" protocol performed by the anesthesiologist, over the "bouncing" protocol. The loss-of-resistance, indicated orally by the anesthesiologist, is consistent with the rapid fall in all three measurements. The oral indication o f the loss-of-resistance slightly lags that o f the measured  values  and  is consistent  with  the  lag  in oral  communication. The  instrumentation o f the loss-of-resistance is further confirmed by direct and indirect measurements from ultrasound images o f the epidural space and needle. However, obtaining good image quality is difficult  due to the steep needle angle and the  surrounding bone structures. A n adaptive spatial compounding algorithm is developed to improve important features such as the bone and epidural space. A specially constructed phantom with speed-of-sound distortion is used to compare several variations o f the algorithm. The adaptive spatial compounding using median-based averaging produced image quality with the best balance for point resolution, edge resolution and noise reduction in homogeneous regions. In porcine studies, the technique shows visible improvements o f the epidural space and surrounding features.  11  T A B L E O F CONTENTS Abstract  •  Table o f Contents  ii  ,  iii  List o f Figures  vi  List o f Tables.....  ix  Acknowledgements 1  2  x  Introduction  ;  1  Epidural Anesthesia Overview  1  1.1  Motivation  3  1.2  Statement o f Problem  7  1.3  Research Objective  8  Instrumentation and Modeling o f the Loss-Of-Resistance Technique 2.1  Introduction  2.2  Instrumentation  :  9 -9 11  2.2.1  Sensors  11  2.2.2  Hardware and Software  13  2.2.3  Testing and Calibration  14  2.3  Modeling  '.  14  2.3.1  Static Model  14  2.3.2 .  Dynamic Model  16  2.3.3  Decay Model  2.4  .'  18  Constant Force Experiment  19  2.4.1  Materials and Method  ....19  2.4.2  Results and Discussion  20  in  2.5  Epidural Experiments  2.5.1  Materials and Method  24  2.5.2  Results and Discussion  28  2.6 3  4  Conclusion  37  Ultrasound Verification of the Epidural Needle Insertion  38  3.1  Introduction  38  3.2  Materials and Method  38  3.3  Results and Discussion  39  3.4  Conclusion  43  Adaptive Spatial Compounding  44  4.1  Introduction  44  4.2  Materials and Method  45  4.2.1  Hardware and Development Tools  45  4.2.2  Image Acquisition and Post-scan Conversion  45  4.2.3  Adaptive Spatial Compounding Method  46  4.2.3.1  Block-based Shift Vector Estimation for Warping  46  4.2.3.2  Interpolation of Shift Vectors  47  4.2.3.3  Image Remapping (Warping)  49  4.2.3.4  Compounding  49  4.2.3.5  Software Application  51  Experimental Verification  52  4.2.4  5  24  4.3  Results and Discussion  53  4.4  Conclusion  65  Conclusions and Future W o r k  66  iv  5.1  Conclusions  66  5.2  Future Work  67  References  69  Appendices  73  Appendix A : Instrumentation Circuits  73  Appendix B : Sensor Calibration  77  v  LIST OF FIGURES Figure 1: A typical epidural needle  2  Figure 2: The loss-of-resistance technique  2  Figure 3: Physical interactions of the epidural needle  10  Figure 4: The S L B - 2 5 force sensor  11  Figure 5: The P X 3 0 2 pressure sensor  :  12  Figure 6: The C S P R 1P65 displacement sensor  12  Figure 7: Force diagram of an angled plunger  15  Figure 8: Pressure profile of fluid in syringe using constant applied force  21  Figure 9: Displacement profile of plunger using constant applied force  21  Figure 10: Plot of resulting force on the fluid against the applied force  22  Figure 11: Pressure decay profiles of a glass epidural syringe...:  23  Figure 12: The instrumentation device  25  Figure 13: A domestic pig (Sus scrofa domestica)  used for the epidural experiments  25  Figure 14: The use of the instrumentation device on the pig  26  Figure 15: Force profile o f epidural procedure using "smooth" technique  28  Figure 16: Pressure profile o f epidural procedure using "smooth" technique  29  Figure 17: Displacement profile of epidural procedure using "smooth" technique  29  Figure 18: Force profile of epidural procedure using "bouncing" technique  30  Figure 19: Pressure profile of epidural procedure using "bouncing" technique  30  Figure 20: Displacement profile o f epidural procedure using "bouncing" technique  31  Figure 21: Comparison of estimated loss-of-resistance times  33  Figure 22: Static and decay modeling of pressure for "smooth" technique  34  Figure 23: Static and decay modeling o f pressure for "bouncing" technique  34  vi  Figure 24: Mean error comparison between the static and decay models  36  Figure 25: R M S error comparison between the static and decay models  36  Figure 26: Ultrasound imaging of the epidural needle  .  :  39  Figure 27: Measurement of the puncture path length between L 3 - L 4 vertebrae  40  Figure 28: Comparison of the puncture path lengths  40  .  Figure 29: Direct measurement of the epidural space depth  41  Figure 30: Indirect measurement of the epidural space depth Figure 31: The concept o f spatial compounding  , .  42 44  Figure 32: Adaptive spatial compounding application  51  Figure 33: Reference image of the phantom  54  Figure 34: Conventional spatial compounding o f the phantom..  54  Figure 35: Warped spatial compounding with averaging o f the phantom  55  Figure 36: Adaptive compounding with gradient-based averaging of the phantom  55  Figure 37: Adaptive compounding with median-based averaging of the phantom...;  56  Figure 38: Selection of spots for evaluation of point features  57  Figure 39: Normalized diameter of spots  '.  .•  57  Figure 40: Selection of edges for evaluation of edge strength  58  Figure 41: M a x i m u m intensity of edges  59  Figure 42: Selection of dark and light homogeneous regions for evaluation o f noise  60  Figure 43: S N R and C N R o f dark and light regions  60  Figure 44: Images o f porcine spinal tissue using different compounding techniques  63  Figure 45: Images of porcine epidural space using different compounding techniques... 64 Figure 46: Instrumentation amplifier circuit diagram  73  Figure 47: ± 15V voltage regulator circuit diagram „  74  vii  Figure 48: 5 V voltage regulator circuit diagram  .  74  Figure 49: 10V voltage regulator circuit diagram  75  Figure 50: Circuit layout  76  Figure 51: Instrumentation circuit boards...  76  Figure 52: Wheatstone bridge circuit for amplifier calibration  77  Figure 53: Calibration plot of the amplifier for the force sensor  78  Figure 54: Calibration plot of the amplifier for the pressure sensor..  78  Figure 55: Calibration plot o f the displacement sensor including built-in amplifier  79  vm  LIST OF TABLES Table 1: The resulting force on the fluid caused by the applied force  22  Table 2: Time o f loss-of-resistance from the two trials shown in Figures 15-20  31  Table 3: Summary o f the statistics o f the decay and static models  37  Table 4: Summary o f the mean epidural depths  42  Table 5: Summary o f the average normalized diameter  58  Table 6: Average maximum intensity of edges  59  Table 7: Average S N R and C N R  61  ix  ACKNOWLEDGEMENTS I owe particular thanks to D r . Rob Rohling for his guidance and patience throughout the years. I thank Dr. Allaudin Kamani for giving insight into the world o f epidurals and for participating as the anesthesiologist in the epidural experiments. I also thank V i c k i e Lessoway for offering her expertise and service as an ultrasonographer.  1 INTRODUCTION Epidural Anesthesia Overview Epidural anesthesia, a form o f regional anesthesia, is an important and widely accepted analgesia technique in obstetrics to effectively alleviate labor pain[l]-[5]. To facilitate the delivery of the local anesthetic, a catheter is inserted through a needle into the epidural space, a narrow space surrounding the dura mater within the spinal column. Although the use o f epidural anesthesia has increased over a few decades, conventional epidural techniques continue to have a failure rate in the range of"6-25%[6][7]. Epidural anesthesia is considered more difficult than other regional anesthetic techniques[8][9]. The  epidural  anesthesia  procedure  (or  epidural)  begins  by  having  the  anesthesiologist perform palpation to identify key anatomical landmarks, generally in the mid-lumbar region o f the patient's back. Palpation identifies the correct vertebral elements such as the spinous processes so the midpoint can be determined for the initial point o f entry for the needle. Usually, the midpoint between the L 3 - L 4 vertebrae or between the L 2 - L 3 vertebrae is chosen for needle entry. Before the epidural needle is inserted, a local anesthetic is injected into the skin using strict aseptic technique. A Tuohy needle with a Huber tip, illustrated in Figure 1, is then inserted and advanced until the tip reaches the epidural space using the loss-of-resistance techriique[10]. The loss-ofresistance technique is a widely accepted method for indicating when the tip o f the needle enters the epidural space[l 1][12]. A syringe, typically filled with air or saline, is attached to the needle and is slowly advanced with relatively little resistance through the skin, fat, and subcutaneous tissue[13]. The needle then encounters the relatively stiff and dense ligament layers known as the  supraspinous  ligament, interspinous ligament and  ligamentum flavum, as illustrated in Figure 2a. Once the needle has encountered the very dense ligamentum flavum, the anesthesiologist feels a high resistance to injection until the needle breaches the ligamentum flavum and enters the epidural space, as shown in Figure 2b and 2c. The loss-of-resistance is felt when the needle enters the epidural space, as the air or saline is easily injected into the epidural space[14]. The syringe is then detached to allow the threading o f the catheter through the needle and into the epidural  1  space. The needle is also withdrawn leaving the catheter in place to allow continuous or repeated administration of anesthetic without any further needle insertions.  Figure 1: A typical epidural needle. The Tuohy needle is a hollow needle with a Huber tip, a very slightly curved tip which is designed to reduce or prevent coring. Images courtesy o f CSE (http://www.csen.com/anesthesia).  Figure 2: The loss-of-resistance technique, (a) The epidural needle is advanced into the interspinal ligament, (b) High resistance is felt and the saline cannot be easily injected when the needle passes through the dense ligaments, (c) The loss-of-resistance is felt when the needle enters the epidural space and the saline is easily injected. Image courtesy of World Anesthesia Online (http://www.nda.ox.ac.uk/wfsa). 2  Like  all  Complications  other  can  obstetric  interventions,  include backache,  epidural  headache,  anesthesia  carries  shivering, hypotension,  risks. bladder  dysfunction and inadequate pain relief[15]. More rare are the inadvertent dural puncture, fetal distress, neurologic injury (from peripheral nerve injury to paralysis), cardiac arrest, allergic shock and maternal death[16][17]. Complications arise from both the dosage o f the local anesthetic and from technical difficulty. The former includes the amount and type o f drug used as the local anesthetic, and the latter encompasses problems with the needle and catheter insertion: The technical difficulty depends entirely on the patient, the equipment and the skill of the anesthesiologist. Patients o f different ethnicity and body mass index have varying anatomical characteristics such as the skin-to-epidural space distance[18]-[21]. Patients having different bony characteristics may require a change in needle puncture site and/or a different needle insertion trajectory. The equipment, such as glass or plastic syringe, also affects the performance o f locating the epidural space due to different physical characteristics[22]. Most importantly, the success o f the procedure is determined by the skill and experience o f the anesthesiologist[23][24]. In routine settings, the anesthesiologist does not have any available detailed knowledge about the patient's internal  spinal anatomy  prior to  the  procedure.  Without such  knowledge,  the  anesthesiologist can only make educated estimates based on experience and external palpation. These skills, including the loss-of-resistance technique, can only be learned through observation and practice on human subjects. The presence o f obesity, scoliosis or edema makes the epidural procedure even more challenging[25].  1.1 Motivation There are several problems associated with traditional epidural anesthesia: •  Obtaining competency requires a relatively high number of attempts and has significant associated risks when compared to other regional anesthetic techniques.  •  The loss-of-resistance technique is the only feedback mechanism for indicating entry of the needle into the epidural space.  3  •  Anesthesiologists determine the location and trajectory, o f the epidural needle solely by palpation and experience. Although the loss-resistance technique has been used for many years, only 6 1 % o f  the punctures are successful at the first attempt[26]. Competency in epidural procedures is obtained by observation and practice. In one study, a success rate o f 60% is achieved after 20 procedures and reaches 80% after 90 attempts[8]. Another study shows 60% success after 10 attempts and 84% after 60 attempts[27]. 90% is considered consistent with competency and is also claimed to require at least 60 attempts by another study[2 8]. A s concluded by several groups, obtaining competency using traditional methods requires a relatively high number o f attempts compared to other regional anesthetic techniques. Although residents can practice on cadavers or simulated tissue and ligaments, none provide accurate haptic feedback. M u c h o f the experience is gained by performing the epidural anesthesia on actual human patients. However, training on human patients clearly carries a high risk o f complications. Furthermore, patients varying in weight, height and ethnicity may have different epidural experiences that are unfamiliar to the anesthesiologist resulting in additional risk o f complications. Since improving the learning curve while avoiding patient risks would be beneficial, there have been a number o f attempts to construct epidural anesthesia simulators[29]-[31]. These simulators provide feedback o f expected forces but have not been widely accepted. Some even provide training for choosing the correct puncture site and needle angle in difficult  patients. However, the force feedback is based on  mathematical models simulating the various anatomical structures with sub-optimal realism[31]. This may be due to subtleties and dynamic interactions that exist only while performing the actual epidural procedure on human subjects in vivo. In the past, studies have focused on physical properties o f the epidural space and surrounding tissues[32][33]. Even the development o f the loss-of-resistance technique was based on the observations o f the different densities o f the tissues, particularly the ligamentum flavum and the epidural space[34]. Anesthesiologists have relied on this technique which has remained virtually unchanged for the past seventy years. Even with 4  the increase in the physiological knowledge involving epidurals, there has been little change to the procedure. Thus, modern epidural anesthesia continues to rely on the loss-of-resistance technique as the only feedback mechanism to indicate entry into the epidural space. Although it is the accepted standard, the technique is not completely reliable[35][36]. There are no external physical characteristics o f the patient that can provide information of the exact location o f the epidural space. It also possible the loss-of-resistance may also occur outside the epidural space[35]. Having to solely rely on this technique means the patient is exposed to any risks associated with the technique including complications from the actual injection o f saline or air into the epidural space[37]. Additional feedback that can be used in conjunction with the loss-of-resistance technique could decrease the risk o f patient complications. Over the years, several research groups have come up with devices to assist in locating the epidural space[38][40]. However, these devices require custom-built equipment and are not widely used today. In  1980,  ultrasonography  was  first  proposed  for  guidance  o f epidural  anesthesia[41]. Ultrasound has several unique advantages over other medical imaging technologies: it is portable, relatively inexpensive, real-time, immediate, and poses no known risk to the patient. Moreover, ultrasound has the potential to depict the spinal anatomy  including the  epidural space  before  or during the  epidural procedure.  Nevertheless, ultrasound guided epidural anesthesia has not found widespread clinical acceptance. A possible explanation is the relatively low image quality o f early generation ultrasound machines. With the latest digital ultrasound systems, several groups have performed research with the use o f ultrasound in regional anesthesia[25][27][42]-[55]. Due to recent successes, there is renewed interest in the use o f ultrasonography[56][57]. The use o f ultrasound in almost all types o f regional anesthetic techniques has been shown to significantly reduce the number o f puncture attempts and puncture planes, and improve quality of analgesia and patient satisfaction. Other expected benefits include a reduction in the frequency and severity o f associated complications, and enhanced education and training. Furthermore, the benefits may provide an overall reduction in the  .5  cost o f patient care, even when the cost o f the equipment and maintenance is included. Thus, continued research o f ultrasound in epidural anesthesia would be very beneficial. Another aspect that anesthesiologists find challenging is the determination o f the needle puncture site and trajectory solely by palpation and experience. If the insertion o f the needle is unsuccessful, the anesthesiologist has to reinsert the needle causing further discomfort to the already stressed patient. Having an additional aid to assist in the guidance would be beneficial and may reduce the number o f unsuccessful attempts. Again, ultrasonography is a very good candidate since rapid anatomical imaging can be used to help the anesthesiologists choose a suitable puncture site. However, one o f the difficulties with ultrasonography is that it cannot image bone and features beyond most superficial bone interfaces[58]. Ultrasonic guidance is further complicated because the epidural space is surrounded by the vertebral bones[58]. Recently, there have been advances in user programmability o f ultrasound systems allowing research groups access and control o f hardware attributes including beam properties[59]. One such property is the probe's beam angle which may be utilized by ultrasonographers to obtain better image quality o f a target feature by selecting the correct reflection angle. One study has shown substantial improvement in the visibility o f a needle by adaptively steering the beam towards the strongest echoes of the needle[60]. An  additional benefit o f being able to perform beam steering is to use spatial  compounding, a technique that combines several images o f the same scene from different view points to form a single scene. Studies have shown that spatial compounding is beneficial in many clinical applications[61]-[66]. Another study has developed an improved spatial compounding technique by introducing an intermediate warping step to produce significant improvement in point resolution, edge sharpness  and speckle  noise[67]. These recent advances in ultrasound research allow for further investigations in many possible applications, including epidural anesthesia.  6  1.2  Statement of Problem N o w that the issues of epidural anesthesia have been discussed, the problem  statements are presented as follows: 1. There has been research and development o f simulators used to improve the learning curve o f the loss-of-resistance technique while reducing patient risk, but the models are based only on properties o f the various anatomical structures. Very little research has been carried out on the quantification o f physical characteristics o f actually performing  the  loss-of-resistance  technique.  This  may  reveal  subtleties  and  fundamental characteristics that may be used to improve accuracy and realism in current simulators. 2. The loss-of-resistance technique is currently the only feedback mechanism for indicating entry o f the needle into the epidural space. Recently, studies have used ultrasound to identify the epidural space and the surrounding structure, but more research is needed to validate the skin-to-epidural space distance and the length o f the puncture path with the simultaneous measurement o f the loss-of-resistance technique. 3. Ultrasound-assisted guidance has not been widely adopted for epidurals because imaging the epidural space in the vertebral interspace has been very challenging due to the surrounding bony structures. Thus, the ultrasound probe location and beam direction are essential for obtaining good image quality. There has been no research pertaining to improving ultrasound image quality specific for epidural anesthesia. Good results may help future acceptance o f ultrasound-assisted guidance in epidural anesthesia. A n additional benefit is that it may be used in other applications other than epidural anesthesia.  7  1.3 Research Objective  .  In conjunction with the problem statements, the dissertation presents the following research objectives: 1. One of the research objectives is to gain insight and understanding of the physical characteristics involved in epidural anesthesia using the loss-of-resistance technique. More specifically, the goal is to measure and analyze physical quantities: the force applied at the plunger by the anesthesiologist, the pressure of the fluid, and the position of plunger relative to the syringe. An instrumentation device is developed to acquire physical data and physical models are used to describe their relationships. The device is designed such that an anesthesiologist may use it in a practical manner • during clinical trials. 2. Another objective is to validate the use of ultrasound images by comparing the depth of the depicted epidural space to the length of the inserted portion of the needle when it has entered the space using the loss-of-resistance technique. Consistency of the epidural space in the ultrasound image and by the loss-of-resistance  technique is  essential to further fundamental research of real-time ultrasound-assisted guidance. 3. The final objective is to develop an adaptive ultrasound imaging technique that can help enhance the overall image quality for epidural anesthesia. Two-dimensional spatial compounding with warping is used as the basis for these investigations. Objectives 1, 2 and 3 are individually described in Chapters 2, 3 and 4, respectively.  t  8  2  INSTRUMENTATION AND M O D E L I N G OF T H E LOSSOF-RESISTANCE T E C H N I Q U E  2.1 Introduction In order to gain an understanding of the physical characteristics involved in epidural anesthesia, initial research begins with the investigation and identification of the characteristics involved in the loss-of-resistance technique. An instrumentation device is constructed to measure and capture the identified characteristics, and designed for the use by an anesthesiologist in clinical settings. Finally, analysis of the loss-of-resistance and several  physical models  relating the  characteristics  are performed using the  instrumentation device in epidural experiments. Physical characteristics are determined by examining the interactions of the anesthesiologist and patient with respect to the syringe, as shown in Figure 3. The anesthesiologist typically supports the barrel and needle with one or both hands while using his thumb to push the plunger. The anesthesiologist applies a force F onto the a  plunger relative to the barrel overcoming the frictional force F to cause a change in f  displacement D of the plunger with respect to the barrel. As a consequence of F , the a  force of the plunger F acts on the fluid inside the barrel resulting in positive pressure of P  the fluid, P. If the needle tip is inserted into the dense ligament flavum, the flow of the fluid, v is significantly impeded causing an increase in the fluid pressure. The anesthesiologist "feels" the resistance because the force applied on the plunger is no longer able to move the plunger due to the high pressure P. Once the needle tip enters the epidural space, the flow of the fluid is no longer impeded and the pressure decreases rapidly causing a substantial displacement of the plunger. The condition is known as the loss-of-resistance.  9  I) V  7 Plunger  Barrel  Needle Tissue Skin  Figure  3:  Physical interactions of the epidural needle.  m e a s u r e d b y the i n s t r u m e n t a t i o n d e v i c e plunger displacement  The  must  are the a p p l i e d f o r c e F , a  three  characteristics  f l u i d p r e s s u r e P,  and  D.  challenge  measurements  The  of  be  developing  performed  instrumentation  in  a  sterile  for  epidural  environment  while  procedures  is  that  minimizing  patient  d i s c o m f o r t . T h e p r e p a r a t i o n t i m e m u s t b e s h o r t , n o part o f the d e v i c e c a n be a t t a c h e d the patient,  a n d the  anesthesiologist  should be  able to p e r f o r m the  to  epidural procedure  u s i n g the d e v i c e w i t h m i n i m a l t r a i n i n g a n d o b s t r u c t i o n .  Considering  the  different  physical  characteristics  and  constraints  for  clinical  the  pressure  a p p l i c a t i o n , it i s r e a s o n a b l e t o m e a s u r e t h e f o l l o w i n g p h y s i c a l c h a r a c t e r i s t i c s :  •  T h e applied force  F.  •  T h e fluid pressure  P.  •  T h e plunger displacement  a  D.  I n c l i n i c a l s e t t i n g s , d i r e c t l y m e a s u r i n g t h e f l u i d p r e s s u r e is d i f f i c u l t b e c a u s e sensing device  i n c l u d i n g the t r a n s d u c e r a n d c a b l e s m u s t b e s t e r i l i z e d . F o r this r e s e a r c h ,  the p r e s s u r e m e a s u r e m e n t s  are u s e d as r e f e r e n c e  10  d a t a f o r a n a l y s i s a n d it w i l l b e  shown  that the pressure can be determined indirectly from the applied force and plunger displacement in certain conditions. Although there are many useful characteristics such as the force o f the needle against the tissue and the position o f the needle tip relative to the patient, measuring these quantities is difficult and impractical because accurate sensing devices require attachment to the patient, cannot be sterilized, or are too large and cumbersome. Only the loss-ofresistance with the plunger is measured in this research.  2.2  Instrumentation Building  the  appropriate  device  to  measure  each  characteristic  requires  appropriate sensors, hardware, software and calibration which are described in the following subsections.  2.2.1  Sensors Measuring the three physical quantities, force, pressure,  and displacement  requires three individual sensors. Each sensor is chosen based on several constraints such as accuracy, range and practicality. The S L B - 2 5 force sensor manufactured by Transducer Techniques (Temecula, C A ) , shown in Figure 4, is used to measure F . The sensor has a mini-spherical load a  button used to measure compression force. This force sensor is very small and has a footprint diameter o f 9.5mm. The S L B - 2 5 has a maximum compression load o f 251bs which is sufficient for measuring the thumb force used in the epidural procedure. A custom-built stainless steel harness that can be fitted on an anesthesiologist's thumb is used to mount the sensor. Sterility is maintained by wearing the sensor under a sterile glove.  Figure 4: The SLB-25 force sensor. The sensor is used to measure the force o f the thumb acting on the plunger. Image courtesy o f Transducer Techniques. II  The P X 3 0 2 pressure sensor manufactured by Omega Engineering, Inc. (Stamford, C T ) , shown in Figure 5, is used to measure P. The sensor uses a corrugated stainless steel diaphragm that is fluid filled and has a pressure range between 0 and 300psi. Typically, the expected pressure range o f the fluid in the epidural syringe is between 0 and lOpsi. A custom-built stainless steel adaptor is used to attach the rubber tube to the epidural syringe.  Figure 5: The PX302 pressure sensor. The sensor is used to directly measure the fluid pressure o f the syringe. Image courtesy o f Omega Engineering, Inc. The C S P R IP65 displacement sensor manufactured by M T S System Corp. (Cary, N C ) , shown in Figure 6, is used to measure D. The sensor, based on magnetostriction principles, uses a small ring magnet situated along the transducer, a thin cylindrical rod. The maximum stroke length is 72.3mm and can sufficiently measure the full extension o f the plunger. The ring magnet is attached to the plunger and the transducer rod is attached to the barrel by a custom-built stainless steel harnesses. The ring need not touch the rod, so friction should be negligible and allows the anesthesiologist to retain the full feeling o f loss-of-resistance. Sterility is maintained by covering the sensor with a sterile drape before mounting it to the sterilized harness attached to the syringe barrel.  Figure 6: The CSPR IP65 displacement sensor. The sensor is used to measure the displacement of the plunger with respect to the barrel. Image courtesy o f M T S System Corp.  12  2.2.2  Hardware and Software Additional circuitry is required to power the sensors and interface with the digital  capture board. The force sensor requires a 5 V voltage regulator and a differential voltage amplifier. The displacement sensor also requires a 5 V voltage regulator, but it already has a built-in voltage amplifier. The pressure sensor requires a 10V voltage regulator and a differential voltage amplifier. Additionally, +15V and -15V voltage regulators are needed to power the two differential amplifiers. The selection o f the circuit components are based on the requirements for optimal operation in epidural procedures. CircuitMaker 2000 (Altium Ltd., Carlsbad, C A ) is used for design o f the circuit layout. T w o identical printed circuit boards are fabricated by A P Circuits (Calgary, A B ) . The circuit components and designs are described in Appendix A. The two assembled circuit boards are housed in a black plastic box with openings to allow entry o f the power and signal cables from the sensors and computer. A single ± 2 5 V (max 1A) power supply unit is required to power the entire instrumentation device. The amplified signal cables, from the box, are connected to the Q8 terminal board (Quansar Inc., Markham, O N ) . The Q8 hardware-in-the-loop control board and its associated terminal board, both manufactured by Quansar Inc. (Markham, O N ) , are used to capture the voltage signals from the sensor to a P C . The control board contains 14-bit analog-to-digital converters that measure the voltage range between -10V and +10V, and can sample data at a rate up to 192kHz. A P C I interface card to the Q8 board is installed into a P C (2.8GHz X e o n H T , 5 1 2 K B L 2 cache, 4 0 0 M H z F S B , 2 G B R A M ) for capture o f the three measurements. The R T X driver (Ardence, Inc., Waltham, M A ) is installed into the P C to provide real-time operation in the Windows X P (Microsoft Corp., Redmond, W A ) operating environment. W i n C o n 4.0 (Quansar, Inc., Markham, O N ) is the real-time control application for Windows that integrates with Simulink (The MathWorks, Inc., Natick, M A ) . The software allows the user to create Simulink models that are automatically built into the C code using the Visual C++ 2003 (Microsoft Corp., Redmond, W A ) compiler. 13  The sensor data is captured in real-time by W i n C o n and stored directly onto the local hard drive in M A T - f i l e s . M o d e l simulation and analysis are performed using M A T L A B 7.0.1 (The Math Works, Inc., Natick, M A ) .  2.2.3  Testing and Calibration The complete treatment o f testing and calibration o f the sensors and amplifiers are  discussed in Appendix B . In summary, the relationships between the physical quantities and the sensor voltage are the following: F =1.283F  o u l > r c e  P = 3-483F  outpressure  a  D = 26.08F F  a  +0.487 +0.2043  o u t d l s p ] a c e m e n l  -31.86  Eq. 1 Eq. 2 Eq. 3  is compression force with lbs units, P is fluid pressure with psi units, D is the  displacement with mm units, and V i is the sensor voltage with V units. ou  2.3  Modeling A  research  goal is to  determine  any  relationship between  the physical  characteristics. In particular, is it possible to use force and displacement measurements to estimate the pressure? If so, it would allow the pressure sensor to be omitted in clinical trials and make the instrumentation even less obtrusive. The next subsections discuss three possible models: the static, dynamic and decay models. Each model incorporates different physical and empirical properties. A n analysis is performed on the models using experimental data to determine their suitability.  2.3.1  Static Model The static model describes a non-dynamic system which assumes the system has  no motion or fluid flow. The static model establishes the basic relationship between the physical characteristics and its principles are used for more complex models. The fundamental relationship describing the pressure P(i) varying over time t o f an incompressible static fluid is  14  P(t)-^p-  Eq.4  where Fp(t) is the force exerted on the fluid over an area A. For the case of the epidural needle, shown in Figure 3 , P(i) is the pressure o f the fluid inside the barrel, F (t) is the P  force exerted by the plunger onto the fluid inside the barrel, and A is the inner crosssectional area o f the barrel. To relate the applied force F (t), a close examination o f the syringe reveals a a  small non-zero angle 0 exists between the central axis o f the plunger and barrel due to design and manufacturing tolerances. Therefore, the plunger can be pushed into the barrel with an applied force FJj) that has a non-zero perpendicular component, as shown in Figure 7. Although it may be possible to push the plunger perfectly parallel to the barrel, it is very unlikely for a human in practical settings, including epidural procedures. F cosf? a  Plunger  Figure 7: Force diagram of an angled plunger. Although exaggerated in the diagram, a very small non-zero angle 9 exists between the central axis o f the plunger and barrel. The perpendicular component o f F (/) is counteracted by the normal force F^(t). a  Since the friction force Ff(t) is proportional to F^(t), the equation relation friction force to the applied force is F (t) = vF (t)sm0 {  a  where p is the coefficient o f friction o f the glass-glass interface. Although 0 depends on the position o f the plunger relative to the barrel, the range is assumed to be small so 0 is 15  assumed to be constant. The force acting on the fluid Fp(/) is the net force o f the parallel components and is given by F (/) = F (Ocos0-//F,(Osin0 P  Eq. 5  a  Let ^ ( c o s ^ s i n ^ ) , then E q . 5 can be written as F {t) = KF (t) v  Eq.6  z  where k describes the complex interactions o f the glass-glass interface o f the plunger and a  barrel. This derivation is an oversimplification of the real interaction, and 9, ju are unknown but allows a correction factor to be incorporated into one parameter, k . The a  value o f k is determined empirically and assumed constant. These complex interactions a  include friction due to the imperfections o f the plunger and barrel, and the "wetting" o f the fluid o f the glass-glass interface. A value o f k close to unity implies little loss o f a  force being transferred from F (i) to F (t). The analysis and estimation of k are discussed a  P  a  i  in Section 2.4. Combining E q . 4 and E q . 6 yields the following: P(t) =  k  *  F  Eq. 7  ^  The relationship shown in E q . 7 is used to compare the force and pressure data measured by the instrumentation device.  2.3.2  Dynamic Model The nature o f the epidural procedure is such that fluid is continuously injected  into the tissue to detect the loss-of-resistance, and therefore, the dynamics o f the fluid must be considered. For simplicity, the fluid is. assumed to be incompressible, nonviscous and has steady flow. From conservation principles, the continuity equation states that the volume flow rate at any point in the fluid is constant: v A = constant where v is the speed of the fluid and A is the cross-sectional area. Another conservation principle, Bernoulli's equation is given by P + p g x + j p v = constant 2  16  where P is the pressure o f the fluid, p is the density o f the fluid, g is the acceleration due to gravity exerted on the fluid, and x is the height o f the fluid. Since the syringe for the epidural is typically inserted horizontally, the change in pressure due to different heights is negligible. If Bernoulli's equation is applied to the fluid flowing through two tubes (i.e., the barrel and the needle) with different crosssectional areas, their relationship is given by P +\pv  =P +\pv  2  Eq.8  2  x  2  2  Similarly, the continuity equation between two tubes is  '  Eq. 9  v, A - v A x  2  2  Combining E q . 8 and E q . 9 yields the following: A  2  P -P< = T P v , ( l - - V )  Eq.10  2  2  E q . 10 can be used to estimate the pressure difference between the barrel and needle. Given the approximate ratio o f the cross-sectional areas o f the barrel and needle is 19, and the upper-limit speed o f the plunger is lOmm/s (verified in later clinical tests), the difference in pressure is calculated to be approximately 0.003psi. The resulting pressure  difference  is  relatively  small  and  does  not  significantly effect  the  instrumentation since the pressure sensor does not measure at that level o f accuracy. For the epidural procedure, the measured pressure difference is approximately in the range o f 0 and lOpsi. Therefore, it can be assumed that the pressures from which the fluid flows from the barrel to needle and other cylindrical connections are approximately constant. Hence, this dynamic model is not relevant and is not used in modeling the physical characteristics. A corollary is that measurements from the pressure sensor attached at the end o f the connector are sufficiently accurate and require no additional compensation due to fluid motion to the sensor.  17  2.3.3  Decay Model Some of the fluid is known to leak past the plunger, s o E q . 7 needs to be corrected  i f the leakage is significant. In general, the leakage is dependant on the plunger force, displacement o f the plunger, and time, so the general pressure decay Pdccay is introduced as follows: " ^ ( 0=  ^ ( ^ ( 0 ^ ( 0 , 0  A simple expression for Pdccay is needed so that F (t) and D{t) can be easily used a  to estimate P{i). T w o cases are investigated: a stationary and a moving plunger. When the plunger is stationary, the pressure is expected to decay exponentially from the initial pressure (at the time when the plunger stops moving) caused by F . Since the plunger is P  motionless, small changes in the applied force F does not affect the initial pressure a  because it is countered by static friction. If the change in F is large, it w i l l cause the a  plunger to move. When the plunger is in motion, pressure does not decay (although some leakage still likely occurs) because it is continually and directly affected by F p . Thus, the pressure decay simplifies to the following: dz>(0  A  P(t) =  *0  «tP(Q _  _ _ _ _ _ _ " ~ 7 ~ 1  Eq. 11  A  At  Therefore, substituting E q . 6 into E q . 11 yields the following: k  a  P(t) =  Fa  (0  dD(i)  •  A  _________ ""P  ' *  *0  _____  > a,  Eq. 12 - 0  where z is the exponential time constant and /, is the time at which the plunger stops moving, T and k are estimated experimentally by applying a range o f constant F 3  a  (see  Section 2.4). The relationship shown in E q . 12 is used to compare the force and distance to the pressure data measured by the instrumentation device.  18  2.4 Constant Force Experiment To estimate k and x, a set o f experiments are performed by applying different a  constant forces to the plunger while measuring the average fluid pressure. The needle end o f the plunger is sealed such that the fluid only leaks through the plunger-barrel interface. A s the fluid leaks continually, the plunger moves until it is fully depressed and stops. The decay time constant is estimated by analyzing the decaying pressure o f the fully depressed plunger. The constant, force experiments mimic to some degree the constantforce protocol ("smooth" technique) o f the anesthesiologist.  2.4.1  Materials and Method The epidural syringe, obtained from the JH-0550 epidural catheterization kit  (Arrow International, Inc., Reading, P A ) is a 5ml glass syringe. The barrel o f the syringe has an inner diameter o f 12.46±0.02mm. The barrel is supported vertically by a clamp with the plunger on the topside. Water is drawn into the syringe while ensuring there is little or no air bubbles. To reduce errors, the barrel and syringe interface is always wetted before each trial. The pressure sensor is attached to the needle-seat using a three-way stopcock. The third opening in the stopcock is closed off to prevent leakage from this end. The displacement sensor is attached to the syringe using the custom-built harness. Using pre-determined weights, a constant downward force is applied to the plunger while the sensor data is acquired and stored to the P C for post-analysis. Three weights 1.40T±0.0021bs, 3.441±0.0021bs and 4.842±0.0021bs are used in the experiment. F o r each weight, five trials are performed and data acquired at a sampling rate o f 0.01s. To estimate k , the average pressure o f each trial is calculated by averaging the a  measured pressures  between the time interval when the readings are stable  (not  oscillating) and the plunger becomes fully depressed and stopped (just before the onset o f decay). Manual  selection o f the time intervals for the averaging is performed.  Additionally, the standard deviation o f the average pressure is also calculated in the same time intervals. The average pressures for each weight are averaged and multiplied with the cross-section area to determine the average force exerted on fluid (see E q . 4). The  19  best-fit line (based on least-squares) is determined for the plot o f the applied force and the force exerted on the fluid. The estimated k is the slope o f the best-fit line. a  To estimate x, the decay portion o f each trial is fitted to ah exponential curve to determine its individual exponential time constants, x is the average o f the time constants for all the trials.  2.4.2  Results and Discussion The pressure and displacement data for a typical experimental trial are shown in  Figure 8 and Figure 9, respectively. A t time ^ O s , the weight has not been added to the system. Once the weight is added, there is a significantly large change in pressure and displacement. For approximately 200 seconds, there are significant pressure oscillations because  the plunger is almost fully  extended causing slight swaying. Since the  anesthesiologist normally inserts the plunger to at least half length (e.g., at ?=300s), the earlier oscillating part o f the data is ignored. When  the displacement  level is at approximately /=580s,  the plunger is  completely depressed and the pressure decay is observed. The fluid is observed to be leaking through the plunger-barrel interface. The leak continues until the fluid pressure equalizes with atmosphere pressure (and fluid friction). The decay is only approximately exponential due to the complex interactions o f the fluid leak along the plunger-barrel surface. In clinical settings, the plunger only remains motionless in the order o f seconds such that only a small amount o f decay is observed and can be approximated using the exponential decay model. The key observations o f Figures 8 and 9 is that there is an interval with constant pressure, followed by an interval with a substantial decay. This supports the use o f E q . 12, which divides the equation into a pseudo-static part and a static part. For the first pseudo-static interval, the constant drop o f D(t) suggests a constant leak rate through the plunger-barrel interface. For the second static-decay interval, the decay suggests the leakage is non-constant and decreases as the pressure decreases.  Since water is close to incompressible, this decay suggests that other  compressibility and viscosity factors are at work, likely from small amounts o f air introduced in the system.  •  s  20  100  200  300  400 500 Time (s)  600  700  800  Figure 8: Pressure profile of fluid in syringe using constant applied force. The applied force acting on the plunger is 3.441bs.  40 i  0' 0  1  100  200  1  300  1  400 500 Time (s)  1  1  600  700  — 800 1  Figure 9 : Displacement profile of plunger using constant applied force. The applied force acting on the plunger is 3.441bs.  21  The mean and standard deviation o f the pressure for each trial are calculated by manually selecting the interval between the non-oscillating pressure and prior to the decay (/=200s to 7=580s). The cross-sectional area o f the inner barrel is 0.1890±0.0004in and is used to compute F . The mean values o f F P  P  and F  a  2  along with their standard  deviations are given in Table 1, and the graph is shown in Figure 10. A linear fit is applied to the plot and its R value is 0.9998 implying a reliable fit and suitable use o f 2  constant k . The slope is & =0.8998, which is approximately 10% o f unity. The pressure a  a  of the fluid is caused by approximately 90% o f the applied force and the rest is lost by frictional forces. It should be noted that for very low values o f F , the relationship is, to a a  slight degree, not directly proportional to F because static friction prevents the plunger p  from moving. In the case o f the epidural procedure, the linear relationship is valid since the anesthesiologist constantly exerts a relatively large amount o f applied force to move the plunger.  Table 1: The resulting force on the fluid caused by the applied force. F (lbs)  F (lbs)  1.401±0.002  1.281±0.005  3.441±0.002  3.08±0.05  4.842±0.002  4.33±0.02  a  P  5  Figure 10: Plot of resulting force on the fluid against the applied force. The slope is of the best-fit line is the estimated k value. a  22  Figure 11 shows the decay portion o f the pressure data for all fifteen trials. The decay time constant was determined for each trial by fitting an exponential curve to the interval when the decay occurs. The plot is intended to illustrate the large variability o f the decay curves which is possibly due to the fluid leaking along different paths in the plunger-barrel interface. Different plunger orientations may cause slight gaps or closures along the imperfect glass-glass interface. It also possible that the syringe was worn down through repeated  use  as it was only designed for one-time-use.  A s mentioned,  compressibility and viscosity factors o f the various materials in the syringe may also play a role.  300  T i m e (s)  Figure 11: Pressure decay profiles of a glass epidural syringe. The decay portions from the profiles (fifteen trials) are plotted for comparison. The average decay constant r is estimated to be 23±8s. The large deviation is not as significant in the actual epidural procedure because the plunger only remains motionless for up to one or two seconds. If the plunger remains motionless for two seconds', the largest error is approximately 7%. Although the decay constant is computed for a completely depressed plunger, the small change in time constant w i l l have little •impact on the calculations in the actual epidural procedure.  23  For real epidural pressures, additional leakage w i l l occur directly into the tissue. For the pseudo-static part o f Eq. 12, the pressure calculations should be unaffected. For the static-decay portion, it is assumed that there is a very small leakage into tissue, especially ligaments. Adding the tissue leakage term would decrease the effective r, but, as mentioned, it should not have a large affect on the pressure calculations for short time intervals.  2.5  Epidural Experiments The objective o f the epidural experiments is to analyze the loss-of-resistance  technique  and physical models on data  from  actual epidurals performed by an  anesthesiologist: The goal is to show the loss-of-resistance from the measured data is consistent with the loss-of-resistance felt by the anesthesiologist. Another goal is to validate the static and decay models with epidural data.  2.5.1  Materials and Method Before performing the epidural procedure, the instrumentation device must be  prepared. The instrumentation system consists o f the sensor devices, circuit and capture box, power supply and P C (see Sections 2.2.1 and 2.2.2). Strict aseptic techniques are not necessary, but for the majority o f the tests, they are still followed so that the procedure remains as similar as possible to the standard procedure. The harness for the force sensor is fitted and attached to the anesthesiologist's thumb. Medical gloves are worn over the harness and sensor to provide non-slip support.to the force sensor and to prevent contamination. The syringe's needle seat is fitted with a three-way stopcock to allow the attachment o f the pressure sensor to its third opening using a 1cm stiff intravenous tube. The displacement sensor harness is attached to both the syringe's barrel and plunger. The epidural syringe is a 5ml glass syringe that obtained from the JH-0550 epidural catheterization kit (Arrow International, Inc., Reading, P A ) . The instrumentation sensors and the epidural syringe are shown in Figure 12.  24  Force Sensor Displacement Sensor  Pressure Sensor  Figure 12: The instrumentation device. The force, pressure and displacement sensor are used to instrument the loss-of-resistance technique. The epidural procedure is performed by an anesthesiologist on two pigs (Sus scrofa  domestica),  as shown in Figure 13. The pigs, obtained from a local meat store,  were culled and prepared for human consumption the same day as the experiments. Organs such as the eyes, stomach and intestines had already been removed, and the pigs had been refrigerated for several hours prior to the experiments.  Figure 13: A domestic pig (Sus scrofa domestica) used for the epidural experiments. 25  The epidural procedure is performed by the anesthesiologist in a manner consistent with clinical practice. H i s hold on the syringe is slightly different to compensate for the instrumentation device, but the loss-of-resistance technique remains unchanged. T w o such motion patterns are used in clinical practice: "smooth" and "bouncing". For the "smooth" technique, the anesthesiologist continuously applies an approximately constant force, and for the "bouncing" technique, the anesthesiologist repeatedly applies and releases the plunger in quick succession. Ten trials are performed using each technique and the punctures take place either between the L 3 - L 4 and L 2 - L 3 interspaces to prevent overuse of one interspace. Figure 14 shows the epidural needle with the instrumentation device injected into the L 3 - L 4 interspace in a typical trial. Water is used as the injection fluid and is carefully filled into the syringe and all other parts including the tubes and pressure sensor. During the procedure, a computer operator monitors the device and acquires the data at a sampling rate o f 0.01s. When the loss-ofresistance is felt, the anesthesiologist orally indicates the event to the operator so that the time is recorded for analysis.  "NS.  _ta  ^>  Figure 14: The use of the instrumentation device on the pig. The epidural needle is inserted into the L 3 - L 4 interspace. Analysis is performed by examining the results for consistency in the loss-ofresistance indicated by the anesthesiologist and the estimations from the profiles. A l l three measurements should show a simultaneous rapid fall when a loss-of-resistance is  26  encountered. T o estimate the loss-resistance for each physical measurement, a moving average filter with an interval size o f 0.1s is used to remove the majority o f the noise. Since the pressure and displacement profiles continually decrease when the fluid is injected into the tissue or ligaments, the time when the minimum slope occurs is chosen to be time when loss-of-resistance also occurs. The force profiles nearby the loss-ofresistance tend to vary depending on the anesthesiologist's actions so the time o f loss-ofresistance is found by averaging the time at 10% o f the local maximum and minimum values. The paired t-test is used to compare all three times obtained from the force, displacement, and pressure profiles. The mean time o f the three estimated times is compared against the time orally indicated by the anesthesiologist. The next step is to examine the physical models discussed in Section 2.3. The estimated pressure is calculated using the force, and displacement profiles, and E q . 7 and E q . 12. The estimated pressure values are compared with the actual values using error statistics. Suppose the error E at time index /, is defined to be h  E = P. i  - P.  /.measured  •  /, estimated  where P,, easurcd is the measured pressure value of the pressure sensor, and P/, timated is the m  cs  pressure estimated by either the static (Eq. 7) or decay model (Eq. 12). Then the mean error £mcan measured over the number o f samples N in the a time interval is given by  i-\  i  The standard deviation OE o f the mean error is defined as  , —  f(E.  -E  f  Eq.14  Another useful measure, the root mean square ( R M S ) error Erms is defined as  ^s=J^5U  2  Eq.15  Both the mean error and its standard deviation are used to measure the average and the spread o f the error. The additional R M S error is also used since the pressure differences 27  can either be positive or negative. The unpaired t-test is used to compare the errors and standard deviations between the "smooth" arid "bouncing" techniques.  2.5.2  Results and Discussion After acquisition o f the raw voltage data, the force, pressure and displacement  data are converted to the appropriate physical values using E q . 1, E q . 2 and E q . 3, respectively. Figures 15-17 show the three profiles for the "smooth" technique o f a typical trial. Similarly, Figures 18-20 show the three profiles for the "bouncing" technique o f a typical trial. The solid vertical line in each plot indicates the time of lossof-resistance determined by the respective profile. The dashed vertical line in each plot indicates the time o f loss-of-resistance orally communicated by the anesthesiologist. The estimated times, shown in Figures 15-20, are summarized in Table 2.  0  5  10  15 Time (s)  Figure 15: Force profile of epidural procedure using "smooth" technique. The solid vertical line indicates the time o f loss-of-resistance determined by averaging the time at 10% o f the local maximum and minimum values. The dashed vertical line indicates the time o f loss-of-resistance orally communicated by the anesthesiologist.  28  0  30  15 Time (s)  Figure 16: Pressure profile of epidural procedure using "smooth" technique. The solid vertical line indicates the time of loss-of-resistance determined by minimum slope. The dashed vertical line indicates the time of loss-of-resistance orally communicated by the anesthesiologist.  15 Time (s)  20  25  30  Figure 17:' Displacement profile of epidural procedure using "smooth" technique. The solid vertical line indicates the time of loss-of-resistance determined by minimum slope. The dashed' vertical line indicates the time of loss-of-resistance orally communicated by the anesthesiologist. 29  0>  o  O UH  0  2  4  6  8 10 Time (s)  Figure 18: Force profile of epidural procedure using "bouncing" technique. The solid vertical line indicates the time o f loss-of-resistance determined by averaging the time at 10% o f the local maximum and minimum values. The dashed vertical line indicates the time o f loss-of-resistance orally communicated by the anesthesiologist.  0  2  4  6  8 10 Time (s)  Figure 19: Pressure profile of epidural procedure using "bouncing" technique. The solid vertical line indicates the time o f loss-of-resistance determined by minimum slope. The dashed vertical line indicates the time o f loss-of-resistance orally communicated by the anesthesiologist. 30  35  -  30  I• i \ •  25  I  i  20  \A  <u o  i  1 r  .22 15 Q  \  \  10  0  1  1  t  2  4  6  i  i  8 10 Time (s)  t  12  i 14  16  1J  Figure 20: Displacement profile of epidural procedure using "bouncing" technique. The solid vertical line indicates the time o f loss-of-resistance determined, by minimum slope. The dashed vertical line indicates the time o f loss-of-resistance orally communicated by the anesthesiologist.  Table 2: Time of loss-of-resistance from the two trials shown in Figures 15-20. Force Profile  Pressure Profile  Smooth  25.0s  24.6s  Bouncing  15.2s  15.3s  .  Displacement Profile  Anesthesiologist  25.2s  26.0s  14.2s  . 15.4s  When the anesthesiologist uses the "smooth" technique, the applied force actually shows significant variability indicating the applied force is not truly constant. Rather, the anesthesiologist is trying to apply the appropriate amount o f force to move the plunger in a slow continuously decreasing manner. The slow changes are used for additional feedback by the anesthesiologist to ensure the plunger is not stuck and to ensure the fluid has consistently high pressure such that the resistance is felt when entering the dense ligaments. The "bouncing" technique differs from the "smooth" technique, but it still provides the same feedback. The plunger's displacement "bounces" because the fluid injected into the ligament is forced back into the syringe because o f ligament's high 31  density and elasticity[68]. Even when the needle has entered the dense ligaments, the plunger's displacement continually decreases, indicating the fluid is still slowly being injected.  '  ' ,  To compare the estimated times when loss-of-resistance occurs over the different profiles, paired t-tests (a=0.05) are performed on each paired set over all trials. There are no significant differences between any o f the three time o f loss-of-resistance obtained from the force, pressure or displacement profile. Therefore, the times o f loss-of-resistance for any o f the profiles are consistent with each other. There is also no advantage o f either the "smooth" or "bouncing" technique in loss-of-resistance analysis. Furthermore, the time o f loss-of-resistance can be sufficiently determined from any o f the three profiles: Since there is no significant difference for the times o f loss-of-resistance between the three profiles, the mean times are calculated and compared with the times orally indicated by the anesthesiologist. The paired t-tests (oc=0.05) results conclude that the times indicated by the anesthesiologist are significantly larger than the estimates from any o f the sensors or the calculated mean times for the sensors. To compare the different values, the mean times are subtracted from each estimated value in the same trial. The relative differences are shown in Figure 21, where trials 1 to 10 consist of values from the "smooth" technique and trials 11 to 20 are from the "bouncing" technique. The first three bars o f each trial are the relative time difference o f the force, pressure and displacement profiles from the mean. The last bar in the set indicates the relative time difference o f the anesthesiologist's oral time, and it lagged, in all trials, the mean time. The times indicated by the anesthesiologist are, on average, 0.7±0.3s later than the mean. This discrepancy is consistent with the time it takes for the anesthesiologist to conclude the needle has reached the epidural space and to orally relay the information to the operator.  32  1.5  _l Force • Pressure BDispl. • Anesth.  -0.5  A  -1.0 -I 1  2  3  4  5  6  7  II  9  10  II  12  13  14  IS'.  16  17  18  19  20  Bouncing  Smooth  Trial  Figure 21: Comparison of estimated loss-of-resistance times. The mean time of lossof-resistance is the average o f the three time estimates o f the force, pressure and displacement profiles. The relative difference o f each o f the four times (including the anesthesiologist's oral time) o f loss-of-resistance with the mean time are shown over all the trials. The static and decay models described by E q . 7 and E q . 12 are then used to estimate the pressure from the force and displacement data. The estimated constants, k  a  and T , from the two models, are discussed in Section 2.4. Because the data from pressure sensor measures the fluid pressure directly, it is the most accurate pressure data and it is used as the reference for comparing the estimated pressures. The estimated and measured pressure profiles for both the "smooth" and "bouncing" technique are shown Figure 22 and Figure 23, respectively. These plots are from the same trials shown in Figures 15-20. The time o f loss-of-resistance from the pressure profile and the orally communication are also shown.  33  0  5  10  15  20  25  30  Time (s)  Figure 22: Static and decay modeling of pressure for "smooth" technique. The solid vertical line indicates the time o f loss-of-resistance determined by pressure profile. The dashed vertical line indicates the time o f loss-of-resistance orally communicated by the anesthesiologist. The arrows point to examples o f when fluid leakage occurs while the plunger is motionless. 10  Time (s)  Figure 23: Static and decay modeling of pressure for "bouncing" technique. The solid vertical line indicates the time o f loss-of-resistance determined by pressure profile. The dashed vertical line indicates the time o f loss-of-resistance orally communicated by the anesthesiologist. The arrows point to examples o f when fluid leakage occurs while the plunger is motionless. 34  For the "smooth" technique, the decay model is clearly a better estimate than the static model. The "smooth" technique has relatively longer constant'displacement and therefore, the decay model is suited for accounting the loss o f pressure from leakage. Although the decay model accounts for leakage, the model only estimates decay with a single time constant. The pressure data shows small variations in the decay rate. Possible explanations are that there are small amounts o f leakage into the tissue and ligaments, and the time constant for the leakage through the plunger-barrel interface is position dependant (how much the plunger is inserted). A t the time when loss-of-resistance occurs, all estimates rapidly fall, but the pressure estimates slightly lag the actual pressure. A likely reason is that the plunger moved too quickly and consequently, the anesthesiologist was unable to properly apply an axial force upon the plunger so the force reading simply show the greater levels o f friction. For the "bouncing" technique, the estimated pressures also follow the rapid oscillations o f the force profile, but shows small oscillations with decaying peaks. In some instances, the  decay model shows the  appropriate  pressure  decay, but it  significantly differs from the measured pressure. The decay model is unable to estimate the decay pressure due to the rapidly changing force and displacement profile. For the majority, the estimates are nearly identical since the plunger is always in motion. A t the time when loss-of-resistance occurs, all estimates fall to zero, but at a slower rate than the oscillations. A possible explanation is that the anesthesiologist is rapidly "bouncing" the plunger until he believes he feels the loss-of-resistance. A t that point in time, he slowly pushes the plunger to confirm his "hunch". The mean errors and standard deviations are shown in Figure 24 and the R M S errors are shown in Figure 25. Using the unpaired t-test (ct=0.05), there are significant reductions in both the standard deviations (by an average o f 31 %) and R M S errors (by an average o f 40%), but not for the mean error values for the "smooth" technique. The results conclude the decay model is more accurate than the static model for the "smooth" technique. However for the "bouncing" technique, there are no significant differences in the standard deviations, mean and R M S errors indicating neither model performs better: On average, the "smooth" technique has smaller errors and standard deviations for both models compared to the "bouncing" technique, as summarized in Table 3. Overall, the 35  decay model is the better pressure estimator and suggests it should be used i n clinical settings to replace the pressure sensor. Furthermore, the "smooth" technique should be used for greater accuracy. 2.5 2.0  • Static  _ Decay  1.5 1.0  'JL 0.5  II.  P  c oo  m  S  in iii in m in I in  1  C  -0.5 -1.0 -1.5 -2.0 -2.5  1  2  3  4  5  7  6  8  9  10  11  12  13  14  15  16  17  18  19  20  Bouncing  Smooth  Trial  Figure 24: Mean error comparison between the static and decay models. The vertical error bars represent the standard deviation of the mean error values.  • Static  • Decay  1.2  E U  0.8  _  0.6  00  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  Bouncing  Smooth  Trial  Figure 25: RMS error comparison between the static and decay models.  36  20  Table 3: Summary of the statistics of the decay and static models. The mean values are computed from the values o f the mean error, standard deviation and RMS error. Mean Error •  R M S Error  Mean Error  R M S Error  Static  Static  Decay  Decay  Smooth  0.1±0.8psi  l.Opsi  -0.1±0.6psi  0.7psi  Bouncing  0.2±1.0psi  1.2psi  0.2± l.Opsi  1.2psi  2.6 Conclusion A n instrumentation device measuring the applied force o f the plunger, pressure o f the fluid and the displacement o f the plunger relative to the barrel was successfully constructed and calibrated. The instrumentation device is simple, unobtrusive and can be used in a sterile clinical setting. Depending on personal preference, the anesthesiologist can apply either a "smooth" or "bouncing" force upon the plunger when performing the loss-of-resistance technique. The times o f loss-of-resistance are estimated for the force, pressure and displacement measurements and shown to be equivalent. Neither the "smooth" nor "bouncing" technique has any distinct advantage for determining loss-ofresistance. The anesthesiologist indicated that he had felt the loss-of-resistance shortly after the sudden drop in the measured values by approximately 0.7±0.3s, which is consistent with the expected oral response time. The static and decay models are used to relate the estimate the pressure from the force and displacement measurements. The static model accounts for friction, and the decay model deals with both friction and fluid leakage. The decay model produced better estimates for the "smooth" technique, but similar estimates for the "bouncing" technique. Overall, the decay model is more accurate o f the two and is should be considered as the replacement measurements in clinical trials.  37  for direct pressure  3  ULTRASOUND VERIFICATION OF THE EPIDURAL NEEDLE INSERTION  3.1 Introduction In the previous chapter, an instrumentation device successfully measured the time of the loss-of-resistance for indicating entry o f the needle tip into the epidural space. This part o f the research is to confirm that the depth o f the epidural space, as depicted in ultrasound, is similar to the actual depth, as measured along the needle. This is similar to a study by Grau et al.[44], except for the use o f the additional loss-of-resistance measurements to confirm the needle has actually entered the epidural space instead o f simply relying on the anesthesiologist's belief. Furthermore, the purpose is to gain an understanding o f the issues involved in ultrasonography o f the epidural space.  3.2  Materials and Method The epidural procedure is performed by an anesthesiologist on two pigs, as  described in Section 2.5.1. A Voluson 730 ( G E Healthcare, Chalfont St. Giles, Buckinghamshire, U K ) with a real-time 4 D convex 1.5-5MHz probe was used to capture ultrasound images o f the puncture site during the epidural procedure. The 17Ga x 8.57cm epidural needle is obtained from the JH-0550 epidural catheterization kit (Arrow International, Inc., Reading, P A ) . Once the needle breaches the epidural space by the loss-of-resistance technique, the needle is marked at the base o f the puncture and ultrasound is used to image the needle and the epidural space, as shown in Figure 26. The built-in software caliper is used to measure the puncture path length, the distance between the base o f the puncture and the tip o f the needle, in the ultrasound image. T o physically measure the puncture path length, the needle is withdrawn and measured with calipers from the mark to the needle tip. A paired t-test analysis is performed on the ten paired measurements (ultrasound and actual needle), and the mean, standard deviation and R M S errors are calculated.  38  In a second, more limited study, the epidural depth is directly estimated by manually identifying the epidural space in the ultrasound image without the needle. The depth is measured vertically to the skin surface (shortest distance) since the needle path is unknown. That depth can then be compared to a depth indirectly measured by estimating the length between the tip o f the needle and the skin directly above it (shortest length). Three trials were performed for each o f the L 3 - L 4 and the L 4 - L 5 interspace.  Figure 26: Ultrasound imaging of the epidural needle. The ultrasound probe is place sagittally between the L 3 - L 4 vertebrae to image the needle and the epidural space.  3.3  Results and Discussion A n ultrasound image o f a typical epidural puncture between the L 3 - L 4 vertebrae  is shown i n Figure 27. The software calipers measure the distance between the two x ' s marking the surface o f the puncture and the tip o f the needle. Figure 28 compares the results o f all the ten paired measurements. The puncture path length varies significantly by up to 16mm because the anesthesiologist is able to choose different puncture sites and needle trajectory. The mean error and standard deviation are 0.0±0.5mm, and the R M S error is 0.5mm. The paired t-test concludes there is no significant difference between the two  measurements  (a=0.0001)  confirming  39  that the ultrasound measurements  are  consistent with the actual measurements when the needle itself is visible in the ultrasound.  Figure 27: Measurement of the puncture path length between L3-L4 vertebrae. The ellipse shows the needle location and trajectory. The two *'s at the ends o f the ellipse mark the puncture path length o f the needle.  • Actual  11 1 1 1  • Ultrasound  [_  2  3  4  5  6  Trial  7  8  1 9  1 10  1  Figure 28: Comparison of the puncture path lengths. The lengths were measured from physical markings o f the needle and the ultrasound image. A l l ten trials are measured from the needle in the L 3 - L 4 interspace. 40  Direct and indirect measurements of the depth o f the epidural space are shown in Figure 29 and Figure 30, respectively. The direct method is performed by manually identifying the epidural space, seen typically as the doublet echoes, and measuring its depth. The indirect method estimates the epidural depth geometrically using the puncture path length o f the needle. The results o f for the L 3 - L 4 and L 4 - L 5 epidural space depth are given in Table 4. The small variation in depth is explained by how hard the probe is depressed into the skin causing deformation. Nevertheless, the mean depth o f the L 3 - L 4 is significantly less than the depth of L 4 - L 5 , which is also consistent with human anatomy[21]. For each interspace, the direct method is similar to the indirect method and within the error tolerance. Therefore, the depth o f the epidural space is consistent with the depth o f the needle tip. Furthermore, the use o f the loss-of-resistance technique to reach the epidural depth is consistent with the measurements from the ultrasound image.  Figure 29: Direct measurement of the epidural space depth. The two x's mark the skin-to-epidural space distance. The ellipse contains the doublet echoes that are typical o f the epidural space.  41  Figure 30: Indirect measurement of the epidural space depth. The ellipse shows the needle location and trajectory. The two x ' s mark the skin-to-epidural space distance. The epidural depth is measured along line from the needle tip to the skin directly above it.  Table 4: Summary of the mean epidural depths. The direct method measures the manually identified epidural depth in the ultrasound image. The indirect method measures the depth by geometrically computing the tip o f the needle. Direct  Indirect  L3-L4  29.5±0.8mm  29±2mm  L4-L5  35.7±1.7mm  37±4mm  In this study, we found that the main difficulty is obtaining good images o f both the needle and epidural space. O n many occasions, several attempts are made to optimally position the probe in order to obtain the strongest echo of the needle. Because the needle and epidural space are surrounded by bone, there is a very small range o f positions which yield satisfactory images. Furthermore, the probe has to be placed alongside the needle making it very difficult to visualize the needle due to the steep angle.  42  3.4 Conclusion Ultrasound measurement o f the puncture path length o f the needle is accurate and reliable. The location o f the needle in the image is consistent with the actual location but the puncture path length varies significantly depending on the choice o f puncture site and trajectory. The depth o f the epidural space is consistent with the measurements o f depth o f the needle using the loss-of-resistance technique. However, obtaining optimal ultrasound images o f the epidural space and needle is very difficult due to the steep angle of the needle and surrounding bone structures. If ultrasound-assisted guidance is to be widely used in epidural procedures, then good image quality depicting the needle and epidural space is needed.  43  4 ADAPTIVE SPATIAL COMPOUNDING 4.1 Introduction The use o f ultrasound imaging to examine the epidural space has been particularly challenging. To image the epidural space, the patient must arch her back causing the spinal elements to move apart. Then the probe must be placed in a specific position and angle to obtain the optimal image o f the epidural space. Other important features such as bony surfaces may not be visualized because the probe is at a sub-optimal angle for good reflection o f the structures. The motivation o f this research is to improve feature visualization by adaptively enhancing features at different beam angles and combining these enhancements to show an overall improved image quality. This is done with a technique called adaptive spatial compounding. The concept o f spatial compounding is illustrated in Figure 31.  Figure 31: The concept of spatial compounding. It is the process of averaging (compounding) multiples views o f the same region taken from different points o f view. For two-dimensional ultrasound, multiple images are obtained by electronically steering the sound beam through a range o f angles while the probe is stationary. A t each angle, the image is constructed. The compounded image is the average o f the set o f beam-steered images.  44  Spatial compounding is a technique that signal-averages the images over varying beam angles. However, this technique often results in blurry compounded images when there is misalignment among the individual images from refraction and speed-of-sound errors. A n improved spatial compounding technique was proposed by introducing an intermediate warping step that non-rigidly realigns the features in each o f the individual image frames before averaging[67]. This warped spatial compounding technique is used as the starting point o f this research to further improve image quality.  4.2 Materials and Method 4.2.1  Hardware and Development Tools The Ultrasonix 500RP (Ultrasonix Medical Corp., Burnaby, B C ) equipped with a  38mm linear 4 - 9 M H z probe and a 40mm curvilinear l - 9 M H z probe is used to acquire the set o f beam-steered images. The pre-scan-cOnverted frames are stored locally onto the system's hard disk drive. The frames are transferred to a standard P C (2.8GHz X e o n H T , 5 1 2 K B L 2 cache, 4 0 0 M H z F S B , 2 G B R A M ) for post-scan conversion (to Cartesian coordinates), compounding and analysis. A l l applications including image acquisition, post-scan conversion, compounding and display are developed using Visual C++ 2003 (Microsoft Corp., Redmond, W A ) . The Microsoft Foundation Class ( M F C ) library is used for G U I development, and the Integrated Performance Primitives (IPP) 2.0 library (Intel Corp, Santa Clara, C A ) is used for high-speed image processing and numerical computation. Evaluation and analysis o f the results are performed using M A T L A B 7.0.1 (The MathWorks, Inc., Natick, M A ) .  4.2.2  Image Acquisition and Post-scan Conversion A n application is developed to acquire pre-scan-converted images from  the  ultrasound system using the application programming interface (API) provided by Ultrasonix. The A P I is used to access various system functions and probe properties. M o r e specifically, the application allows the user to select the beam angle sweep range and the size o f the angle increment. Once the user begins the capture process, the application automatically selects the lowest beam angle, and captures the pre-scan-  45  converted frames (individual beam-steered image). Then the next beam angle o f the probe is set to capture the next frame. The process is repeated until it captures the frame of the final beam angle o f the specified range. In this research, the captured frames consist o f the reference frame o f angle 0°, and eight beam-steered frames o f angles ± 2 ° , ± 4 ° , ± 6 ° and ± 8 ° . Frames with beam-steered angles beyond ± 1 0 ° degraded significantly. The pre-scan-converted data frames are received as a series o f rectangular gray-scale data for a given beam angle. Typically, it can take up to one second for each frame capture because the Windows Messaging System is used as the communication protocol between the software application and A P I .  .  The pre-scan converted frames are copied from the ultrasound system to the P C for scan-conversion and processing. Scan-conversion involves transforming the pre-scanconverted frames, by using the beam-angle and probe type, into either into a trapezoidal or curved image (depending on the type o f probe) in Cartesian coordinates for further processing or display.  4.2.3  Adaptive Spatial Compounding Method The spatial compounding technique uses non-rigid (warped) image registration  prior to compounding. The warped images are then compounded using one o f several possible methods, each with its own merits and demerits. First, warping is described, then several compounding techniques.  4.2.3.1 Block-based Shift Vector Estimation for Warping The warping process corrects misalignment o f features prior to compounding the frames. The basic principle is to divide each frame into small blocks and determine the optimal alignment for each block to the reference image. Warping is described by the set o f registration vectors from the blocks. This means after scan-conversion, all beamsteered frames (±2°, ± 4 ° , ± 6 ° and ± 8 ° ) are warped with the registration vectors to match the reference frame (0°). Registration is based on correlating blocks o f pixels between the beam-steered frames and pixels in a predefined search area o f the reference frame. The blocks are defined such that the centers are evenly spaced horizontally and vertically, and may overlap each other depending on the size and number. The size o f each block is 96 46  by 96 pixels to ensure that each block contains significant features. A 5 by 5 set o f blocks are thus defined on each target frame. Each block in the beam-steered frame is compared to a corresponding block o f the same location in the reference frame. It is also compared around neighboring locations based on a horizontal and vertical search range o f ± 1 0 and ±4  pixels,  respectively. This  search  range  encompasses  reasonable  translational  misregistration (relative to refraction and speed o f sound maximum errors) and assumes that rotation and shear is small relative to the block size. Matching is based on the statistical correlation between the target and reference frames. Given two blocks, the reference block A and the beam-steered block B, and a shift vector (Ax, Ay), then the pixel A(x,y) corresponds to pixel B(x+Ax, 7+Ay). Let I denote the set o f all indices where B contains a valid ultrasound pixel that is within the borders o f the ultrasound image. These corresponding pixel pairs can be arranged into vectors A-, and B where /el. Let fx and p be the respective averages o f Aj and B over all h  A  B  t  /el. Then the correlation coefficient C is defined by  c=  Eq. 16  The value o f C ranges between -1.0 to +1.0, where a value o f +1.0 implies a perfect match o f the two image blocks. The best match and its associated shift vector are determined by finding the highest correlation value within the search range. The process is repeated over all blocks for each beam-steered image.  4.2.3.2 Interpolation of Shift Vectors Once all the shift vectors for each block have been determined for each beamsteered image, a shift vector for each pixel is computed using radial basis function ( R B F ) interpolation  technique.  The  R B F technique  offers  smooth  interpolation and  is  computationally practical for the relatively small number o f points in this application. The radial basis function approximation is described here for the two dimensional case. Let x=(x,y) be a two-dimensional point (in a Cartesian coordinate system) and  47  (fi,...fy) be the set o f N two-variable real-valued functions with corresponding distinct points {xi,.. .,x ] such thatfrflxi).  Then the radial basis function s(x) is  N  Eq. 17 where p is a low-degree polynomial o f degree M,  is a real-valued constant, || • || denotes  the Euclidean norm, and (f> is single-variable real-valued function. The space o f all polynomials o f at most M degrees in 2 variables is denoted by n . The solution can be 2  M  found by satisfying the interpolation condition s(x ) i  / = ! , . . . , TV  = f  i  Eq. 18  and applying the side condition  £  A,. _,(%,) = 0  V  ?  Eq. 19  e.  There are several choices for <f> and p. For two-dimensional registration, a common choice is the thin-plate spline, where $>)=r log(>) is the biharmonic equation 2  and p(x)=ao+ci]X+a2y is the affine trend function[69][70]. Thus, E q . 18 and E q . 19 imply the coefficients o f the radial basis functions and the affine trend function can be solved using following linear system ' A  )  Q W T  0  ff^  Eq.20  V  where  i,j = \,...,N  A = (a,,) = Wx,. 1 Q =  \ -  (X ,...,A. )  J  X  N  a = (a ,a,,a )  T  f = (/„...,  T  0  2  48  f) N  T o obtain interpolation o f the shift vectors for each pixel, the R B F technique is applied separately to the horizontal and vertical components. I f the set o f vertical components from the shift vectors for a single beam-steered image is represented as f with the corresponding block location (at the center), then X and a can be solved using E q . 20. A fast matrix inversion routine provided by the IPP library is used to solve the linear system. The technique is repeated for the horizontal component for the same image. Once X and a have been determined for both components, the shift vectors for all pixels are interpolated using E q . 17.  4.2.3.3 Image Remapping (Warping) Warping is performed by remapping the pixels using their corresponding shift vectors  and resampling to a regular  grid  is performed  using  nearest-neighbor  interpolation. This step is performed using the image-processing routines o f the IPP library.  4.2.3.4 Compounding Both conventional and warped spatial compounding perform a basic signalaveraging step where the valid pixel intensity values for all beam-steered and reference images are averaged to form the final compounded image. More formally, let Pi(x,y) be the valid pixel intensity value at coordinates (x,y) where i is the image index in I(x,y), which is the set valid pixels (within the image border) o f all the images. Then the intensity o f the pixel o f the compounded image is given by  P* &( >y) x  vm  =i , T  1  ,i Z J O  Eq.21  where | • | denotes the cardinality o f the set. One o f the problems with this method is that features present i n some frames are reduced i n overall intensity after averaging. Edge responses may appear stronger i n some beam-steered images than others because an edge perpendicular to the echo plane reflects back a higher energy echo. The idea is to develop methods that adaptively enhance edges perpendicular to the echo plane when the images are compounded. T w o new adaptive  49  methods  are  developed in this research:  a gradient-based  and  a  median-based  compounding technique. The gradient-based compounding method is used to sharpen edges including point features (spots). T o detect the edges o f features, the Laplacian o f Gaussian filter is initially convolved with each warped image to obtain an edge response while  filtering  speckle noise. The suitable kernel size for speckle reduction is determined empirically to be a 9 by 9 mask with a standard deviation o f 1.5 pixels in order to obtain the strongest gradient or edge response o f the significant features while ignoring the smaller size speckle noise. The values o f the computed gradient at each pixel location are used as weights for computing the weighted-average o f each compounded pixel. The values o f the weighted-average are used as the final intensity value o f the compounded image. The gradient value produced by the Laplacian o f Gaussian at each pixel o f an image is G,(x,y). Then the weighted-average for the pixels o f the compounded image using the .gradientbased technique is given by  ]^G,(x,y)/?,.(*, 7) ^gradient (*, X> =  '  1 ( j c y  )  Eq.  22  The goal o f this approach is to retain strong reflections/edges in the compounded image by weighting their contributions more than weak reflections/edges at the same anatomical locations. The median-based compounding method is an extension o f the gradient-based method. Once the gradient responses G,(x,v) have been computed, an additional decision making step is introduced for each pixel. Given a set o f overlapping pixels at a particular location, i f more than half o f the frames that have a pixel value above the threshold value ^threshold, then the median intensity for that pixel Over all the images is used as the pixel intensity o f the compounded image. Otherwise, the gradient weighted-average of the intensities is used as the pixel intensity o f the compounded image. Gthrcshoid is determined empirically by choosing a suitable value that gives the best edge response without introducing speckle noise. A g a i n , the goal is to further improve the edge response by  50  performing median computation on images with stronger reflections/edges rather than weighted-averaging which tends to blur the edge responses. More formally, define the set o f pixels P(x,y) to be P(„, y) = {G (x,y) | G,(x,y)>G t  threshold '  Then the weighted-average for the pixels in the compounded image using the medianbased technique is given by  median (x,y)  =  JMedian(P(x,v))  ,|P(x,v)| >  \Pp*m*(*»y)  .otherwise  ^  Eq. 23  4.2.3.5 Software Application A multi-threaded, object-oriented  M F C application, shown i n Figure 32, is  developed to perform scan-conversion, adaptive spatial compounding algorithms and image display. The application is able to load one or more beam-steered images acquired by a linear or curvilinear probe, and view the pre-scan converted or scan-converted image(s) and the resulting compounded image.  O tonv. cane Qw_fpcw-f  lin  M-MI*I»|  [  J  i-**JI*fkfJ\-  *S4  M.QQmt Mod-;hijiCunfcUrd  fcflt*  cwtktt:. 1**1 t «n*ptf.  s' «c!.  >*iMM«) a-rjt CVr^Hnq ruw WP*-  : Uudhg i..«««Me. Tot* 1 ttwjn.  Figure 32: Adaptive spatial compounding application. The application can compute and display beam-steered images, conventional and adaptive spatial compounded images for the linear and curvilinear probes. 51  4.2.4  Experimental Verification A number o f experiments are conducted to evaluate image quality o f five  available methods: no compounding, spatial compounding, warped spatial compounding with averaging, adaptive  spatial compounding with gradient-based  averaging  and  adaptive spatial compounding with median-based averaging. Experimental verification is performed on the data o f a specially-constructed agar phantom obtained from the experiments in [67]. The phantom consists o f 39% glycerol (by mass) mixed with water to form the solvent. Square columns o f "white agar", consisting o f 30 g / L cellulose fibre, were embedded in the clear agar substrate. Small bright points were created by stirring air bubbles into the agar mixture just before pouring. This phantom was specifically designed to investigate image quality for point features, edge features and homogeneous regions. To evaluate point features, bounding boxes over manually selected air bubbles from the test phantom are established. Pixels that have intensity values that are at least half as bright as the brightest pixel in the bounding box are counted. The normalized diameter is computed and expressed as the diameter o f a circle with the same area as the counted pixels. The normalized diameters are compared over all the compounding methods using the paired t-test. Edge sharpness is quantified by measuring the intensity transition o f a manually chosen boundary. The average intensity profile is the average o f 30 intensity profiles evenly spaced, 2.2mm wide that perpendicularly crosses the boundary. The maximum value o f the average intensity profile convolved with the derivative o f a Gaussian with (7=2 is compared over all the compounding methods using the paired t-test. The amount o f speckle within a homogeneous region is measured using the signal-to-noise ratio (SNR). The signal-to-noise ratio for a region is defined as  SNR =  where x  a v g  Eq. 24  is the average intensity o f the region and cr is its variance. S N R is computed x  for both the clear and white homogeneous regions o f the image.  52  The contrast-to-noise ratio ( C N R ) is used to compare a light against a dark region. The contrast-to-noise ratio is defined as  CNR =  where x  a v g  and y  a v g  x.avg -y, avg  Eq.25  are the average intensity o f the light and dark regions, respectively,  and o and o are their respective variances. C N R is computed on manually selected dark x  y  regions consisting o f a clear homogeneous regions, and light regions consisting o f white homogeneous regions. A qualitative analysis is also performed on porcine tissue. The ultrasound images are acquired during the epidural experiments described in Section 2.5 and 3.2. A n ultrasonographer steadily positions the probe to minimize motion error during frame acquisition. Acquisition requires several seconds due to the slow rate o f change i n the beam angle. Features such as muscle tissue, bone structures and the epidural space are qualitatively compared.  4.3 Results and Discussion The phantom used for experimental verification is depicted in Figure 33 using standard ultrasound. The different spatial compounding techniques, applied to the set o f phantom images, are shown in Figures 34-37. Qualitatively, the resulting images show remarkable differences relative to each other. Conventional spatial compounding appears to be the most blurred, and warped spatial compounding appears to recover some image quality, while the adaptive spatial compounding techniques recover most o f the sharpness. The amount o f speckle noise present in the compounded images also varies substantially.  53  Figure 3 3 : Reference image of the phantom.  Figure 35: Warped spatial compounding with averaging of the phantom.  Figure 37: Adaptive compounding with median-based averaging of the phantom.  Manual selections o f spots are shown in Figure 38, their normalized diameters are plotted in Figure 39, and the summary  of their averages are given in Table 5.  Conventional compounding has the most blurring and hence a larger average spot diameter. A p p l y i n g the paired t-test (a=0.05), shows that both the conventional and warped diameter  spatial compounding with averaging have relative to the reference  significantly larger normalized  image. Both gradient-based  and  median-based  techniques have no significant difference relative to the reference image implying that both techniques are able to recover the resolution o f the point features. Furthermore, the normalized diameters from both techniques are significantly smaller than those o f the warped spatial compounding with averaging.  56  Figure 38: Selection of spots for evaluation of point features.  1.6  1.4  • Reference  • Conventional Comp  B Warped Comp w/ A v g  • Adaptive Comp w/ Grad  • Adaptive Comp w/ Med  1.2  1.0  J]  0.8  ILJI  —I  u  "c3  0.6  Jl  o 0.4  0.2  0.0 1  2  3  4  5  6  7  8  Feature Number  Figure 39: Normalized diameter of spots.  57  9  10  11  12  13  Table 5: Summary of the average normalized diameter. Image Type  Average Normalized Diameter (mm)  Reference  0.86±0.17  Conventional Comp.  1.1 ±0.2  Warped Comp. w/ A v g  0.93±0.18  Adaptive Comp. w/ Grad  0.87±0.17  Adaptive Comp. w/ M e d  0.87±0.18  Manual selections o f edges are shown in Figure 40, their maximum slopes are plotted in Figure 41, and the summary o f their averages are given in Table 6. A g a i n , conventional compounding produces edges with the least edge strength. The paired t-test (et=0.05) shows  that the  maximum  slopes  from  conventional  compounding  are  significantly less than those o f the reference image. A l l three warped compounding methods recover most o f the edge sharpness o f the reference image.  Figure 40: Selection of edges for evaluation of edge strength.  58  300  • Reference  • Conventional Comp  B Warped Comp w/ A v g  • Adaptive Comp w/ Grad  • Adaptive Comp w/ Med  9  10  II  12  Figure 41: Maximum intensity of edges.  Table 6: Average maximum intensity of edges. Image Type  Average Max Slope (intensity/mm)  Reference  170±40  Conventional Comp.  140±50  Warped Comp. w/ Avg  160±50  Adaptive Comp. w/ Grad  160±50  Adaptive Comp. w/ Med  160±50  Manual selections of dark and light regions are shown in Figure 42, the results of the SNR and C N R calculations are plotted in Figure 43, and the summary of their averages are given in Table 7. The paired t-test (a=0.05) shows that only the gradientbased technique is not significantly improved over the reference. All other techniques have significantly better noise reduction.  59  Figure 42: Selection of dark and light homogeneous regions for evaluation of noise. The lines connecting the rectangles indicate the pairings used in the C N R evaluation.  • Reference  •Conventional Comp  5 Warped Comp w/ Avg  • Adaptive Comp w/ Grad  • Adaptive Comp w/ Med  S N R 1 (light) S N R 2 (light) S N R 3 (light) S N R I (dark) S N R 2 (dark) S N R 3 (dark)  CNR I  CNR 2  CNR 3  Figure 43: SNR and CNR of dark and light regions. The C N R values are calculated using the paired regions shown in Figure 42.  60  Table 7: Average SNR and CNR. Image Type  Average S N R - L i g h t  Average S N R - D a r k  Average C N R  Reference  10±2  6.5±0.7  6.3±1.0  Conventional Comp.  16±4  11±3  9±2  Adaptive Comp. w7 Avg  15±4  11±3  9±2  Adaptive Comp. w/ Grad  12±2  8.9±1.8  6.8±1.7  Adaptive Comp. w/ Med  13±3  9.2±2  7.2±1.9  Test data sets are acquired from a porcine specimen and the resulting images are shown in Figure 44. Conventional compounding produces an image consisting o f slightly blurred bone structure, reduced speckle, and slightly better defined muscle striations. Warped compounding with averaging improves the image with some sharper muscle definition, but still contains blurred bone structure. Adaptive compounding with gradient averaging further sharpens edges o f the bone and muscle. Adaptive compounding with median averaging produces similar results to the image from the gradient averaging. Another set o f the images consisting o f the epidural space and surrounding bone are shown in Figure 45. Conventional compounding produces blurry images with poor visualization o f the epidural space. Warped compounding with averaging slightly recovers the epidural space feature, but some significant blurring occurs in the featureless regions. Adaptive compounding with gradient averaging produces slightly sharper edges on the bone and epidural space, but the blurring in the featureless regions remain. Adaptive compounding with median averaging produces sharper edges along the bone and epidural space, and the contrast around those features is significantly higher which brings out some more detail around the features. Furthermore, the blurring in the featureless regions is noticeable reduced. Overall for the porcine test data, the adaptive spatial compounding with medianbased averaging produced the best compounded image with similar or better image  61  quality than the reference image depending on the region. However, the improvements are modest, but a small improvement can have a large impact for this application. In Figure 45, the epidural space can be seen in the reference  image because  the  ultrasonographer took great care in the positioning o f the probe. For an anesthesiologist with limited experience in ultrasonography, the epidural space may not appear in the reference  image  so the  adaptive  spatial compounding technique  may help  the  anesthesiologist image the epidural space more quickly and without the need for optimal probe placement. However, one o f the issues with warping is that significant misregistration may .occur in featureless regions because the block matching algorithm is unable to determine the best match. Since there are little or no features in such regions, the correlation values are very low resulting in possible misregistration, which may actually blur the image more than conventional compounding. Although this can occur, it is not as important since the region is presumed featureless and o f less interest. Due to the lengthy acquisition time, the images may possibly suffer from slight motion error. However, the process o f non-rigid registration and warping allows for correction o f a small degree o f motion error. This additional benefit is well suited for clinical settings where tissue motion may be even more significant.  62  (d) (e) Figure 4 4 : Images of porcine spinal tissue using different compounding techniques. Two vertebral elements are shown with overlying muscle, fat and skin, (a) Reference, (b) conventional, (c) warped with averaging, (d) adaptive with gradient averaging and (e) adaptive with median averaging. 63  Figure 45: Images of porcine epidural space using different compounding techniques, (a) Reference, (b) conventional, (c) warped with averaging, (d) adaptive with gradient averaging and (e) adaptive with median averaging. 64  4.4 Conclusion Conventional spatial compounding performed the worst in point and edge features, but it performed the best in noise reduction of homogeneous regions. Warped spatial compounding with averaging can satisfactorily recover point and edge features with excellent noise reduction in homogenous regions. Adaptive spatial compounding with gradient-based averaging can excellently recover point features but at the cost of some increased noise in homogenous regions. Adaptive spatial compounding with median-based averaging performed the best in point feature recovery while maintaining excellent edge features with good noise reduction in homogenous regions. For imaging specific features, such as the epidural space, point and edge resolution is likely more important than noise reduction in homogenous  regions. The adaptive spatial  compounding with median-based averaging also performed the best with the porcine data by sharpening bone, muscle and epidural structures, and increasing the contrast in particularly noisy areas. Therefore, adaptive spatial compounding with median-based averaging is the overall best compromise but it comes at the cost of increased computational power.  65  5  CONCLUSIONS AND FUTURE WORK  5.1 Conclusions The loss-of-resistance, together with the applied force, fluid pressure and plunger displacement are successfully instrumented in porcine studies. The times o f the loss-ofresistance characterized by the rapid fall o f the force, pressure and displacement profiles are equivalent and very close to the oral indication o f the loss-of-resistance felt by the anesthesiologist. Static and decay models are developed to obtain reasonable estimates o f the pressure from the force and displacement measurements. The decay model is more accurate and offers better estimates compared to the static model. Furthermore, accuracy is further increased when the "smooth" technique is used in epidural  procedures  compared to the "bouncing" technique. Therefore, the pressure can be reasonably estimated by using only the force and displacement. Because the instrumentation device is simple, unobtrusive and sterilizable, and the pressure sensor can be omitted, the instrumentation device can be used in clinical trials. It is also recommended that anesthesiologists use the "smooth" technique during clinical trials to improve the accuracy o f the pressure estimates. Ultrasound can reliably and accurately measure the puncture path length o f the needle. Furthermore, the depth o f the epidural space is consistent with ultrasound measurements and the loss-of-resistance technique (in porcine studies). However, it is very difficult to use ultrasound to visualize the epidural space and needle due to the steep needle angle and surrounding bony structure. The angle and position dependencies result in sub-optimal image quality. Therefore, there is a need to improve ultrasound image quality for epidurals. N e w algorithms for adaptive spatial compounding are developed to improve several aspects o f image quality. The adaptive spatial compounding using a median-based averaging gives the best balance for point resolution, edge resolution and noise reduction in homogeneous regions. This algorithm also provides the best image quality o f the . epidural space for the porcine studies because point and edge resolution are especially important.  66  5.2  Future Work One o f the future goals is to use the instrumentation device in clinical trials to  study the loss-of-resistance technique on pregnant women. Further epidural studies are needed to gain more insight in the dynamics o f the loss-of-resistance  technique.  Additionally, it would be beneficial to consider measuring other physical characteristics such as the elasticity o f the tissues or the needle position with respect to the patient. M o d e l improvement is another aspect o f future study so that simulations can be made more realistic and accurate. The use o f ultrasound can be beneficial in epidural procedures for image-assisted guidance. It has been shown that the needle and epidural space can be accurately measured. So the next step is to track the needle using an automated technique. A needle enhancement using beam steering has already been developed by others, but it must be adapted for use in epidural anesthesia to account for anatomy such as bones and the steep needle angles. Detection o f the epidural space with ultrasound is mainly a noise-limited and a human-perception problem, which is especially obvious in the human study. Acceptance o f ultrasound-assisted guidance is possible when it can be used to reliably detect the epidural space, especially by an anesthesiologist with limited experience in ultrasound interpretation. The adaptive spatial compounding algorithm is a step in the right direction, but there are several areas for future work in improving the algorithm including real-time implementation and registration. W i t h the recent introduction o f commercial multi-core C P U s , implementation o f special-purpose threading tasks would greatly speed up computation. For example, cross-correlation can be performed on one C P U while R B F interpolation can be performed in another C P U . Frames can be sent through a pipeline architecture that performs compounding "on-the-fly" as new frames are acquired. Another area for future work is to improve registration by developing an adaptive technique that improves matching in near or completely featureless regions. Furthermore, an adaptive technique can be developed to automatically choose the optimal parameters (i.e., filter size,  Gthrcshoia)  for the gradient and median-based averaging algorithms.  Although the ultrasonographer who participated in the studies prefers the images  67  produced  by  investigation  the in  adaptive the  image  spatial  compounding  assessment  by  beneficial.  68  many  technique  over  the  ultrasonographers  others, would  further also  be  REFERENCES [I]  Anim-Somuah M , Smyth R, H o w e l l C . Epidural versus non-epidural or no analgesia in labour. 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Identification o f the epidural space. B r J Hosp M e d , 1991;46:60-3. [41] Cork R, K r y e J, Vaughan R. Ultrasonic localization o f the lumbar epidural space. Anesthesiology, 1980:52;513-6. [42] Rapp H J , Folger A , Grau T. Ultrasound-guided epidural catheter insertion in children. Anesth Analg, 2005;101;333-9. [43] Rapp H J , Grau T. Ultrasound imaging in pediatric regional anesthesia. Can J Anesth, 2004;51:277-8. [44] Grau T, Leipold R W , Fatehi S, Martin E , Motsch J. Real-time ultrasonic observation o f combined spinal-epidural anaesthesia. Eur J Anaesthesiol. 2004;21:25-31. [45] Grau T. The evaluation o f ultrasound for neuraxial anesthesia. Can J Anesth, 2003 50:6,Rl-8. [46] Grau T, Leipold R W , Conradi R, Martin E , Motsch J. Efficacy o f ultrasound imaging in obstetric epidural anesthesia. J C l i n Anesth, 2002;14:169-75. [47] Grau T, Leipold R W , Horter J, Conradi R, Martin E , Motsch J. Paramedian access to the epidural space: the optimum window for ultrasound imaging. J C l i n Anesth, 2001;13:213-7. [48] Grau T, Leipold R W , Conradi R, Martin E , Motsch J. Ultrasound imaging facilitates localization o f the epidural space during combined spinal and epidural anesthesia. Reg Anesth Pain M e d , 2001;26:64-7. [49] Grau T, Leipold R W , Horter J, Conradi R, Martin E , Motsch J. The lumbar epidural space in pregnancy: visualization by ultrasonography. B r J Anaesth, 2001;86:798804. [50] Perlas A , Chan V W , Simons M . Brachial plexus examination and localization using ultrasound and electrical stimulation: a volunteer study. Anesthesiology, 2003;99:429-35. [51] Chan V W . A p p l y i n g ultrasound imaging to interscalene brachial plexus block. Reg Anesth Pain M e d , 2003;28:340-3. [52] Chan V W , Perlas A , Rawson R , Odukoya O. Ultrasound-guided supraclavicular brachial plexus block. Anesth Analg, 2003;97:1514-7. [53] Schafhalter-Zoppoth I, M c C u l l o c h C E , Gray A T . Ultrasound visibility o f needles used for regional nerve block: an in vitro study. Reg Anesth Pain M e d , 2004;29:480-8.  71  Gray A T , Collins A B , Schafhalter-Zoppoth I. Sciatic nerve block in a child: a sonographic approach. Anesth Analg, 2003;97:1300-2. Wallace D H , Currie J M , Gilstrap L C , Santos R. Indirect sonographic guidance for epidural anaesthesia in obese pregnant patients. Reg Anesth, 1992;17:233-6. Marhofer P, Willschke H , Greher M , Kapral S. N e w perspectives in regional anesthesia: the use o f ultrasound - past, present, and future. Can J Anaesth, 2005;52:R1-R5. Marhofer P, Greher M , Kapral S. Ultrasound guidance in regional anaesthesia. B r J Anaesth, 2005;94:7-17. Cittadini G , Martinoli C . Ultrasound and the bone: a difficult relationship. Radiol M e d , 1995;89:12-7. Rohling R , Fung W , Lajevardi P. P U P I L : programmable ultrasound platform and interface library. Proc. o f Medical Image Computing and Computer A i d e d Interventions, 2003, L N C S 2879. Cheung S, Rohling R. Enhancement o f needle visibility in ultrasound guided percutaneous procedures. Ultrasound M e d B i o l , 2004;30:617-24. L i n D C , Nazarian L N , O ' K a n e P L , McShane J M , Parker L , Merritt C R B . Advantages o f real-time spatial compounding sonography o f the musculoskeletal system versus conventional sonography. A R J 2002;179:1629-31. Huber S, Wagner M , M e d l M , Czembirek H . Real-time spatial compounding imaging in breast ultrasound. Ultrasound M e d B i o l , 2002;28:155-63. Entrekin R R , Porter B A , Sillesen H H , W o n g A D , Cooperberg P L , F i x C H . Realtime spatial compounding: application to breast, vascular, and musculoskeletal ultrasound, Semin Ultrasound C D M R , 2001;22:50-64. Entrekin R , Jackson P, Jago JR, Porter B . Real time spatial compounding imaging in breast ultrasound: technology and early clinical experience. 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Imag., 1997;16:96-107.  72  APPENDICES Appendix A : Instrumentation Circuits The differential amplifier design for the sensors is illustrated in Figure 46. The amplifier exhibits high S N R , linear frequency response, and high input impedance. The voltage gain is adjusted by varying the resistor R. + 15 V  -15 V  Figure 46: Instrumentation amplifier circuit diagram. The circuit is designed to amply the small, differential output voltages of both the force and pressure sensors.  73  Figure 47, Figure 48 and Figure 49 illustrate the circuits for regulating specific voltages. The regulators exhibits low drift, high SNR and can be powered by a ±25V power supply unit. Adjusting the resistor R for the 10V voltage regulator fine tunes the output voltage.  LM7815 Input (~^~V pp|y)  GND  SU  0.33 nF  0.01 HF  2.3 nF  1.5 nF Tant.  Tant.  _k  Output (+15V)  1N4005  1N4005  GND  Input ("V pp|y)  v  SU  in  . v„  •  Output (-15V)  LM7915  Figure 47: ±15V voltage regulator circuit diagram. The circuit is designed to power the.differential amplifiers of both the force and pressure sensors.  Input  Output (+5V)  ("*~V pply) SU  0.01 uF  Figure 48: 5V voltage regulator circuit diagram. The circuit is designed to power both the force and displacement sensor.  74  1N4005  LM317 Input—  Output (+10V)  ADJ  (~*~V pp|y) SU  '2kO.  1.5 uF  5.9V Zener  Tant.  1 5  1N4005  .3kn  1.5 uF Tant.  M F  Elect.  5 C  K  Figure 49: 10V voltage regulator circuit diagram. The circuit is designed to power pressure sensor. The P C B layout and fully assembled circuit board are shown in Figure 50 and Figure 51, respectively. The two P C B s are identical, but the circuit configuration differs for the different sensors. The power, signal, ground and shield cables are also connected to the circuit boards using banana plugs.  75  Figure 50: Circuit layout. The layout is designed for two different circuit configurations. The red paths are for the top layer and the blue paths are for the bottom layer.  Figure 51: Instrumentation circuit boards. The two identical circuit boards each have different circuit configurations allowing for complete power and amplification o f the instrumentation device. 76  Appendix B: Sensor Calibration T w o calibration stages are required for each sensor subsystem: the sensor device and the amplifier circuit. A l l the sensors are pre-calibrated by the manufacturers and are reported to have insignificant non-linearity errors. However, the amplifiers require gain adjustment and calibration in order to amplify signal voltages o f the sensors to the appropriate levels. The gain is adjusted such that the maximum output voltage is 10V since it is the maximum allowable voltage for the Q8 control board. The amplifier is calibrated using a Wheatstone bridge configuration, as shown in Figure 52. The resistor, Rl is adjusted around the value o f Rl such that the differential voltage AV  0Xlt  is desired. A  range o f differential voltages are applied to the inputs o f each amplifier and the resulting output voltages are measured and plotted. The plots o f the output voltage against the differential input voltage and their calibration curves are shown in Figure 53, Figure 54 and Figure 55. Because the amplifier for the displacement sensor has a built-in amplifier, its calibration differs from the calibration o f the amplifiers for the force and pressure sensors. Calibration is performed by measuring (with calipers) the positions o f the magnet with respect to the transducer, and also measuring the resulting output voltages.  Figure 52: Wheatstone bridge circuit for amplifier calibration. The circuit is used to calibrate the amplifiers by creating small differential voltages in the order o f millivolts.  77  12 l  AV , in  force  (raV)  Figure 53: Calibration plot of the amplifier for the force sensor. A reference differential voltage source is applied to the input o f the amplifier, and the resulting output voltages are measured. 12 1  Figure 54: Calibration plot of the amplifier for the pressure sensor. A reference differential voltage source is applied to the input o f the amplifier, and the resulting output voltages are measured.  78  1.0 -  0.5 -  0.0  -I  ,  0  10  1  :  1  20  1  i  30  40 .  1  50  :  60  1  1  70  80  D (mm)  Figure 55: Calibration plot of the displacement sensor including built-in amplifier. The position o f the ring magnet is varied, and the resulting output voltages are measured. The R values o f the linear calibration plot o f Figure 53, Figure 54 and Figure 55 2  are  0.9996, 0.999997  and  0.99996,  respectively. A s expected, the linear calibration  curves are reliable and can be used for establishing a linear relationship between the input and output values. The amplifier for the force sensor is slightly less reliable than the amplifier for the pressure sensor since it needs to amplify smaller differential voltages which are more susceptible to noise. The linear relationship for the amplifier o f the force, pressure and displacement sensors are respectively ^out, force J o ,p  1 .V1 12 A \f  U l  - 0.3794  0Ke  /  r e S  s  u r e  =0.1436A^  ^dbpu-_=0.0383D  p r e s s u r e  -0.0586.  + 1.2212  Eq. E  q.  26 27  Eq. 28  A Fin is the input differential voltage with m V units, D is the displacement with mm units, and  F ut 0  is the output with V units. The calibrated values reported by the manufacturers  for the force and pressure sensor are respectively F = 2.195 A F a  i n > r c e  79  Eq.29  P = 0.5000 A ^  Eq.30  p r e s s u r e  F is compression force with lbs units and P is fluid pressure with psi units. The physical a  characteristics F , P and D must be a function o f V , since the output voltages are the a  oul  only values captured by the computer for analysis: After substituting E q . 26 into E q . 29, and E q . 27 into E q : 30, and performing algebraic rearrangement o f Eq. 28, the equations for the three sensors are as follows: F =1.283F  ouliforce  P = 3-483 F  out>pressure  a  D = 26.08F  + 0.487 + 0.2043  oul>displacenient  -31.86  The three equations are the basis for converting the raw voltage values captured by the computer into meaningful physical quantities for simulation and analysis o f the physical models.  80  

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