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UBC Theses and Dissertations

A study of the motor unit potential for application to the automatic analysis of clinical EMG signals Boyd, David Colin 1976

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A STUDY OF THE MOTOR UNIT POTENTIAL FOR APPLICATION TO THE AUTOMATIC ANALYSIS OF CLINICAL EMG SIGNALS by David Colin Boyd •Sc. (Hons.), The Queen's University of Belfast, 1974 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of E l e c t r i c a l Engineering We accept this thesis as conforming to . the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1976 (c) David Colin Boyd, 1976 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is for f i nanc ia l gain sha l l not be allowed without my writ ten permission. Department The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e V a n c o u v e r , C a n a d a V6T 1W5 0 ABSTRACT A computer model of the human single motor unit potential has been created for the purpose of developing methods of automated analysis in c l i n i c a l electromyography. This approach was taken in order to examine the effects of pathological changes on the electromyographic potentials. A comprehensive review of the previous methods of automatic analysis of c l i n i c a l EMG signals described in the literature has been presented and discussed, together with the relevant work on the production and detection of ele c t r i c a l activity with intramuscular electrodes. A methodology has been devised for the collection and prepro-cessing of the electromyographic signals and an . EMG data base establish-ed at U.B.C. An interactive graphics routine was developed to display the EMG waveform and allow the extraction of single motor unit potentials for further analysis. A computer model has been proposed for the generation of single motor unit potentials observed during c l i n i c a l EMG examinations of the normal biceps brachii muscle. This model was based on physiological find-ings. In the model the single fiber activity was represented by a dipole current source and the motor unit was constructed from a uniform random array of fibers. Motor unit potentials generated from this array were examined at various points both inside and outside the array and the effects of single fiber axial dispersion.,were investigated. The simu-lated motor unit potentials generated by the model have been compared with existing data from multielectrode studies in biceps brachii. The hypothesis that there is a variation in motor unit poten-t i a l shape at successive discharges was investigated and the model em-ployed for this purpose. It has been shown that for the normal motor i i unit potential, one major contributor to the shape variance i s electro-myographic j i t t e r . The predictions from the model were compared with human experimental data. These results reveal that the variance may be a useful diagnostic indicator, although further research is warranted. i i i TABLE OF CONTENTS Page ABSTRACT 1 1 TABLE OF CONTENTS - i v LIST OF ILLUSTRATIONS . . v 1 1 ACKNOWLEDGEMENTS . . x I. INTRODUCTION . 1 1.1 Overview of Electromyography 1 1.2 Generation and Detection of the EMG . . . . . . . . . 1 1.3 A Review of Previous Methods of Automatic Analysis . . 5 1.3.1 Special Purpose Analysers . . . . . . . . . . . 5 1.3.2 Measurement Analysis by Computer 13 1.4 Scope, of the Thesis • • • • 18 1.4.1 Thesis Objective 18 1.4.2 Thesis Outline . . . . . . . . . . . . . . . . 19 II TkE ACQUISITION AND PREPROCESSING OF THE EMG DATA . . . . . 21 2.1 Introduction 21 2.2 Recording and Digitization of Data . . . . . . . . . . 24 2.2.1 Analog Recording of EMG Data . 24 2.2.2 Digitization of the EMG Waveform 27 2.3 EMG Data Base . . 28 2.4 The Averaging of Single Motor Unit Potentials . . . . 28 2.4.1 The Interactive Graphics Routine 28 2.4.2 Averaged Motor Unit Potential (AMUP) 29 III A MODEL FOR THE GENERATION OF SINGLE MOTOR UNIT POTENTIALS. 34 3.1 Introduction . . . 34 iv 3.1.1 Single Fiber Action Potential Models . 34 3.1.2 Previous Single Motor Unit Models 36. 3.1.3 Description of the Model 36 3.2 Development of the Model 37 3.2.1 Single Fiber Potential Representation . . . . . 37 3.2.2 The Fiber Array . . . . . . . . . . 39 3.2.3 The Motor Unit Potential 41 3.3 The Motor Unit Potential Amplitude and Duration . . . 41 3.4 Axial Dipole Dispersion 47 3.5 Comparison with Experimental Data . . . . 53. 3.6 Discussion 56 3.6.1 Validity of the Model 56 3.6.2 Implications of the Model 58 IV AN INVESTIGATION OF THE VARIATION IN SHAPE OF THE MOTOR UNIT POTENTIAL . 6 1 4.1 Introduction . ^1 4.1.1 Motivation ^ 1 4.1.2 The J i t t e r Phenomenon 6 2. 4.2 Simulation of Electromyographic J i t t e r 65; 4.2.1 Calculation of J i t t e r for Use in the Model . . 6 6' 4.2.2 Circular Array of Fibers 70 4.2.3 Motor Unit Fiber Array 7 4 4.2.3.1 No Axial Potential Dispersion . . . . 7 4 4.2.3.2 With Axial Potential Dispersion . . . 7 4 7 8 4.3 Experimental Results From Human Subjects 4.3.1 Determination of the Number of Motor Unit Potentials . . . . . . . . . . . 78 v 4.3.2 Normal Subjects 81 4.3.3 Patients With Muscle Disease 85 4.4 Discussion . . . . . -. . 4.4.1 General Discussion 5.1 Synopsis of the Thesis ... ..... . . . . . . 5.2 Contributions of the Research . . . . . . . . 5.3 Directions for Further Research . . . . . . . 5;3.1 Expansion of the Data Base 5.3.2 Interactive Graphics Routine 5.3.3 Motor Unit Potential Model 5.3.4 Study of Motor Unit Potential Variance APPENDIX D COMPUTER LISTING OF THE MOTOR UNIT POTENTIAL SIMULATION MODEL . . . APPENDIX E COMPUTATION OF THE AVERAGED POTENTIAL, THE VARIANCE AND THE PLOTTING OF RESULTS . . . REFERENCES . . 84 84 4.4.2 Extensions of this Work ?1 V. CONCLUSIONS AND DIRECTIONS FOR FURTHER RESEARCH 9 ^ 94 95 96 96 96 97 97 APPENDIX A TERMS AND DEFINITIONS OF ELECTROMYOGRAPHY 9 ? APPENDIX B EMG RECORDING - INFORMATION SHEET 1 0 0 APPENDIX C DOCUMENTATION ON THE INTERACT GRAPHICS ROUTINE . . 103 109 113 115 v i LIST OF ILLUSTRATIONS 1.1 Diagram of the Single Motor Unit: The Anterior Horn Cell, Axon, and a l l the Muscle Fibers Innervated by the Axon • 2 1.2 Block Diagram of the Analyser Used by Fitch [26] . . . . 6 1.3 Apparatus of Dowling, Fitch and Willison (1968) [31] . . 8 1.4 Method of Lang e_t a l . to Obtain an Averaged Muscular Potential (A.M.P.) . 11 1.5 Method Used by Rathjen et a l . (1968) to Measure Duration 14 1.6 Block Diagram of the Apparatus as Described by Kopec and Hausmanowa-Petrusewicz [55] 15 2.1 (a) Typical Single Motor Unit Potentials Recorded from the Normal Human Muscle (Biceps Brachii) 22 (b) Abnormal Potentials Recorded from a Patient with Polymyositis (Biceps Brachii) 22 2.2 (a) The Equipment Used for Data Acquisition 25 (b) Diagram of a Concentric Needle Electrode 26 2.3 (a) Selection, Centering and Enlargement of a Single Motor Unit Potential 31 (b) Choosing the Portion of the Potential to be Extracted from the Waveform for Further Processing 32 (c) Averaging of a Motor Unit Potential . . 33 3.1 The Single Fiber Dipole 38 3.2 Single Fiber Action Potential Computed at Different Distances from the Dipole . . . . . . . 40 3.3 Typical Random Array Representing a Motor Unit in the Human Biceps Brachii Muscle (163 Muscle Fibers) 42 3.4 A Motor Unit Potential - Computed at (2.5, 2.5) in the Array Shown in Fig. 3.3 Scaling as in Fig. 3.2 . . . . . 43 3.5 Peak to Peak Duration Outside the Motor Unit as a Function of Distance 45 •3.6 Peak to Peak Amplitude outside the Motor Unit as a Function of Distance • 46 v i i 3.7 Diagrammatic Representation of the Motor Unit Anatomy . . 48 3.8 Effect of Dipole Scatter on the Slope of the Motor Unit Potential . 49 3.9 Ef fecit of Increasing the Dispersion of the Dipoles on the Peak to Peak Amplitude 50 3.10 Effect of Increasing the Dispersion of the Dipoles on Peak to Peak Duration . 51 3.11 Effect on the Motor Unit Potential Slope for Large Values of Axial Dipole Dispersion 52 3.12 Comparison with Experiments of Buchthal [84] "54 3.13 Comparison with Experiments of Buchthal [84] 55 4.1 The J i t t e r in a Potential Pair in the Biceps Brachii Muscle . . . . "64 4.2 Calculation of Electromyograplic J i t t e r 68 4.3 Variance in an Ensemble of Summated Potentials Computed at the Center of Circles Radius R . 71 4.4 Variance in the Motor Unit Potential Amplitude Due to Electromyographic J i t t e r . . . 75 4.5 Peak Variance Due to Electromyographic J i t t e r as a Function of Distance Outside the Motor Unit Territory . . 7 7 4.6 Variance in the Motor Unit Potential Due to Effects of (1) Electromyographic j i t t e r at each successive generation (2) Scatter of dipoles (a = 0.7 mm) . . . . . . . . . . 79 4.7 Effect of Increasing the Number of Motor Unit Potentials to Estimate Variance, on the Confidence Interval for a 95% Confidence Level. Subject T.M. 82. 4.8 As in Fig. 4.7. Subjects.B 83 4.9 As in Fig. 4.7. Subject P.L 84 4.10 Motor Unit Potential Variance in Amplitude from Normal Subject T.M 86 4.11 As in Fig. 4.10. Subject P.B 86 4.12 Motor Unit Potential Variance in Amplitude from Normal Subject P.L 87 4.13 As in Fig. 4.12 Subject P.L. 87 v i i i 4.14 Modelling of Myasthenia Gravis - The Variance Due to Increased J i t t e r 88 4.15 Variance of Motor Unit Amplitude in a Patient with Myasthenia Gravis . . . . . . . 88 4.16 Simple Generator Model Representing the Recorded Motor Unit Potential 92 / C.l Function Buttons - Layout and Assignment . 105 C.2 Variable Potentiometer Control Dials . . 105 ix ACKNOWLEDGEMENTS I would l i k e to express my s i n c e r e thanks to Dr. P. D. Lawrence f o r h i s constant encouragement, i n v a l u a b l e suggestions and enduring patience throughout the course of t h i s research. Much has been learned from h i s vast wealth of experience. Thanks are a l s o due to Dr. P. A. J . B r a t t y of the Department of Medicine, U n i v e r s i t y of B r i t i s h Columbia, f o r h i s p a r t i c i p a t i o n i n the research and many s t i m u l a t i n g d i s c u s s i o n s . I would l i k e to thank Mr. Mike Koombes f o r p r o v i d i n g the software to d i g i t i z e the EMG data and f o r h i s a s s i s t a n c e during t h i s process, and Mr. A l MacKenzie f o r transforming the crude sketches i n t o f i n e l i n e s . I wish to express a p p r e c i a t i o n to a l l my colleagues at the E l e c t r i c a l Engineering Department, p a r t i c u l a r l y Mr. James Yan, f o r c r e a t i n g an enjoyable and s t i m u l a t i n g environment. I would l i k e a l s o to thank the s e c r e t a r i e s at the E l e c t r i c a l Engineering Department, Ms. Flanagan, Ms. Louie and Mrs. Semmens, f o r t h e i r e f f i c i e n t t y p i n g of the manuscript, and Mr. Ron Mackinnon f o r proofreading. F i n a l l y , I am indebted to the Commonwealth Scholarship Committee f o r t h e i r monetary a s s i s t a n c e . x to my mother x i 1 CHAPTER I INTRODUCTION 1.1 Overview of Electromyography Electromyography is the detection and recording of ele c t r i c a l activity from a portion of a contracting muscle. It is a method of study-ing the state of a muscle from the recorded action potentials. The ear-l i e s t extensive study of the human electromyogram (EMG) was made by Piper in 1912 [1], although human action potentials had already been observed many years previously. Piper recorded potentials during voluntary con-traction using surface electrodes and a galvanometer. In 1929, Adrian and Bronk [2] introduced the concentric needle electrode which can be inserted through the skin into the muscle to obtain a more selective picture of the internal activity. The motor unit i s the functional unit of the neuromuscular system and i t consists of the anterior horn c e l l , i t s axon and a l l muscle fibers innervated by that axon [3,4];. This i s represented diagramatically in Fig. 1.1. The EMG is of proven value to determine malfunction of the motor unit since neuropathic and myopathic diseases cause physiological changes which may reflect in the electrical activity although not sine  qua non. This i s the basis of electrodiagnosis of neuromuscular diseases. For more fundamental information the reader is referred to references on general electromyography and electrodiagnosis [5,6,7,8]. Definitions of the more important terms in Electromyography used in this thesis have been included in Appendix A. 1.2 Generation and Detection of the Cl i n i c a l EMG The bioelectric phenomena observed by the electrode are;pro-2 SPINAL. CORD FIG. 1.1 DIAGRAM OF THE SINGLE MOTOR UNIT: THE ANTERIOR HORN CELL, AXON, AND ALL THE MUSCLE FIBERS INNERVATED BY THE AXON. 3 duced by a summation of electrical events within the muscle. Each active muscle fiber contributes to the production of a time-varying f i e l d . The electrode samples this potential f i e l d producing an observed action poten-t i a l . The age, temperature and physiological characteristics of the mus-cle determine the potential f i e l d generated (Buchthal et^ al.[9]). The distance of an electrode from the fibers composing the motor unit, and the size, shape, configuration and orientation of the electrode are of importance in the time course of the observed signal. Conventionally a concentric needle electrode i s used intramuscularly for routine electro-myography (Buchthal [10]). Guld e_t al. [11] have prepared a report on technical factors involved in EMG instrumentation. According to i t s geometry and location, the electrode acts as a f i l t e r on the motor unit action potential to produce the observed sig-nal (Lindstrbm [12]). With a knowledge of the f i l t e r transfer function, signal processing techniques can be employed to select physiological characteristics reflecting the state of the muscle. For example the propagation velocity of the signal along the fibers can be determined by observation of the Fourier power spectra of the electrode signal (Lind-strom [12]). Literature exists in some of these areas and can be pro-ductively employed in design considerations. Lorente de N6 [13] determined the potential changes surrounding a single nerve fiber in an i n f i n i t e , homogeneous volume conductor. Krakau [14,15] extended the analysis by applying Fourier transform techniques indicating the applicability to the radial decline of the potential f i e l d in the muscle experiments of Hakansson [16]. In his 1969 monograph, Rosenfalck [17] compared the various models for determining the external action potentials of nerve and muscle in volume conductors, including the 4, work of Clark and Plonsey [.18,19], and extended the analysis to include the effects of muscle fiber thickness and anisotropic media. R.E. George [20] investigated the summation of muscle action potentials for fibers with a Gaussian distribution of axial scatter. George showed that this gives rise to the c l i n i c a l l y observed extended duration of a motor unit action potential over a single fiber potential. Based on the expression for the external single fiber action potential derived by Rosenfalck [17], Ekstedt and Stalberg [21] have described the effects of size, shape and orientation of the leading-off surface of a concentric electrode on the observed single fiber action potential. Using frequency domain analysis, Lindstrom [12] has determined the relationship between the fiber surface power spectrum observed through a concentric and a surface electrode, and explained the occurrence of dips in the EMG frequency spectrum and the f i l t e r i n g effect of the electrode geometry. Broman and Lindstrom [22] have described the composition of the single fiber signals into a motor unit power spectrum taking into account the temporal and spatial dispersion of the single fiber action potentials, as well as velocity dispersion among fibers of a motor unit. A model for the summation of motor units in the generation of a power spectrum for intramuscular and surface electrodes has been proposed by Lindstrom and Broman [22,23]. The application of automatic signal analysis techniques to diagnosis is becoming more common in medicine and i s particularly con-venient where the basic signal sources are electrical in nature. Such techniques have been applied to the electrocardiogram and electroencepha-logram. Much of the present day diagnosis of neuromuscular diseases via the electromyogram is based on a purely subjective examination by the 5 clinician. Often i t i s d i f f i c u l t for the clinicians to distinguish be-tween different types of diseases and sometimes between the diseased and normal states. A knowledge of the disordered physiology of the disease state coupled with the transformation induced on the motor unit potentials by the factors mentioned in the preceeding paragraphs, can assist in the selection of automatic techniques of analysis to be applied to the elec-tromyogram. 1.3 A Review of Previous Methods of Automatic Analysis 1.3.1 Special Purpose Analysers Since the summated action potential recorded from a motor unit includes a potential contribution from each individual muscle fiber, then any f a l l out of these fibers such as in the myopathies, may reduce the amplitude and duration of the motor action potentials. Even at levels of voluntary activity at which i t is not possible to identify individual action potentials, the complex waveform or interference pattern may be affected. Willison [24] in 1963 described a manual method of analysing an EMG record by means of a cursor and a mechanical counting device. This apparatus was used to examine the recordings on 35 mm film which were enlarged by projection. The method involved counting each potential change greater than 100 uV, and recording separately the amplitude of each potential. He was able to demonstrate by this technique those.for a patient with muscular dystrophy, the potential changes per second and the mean amplitude of the EMG activity had greater values than that shown by a healthy subject. However, the method was tedious and an automatic electronic analyser was developed by Fitch and Willison [25], to replace the mechanical counter. This analyser was electronic and could be used in real time with the patient. Fitch [26] describes the electronic c i r c u i t in greater detail. Briefly, in Fitch's c i r c u i t Fig. 1.2, the EMG signal from an intramuscular concentric needle electrode is amplified. The output from the amplifer i s applied via an RC network to a pair of Schmitt trigger circuits which w i l l respond when a 100 yV positive or negative level appears at the recording electrode. The trigger outputs are fed to a bistable such that i t w i l l change state when a positive trigger follows EMG ACTIVITY 0"^  AMPLIFIER I +ve triggered circuit -ve triggered circuit AMPLITUDE COUNTER MONO FIG. 1.2 BLOCK DIAGRAM OF ANALYSER USED BY FITCH [26]. a negative one, or a negative trigger follows a positive one. Two AND gates are driven from the outputs of the Schmitt trigger circuits and the bistable. Hence the TURNS counter w i l l only receive a pulse when there is a change in polarity of two successive 100 yV increments of the signal. The operation of either trigger c i r c u i t also clamps the point A to zero 7 volts, thus allowing the next increment of the input signal to be ex-amined. Each operation of the clamp is counted, the total representing the sum of the 100 uV increments. Rose and Willison [27] used this electronic analyser to quan-t i f y the EMG in terms of frequency and amplitude of potential changes during voluntary effort. Standard loads of 2 kg for the biceps, triceps and t i b i a l i s anterior and 5 kg for the vastus medialis, were used since the frequency and mean amplitude increased with^voluntary effort (Willison [28], Hayward and Willison [29]). The EMG activity of 45 control subjects and 20 patients with muscular dystrophy or polymyositis was analysed. An average of 16 samples for each muscle was taken using a concentric needle electrode. The electronic analyser measured the number of potential changes and the amplitude of every potential change greater than 100 uV (referred to as TURNS COUNT and AMPLITUDE COUNT respectively) per second while the recording was being made. Rose and Willison presented evidence that the frequency of potential changes was often increased in their patients. They also showed that in the cases they examined, the disease was not sufficient-ly advanced enough that low amplitudes became more important than high counts. Since high count rates might also be shown by patients with chronic partial denervation, i t was suggested that the amplitude measure-ment may help to distinguish between such patients and those with myopathy. When a motor neuron dies collateral branches are sent out from nearby healthy axons. These additional fibers w i l l increase the amplitude as well as the duration of the summated potential (Ermino, Buchthal and Rosenfalck [30]). Thus i t seems important to have some measure of the amplitude of a potential. Later, Hayward and Willison [29] showed that the AMPLITUDE COUNT o measurement could distinguish between chronic partial denervation and myopathy. It was found that even i n milder cases of parti a l denervation, there was an increase in the mean amplitude of the EMG, They also found that the mean amplitude increased as the muscle became weaker, but that such a measurement could not differentiate anterior horn c e l l disease from peripheral neuropathy. Dowling, Fitch and Willison [31] used a d i g i t a l computer together with the analyser to make further measurements on the EMG record (Fig. 1.3). TAPE AMPLITUDE COUNT PULSES BIOKAC 500 COMPUTER t  CHART RECORDER FIG. 1.3 APPARATUS OF DOWLING, FITCH AND. WILLISON (1968) [31] The object of the computer was to accumulate histograms of the time i n -tervals between successive TURNS pulses. The computer used was the Biomac 500 (Data Laboratories Ltd.) as described by Edwards and Aspinall [32]. A TURNS pulse started the sequential addressing of an area in mem-ory at the rate of 64 addresses per millisecond. The next TURNS pulse incremented the content of the memory address reached at that time by one, 9 and restarted the address sequence. Since addressing intervals are 15.6 usee, a histogram of the interval between TURNS in sections of 15.6 usee was built up. Using such a histogram, Dowling et al-revealed that in a patient with dystrophy, there was a marked shift to lower values of TURNS count intervals compared to healthy subjects. Another form of histogram was available as indicated by the switch in Fig. 1.3. The TURNS pulse started the addressing sequence of the memory, while the AMPLITUDE pulses were used to increment and restart the addressing. This histogram provid-ed a means of differentiating between healthy persons and patients with chronic partial denervation. The work of Hirose and Sobue [33] was similar in principle to that of Willison [24]. Instead of converting the EMG waveform into pulses representing TURNS and AMPLITUDE counts, an analog/digital converter and a JEC-6 spectrum computer (Nippon-denshi) were used to store the actual sampled points as an i n i t i a l step. The points of each positive and neg-ative peak, in the sampled waveform were then selected. Then, the d i f f e r -ence between the f i r s t negative and positive peak or vice versa and each subsequent pair was calculated. If this difference was less than 100 yV the pair of peaks was ignored i.e. potential changes of less than 100 yV were ignored. A modified waveform was constructed from the significant pairs of peaks and then the number of potentials, the mean amplitude and interval were calculated. A l l recordings of potentials were carried out under maximum muscle effort. Hirose et al. later compared manual values with this computer analysis (Hirose, Uono and Sobue [34]) and report an application to patients with progressive muscular dystrophy (Hirose, Uono and Sobue [35]). The duration of the individual motor unit potential i s often a 10 good i n d i c a t o r of disease states, (Buchthai e t / a l . [ 9 ] ) but the i n d i v i d u a l motor u n i t p o t e n t i a l s are o f t e n d i f f i c u l t to d i s t i n g u i s h at high l e v e l s of c o n t r a c t i o n . Moosa and Brown [36] used a pur e l y "analog analyser to detect i n d i r e c t l y changes i n the a c t i o n p o t e n t i a l d u r a t i o n w i t h maximum streng t h of c o n t r a c t i o n i n the muscle. This analyser was used to o b t a i n an index representing the r e c i p r o c a l of the mean phase d u r a t i o n . The index was based on a s i m i l a r one, <j>, presented by Van den Bosch [37], where S i + S 2 - - - S n 1 . (1.1) * T,+T0...T Mean du r a t i o n of the phases and T n, *-S are the d u r a t i o n and the number of p o s i t i v e and negative peaks r e s p e c t i v e l y i n the nV^. d e f l e c t i o n of the waveform. Moosa and Brown avoided the problem of d i s t i n g u i s h i n g between a c t i o n p o t e n t i a l s arid s m a l l noise d e f l e c t i o n s by weighting the mean d u r a t i o n according to the ampli-tudes of the d e f l e c t i o n s . Hence, n=N I a n ^ = n ^ ^ ( 1 ' 2 ) V a T u. n n n=l where TJJ i s the symbol used f o r the index, and a n i s the amplitude of the til n d e f l e c t i o n of the waveform. I f i t i s assumed the waveform p ( t ) i s s i n u s o i d a l , they show can be represented by fl li>(t)| dt rr / Q I P O O I dt A simple analog computer c i r c u i t implementing t h i s expression was the ba s i s of the analyser and the value f o r ij> could be continuously d i s p l a y e d 11 by a chart recorder. Moosa and Brown claimed that this index was nearly independent of the strength of contraction of the muscle. The index could differentiate between normal and myopathic EMG signals. Moosa, Brown and Dubowitz [38] applied the analyser to carrier detection in Duchene type muscular dystrophy. The index was significantly higher in a proportion of the cases examined. However, they advise the estimation of serum creatine phosphokinase to supplement this EMG analysis to give an 80% rate of carrier detection. In contrast to the previously discussed methods, Lang and Vaahtoranta [39] used the principle of sampling and averaging voluntary EMG activity to create an average motor unit action potential. The elec-trode was kept at a constant site in the muscle and the sum of different motor unit potentials (MUP'S) obtained. This sum they termed the averaged muscular potential (AMP). The method is illustrated in Fig. 1.4. EMG ACTIVITY 4> TRIGGERING DEVICE COMPUTER ' TRIGGER AMPLIFIER PULSE 10 MSEC DELAY LINE A|D CONVERTER OSCILLOSCOPE FIG. 1.4 METHOD OF LANG ET AL^ TO OBTAIN AN AVERAGED MUSCULAR POTENTIAL (A.M.P.) The EMG signal was amplified and connected to a device which would trigger the computer when the rapid negative phase satisfied the amplitude condition (see Lang, Nurkkanen and Vaahtoranta [40]). The sig-nal was then fed through a 10 msec hardware delay, such as that described by Nissen-Petersen et a l . [41], to the oscilloscope and to the analog/dig-i t a l converter of the computer. Thus the 10 msec of the signal before the trigger was recorded. Single MUP's were recorded during weak muscle con-traction. Normally about 100-200 signals were summed with the computer set at 200 usee address time. Advantages of this method are that the parameters such as shape, duration and amplitude are averaged, and that further computer analysis could be employed since the signal i s in a di g i t a l form. Lang and Tuomola [42] showed very clearly that the AMP recorded from neuropathic, myopathic and normal muscles significantly diffe r . The signal/noise ratio i s improved and the baseline preceding the signal be-comes more exact. Parameters dependent on the r e l i a b i l i t y of a baseline may then be more easily defined. Another special purpose EMG analyser was described by Kunze [43] Briefly, the analyser transformed the action potential into pulses for the different measurements: potential duration, polarity of the f i r s t phase, number of phases and the amplitude integral. The pulses were then counted and x-y plots could be made for the following parameters while isometric contraction was varied: the amplitude integral versus the number of phases; potential time (the sum of the pulses in a l l valid po-tential durations within the analysis interval) versus the number of phases potential time versus amplitude. Using such plots Kunze then showed the difference in patterns of a patient with myogenic muscle disease (poly-13 myositis) and one with a neurogenic muscle disease (neural muscular atrophy), and how these patterns differed from those in the normal control group. Frequency analysis of the EMG waveform may also provide infor-mation about the state of a muscle. It has been shown by Larsson [44] using a frequency analyser of the type described by Kaiser and Petersen [45,46], and by integrating the output from the f i l t e r s , that in myopath-ies there was an increase of activity in the high frequency f i l t e r s as com-pared to normals. Larsson also pointed out that denervated muscles tended to show a decrease in the output at high frequencies. Larsson [47] pre-sents further evidence of this in a later paper and indicates that the frequency spectrum depends on the duration of the symptoms. A l l of the above methods use electronic circuits to detect spec-i a l features of the EMG waveform. Some investigators, however, use the computer directly as a tool to measure EMG characteristics as w i l l be discussed in the next section. 1.3.2 Measurement Analysis by Computer Many of the characteristics of muscle action potential described by Buchthal, Guld and Rosenfalck [48], are affected by disease (Kugelberg [49], P i n e l l i and Buchthal [50], Buchthal and P i n e l l i [51,52]). The actual measurement of these parameters proved to be laborious and time consuming. Fortunately they are suitable for computer automation. A common d i f f i -culty, however, is the automatic detection of the onset and end of the action potential. This problem was approached in several different ways by various investigators. Rathjen, Simons and Peterson [53] used a minicomputer (Digital Equipment Corp. PDP-8) to measure and print out the duration parameter. Single motor unit potentials were picked up by a bipolar coaxial electrode and amplified. An analog/digital converter then sampled the signal and a computer program examined each digitized sample to look for valid durations. A valid duration existed i f the signal had exceeded an amplitude threshold or trap level and returned to the trap for a certain number of samples. U l r T \ A B /" Kt—t, — "Vc , D V > « M 4 W V U M J \ J | ^ ^ * * J V A " **t*h— W W * " -! B \ / A i \t D U R A T I O N — — T T R A P 1. FIG. 1.5 METHOD USED BY RATHJEN ET AL (1968) TO MEASURE DURATION In any time PERIOD AB there are not enough samples within the trap to terminate sampling. This only happens during the time PERIOD CD. Thus the duration is given by T - t ^ This is indicated in Fig. 1.5. The purpose of this trap was to eliminate baseline d r i f t and low amplitude noise. Once the signal had l e f t the trap, an internal clock in the computer was started, and stopped only when the program had found a valid return. Further checks were made on the duration. The program established i f i t was greater than a minimum duration. This was to eliminate high frequency noise potentials. Also, the amplitude had to be larger than a preset value to avoid distant motor unit potentials. There was no discussion of the accuracy of the method reported. Automatic recording of histograms of the motor unit potential duration was developed by Hausmanowa-Petrusewicz et^ a l . [54] and Kopec 15 and Hausmanowa-Petrusewlcz [55,56] to study as large a number as possible of the potentials. Kopec and Hausmanowa-Petrusewicz [55] applied the Polish Averaging Computer, ANOPS (Analyser of Perodic Noise discharges) for this purpose. The amplified EMG was fed to special input circuits before entering the computer, as shown in Fig. 1.6. These input circuits EMG ACTIVITY AMPLIFIER TRANSFORMATION TO PULSES DECISION CIRCUIT >100 'uV? INPUT CIRCUITS to COMPUTER MEMORY D|A CONVERTERS OSCILLOSCOPE FIG. 1.6 BLOCK DIAGRAM OF THE APPARATUS AS DESCRIBED BY KOPEC' AND HANSMANOWA-PETRUSEWICZ [55] transformed the motor unit potentials into rectangular pulses equal in width to their duration at a 20 uV level. A decision ci r c u i t 'AND' gated only those potentials with absolute amplitudes higher than 100 uV, which were then fed in pulse form to the computer. In the computer the pulses were summed and stored in memory locations according to their duration. When the histograms were to be displayed, the content of memory was output to a digital/analog converter which was connected to the vertical and horizontal amplifiers of the computer oscilloscope. The vertical bar represented the number of motor units of that memory location and the horizontal corresponded to the duration of the measured 16 pulse in 0.8 msec intervals. A pilot study was carried out on a number of subjects including healthy ones, various cases of myopathy and cases of neurogenic muscle atrophy. Histograms of the healthy subjects showed peaks in the range 6 to 12 msec with the spectral width, estimated at the 50% level of the maximum height, of 4 to 15 msec. In the cases of myop-athy there was a definite shift to the l e f t of the histogram with peaks lying from 3 to 6 msec and the spectral width from 2 to 11 msec. On the other hand, in cases of neurogenic atrophy the histograms were shifted to the right having peaks in the range 8 to 19 msec and a spectral width of 5 to 26 msec. The above method was later extended by Kopec, Hausmanowa-Petrusewicz, Mawski and Wolynski [57], to include histograms of the num-ber of phases per unit time. Lee and White [58] used the slope to determine the beginning and end of a computer-identified motor unit potential, for measuring dur-ation and peak to peak amplitude. A number of sampled points was ex-amined by a PDP-12 computer for a voltage change exceeding a preset level. When the slope exceeded this l i m i t , the beginning of that section was marked as the onset of the potential. As most potentials have a gradually sloping t a i l , a different slope was used to find the end. A display of the potential, together with measured parameters and cursors indicating the onset and the end, was also available which allowed the operator to check the computer. Lee and white's c l i n i c a l result on one patient with polymyositis supported the work of Koped, although the method of duration computation differed. Computer analysis described previously have certain limitations. There is no computer check that identified potentials are of one single 17 motor unit, and thus artifacts and potentials due to a superposition of two different motor unit potentials, are not always rejected. Also, the part of the signal that occurs before the triggering level i s reached w i l l be lost. Bergmans [59,60] used a software delay line which would allow values of the signal to be kept ahead of the trigger. To be sure the potentials were representative of only one single motor unit, a computer program required that the waveform should occur twice before i t s para-meters were measured. The parameters of duration, amplitude, polarity of the i n i t i a l phase, number of phases and the number of peaks were then measured. The EMG activity was recorded during slight voluntary con-traction, amplified and sent to an analog/digital converter connected on-line to a PDP-12 computer. The f i r s t function of the computer was to isolate one potential out of the EMG record using an interactive display to adjust a threshold criterion. The second function was to identify, i f possible, subsequent potentials as belonging to the same motor unit and average the stored and new potentials together to improve the signal-to-noise ratio. The third function was to recognize that an isolated potential did not belong to a stored average motor unit potential and to generate a new motor unit pattern in storage for identification with subsequent isolated potentials. The f i n a l function was that of compu-tation and display. Usually 5 different motor unit potentials were ob-tained and each displayed in turn after parameter measurements were made. In this method, duration was measured between the f i r s t n consecutive points exceeding a threshold and the last m consecutive points exceeding the same threshold. The interactive display again allowed the operator to adjust these points or to verify duration had been measured correctly. Histograms of the parameters could later be generated. 18 In the EMG analysis described by Bergmans, there was close i n -teraction of not only the operator with the computer but also between the patient and the computer. In another program developed by him, the task of recognizing the different motor unit potentials was l e f t solely to the operator who rejected or accepted a potential. Thus, further intervention of the operator meant that the errors were reduced. 1.4 Scope of the Thesis 1.4.1 Thesis Objective Few of the methods of automatic analysis of the electromyogram described above, with the exception of Willison's, are c l i n i c a l l y practi-cal. Motivation does exist to develop c l i n i c a l l y practical and reliable automatic methods as an adjunct to normal c l i n i c a l assessment of neuro-muscular diseases and integrate these with existing equipment. Boyd, Bratty and Lawrence [61] have proposed a number of design features re-quired by such a system. Before a system is realized however, a basic understanding of the spread of e l e c t r i c a l activity in the tissues, elec-trode properties and the pathophysiology of the diseased state, is re-quired. None of the automatic methods discussed in section 1.3 were based on a quantitative relationships to the physiological effects-of disease on electrical activity. The approach that was taken here was to construct a model of the single motor unit as seen by an electrode in the muscle. This model was then compared to physiological data that was recorded from normal motor units in the human and also to the data of other i n -vestigators. By using this model changes in the diseased state could be predicted. To the knowledge of the author, this approach has not been taken previously. Thus the overall objective of the research described in this dissertation i s to contribute to our understanding of the human 19 motor unit potential in the normal and abnormal states in order to shape the development of a c l i n i c a l system. 1.4.2 Thesis Outline A data base has been established containing normal and patho-logical EMG activity. The method used to collect this data is the sub-ject of Chapter II. This chapter also describes the use of interactive graphics to isolate single motor unit potentials from the recorded EMG activity for averaging and further processing. Chapter III describes the development of a computer simulation model of the human motor unit in the biceps brachii muscle. This model is an attempt to understand the single motor unit potential and how the electrode affects this potential. The model i s compared with the real data and with other c l i n i c a l investigations given in the literature. It has been observed c l i n i c a l l y that the shape of the motor unit potential varied in subsequent firingsin the diseased state [62]. Chapter IV investigates this hypothesis by studying the variance in shape of the single motor unit potential at each f i r i n g . The model developed in Chapter III i s used to show the effect of ' j i t t e r ' of the single fiber potential on the variance in shape of the motor unit potential. A summary of the contributions of this research together with conclusions i s given in Chapter V. Suggestions for further work are also outlined in this chapter. A number of appendices are included for reference purposes. Appendix A contains definitions of some of the more important terms used in electromyography. Appendix B is a copy of the 'EMG RECORDING - INFOR-MATION SHEET' which was used during the analog recording of the EMG data. Documentation for the interactive graphics program has been included in Appendix C for the use of other researchers, and Appendices D and E con-t a i n the computer program l i s t i n g s f o r the s i m u l a t i o n and p l o t t i n g of s i n g l e motor u n i t p o t e n t i a l s . 21 CHAPTER II THE ACQUISITION AND PREPROCESSING OF THE EMG DATA 2.1 Introduction In this chapter the acquisition of the EMG and the subsequent preprocessing used to test the models developed in later chapters is described. Samples of EMG activity, at low level contraction, from both normal and pathological muscle were recorded in analog form and digitized for further analysis on the computer. The objective was to obtain action potentials from a single motor unit. Action potentials were recorded from the biceps brachii muscle which is the principle flexor of the elbow joint [63]. This muscle was chosen as i t was easily identified and examined. In the normal electro-myogram recorded from this muscle, the single motor unit potential can be bi- or triphasic, with monophasic potentials being less common [64]. Polyphasic potentials which contain more than four phases occur in approximately 4% of the motor units. For-a weak volitional effort, the frequency of f i r i n g of a motor unit potential i s between 5-15/sec. With increased effort, the rate of discharge increases and also add-itional motor units are recruited. The observed amplitude of the action potentials recorded intramuscularly with a concentric electrode ranges from a few microvolts to about 5 mV, with a total duration of 3-16 msec in the normal biceps brachii [9]. The duration of the positive to neg-ative deflection i s in the order of 100-200 usee. Typical EMG activity recorded from a normal biceps brachii of a male subject at a low muscle contraction level i s shown in Fig. 2.1 (a). Recordings were also made of patients with polymyositis. This i s a muscle disorder in which there is muscular weakness and i s one of 22 " FIG. 2.1 (a) TYPICAL SINGLE MOTOR UNIT POTENTIALS RECORDED FROM THE NORMAL HUMAN MUSCLE (BICEPS BRACHII) FIG. 2.1 (b) ABNORMAL POTENTIALS RECORDED FROM A PATIENT WITH POLYMYOSITIS (BICEPS BRACHII) 23 the most frequently occurring primary myopathies in adults. The motor unit potentials are polyphasic and usually of shorter duration than the normal. As electromyographic changes in. polymyositis are patchy in distribution within the muscle, the muscle must be explored to un-cover abnormal potentials before recording. The EMG activity recorded from such a diseased biceps brachii muscle is shown in Fig. 2.1 (b). Section 2.2.1 of this chapter describes the method used for analog recording of this EMG data while section 2.2.2 outlines the pro-cedure used for digitization. Single motor unit potentials may be isolated from the recorded EMG activity due to the following considerations: (1) At low levels of muscle contractions only a few motor unit potentials f i r e to maintain the contraction. (2) By slight movement of the electrode under the condition given in (1), the clinician can move to within the pick up range of one unit. (3) Often the subject while viewing the oscilloscope trace of his e l e c t r i c a l activity can isolate a motor unit potential by vary-ing the contraction level of his muscle. (4) Motor unit potentials f i r i n g within the range of the electrode can usually be distinguished by a characteristic shape. (5) Since each motor unit fires repetitively and usually out of synchronism with other motor units, a single motor unit potential can be identified. A method has been developed using interactive graphics to extract identified action potentials from the digitized EMG activity. This method is described in Section 2.4.1. 24 For f u r t h e r a n a l y s i s , i t i s r e q u i r e d to form the averaged motor u n i t p o t e n t i a l . Before averaging,the e x t r a c t e d s i n g l e motor u n i t poten-t i a l s must be a l i g n e d i n the formation of an ensemble. The procedure f o r alignment of these p o t e n t i a l s i s discussed i n S e c t i o n 2.4.2. 2.2 Recording and D i g i t i z a t i o n of the Data 2.2.1 Analog Recording of EMG Data A data base c o n s i s t i n g of the EMG a c t i v i t y recorded from norm-a l and diseased muscle has been e s t a b l i s h e d f o r use i n t h i s research. Recordings were made at the Vancouver General H o s p i t a l under the super-v i s i o n of an experienced neurologist"'". F i g . 2.2 (a) shows the equipment used during the data a c q u i s i t i o n . A DISA, 3 channel Electromyograph Type 14A30 was used to amplify and v i s u a l l y d i s p l a y the EMG a c t i v i t y . The f i l t e r s on the DISA Electromyograph were set w i t h the high pass at 20 Hz, to avoid s h i f t i n g of the b a s e l i n e due to e l e c t r o d e movement, and the low pass f i l t e r at 1 KHz thereby reducing high frequency noise com-ponents. A Hewlett-Packard 3960A FM i n s t r u m e n t a t i o n tape recorder was connected to the electromyograph and used to record the EMG a c t i v i t y on 3M TYPE 871 instrumentation tape at a speed of 15 i . p . s . The e l e c t r o d e used was the standard c o n c e n t r i c needle e l e c t r o d e used f o r intramuscular re c o r d i n g (DISA ELEKTRONIK 13K51). The diameter of the needle was 0.65 2 mm, the i n n e r conductor being 0'.07 mm . This e l e c t r o d e has been repre-sented d i a g r a m a t i c a l l y i n F i g . 2.2 ( b ) . S t a n d a r d i z a t i o n of the electromyographic examination cannot be complete as i n electroencephalographic examinations, f o r example, be-cause standard e l e c t r o d e p o s i t i o n s are not a p p l i c a b l e . Though recordings 1 Dr. P.J.A. B r a t t y , C l i n i c a l A s s o c i a t e P r o f e s s o r of Medicine (Neur-ology) , U n i v e r s i t y of B r i t i s h Columbia. F i g . 2.2 (a) THE EQUIPMENT USED FOR DATA ACQUISITION 26 CANULA F i g . 2.2 (b) DIAGRAM OF A CONCENTRIC NEEDLE ELECTRODE T h i s t y p e o f e l e c t r o d e was used f o r r e c o r d i n g t h e EMG. 27 were usually taken from the biceps brachii muscle, no attempt was made to standardize the position of the electrode in this muscle, or the place of insertion, except that the innervation zone and ends of the muscle were avoided. The EMG activity was recorded in the following manner. The subject was asked to make the weakest possible muscle contraction and by slowly changing the position of the needle electrode, a point was reached at which i t was possible to record a single.motor unit potential or at least one of considerably larger amplitude than the others. The gain of the DISA Electromyograph was altered to give a signal 0.5 volts peak to peak. Changes of the electrode position and details of the re-cording equipment settings were noted in accordance with the 'EMG RECORD-ING - INFORMATION SHEET', shown in Appendix B. 2.2.2 Digitization of the EMG Waveform The recorded EMG activity which was stored in analog form was digitized for further processing using the Data General Nova 840 system at the U.B.C. Elec t r i c a l Engineering Department. This was accomplished by f i r s t reproducing the recorded EMG activity on the tape recorder at the lower speed of 15/16 i.p.s., to reduce the effective sampling rate by a factor of 16. The signal was then low pass fi l t e r e d at 62.5 Hz with a f i l t e r gain of 20 dB iising the Krohn-Hite 3342R f i l t e r s and subsequently digitized. The digitized samples were then stored on 9-track IBM compatible magnetic tapes by using the Nova 840 computer sys^ tern. The analog waveform was sampled at a frequency of 512 Hz (giving a factor of >8 improvement over the Nyquist sampling rate), and conver-ted to a 12 bit binary number. Although the resolution was 12 bits, reach sample was stored on the magnetic tape as two 8: b i t bytes, right adjusted 28 with the other 4 bits being a copy of the sign b i t (2's complement format). This simplified the programs described in later chapters. An end—of—file mark on the magnetic tape was established to indicate a change of subject, or a change of the electrode position in the same subject. This was in accordance with the 'EMG RECORDING - INFORMATION SHEET' (see Appendix B). 2.3 EMG Data Base Sample EMG activity was obtained from the biceps brachii muscle of three normal male subjects and two female subjects. Several different motor unit potentials were selected for recording from each subject. Re-cordings of EMG were also made from the same muscle of one male and one female with previously established diagnoses of polymyositis. Only ab-normal EMG was recorded from these two patients. To test predictions made in Chapter IV, EMG was recorded from a patient with Myasthenia Gravis, a neuromuscular transmission disease. Examples of some of the recorded activity are shown in Fig. 2.1 (a) and Fig. 2.1 (b). 2.4 The Averaging of Single Motor Unit Potentials 2.4.1 The Interactive Graphics Routine To extract single motor unit potentials from the time series EMG waveform an interactive graphics routine known as INTERACT was de-veloped for use at the Adage Graphics Terminal, U.B.C. Computing Center. Documentation for the use of this program is given in Appendix C. This method was adopted for several reasons: (1) Artifacts, such as distant motor unit potentials, the superposition of two motor unit potentials or an unsteady baseline due to electrode movement, could be eliminated by visual assessment. 29 (2) By storing one motor unit potential on the screen, and by superimposing another potential on i t , a decision could be made on the basis of shape i f the second potential was from the same motor unit. (3) The portion of the motor unit potential to be analysed could be chosen visually and other potentials matched to have the same time period. The EMG waveform was displayed on the screen, one record at a time (4096 bytes or 2048 sample points), being read directly from the digital magnetic tape. A single motor unit potential was then selected, centered on the screen and enlarged. The result of this procedure i s shown in Fig. 2.3 (a). The section of the potential to be analysed was visually chosen by means of hairline cursors (Fig. 2.3 (b)), and the potential extracted and stored on magnetic disk for further processing. The selected potential was also 'stored' on the screen and other action potentials from the same motor unit matched to i t . An ensemble of single motor unit potentials was formed in this manner. 2.4.2 Averaged Motor Unit Potential (AMUP) As stated previously, single motor unit potentials were align-ed visually using the interactive graphics routine (Appendix C). To reduce alignment error, the mean square difference between the two poten-t i a l s was minimized. This was achieved by the following method. A window of N-10 sample points, where N i s the total number of sample points of the action potential was considered, such that up to 5 sample points on each side of this window could be moved into i t , or out of i t . The coefficients were then computed: 30 k = 0, 1 ... 5 sample points, and B L 0 O = f ;!i <-i+k " y ± ) 2 (2.2) i=l k =0, 1 ... 5 sample points where N is the number of sample points, y ( l , ... N) i s the potential to be aligned, and x ( l , ... N) is the potential to which y is aligned. The MINIMUM (RL(k), RR(k)) k = 0, 1 ... 5 was chosen and the potential y moved k sample points in the direction of the minimum coefficient. It was found that the visual method of align-ment satisfied the mean square difference criterion within 1 or 2 sample points. Finally an averaged motor unit potential was computed from the ensemble of aligned potentials. Fig. 2.3 (c) summarizes the procedure for obtaining the averag-ed motor unit potential from the digitized EMG waveform stored on mag-netic tape. 31 s^§»» FlG. 2.3 (a) SELECTION, CENTERING AND ENLARGEMENT OF A SINGLE MOTOR UNIT POTENTIAL. A s i n g l e motor u n i t p o t e n t i a l has been s e l e c t e d from the EMG waveform and enlarged on the screen. The peak of the p o t e n t i a l i s centered on the screen by means of the x h a i r l i n e cursor (the v e r t i c a l l i n e ) . SI F I T . 2.3 (b) CHOSING THE PORTION OF THE POTENTIAL TO BE EXTRACTED FROM THE WAVEFORM FOR FURTHER PROCESSING The x ha . r l i n e c u r s o r ( t h e v e r t i c a l l i n e ) i s used to s e l e c t the b e g i n n i n g and end o f the a c t i o n p o t e n t i a l . In t h i s f i g u r e , the b e g i n n i n g o f the p o t e n t i a l has been chosen and marked by a p u l s e . MAGNETIC TAPE GRAPHICS COMPUTER COMPUTER PROGRAM. COMPUTER PROGRAM VISUAL ALIGNMENT OF MOTOR ACT/ON POTENTIALS AND EX TRACTION HUMAN INTERACTION ALIGNMENT BY MINIMIZATION OF MEAN SQUARE DIFFERENCE AVERAGING FIG. 2.3 (c) AVERAGING OF A MOTOR UNIT POTENTIAL 34 CHAPTER III A MODEL FOR THE GENERATION OF SINGLE MOTOR UNIT POTENTIALS 3.1 Lntroduction Electromyography has achieved widespread application as an aid to the diagnosis of neuromuscular diseases. In many of the standard methods of c l i n i c a l EMG examinations, i t i s the shape of the action po-tential that i s analysed. For this purpose the study i s carried out with the EMG signal recorded at low contraction levels of the muscle, usually such that only one single motor unit potential i s distinguishable. In order to give a better understanding of the form of the action potential that i s recorded from a motor unit, a simulation model can be developed. Such a model may be applied to study how disease mechanisms affect the recorded motor unit potential. A motor unit action potential i s the result of a summation of ele c t r i c a l activity within the muscle. Each active fiber belonging to the motor unit contributes to the production of a time varying potential f i e l d . The time course of the single fiber potential thus determines the overall motor unit potential. Many studies, both experimental and theoretical of the single fiber action potential of the nerve and muscle have been presented in the literature. 3.1.1 Single Fiber Action Potential Models Lorente de No [13] showed mathematically that the potential at any point in an i n f i n i t e volume conductor surrounding a nerve fiber can be related to the membrane current density distribution. He showed that the form of thevolume conducted action potential was triphasic i n the nerve. He also described how the membrane current density can be determined by experimental measurement of the second derivative of the 35 surface a c t i o n p o t e n t i a l w i t h respect to a x i a l distance along the e x c i s e d nerve i n a i r . Plonsey [65] i n 1964, f u r t h e r extended the formula of Lorente de N6, and derived equations dependent upon i n s i t u measurements: the membrane current d e n s i t y and the i n s i t u surface p o t e n t i a l . In the f o l l o w i n g y e a r , u s i n g the concept that the p o t e n t i a l i n a volume conduct-or can be expressed i n terms of the s o l i d angle subtended at any p o i n t i n the f i e l d by each a c t i v e area element of the membrane, Plonsey [66] ex-tended the a n a l y s i s to the case of unequal i n t e r n a l and e x t e r n a l conduc-t i v i t i e s . C l a r k and Plonsey [18] gave a mathematical e v a l u a t i o n of the core conductor model of a nerve f i b e r put forward by Hermann i n 1879 [67]. They concluded that the core conductor model i s a good approximation f o r the i n t e r n a l but not the e x t e r n a l parameters. R e s t r i c t i n g the a n a l y s i s to only the i n t e r n a l parameters of the core conductor model, C l a r k and Plonsey [19] showed that i t p r e d i c t e d the r e l a t i o n s h i p between the mem-brane current and the second d e r i v a t i v e of the transmembrane p o t e n t i a l . This r e l a t i o n s h i p had been experimentally shown by Tasaki [68]. In the study of muscle f i b e r s , H&kansson [16] examined e x p e r i -mentally the volume conducted a c t i o n p o t e n t i a l of an i s o l a t e d f r o g mus-c l e f i b e r . He demonstrated that the i n t r a c e l l u l a r a c t i o n p o t e n t i a l had a monophasic time course and that the e x t r a c e l l u l a r a c t i o n p o t e n t i a l was d i p h a s i c . He pointed out that the t h i r d p o s i t i v e phase which was present i n the volume conducted p o t e n t i a l of the nerve d i d not appear f o r the muscle because, he e x p l a i n e d , of the slower course of r e p o l a r i z a t i o n . Rosenfalck [17] mathematically accounted f o r the e x t r a c e l l u l a r a c t i o n p o t e n t i a l recorded by H&kansson i n terms of the i n t r a c e l l u l a r p o t e n t i a l , and he f u r t h e r compared h i s f i n d i n g s w i t h the core conductor model and the theory of Lorente de No. He a l s o i n d i c a t e d that the d i p o l e concept 36 presented by other investigators [69,70,71] can be used to approximate the extracellular action potential of the muscle fiber. More recently, Dimitrova [72] proposed a model of the single muscle fiber taking into account fi n i t e length, and the presence of two depolarized zones which spread in opposite directions when a nerve impulse arrives at the motor end plates [73,74]. 3.1.2 Previous Single Motor Unit Models Relatively few models of the single motor unit potential in muscle, have been described in the literature. Lindstrom [12] proposed a power spectrum model ofthe single fiber and in a later paper, Broman and Lindstrom [22] extended the expressions derived for the single muscle fiber to a mathematical model for the Fourier transform and power spec-trum of a motor unit action potential. The influence of dispersion of the individual fiber signals, the spatial arrangement of those fibers and the action potential velocity, on the power spectrum of the motor unit signal, was studied. R.E. George [20] investigated the simulation of single muscle fibers using a dipole model in the time domain. He con-sidered the summation of the single fiber potentials at a point situated at the center of a cylindrical dipole array. He also explored how small amounts of scatter in the axial position affect the spreading of the potential peaks. 3.1.3 Description of the Model In this chapter, a model for the generation of the action po-tential from the single motor unit i s proposed. This model incorporates known physiological parameters such as the spatial arrangement of the fibers,the velocity of the fiber action potential and the axial scatter of the single fiber potentials. A dipole model for the single fiber 37 potential i s used as an approximation to the action potential. The form of the motor unit potential (MUP) is studied at points inside and outside the motor unit territory. The effect on the amplitude and duration of the MUP viewed from outside the motor unit, is discussed. In addition, an approximation to the multielectrode as described by Buchthal [75] is used to compare his experimental data with the results obtained from the motor unit model. 3.2 The Development of the Model 3.2.1 Single Fiber Potential Representation In his studies on normal human single muscle fibers in sit u , Ekstedt [76] showed that both during voluntary and chemical activation the action potential shape recorded was_ a clean and smooth blphasic, spike. He also pointed out that for an electrode kept in a constant position relative to the fiber, each consecutive single fiber action potential had an identical shape. The dipole model was thus chosen as a f i r s t approximation to simulate the extracellular action potential of the human muscle fiber. A dipole generator may be considered as consis-ting of a source of current I and a sink of current I at a distance 2b apart as shown in Fig. 3.1. A current source I would produce a spherically symmetric poten-t i a l f i e l d <}> given by where r i s the distance from the source and v i s the conductivity of the medium surrounding the fiber. Thus the potential produced at a point (x,y) (Fig. 3.1) from a dipole with source at (0,-b) and sink at (0,b) i s 38 FIG. 3.1 THE SINGLE FIBER DIPOLE 39 <!>(x,y) <f>(x,y) I 1 1 •1 (3.1) 4TTV (x + b ) 2 + y' 2 / (x - b ) 2 + y 2 Since the motor unit structure of the biceps brachii muscle has been de-scribed in the literature, this muscle was chosen as the basis for the model. In the biceps brachii muscle, the mean propagation velocity for motor unit potentials was given by Buchthal [77] to be 4.1 m/sec (at 36.5°C) and thus the single fiber potential can be assumed to have the same velocity. The peak to peak duration close to the fiber is depend-ent upon the length of the dipole. The separation of the source and the sink of the dipole was chosen to be 0.5 mm (i.e. b - 0.25 mm). At the d3r propagation velocity of 4.1 m/sec the minimum peak to peak duration was therefore. 121 ysec. This result l i e s within the range as observed by Ekstedt [75] (see also Rosenfalck [17]). Using this dipole model, ex-amples of the action potential computed at different distances from the fiber are shown in Fig. 3.2. 3.2.2 The Fiber Array Buchthal et a l . [78] reported that the territory of one motor unit in the normal human brachial biceps muscle i s nearly circular with a mean diameter of 5 mm. It has been estimated that a motor unit in this muscle contains an average 163 fibers [73]. The spatial arrangement of the fibers in a motor unit has also been explored. In the histolog-i c a l studies of glycogen depleted rat fibers, Brandstater and Lambert [79] showed that the fibers are uniformly scattered throughout the motor unit area. More recently, Stalberg et a l . [80] report that the fibers a a. - o *" - . a ( U n -ci >— —I a. a • '" —I 1" i-a — i ; — i 0.0 4.0 B.O DISl (MILLIMETERS) 16.0 24.0 1 1 i — 1 — 0-0 4.0 8.0 12.0 16.0 DIST(MILLIMETERS) 20.0 24.1 0.1 mm FROM THE DIPOLE 0.2 mm FROM THE DIPOLE U i a ' O 3 o —I a. 1 1 1 — — i 1 1 o.o 4.o e.o i2.o is.a zo.o 24.0 DIST(MILLIMETERS) 1 , , — , — 0-0 4.0 6.0 12.0 16.0 DIST(MILLIMETERS) 20.0 24.1 0.3 mm FROM THE DIPOLE 0.4 mm FROM THE DIPOLE FIG. 3.2 SINGLE FIBER ACTION POTENTIAL COMPUTED AT DIFFERENT DISTANCES FROM THE DIPOLE I ORDINATE: POTENTIAL AMPLITUDE IN UNITS OF 4TTV ABSCISSA: DISTANCE'ALONG AXIS OF THE DIPOLE IN MILLIMETERS (DISTANCE TO TIME RELATED BY CONDUCTION VELOCITY OF 4.1 m/s) 41 in the human bicep brachii have a similar scatter with no tendency, for grouping. To simulate this spatial scatter of the fibers in the motor unit, an array of 163 fibers was computer generated to l i e with a uniform random distribution within a circle of 5 mm diameter. Fig. 3.3 shows a representative array. Each muscle fiber is represented by a circle of diameter 50 ym, which is the average fiber diameter in the biceps brachii [81]. It was observed from this random array that the percentage of adjacent fibers was similar to the experimental findings of Brandstater and Lambert. 3.2.3 The Motor Unit Potential Assuming that the fiber array l i e s within an extensive homo-genous volume conductor, then Helmholtz' Principle [82] that the voltage at a point caused by more than one source of electromotive force (gpff) -is given by the algebraic sum of the voltages caused by each emf acting alone, can be applied. A FORTRAN computer program to run on the IBM .370/ 168 has been written which can input the coordinates of a point electrode placed inside or outside the fiber array and sum the potential contrib-uted by each single muscle fiber to produce the motor unit potential at that point. An example of a.MUP computed at the center of the array of Fig. 3.3 (at (2.5, 2.5)) i s shown in Fig. 3.4. It i s observed that not only the amplitude of this potential has increased over the single fiber as anticipated, but also the total duration. 3.3 The Motor Unit Potential Amplitude and Duration Motor unit potentials for a set of points at increasing distance from the array center were generated for 15 individual random muscle fiber arrays. The maximum, minimum and mean of the peak to peak amplitude and peak to peak duration at each point were then calculated and plotted as 42 o in" ft a O >— or O o or or o 0 0 a o o ft o • 0 • a 0 0 ft ft c 0 0 0 0 0 . ft o 0 ft 0 ft or o I— o • ft 0 ft ft 0 * » ft ft ft 0 0 0 ~i 1 1 r— l.O 2.0 3.0 4.0 MOTOR UNIT TERRITORYIMMJ o.o 5.0 FIG. 3.3 TYPICAL RANDOM ARRAY REPRESENTING A MOTOR UNIT IN THE HUMAN BICEPS BRACHII MUSCLE (163 MUSCLE FIBERS) FIG. 3.4 A MOTOR UNIT POTENTIAL - COMPUTED AT (2.5,2.5) IN THE ARRAY SHOWN IN FIG. 3.3. SCALING AS LN FIG. 3.2. 44 a function of distance (Fig. 3.5 and Fig. 3.6). Due to the great vari-a b i l i t y inside the motor unit caused by the close proximity of the fibers, only points outside the motor unit territory are shown.in these figures. The relationship between the mean single motor unit potential peak to peak duration and the single fiber peak to peak duration i s shown in Fig. 3.5. Consider one single fiber placed at the center of the array. By differentiating equation (3.1) with respect to x and setting: i i . o dx i t can be shown (George [20]) that when x >> b, the position of the peaks of the single fiber potential i s approximated by: x = ± (3.2) >/2 where y i s the distance from the dipole and x lie s on the axis of the dipole. The peak to peak duration of the potential (2y/v/2'V) has. been plotted as a function of distance outside the motor unit territory in Fig. 3.5. Near the edge of the motor unit territory, the duration of the motor unit potential is decreased from the single fiber potential due to the influence of nearby fibers. A comparison between the peak to peak amplitude of a single fiber at the center of the array and the mean single motor unit peak to peak amplitude pan also be made (Fig. 3.6). By substitution of equation (3.2) into equation (3.1), and multiplying the result by 2 x 163, the peak to peak amplitude as a function of distance extraterritorially from the motor unit can be calculated. It can be seen that peak to peak amp-litude i s increased from the fiber array near the edge of the motor unit due to greater influence of fibers at the boundary. 45 FIG. 3.5 PEAK TO PEAK DURATION OUTSIDE THE MOTOR UNIT AS A FUNCTION OF DISTANCE SINGLE FIBER POTENTIAL . MOTOR UNIT POTENTIAL 46 FIG. 3.6 PEAK TO PEAK AMPLITUDE OUTSIDE THE MOTOR UNIT AS A FUNCTION OF DISTANCE. (AMPLITUDE IN ARBITRARY UNITS) , SINGLE FIBER POTENTIAL MOTOR UNIT POTENTIAL 47 3.4 Axial Dipole Dispersion At any instant of time, the activity centers of a l l the fibers in a single motor unit do not l i e in the same plane normal to the direc-tion of propagation. This i s due to differences in conduction time along branching motor nerve fibers, differences in the axial position of the motor end plates they innervate [74] and f i n a l l y , differences in conduc-tion velocity of the muscle fibers within the motor unit. The result of these three factors i s a temporal dispersion of arrival times of the fiber dipoles at the plane of electrode. This i s indicated in Fig. 3.7. To study the effects of dispersion on the motor unit potential, a Gaussian distribution of the fiber dipole locations i s assumed. Fig. 3.8 shows the motor unit potentials calculated at distances from the cen-ter of the fiber array (2.5, 2.5 mm), and compares the application of a normal distribution of dipole positions (standard deviation of 0.7 mm) with no dipole scattering. It i s to be noted, that the sampling electrode is assumed to be placed outside the zone of innervation. The effect of the dispersion i s to elongate the potential and decrease i t s amplitude [20]. A further outcome of this distribution i s to introduce irregulari-ties in the form of spikes and notches within the motor unit. Outside the motor unit, however, the potentials become smooth and diphasic. Fig. 3.9 shows the peak to peak amplitude as a function of distance out-side the motor unit territory for different values of standard deviation. The effect of axial scatter of the fiber dipoles on the peak to peak duration of the motor unit potential i s shown in Fig. 3.10. In-creasing the standard deviation of the fiber dipole distribution, results in irregularities in the motor unit potential and eventual spl i t t i n g of the potential. This i s shown in Fig. 3.11. 48 MOTOR NERVE MOTOR UNI POTENTIAL MOTOR END-PLATES SAMPLING EL ECTRODE REGION OF 'INNERVATION' MUSCL E FIBERS (SPAT/ALLY DISPERSED) FIG. 3.7 DIAGRAMMATIC REPRESENTATION OF THE MOTOR UNIT ANATOMY CONTRIBUTING TO THE DISPERSION OF THE SINGLE FIBER POTENTIALS 49 (2.5,2.5) (3.0,2:5) (3.5, 2.5) (4.0, 2.5) (4.5, 2.5) (5.0,2.5) (5.5,2.5) (6.0,2.5) (7.0,25) (8.0, 2.5) (9.0,2.5) (a) 20 0). 10.0 r C 3 •s.ol* -20.0V -35.0 0.0 0-4 0-8(mm) (b) FIG. 3.8 EFFECT OF DIPOLE SCATTER ON THE SHAPE OF THE MOTOR UNIT POTENTIAL (a) NO SCATTER (b) GAUSSIAN SCATTER WITH STANDARD DEVIATION = 0.7 mm. CO-ORDINATES REFER TO THE SAMPLING POSITION WITH RESPECT TO THE FIBER ARRAY. 50 FIG. 3.9 EFFECT OF INCREASING THE DISPERSION OF DIPOLES ON PEAK TO PEAK AMPLITUDE ' ' •(AMPLITUDE IN ARBITRARY UNITS) " • o Cb 10 O •Q: >^ Q UJ o 2 2.50 2.25 2.0 175 < 1.50 1.25 1-0 0.75 0.5 0.25 51-2.5 3.5 4.5 5.5 6>5 7.5 DISTANCE FROM ARRAY CENTER (mm) ~ FIG. 3.10 EFFECT OF INCREASING THE DISPERSION OF THE DIPOLES ON PEAK TO PEAK DURATION 52 03 GAUSSIAN DISPERSION OF THE DIPOLES WITH STANDARD DEVIATION = 2.0.mm W-j , 1 1 1 1 1 0.0 4.0 8.0 12.0 16.0 20.0 24.0 DIST(MILLIMETERS) GAUSSIAN DISPERSION OF THE DIPOLES WITH STANDARD DEVIATION = 5.0 mm FIG. 3.11 EFFECTS ON THE MOTOR UNIT POTENTIAL. SHAPE FOR LARGE VALUES OF AXIAL DIPOLE DISPERSION ORDINATE: AMPLITUDE IN ARBITRARY UNITS. ABSCISSA: DISTANCE IN MILLIMETERS (CONDUCTION VELOCITY=4.1 m/s MOTOR UNIT POTENTIALS COMPUTED AT CENTER OF MUSCLE FIBER ARRAY (2.5,2.5) 53 3.5 Comparison With Experimental Data Buchthal has explored the territory of the motor unit in the biceps brachii by means of a multielectrode [83,75]. He describes this electrode [75] as having twelve 1.5 mm long leads, each placed 0.5 mm apart over a length of 25 mm. The electrode was inserted at right angles to the longitudinal axis of the muscle fibers and the peak to peak amp-litude through the motor unit area was plotted against distance. His results [84, Fig. 3] outside the motor unit territory are compared with those obtained from the model for several dispersions of the motor end-plates. These plots are shown in Fig. 3.12. Each graph has been norm-alized to the peak to peak amplitude at 7.5 mm from the array center. If i t i s assumed that the voltage led off from any electrode surface is equal to the average voltage in the volume conductor over the recording area, then the multielectrode may be better simulated by taking potential values at points and averaging the computations over the area of the electrode. Such a technique has been employed by Ekstedt and Stilberg [21] and was originally proposed by Hakansson [85]. Using the dimensions given for the multielectrode, an average of 15 points was taken for each recording surface and the peak to peak amplitude was plotted against distance through the motor unit territory and compared with the findings of Buchthal in Fig. 3.13. The plots have been normalized to the center of the motor unit territory where the motor unit potential had the larg-est amplitude. 54 FIG. 3.12 COMPARISON WITH EXPERIMENTS OF BUCHTHAL [84]*-- - - - EXPERIMENTAL DATA — POTENTIAL AT A POINT (PLOTS ARE NORMALIZED TO PEAK TO PEAK AMPLITUDE AT 7.5 mm FROM ARRAY CENTER.) 5.5: FIG. 3.13 COMPARISON WITH EXPERIMENTS OF.BUCHTHAL [84] EXPERIMENTAL DATA — ! SIMULATION OF THE MULTIELECTRODE (PLOTS ARE NORMALIZED TO THE MAXIMUM PEAK TO PEAK AMPLITUDE AT THE CENTER OF THE ARRAY) 56 3.6 Discussion 3.6.1 Validity of the Model The biphasic form of the single fiber action potential i s rep-resented by a longitudinally orientated dipole, .travelling along i t s axis. Thus, at any time,.one part of the muscle fiber i s considered as a source of current giving rise to an emf, while another part is acting as a sink. The action potential i s a transient disturbance of the resting state such that the sources and sink- must be equal. In this simple represen-tation, the f i n i t e diameter of the muscle fiber i s not considered. Other considerations which have not been incorporated into the model are the effects of inhomogeneity, anisotropy, the effects of other active fibers in the vi c i n i t y and the effects of the fiber potentials propagat-ing in the other direction from the innervation points. Since the form of the fiber potential is of similar shape as recorded by Ekstedt [76], the author considers these effects to be second order. The territory of the motor unit in the biceps brachii has been estimated to be circular with an average diameter of 5 mm. Stalberg et al . [80] using single fiber electromyography, have recently reported that the muscle fibers of one motor unit are scattered over a distance of less than 8 mm in the biceps brachii. The fiber array used in this model is based on the mean value given for the motor unit territory, although variations from 2-14 mm have been reported [86]. Histological mapping of the motor unit in man has not been made. The number of muscle fibers within a motor unit i s thus based on an e s t i -mate. Buchthal and Madsen [87] in 1950, f i r s t suggested that there was an average of 1000 muscle fibers in a motor unit of the biceps brachii muscle. They based this on an estimate of the total number of muscle 57 fibers in man and the total number of myelinated nerve fibers, giving an average of 700 fibers per motor unit in the human body. They icon elude that, " i t seems therefore, reasonable in a large muscle like the brachial biceps to reckon with an average of 1000 fibers per motor unit". The number of 163 fibers chosen for the model is based on the histological examinations of Christensen [73] and is calculated from counting the total number of neurofibrils and the total number of muscle fibers of the biceps brachii muscle. Using the investigations of Feinstein et a l . [88], 60 per cent of these neurofibrils are considered as motor nerves and hence from the total number of muscle fibers, the number of fibers per motor unit can be found. There is no correction however, for the small motor nerve fibers supplying the intrafusal muscle fibers of the muscle spindles [89] and for the fact that multiple innervation may occur [74]. It should be further pointed out that no indication of the varia b i l i t y between different subjects i s given. It i s also unlikely that every motor unit in the biceps brachii has the same number of fibers. The velocity of the action potential was chosen as 4.1 m/sec, which i s based on the results of the experiments by Buchthal et a l . [81] on e l e c t r i c a l l y evoked action potentials. Using this value, the sum-mated motor unit potentials calculated from the fiber array were found to be within the total duration range reported by Buchthal [10]. This range is from 2-20 msec total duration in the normal motor unit potential recorded in the biceps brachii muscle. Short durations are found near and within the motor unit and long durations further away. In comparing the peak to peak amplitude as a function of dis-tance through the motor unit territory with experimental findings, a similarity was observed for both the potential at a point and with the 58 simulation of the multielectrode.' Correction for the effect on the volume conducted f i e l d of introducing an electrode of relatively large dimensions, such as the multielectrode has not been considered in the simulation. 3.6.2 Implications of the Model The motor unit potential calculated from the uniform randomly distributed muscle fiber array has a diphasic form (Fig. 3.3) and cor-responds to normal findings in c l i n i c a l electromyography. The summation of the contribution from the individual muscle fibers shows clearly and explains -the finding in electromyography that the total duration of the motor unit potential is longer than.the fiber action potential duration. The effect of volume conduction on this summation has been demonstrated by plotting the peak to peak duration and amplitude as a function of distance. The results show that the duration increases with distance while amplitude decreases. Bauwens [90] described an experiment in which ten distinct diphasic potentials of 1 msec total duration were generated and summated electronically. As the potentials were merged together, they formed a diphasic potential of greater amplitude and duration. He sug-gests however, that the blending of these potentials cannot account for a duration of more than 3 milliseconds, and the explanation for longer durations is related to the e l e c t r i c a l characteristics of the tissue and also the position of the electrode. The model described here accounts for total durations larger than 3 milliseconds, because potentials from the dipoles at'adistance from the computation point contribute to the low amplitude i n i t i a l and f i n a l phases of the motor unit potential. The position of the electrode outside the motor unit territory increases duration confirming Bauwen's prediction. 59 A Gaussian scatter of the dipoles along the fiber axis was applied to simulate the differences of the arrival at the electrode of the single fiber action potentials. This accounts for the combined effects of the motor end-plate dispersion, any conduction velocity differences of the muscle fibers and differences in the conduction time along the terminal nerve endings from the motor nerve to the end-plate.1 The results from the model have shown that the duration of the motor unit potential increased with increasing dispersion and :that the amplitude decreased. In the biceps brachii there is a three-fold variation in muscle fiber diameter, and the investigations of Hakannson [85] on an isolated frog muscle fiber in Ringer's solution have shown that the conduction velocity was a linear function of the fiber circumference. Despite these facts, the conduction of the human brachial biceps only varies between 4-5.5 meters/sec. This small variation may be accounted for by the i n -fluence of other muscle fibers in situ. Buchthal et a l . [77] did not consider this difference in propagation velocities of the muscle fibers important in the exploration of the dispersion in arrival times at the electrode of the single fiber potentials. They also said that the prop-agation times in the terminal nerve did not contribute to the action potential duration. Under these assumptions, the nerve impulse would arrive almost synchronously at a l l the end-plates in a motor unit. This opinion has been shared by other investigators [91,6]. Buchthal et a l . [77], who recorded the action potentials within the innervation zone found there was an almost simultaneous i n i t i a l deflection to within 0.5 msec for a distance of up to 40 mm, when recording from the same motor unit. Thus, they concluded this distance i s the extent of the end-plates for a motor unit. If the basic assumptions of these investigators are 60 correct, then on the basis of the model described here the extent of the motor end-plates cannot be greater than 10 mm otherwise the motor unit potential w i l l be severely s p l i t (Fig. 3.11), such that i t does not com-pare with c l i n i c a l findings. This smaller predicted value for the extent of end-plates in one motor unit compares with histological findings in infants [74]. Increasing the number of dipoles within the array to 1000 results in an action potential of the same form, and therefore predicts a similar value. 61 CHAPTER IV AN INVESTIGATION OF THE VARIATION IN SHAPE OF THE MOTOR UNIT POTENTIAL 4.1 'Introduction 4.1.1 Motivation Cl i n i c a l observations of EMG data have indicated that in suc-cesive firings of the single motor unit potential, there is a variation in i t s shape [76]. It has also been observed that, in certain diseased states of the muscle, this v a r i a b i l i t y of the motor unit potential i n -creased [59-P169,62]. To the knowledge of the author, there has been no investigation of this variation in shape or of the factors that may contribute to i t . One l i k e l y factor that may vary the shape of the motor unit potential at each discharge, is electromyographic j i t t e r . This electro-myographic j i t t e r i s the variability in the time interval between two action potentials, from two muscle fibers of the same motor unit, at consecutive discharges [92]. Thus any small variation about.a mean time interval between the single fiber potential firingswould give rise to summated motor unit potentials each of a slightly different shape. At present, the study of the j i t t e r phenomena is achieved by means of a special electrode (single fiber electrode) which can record single muscle fiber potentials. In standard electromyographic procedures however, a concentric needle electrode is used, which samples the summated activity from many muscle fibers. An outcome of an investigation of the variation in the shape of the motor unit potential, i f j i t t e r can be attributed to i t s cause, is that i t may be possible to examine the effects of j i t t e r without the use of the single fiber electrode. Recently, electromyo-62 graphic j i t t e r has proved to be of use in the diagnosis of disease, par-ticularly in disorders of neuromuscular transmission, such as myasthenia gravis. If the j i t t e r changes in the diseased state, this effect may become evident in the motor unit potential v a r i a b i l i t y . In different types of diseases, there may be other physiological mechanisms that may also change the shape of motor unit potential on suc-cessive discharges. Investigation of the pathological processes is neces-sary before the shape of the potential in the diseased state can be ful l y understood. If the vari a b i l i t y in motor unit potential shape can be proven to be an indicator of abnormality, this would become a useful add-iti o n to an automatic analysing system to aid the clinician in his diag-nosis. With the above motivations, and the tools developed in the pre-ceeding chapters, the variation in the shape of the motor unit potential on consecutive firings, was investigated. 4.1.2 The J i t t e r Phenomenon In 1964, Ekstedt [76] observed that when he recorded the action potentials from two muscle fibers from the same motor unit there was a l -ways a vari a b i l i t y in the time intervals between the two potentials. This var i a b i l i t y he termed " j i t t e r " . His recordings were performed with a special type of multielectrode [93], with up to 14 leading-off surfaces 2 of 25 ym >adjacent electrodes being placed 60 ym apart. These dimensions are of the same order as the muscle fiber diameter (40-80 ym) . When the multielectrode is inserted into the muscle i t i s possible to have two muscle fibers from the same motor unit so close that their potentials could be picked up with one electrode, or i f the fibers were more sep-arated, from the leading off surfaces closest to the fibers. If the 63 sweep of an oscilloscope was triggered by the f i r s t potential, then the second potential of a pair for each consecutive discharge appeared to move or " j i t t e r " about the screen (Fig. 4.1). As mentioned in section 3.4, the single muscle fiber potentials arrive at the electrode with a mutual time difference (Fig 3.7). The reasons for this may be: (1) different propagation times in the terminal nerve endings, (2) the synaptic delay of the motor end-plates may be d i f -ferent, (3) the position of the motor end-plates on the muscle would give rise to an unequal distance for the potentials to travel to the electrode, and f i n a l l y (4) the propagation velocity of the two fibers may be di f f e r -ent. However, the j i t t e r phenomenom could only be explained by a varia- b i l i t y in each successive discharge of anyof the above factors. Provided there i s a steady contraction of the muscle, Stalberg et a l . [92] have shown that a va r i a b i l i t y in the normal muscle of the propagation velocity i s not an important factor. By.. analogy^Ekstedt and Stalberg [94] assume that the var i a b i l i t y in propagation velocity of the terminal nerve end-ings i s probably not important. Since the distance from the nerve to the sampling electrode remains the same, i t is reasonable that there is a variability in the synaptic delay of the normal end-plate. It has also been shown by Ekstedt and Stalberg [95] that injection of D-tubocurarine, which only affects the motor end-plate transmission, increases the j i t t e r . J i t t e r is found to be increased in myasthenia gravis although normal values of j i t t e r may be found [96]. In more severe cases of this dis-order, the j i t t e r increases further and fewer normal values are found, but there is an occasional misfiring or blocking of the^single fiber action potential. In these cases the j i t t e r phenomenon is more d i f f i -cult to measure. In the less severely affected cases of myasthenia 6 4 FIG. 4 . 1 THE JITTER IN A POTENTIAL PAIR IN THE BICEPS BRACHII MUSCLE. A. Two discharges of the p a i r . The sweep i s t r i g g e r e d by the f i r s t a c t i o n p o t e n t i a l and the second appears w i t h d i f f e r e n t time delays i n the two discharges. C a l i b r a t i o n : 4 MV and 1 , 0 0 0 psec. B. The second a c t i o n p o t e n t i a l i n the p a i r . About 4 0 0 discharges are superimposed. The f i r s t p o t e n t i a l i n the p a i r i s constant on the screen. The second does not have a constant p o s i t i o n due to the j i t t e r phenomenon. [From S t a l b e r g e t a l , 1971] 65 gravis the measure of j i t t e r i s a sensitive diagnostic indicator [97,98]. Stalberg and Ekstedt [96] have shown that in muscular dystrophy, there is an increase of the j i t t e r in 10-15% of the recordings. They suggest this may be due to changes in the nerve twigs and/or the motor end-plates. They also report findings of markedly increased j i t t e r in neurogenic disorders and propose that this may be due to disturbed trans-mission in the nerve endings and to unreliable transmission across the neuromuscular juction. 4.2 Simulation of Electromyographic J i t t e r As an i n i t i a l step towards the study of variation in the motor unit potential shape at consecutive discharges, the computer simulation model described in Chapter III was modified to include electromyographic j i t t e r of the single fiber potentials. An ensemble of motor unit poten-ti a l s were generated and the variance as a function of time computed. By this method, the contribution of j i t t e r to the variance for different positions of an electrode, and different fiber^ arrays, could be examined. Appendix D contains the computer program l i s t i n g that was used in this investigation. 4.2.1 Calculation of J i t t e r for Use in the Model Many of the single fiber electromyographic recordings from normal muscle show the interval between the action potentials of two muscle fibers at consecutive discharges, the interpotential interval, to be grouped about a stable mean. This interpotential interval has been analysed during recordings in which the mean did not vary and tests show the distribution may be considered as approximately Gaussian [99]. • An estimate of the standard deviation (s ) in the interpotential inter-66 val for a f i n i t e number of action potential discharges N, (N >> 1) is defined as 8 , = N N 9 - (4.1) D N Where is the interpotential interval of the i discharge, and D is the mean interpotential interval. However, Ekstedt [76] reports findings in which the mean time interval between the potentials, would gradually increase or decrease during several hundred discharges. In the presence of slow variations or trends in the mean interpotential interval during measurement, the standard deviation would be overesti-mated. In a recent paper, Ekstedt et a l . [99] present the different methods of expressing the j i t t e r . In conclusion, they suggest that the Mean Consecutive Difference should be used as the measurement of the j i t t e r . This i s defined as follows. N-l I |D. - D. | MCD = — (4.2) N - l til where D^  is the interpotential interval of the i discharge. For a Gaussian distribution without trends, an estimate of the standard de-viation of the interpotential interval i s given by [100]':-s D = 0.886 x MCD (4.3) g In the normal bicepsbrachii muscle the mean value of j i t t e r reported by Stalberg et a l . [92] from twenty-seven experimental subjects is 15.7 ysec expressed as the Mean Consecutive Difference. To incorporate the j i t t e r effect in the simulation model of the motor unit, the contribution of one single fiber action potential must be 67 calculated. Consider two action potentials such that their mean position from an arbitrary axis i s a^ and a2 as shown in Fig. 4.2. Let x^ and y^ be the intervals from the mean position of each potential due to ' j i t -tering' at the i * " * 1 discharge. The interpotential interval i s given by D i = ( a2 + ?1> ~ ( a l + Xi> ' ( a2 " a l } + ( yi " V = K + (y. - x.) An estimate of the mean interpotential interval denoted by D i s N 1=1 • N 1 N x N = N ^ K + N ^ y i " N E X i N i=l N i=l 1 N i=l 1 = K by definition of the mean. 2 2 2 2 Since = E[D ] - y^ where y^ and are the population mean and variance respectively and the estimate of the variance of the inter-2 potential interval is s^ then, ° D 2 - i f \ < V 2 - *2 i=l - | I (K+ (y - x ) ) 2 - K 1=1 1 1 9 N N 4 I K(y. - x.) + ± 7 (y. - x.r N # ^ J i l N . L. w i l 1=1 1=1 6.8 MEAN POSITION, ARBITRARY MEAN POSITION AXIS FIG. 4.2 CALCULATION OF ELECTROMYOGRAPHIC JITTER 69 the f i r s t term is zero and the second can be written N N N SD = N / y i + N X X i N X X i y i i = l 1=1 1=1 If we assume that and y^ are independent, i.e. the end-plate delay for one muscle fiber is not dependent on any other, then i N W I- x i y i = ° i=l 2 The estimate of the variance of x, denoted by s x is 1 N 2 « • *> x. (as the mean i s zero) 1=1 1 Then, under the assumption that x and y are both identically G&. . ^.-..-.y distributed, 2 1 2 S x = 2 S D SD s •' = —-X 72 From equation (4.3), f i n a l l y for a Gaussian distribution, s - ^ i x H C D (4.4) X Jl Using the mean value of MCD in the normal biceps brachii muscle, 8 ^ = 9.8 usee. Thus a Gaussian scatter of the single fiber action p o t e n t i a l s w i t h stand= ard deviation of 9.8 usee.was applied for each successive generation of the motor unit potential. 70 4.2.2 Circular Array of Fibers In order to examine the effects of j i t t e r on variance detected by fibers at different distances, the variance of the summated potential along the axis of a cylinder of fiber dipoles was computed. Several circular arrays of dipoles, representing muscle fibers, were formed such that the number of dipoles in a circle was proportional to the radius. The muscle fiber diameter was chosen to be 0.80 ym, and each circular ar-ray contained the maximum number of fibers for that circle radius. Elec-tromyographic j i t t e r was applied to each single muscle fiber potential as described in section 4.2.1, and the summated action potential was com-puted along the axis of the array. For each array, an ensemble of 50 summated potentials was generated and the average of the ensemble calcu-lated. The variance was then computed as a function of distance along the muscle fiber axis (related to time by the conduction velocity which was chosen to be 4.1 m/sec), according to the equation M S(d) 2 = i I (P.(d))- P(d)) 2 (4.5) i=l where P^(d) i s the amplitude of the potential at the i generation, P(d) i s the amplitude of the averaged potential and d represents the discrete distance steps [d, d+0.1, d+0.2 ...;in mm] from an arbitrary reference point. M is the number of generated summated potentials in the ensemble. Appen-dix E contains a l i s t i n g of the program which computes the averaged poten-t i a l , the variance of the ensemble and plots the results. Fig. 4.3 shows the plots of the variance for various r a d i i of the circular array. The contribution of the j i t t e r to the variance of the summated potential, for different fiber distances from the sampling point, is thus observed.- The j i t t e r of fiber potentials close to the -71 i — 1 . 0 J . O 3 .0 4 .0 DJ5T(MILLIMETERS) R = (a) 0.1 mm F = 8 -1 5 .0 To ~I V 1 " I — 1 . 0 2 . 0 3 .0 4 .0 DIST(MILLIMETERS) (b) R = 0.15 mm F = 12 — i E.O 0 . 0 0 J ? .0 3 .0 4 .0 DJST(MILLIMETERS) (c) R = 0.2 mm F = 16 FIG. 4.3 VARIANCE IN AN ENSEMBLE OF SUMMATED POTENTIALS COMPUTED AT THE CENTER OF CIRCLES RADIUS R. ' F IS THE NUMBER OF MUSCLE FIBERS IN THE CIRCLE. ORDINATE: ..AMPLITUDE OF VARIANCE (IN ARBITRARY UNITS - NOTE CHANGE IN SCALES) ABSCISSA: DISTANCE ALONG THE MUSCLE FIBER (RELATED TO TIME BY THE CONDUCTION VELOCITY OF THE ACTION POTENTIAL). R = 0.3 mm R = 0.35 mm F = 24 F = 28 t r. U J o I 1.0 I r^= 2 .0 3 .0 4 .0 DIST (M1LUMETERS) R (g) 0.4 mm F = 32 FIG. 4.3 (Cont'd) - i 1 DISTCMIUWTERS) ' ' •ft) R = 1.0 mm F = 78 73 R = 2.0 mm R = 3.0 mm F = 156 F = 236 FIG. 4.3 (Cont'd) 74?. sample point, cause two peaks in the variance (Fig. 4.3 (a)). As the radius i s increased, the two peaks form one peak and side lobes are formed (e.g. Fig. 4.3 (d)), while at s t i l l greater distances, the variance be-comes very small and has only one distinct peak. 4.2.3 Motor Unit Fiber Array 4.2.3.1 No Axial Potential Dispersion The variance generated by the anatomical model of the motor unit was next examined. Electromyographic j i t t e r was applied to the single fiber potentials of the random array of 163 fibers described in section 3.2.2, which was used to represent a motor unit in the normal human brachial biceps muscle. Different, Gaussianly distributed (a = 9.8 ysec) j i t t e r values were applied to the single fiber potentials for each suc-cessive generation of the motor unit potential. An ensemble of 50 motor unit potentials was computed for various distances from the motor unit territory. Variance was computed using equation (4.5) and the plotted results are shown in Fig. 4.4. The peak variance as a function of dis-tance outside the motor unit territory has been graphically represented in Fig. 4.5. 4.2.3.2 With Axial Potential Dispersion Recall from Chapter III that to account for different arrival times at the electrode of the fiber potentials due to conduction time differences in the terminal nerve endings, differences in the axial position of the motor end plates and differences in conduction velocity of the muscle fibers, a Gaussian scatter of the potentials was assumed. Gaussian scatter with a standard deviation of 0.7 mm was applied to the fiber potentials in the motor unit array, together with electromyographic j i t t e r for each successive motor unit potential generated. Fig. 4.6 75-l iJo e.o 12.0 16.0 OJST(MILLIMETERS) B.D 12.0 1G.D D)ST(MILLIMETERS) 1 21.0 (a) D = 1.5 mm (Insi d e Motor Uni t T e r r i t o r y ) (b) D = 2.5 mm (Edge of Motor Uni t T e r r i t o r y ) _1— 4.0 8.0 12.0 1G.0 DJSTIMILL1METERS) (c) ~1 24.0 1 4.0 D = 3.0 mm (Just-Outside Motor U n i t T e r r i t o r y ) i 1 — = 1 — 6.0 12.0 1E.0 DJST(MILLIMETERS) (d) D = 3.5 mm ~ i — 20.0 FIG. 4.4 ORDINATE: ABSCISSA: VARIANCE IN THE MOTOR UNIT POTENTIAL AMPLITUDE DUE TO ELECTROMYO-GRAPHIC JITTER(D -IS DISTANCE FROM THE CENTER OF THE MOTOR UNIT TERRITORY). AMPLITUDE OF VARIANCE (IN ARBITRARY UNITS - NOTE SCALE CHANGES) DISTANCE ALONG THE MUSCLE FIBER (RELATED TO TIME BY THE CONDUCTION VELOCITY OF THE ACTION POTENTIAL). 76 S.O ~V2.0 IG.O DIST(MILLIMETERS) T 4.0 i r C O 12.0 lfl.0 DJST(MILL)METERS) D = 4.5 mm D = 5.5 mm ~ i — 4.0 - l :—i 1 8.0 12.0 16.0 D 1ST(MILLIMETERS) 0.0 ~i r 8.0 12.0 16.0 DIST(MILLIMETERS) 1 24.0 D = 6.5 mm D = 7.5 mm FIG. 4.4 (Cont'd) 77. -7-0 o <: 2 a. o CD O -4 -2-0 - 5 0 70 FIG. 4.5 2-5 3-5 4-5 5-5 6-5 . 7 5 DISTANCE FROM THE MOTOR UNIT CENTER (mm.) PEAK VARIANCE DUE TO ELECTROMYOGRAPHIC JITTER AS A FUNCTION OF DISTANCE OUTSIDE THE MOTOR UNIT TERRITORY. O NO AXIAL DISPERSION A AXIAL DISPERSION WITH STANDARD DEVIATION = 0.7 mm 78 shows the variance due to these effects at several distances from the motor unit territory. In Fig. 4.5 the peak variance with potential scatter as a function of distance outside the motor unit area, is com-pared with no Gaussian axial scatter. 4.3 Experimental Results From Human Subjects 4.3.1 Determination of the Number of Motor Unit Potentials In order to compare the experimental data with the simulation results, i t was desired to determine the number of motor unit potentials with which to estimate the variance. Confidence intervals for the true variance of a normal variate can be found using the chi - square d i s t r i -bution [101]. If there are n motor unit potentials in an ensemble, the 2 confidence interval for the true variance cr^ of the amplitude at each sample point in time i s 2 2 n S A 2 n S A • < at < -= (4.6) 2 — "A — 2 X p (n-l) X p (n-l) r l *2 2 where S^ is the variance of the ensemble amplitude for each sample point 2 in time and xp (n-l) is the value of chi - squared for (n-l) degrees of *1 freedom evaluated at P = P^ where 100% F1 = 1/2 (100% - confidence level) 2 Similarly, xp (n-l) is evaluated for (n-l) degrees of freedom for P = P_ 2 ' Z where 100% P 2 = 1/2 (100% + confidence level). Using the interactive graphics routine described in section 2.4.1 single motor unit potentials were extracted from the digitized 79 —I— 4.0 B.O 13.0 IG.O DIST [MILUMETERS) (a) D = 1.5 mm ( I n s i d e Motor U n i t T e r r i t o r y ) U l o ' 1 Q " I 1 6.0 12.0 16.0 DlSTtMILU METERS) o.o (b) D = 2.5 mm (Edge of Motor U n i t T e r r i t o r y ) D = 3.0 mm D = 3.5 mm (Just Outside Motor U n i t T e r r i t o r y ) FIG. 4.6 VARIANCE IN--THE MOTOR UNIT POTENTIAL DUE TO EFFECTS OF (1) ELECTRO-MYOGRAPHIC JITTER AT EACH SUCCESSIVE GENERATION (2) SCATTER OF DIPOLES (arv= 0.7 mm) . ORDINATE: AMPLITUDE OF VARIANCE (IN ARBITRARY UNITS - NOTE SCALE CHANGES). ABSCISSA: DISTANCE ALONG THE MUSCLE FIBER (RELATED TO TIME BY CONDUCTION VELOCITY OF THE ACTION POTENTIAL). 80 (e) ( f ) D = 4.5 mm D = 5.5 mm — r — 4.0 6.0 12.0 IB.O DIST(MILLIMETERS) (g) D = 6.5 mm fl.O 12.0 16.0 DIST(MILLIMETERS) •(h) D = 7.5 mm FIG. 4.6 (Cont'd) 81 time series EMG waveform recorded from normal subjects, and the averaged motor unit potential calculated by the procedure outlined in Fig. 2.3 (c). The variance for each amplitude sample was then computed. Under the assumption that each amplitude sample.of the motor unit potential may be considered as a normal variate, the confidence interval for a 95% confi-dence level was found using the chi - squared distribution. To determine the number of motor unit potentials to use for variance estimation, the largest confidence interval (worst case condition) was selected and plot-ted as a function of the number of potentials. The results of this i n -vestigation from three normal subjects are given in Fig. 4.7 to Fig. 4.9. The results clearly indicate the desirability of using greater than f i f t y motor unit potentials to estimate the variance in an ensemble. Eighty motor unit potentials were chosen. It should be pointed out, in the implementation of a c l i n i c a l system for variance estimation i t i s desirable that the number of motor unit potentials required for analysis should be small for practical reasons. Routine examinations would be less demanding for the patient and the clinician may carry out the test in a short period of time. 4.3.2 Normal Subjects Using the interactive graphics routine, eighty potentials from the same single motor unit were extracted from the EMG time series waveform that had been recorded from the biceps brachii muscle of a nor-mal subject. After alignment, the averaged motor unit potential was computed and the variance was calculated for comparison with the pre-dictions from the simulation model. During the recording of the EMG activity no attempt was made to examine only diphasic potentials such as given by the simulation model (see section 4.4). The plots of the 82 FIG. 4.7 EFFECT OF INCREASING THE NUMBER OF MOTOR UNIT POTENTIALS TO ESTIMATE VARIANCE^ ON THE CONFIDENCE INTERVAL FOR A 95% CONFIDENCE LEVEL. SUBJECT T.M._ 83 FIG. 4.8 AS IN FIG. 4.7. SUBJECT P.B.. 84 ; I L 1 i j i i L fO 20 30 AO 50 60 70 80 No. OF MOTOR UNIT POTENTIALS -FIG. 4.9 AS IN FIG. 4.7. SUBJECT PjL. 85 variance against time, together w i t h the averaged motor u n i t p o t e n t i a l are shown.for 4 d i f f e r e n t motor u n i t s (3 subjects) i n F i g . 4.10 to F i g . 4.13. 4.3.3 P a t i e n t s w i t h Muscle Disease In p a t i e n t s w i t h myasthenia g r a v i s , Ekstedt and S t a l b e r g [94] and S t a l b e r g et a l . [98] found that the j i t t e r i n many s i n g l e f i b e r po-t e n t i a l p a i r s was h i g h l y increased from the normal. This j i t t e r was u s u a l l y above 100 ysec (MCD). Using equation (4.4), an; ' increased j i t -t e r of 100 ysec (MCD) was incorporated i n t o the s i m u l a t i o n model and the v a r i a n c e of the motor u n i t p o t e n t i a l c a l c u l a t e d f o r various p o i n t s i n s i d e and outside the motor u n i t area. The r e s u l t s r e v e a l that there i s a l a r g e increase i n peak variance w i t h i n and near the motor u n i t t e r r i t o r y . F i g . 4.14 shows a t y p i c a l averaged motor u n i t p o t e n t i a l computed at a point i n s i d e the motor u n i t t e r r i t o r y and a l s o the amplitude variance c a l c u l a t e d from the motor u n i t p o t e n t i a l ensemble ( u n i t s of amplitude as i n the normal model case). Repeating the procedure of the preceeding s e c t i o n f o r a p a t i e n t w i t h myasthenia g r a v i s , the experimental r e s u l t s f o l l o w the p r e d i c t i o n s of the model. F i g . 4.15 shows an averaged motor u n i t p o t e n t i a l which i s d i p h a s i c and appears to be c l i n i c a l l y normal yet the peak vari a n c e i s much greater than that from the normal subjects (same u n i t s of amplitude as recorded i n the normal experimental s u b j e c t s ) . I n i t i a l r e s u l t s from the p o l y m y o s i t i s EMG data show there are s e v e r a l l a r g e peaks of v a r i a n c e . Further i n v e s t i g a t i o n s are r e q u i r e d to q u a n t i f y t h i s e f f e c t . 1 1 1 1 1 2.0 4.0 CO a.o 10.0 TIHEIH1LL1SEC) AVERAGED MOTOR UNIT POTENTIAL — i — 2.0 4.0 6.0 8.0 T1HEIH1LLISEC) VARIANCE FIG. 4.10 MOTOR UNIT POTENTIAL VARIANCE IN AMPLITUDE FROM NORMAL SUBJECT T.M. (RECORDINGS FROM THE BICEPS BRACHII MUSCLE) -4 Amp(mV) = 2.44 x 10 x Amp(units) 87 T 2.0 -i 1 r 4.0 s.o a.o TIHEIMILLISEC) 3; I X AVERAGED MOTOR UNIT POTENTIAL -1 1 1 1— a.o 4 . 0 6.o a.o TIMECM1LISEC) VARIANCE i — 1 0 . 0 1 2 . 0 FIG. 4.12 MOTOR UNIT POTENTIAL VARIANCE IN AMPLITUDE FROM NORMAL SUBJECT P.D. (RECORDING FROM THE BICEPS BRACHII MUSCLE) -4 Amp(mV) = 2.44 x 10 x Amp(units) ! . 0 AVERAGED MOTOR UNIT POTENTIAL VARIANCE FIG. 4.13 AS IN FIG. 4.12. SUBJECT P.L. 88 S.D 20.0 24-0 (a) AVERAGE MOTOR UNIT POTENTIAL <b) VARIANCE FIG. 4414 MODELLING OF MYASTHENIA GRAVIS - THE VARIANCE DUE TO INCREASED JITTER. AXIAL DIPOLE DISPERSION = 0.7 mm JITTER = 100 ysec (MCD) COMPUTED INSIDE THE MOTOR UNIT AREA ' (a) AVERAGED MOTOR UNIT POTENTIAL (b) VARIANCE FIG. 4.15 VARIANCE OF MOTOR UNIT AMPLITUDE IN A PATIENT WITH MYASTHENIA GRAVIS Amp(mV) = 2.44 x 10 ^  x Amp(units) 89 4.4 Discussion 4.4.1 General Discussion The computer simulation model of the motor unit potential has been employed to investigate the observation that in each successive f i r i n g of the motor unit potential, there is°a variation in i t s shape and that this v a r i a b i l i t y may be increased in certain diseases. Using the techniques of single fiber electromyography other investigators have shown that there i s a j i t t e r of the time interval between two fiber action potentials at consecutive discharges. This j i t t e r may be due to some variability in the synaptic delay of the normal end-plate [94]. It is a reasonable assumption that inthenormal human muscle the j i t t e r phenomenon would be a factor l i k e l y to alter the contour of a summated potential. As an i n i t i a l approach to the investigation of shape varia-b i l i t y of the motor unit potential, this hypothesis was tested by simu-lating electromyographic j i t t e r and investigating the effect on the v a r i -ance of the motor unit potentials generated. It has been reported that the interpotential interval between two fiber potentials may be considered to be approximately Gaussianly distributed [99]. In the literature some interpotential intervals have been found with distributions which had skewness, positive kurtosis or more commonly, negative kurtosis. Some bimodal distributions were also found [102]. The calculation of j i t t e r for use in the model was based on the assumption that the interpotential interval has a Gaussian dis-tribution. The value of j i t t e r used in the model was 15.7 ysec (MCD) which is the mean value reported [92] for the normal biceps brachii muscle from 27 experimental subjects. The range given is 2.6 - 37.1 ysec (MCD). 90 The e f f e c t of j i t t e r on the variance of the summated p o t e n t i a l s from a c i r c u l a r array of d i p o l e s was f i r s t s t u d i e d . Using t h i s array s t r u c t u r e , the variance caused by j i t t e r of the volume conducted s i n g l e f i b e r p o t e n t i a l s at d i f f e r e n t distances/-, was examined. The r e s u l t s i n -d i c a t e that j i t t e r i n g of p o t e n t i a l s from a nearby e l e c t r o d e gives r i s e to s e v e r a l peaks i n variance ( F i g . 4.3 ( b ) ) . At greater distances one variance peak becomes more dominant ( F i g . 4.3 ( i ) ) . The random f i b e r array representing a motor u n i t i n human biceps b r a c h i i muscle shows tha t there i s a peak vari a n c e i n the r i s i n g edge of the d i p h a s i c motor u n i t p o t e n t i a l . This peak variance decreases r a p i d l y w i t h distance out-s i d e the motor u n i t t e r r i t o r y ( F i g . 4.5). With the i n t r o d u c t i o n of ax-i a l d i s p e r s i o n i n the manner described i n s e c t i o n 4.2.3, some asymmetry i n the lobes of the variance p l o t s was observed ( F i g . 4.6 ( c ) ) . Before comparing the experimental data w i t h the model, a t e s t was performed on the variance confidence i n t e r v a l s to f i n d the number of motor u n i t p o t e n t i a l s r e q u i r e d to estimate v a r i a n c e . The t e s t revealed t h a t f o r a 95% confidence l e v e l at l e a s t f i f t y p o t e n t i a l s mere s u f f i c i e n t f o r the e s t i m a t i o n . I t i s d e s i r a b l e f o r p r a c t i c a l reasons to keep t h i s number to a minimum. Ensembles of e i g h t y motor u n i t p o t e n t i a l s were chosen to compute the variance i n amplitude f o r s e v e r a l normal s u b j e c t s . The variance r e s u l t s c l e a r l y agree w i t h model p r e d i c t i o n s . A l a r g e peak of the variance i s dominant on the r i s i n g edge of the motor u n i t p o t e n t i a l w i t h asymmetrical lobes. In the modelling of myasthenia g r a v i s , the j i t t e r value was increased but a Gaussian d i s t r i b u t i o n was s t i l l assumed. I t i s more common i n the p a t h o l o g i c a l s t a t e f o r the i n t e r p o t e n t i a l i n t e r v a l to have a d i s t r i b u t i o n which i n not Gaussian , [ 9 9 ] . The model however, p r e d i c t s 91 a large Increase in peak variance. Motor unit potentials recorded from a myasthenic muscle, did show a large increase in peak variance from that of the normal. It must be pointed out that in myasthenia gravis there is also a neuromuscular blocking when the single fiber potential does not f i r e for several motor unit discharges. This w i l l also add to the v a r i -ance . The experimental results show that the baseline of variance i s non-zero. This can be modelled rin the following way (see Fig. 4.16). Let G represent a deterministic action potential generator. N represents the generator noise due to electromyographic j i t t e r , while B is the bio-logical noise source added by distant motor unit potentials, the recording apparatus and digitizing process. The total variance then w i l l be the sum of the generator noise variance and the biological noise variance which w i l l contribute to the baseline. In the pathological state, the generator noise increases due to increased electromyographic j i t t e r , blocking of single fiber potentials or amplitude variation in successive figures of the single fiber potentials. 4.4.2 Extensions of this Work The i n i t i a l results of this investigation should provide excit-ing stimulus for further work. It has been beyond the scope of this thesis to quantify this variance. A further expansion of the data base is necessary to establish limits for normal variance in motor unit poten-ti a l s and variance due to pathological conditions. A study of other physiological factors in the generation of motor unit potentials which affect the variance should be undertaken. The model developed in this thesis may be usefully employed for this purpose. In an attempt to compare normal motor unit potentials recorded MOTOR UNIT POTENTIAL l o FIG. 4.16 SIMPLE GENERATOR MODEL REPRESENTING THE RECORDED MOTOR UNIT POTENTIAL NO 93 from the experimental subject, i t was found that many did not have a symmetrical biphasic shape. Some potentials demonstrated a large i n i t i a l phase (Fig. 4.12) or a large second phase (Fig. 4.10). Several motor unit potentials had an almost monophasic time course (Fig. 4.11, Fig. 4.13). It is fundamental to any further investigation of variance to understand how these shapes of the action potentials are produced. One possible area deserving further exploration i s the transformation induced on the motor unit potential by the sampling electrode, and how this elec-trode distorts the volume conducted electric f i e l d . 94 CHAPTER V CONCLUSIONS AND DIRECTIONS FOR FURTHER RESEARCH 5.1 Synopsis Of the Thesis The o b j e c t i v e of the work described i n t h i s t h e s i s was to study the production of the motor u n i t p o t e n t i a l i n order that the knowledge gained may be used i n the development of p r a c t i c a l system f o r automatic a n a l y s i s of EMG to a i d the c l i n i c i a n i n h i s d i a g n o s i s . Methods f o r the a c q u i s i t i o n and subsequent preprocessing of s i n g l e motor u n i t p o t e n t i a l s were devised. An EMG data base c o n s i s t i n g of normal and p a t h o l o g i c a l EMG a c t i v i t y from the biceps b r a c h i i muscle has been e s t a b l i s h e d and an i n t e r a c t i v e graphics r o u t i n e developed to v i s u a l l y e x t r a c t p o t e n t i a l s from the same motor u n i t f o r f u r t h e r a n a l y s i s . . A computer model was pro-posed f o r the generation of motor u n i t p o t e n t i a l s observed i n the c l i n i -c a l EMG examination of the normal biceps b r a c h i i muscle. V a r i a t i o n s i n the peak to peak amplitude and peak to peak d u r a t i o n at d i f f e r e n t a x i a l p o t e n t i a l d i s p e r s i o n s were i n v e s t i g a t e d f o r p o i n t s at i n c r e a s i n g d i s -tance from the motor u n i t a x i s . This model has a l s o been compared w i t h e x i s t i n g experimental data from m u l t i e l e c t r o d e s t u d i e s of the" muscle. The model was f u r t h e r employed i n the i n v e s t i g a t i o n of the v a r i a t i o n i n the shape of the motor u n i t p o t e n t i a l due to the e f f e c t s of EMG j i t t e r . The acquired experimental data has been analysed and compared w i t h the p r e d i c t i o n s of the model concerning the v a r i a t i o n i n shape of normal motor u n i t p o t e n t i a l s due to electromyographic j i t t e r . This i n v e s t i g a -t i o n i n i t i a l l y has demonstrated that i n myasthenia g r a v i s , a disease i n which electromyographic j i t t e r i s inc r e a s e d , the peak v a r i a n c e a l s o increased. Further work has been i n d i c a t e d i n t h i s area. 95 5.2 Contributions of the Research The author considers the main contributions of this research may be summarized as follows: (1) A comprehensive review of the methods of automatic analysis in c l i n -i c a l electromyography has been added to the current literature [62] including the proposal of a set of design requirements for automated analysis of EMG signals. (2) Methods for the acquisition and preprocessing of c l i n i c a l EMG a c t i -vity have been established at U.B.C. (3) An interactive graphics routine to extract single motor unit poten-t i a l s has been developed. To the knowledge of the author, such a method has not been reported before. (4) A model for the generation of the motor unit potential based on phy-siological findings has been proposed and investigated for the f i r s t time. (5) The f i r s t investigation into the variation in motor unit potential shape at successive discharges due to electromyographic j i t t e r has been made. (6) The observation has been made that the variance in motor unit poten-t i a l amplitude was greatly increased in a case of myasthenia gravis. The reason, i t was suggested, was due partially to an increase in electromyographic j i t t e r . A review of the methods of automatic analysis in c l i n i c a l EMG revealed that many were unreliable and, with the exception of Willison's, -lacked c l i n i c a l significance. Many of the methods described use heuris-t i c a l l y derived indices not based on a fundamental understanding of how disease affects the recorded activity. This research represents a new 96 approach. A knowledge of the production of the motor unit potential, together with how the disordered physiology affects the fiber potentials, can give more foundation to the selection of the appropriate signal processing techniques. 5.3 Directions for Further Research The following areas are suggested for further work. (a) Expansion of the EMG Data Base (b) Improvements in the method to extract single motor unit potentials. (c) Further extensions of the motor unit potential model and human ex-perimental verification. (d) Study of the variance in motor unit potentials in myopathy and neuropathy and of i t s diagnostic usefulness. 5.3.1 Expansion of the Data Base The success of^ahyfurther work in this research i s dependent upon the expansion of the EMG data base. One improvement that would be of benefit to this goal i s the development of on-line digitization of the EMG data at Vancouver General Hospital. IBM compatible tapes may be taken directly to the U.B.C. computer center for further analysis and the analog stage eliminated. 5.3.2 Interactive Graphics Routine The extraction of eighty motor unit potentials from the EMG waveform is time consuming and laborious. Thus, computer routines to automatically align the motor unit potentials would leave the operator after i n i t i a l i z a t i o n with an accept/reject decision. Application of pattern recognition techniques is necessary for 97 the e x t r a c t i o n of the motor u n i t p o t e n t i a l s i n a p r a c t i c a l c l i n i c a l s y s -tem. In t h i s regard, the computer programs should use a minimum amount of memory such that the system may be m i n i or microcomputer based. 5.3.3 Motor Unit P o t e n t i a l Model This model has proved to be u s e f u l i n the study of the e l e c t r i c a l a c t i v i t y from the normal motor u n i t . The p r o p e r t i e s of the el e c t r o d e and subsequent a m p l i f i e r s must be examined i n order that the d i s t o r t i o n on the motor u n i t potential." be compensated. Further experimental v e r i f i c a t i o n of the model from human s u b j e c t s , such as amplitude versus d u r a t i o n p l o t s would be b e n e f i c i a l . 5.3.4 Study of Motor U n i t P o t e n t i a l Variance Using the model, p a t h o l o g i c a l processes can be simulated and the e f f e c t s on vari a n c e tes t e d f o r d i a g n o s t i c s i g n i f i c a n c e . 98 APPENDIX A TERMS AND DEFINITIONS OF ELECTROMYOGRAPHY Some of the more important terms and definitions of electromy-ography used in this thesis are given below for reference. Further i n -formation on the terminology may be obtained from [103] or from any of the more general texts [5,6,7]. A.l PHYSIOLOGY A. 1.1 Biceps Brachii One of the muscles of the upper arm. It flexes the forearm and i t turns the hand_so that the palm can face upwards. A.1.2 Motor end-plate The f l a t expansion ending a motor nerve fiber where i t connects with a muscle fiber and includes portions of nerve and muscle. A.1.3 Motor Unit This i s the functional unit of the neuromuscular system consisting of the anterior horn c e l l in the spinal cord, i t s axon and a l l the muscle fibers innervated by that axon. A. 2 ACTION POTENTIALS A.2.1 Motor Unit Potential The-action potential expressing the ac-t i v i t y of that part of a single motor unit which i s within the recording range of an electrode. A.2.2 Total duration As defined by Buchthal [10], this i s the time interval between the i n i t i a l deflection from the baseline and the point at which the terminal deflection again returns to the base-line." A72.3 Monophasic action potential An action potential with a deflec-tion to one side of the baseline. A.2.4 Biphasic action potential An action potential with a deflect-tion f i r s t to one side then to the other side of the baseline 99 (usually a positive-negative sequence). A.2.5 Polyphasic Action Potential An action potential having more than four phases. A. 3 RECORDING EQUIPMENT A.3.1 Concentric needle electrode Variations in voltage are measured between the bare tip of an insulated wire, usually stainless steel, or platinum, and the bare shaft of a steel cannula in which i t i s inserted. The bare tip of the central wire (exploring electrode) i s flush with the level of the cannula (reference electrode). A.3.2 PISA electromyograph Instrument used to amplify and display the EMG signals. It also includes an audio amplifier and speaker to allow acoustic monitoring of the potentials. A.4 MUSCLE DISORDERS A.4.1 Polymyositis A muscle disease in which there is muscular weak-ness. It i s classified in four groups. In the f i r s t , there are muscular changes without involvement of skin. In the second group, skin changes are a feature, although muscular weakness i s again dominant. In the third group, muscle changes occur as a feature of a predominantly connective tissue disorder. In the fourth group, polymyositis occurs in association with malignant disease. A.4.2 Myasthenia Gravis This i s a neuromuscular transmission disorder involving the myoneural junctions. Nerve impulses f a i l to induce normal muscle contraction. The disease i s characterized by great muscular weakness (without atrophy) and progressive fatigability. A.4.3 Neuropathy Any disease of the nerves. A.4.4 Myopathy Any disease or abnormal condition of the striated muscle. 100 APPENDIX B EMG RECORDING - INFORMATION SHEET SUBJECT ..... Date TITLE OF ANALOG TAPE SIDE OF TAPE REVOLUTION COUNTER START 1. SECTION END COMMENTS SECTION END COMMENTS 3. SECTION END COMMENTS 4. SECTION END COMMENTS 5. SECTION END COMMENTS DIAGNOSIS DOCTOR IN CHARGE - 3 -PISA ELECTROMYOGRAPH FREQ. LIMITS SENSITIVITY COMMENTS^  TAPE RECORDER SPEED . .' CHANNEL NO. 103 APPENDIX C DOCUMENTATION ON THE INTERACTIVE GRAPHICS ROUTINE INTERACT - A program to interactively select motor unit potentials from an EMG time series waveform. C.l Introduction INTERACT i s an interactive graphics program developed for use at the Adage Graphics Terminal, U.B.C. Computing Center. Its purpose is to allow the selection of a single motor unit potential from the EMG time series waveform which is stored in a f i l e record. The potential may be enlarged on the screen and by means of a cursor the operator may select the beginning and end of a f i r i n g interval which can be extracted and stored in another f i l e for future analysis. The program further allows the operator to 'store' the potential on the screen and thus other poten-t i a l s may be matched, aligned to i t and extracted. C.2 Running the Program The program is initiated by an MTS command: $RUN INTERACT 1=WAVEFORM 2=P0TENTIALS WAVEFORM and POTENTIALS are the names of two sequential f i l e s , the for-mer containing the EMG waveform to be examined and the other w i l l contain the extracted action potentials. The f i l e WAVEFORM should have data in the form of 2 bytes/integer and 4096 bytes/record. The f i l e POTENTIALS w i l l contain one motor unit potential per record, each sample being a 2 byte integer. The operator w i l l be asked to ENTER SCALING FACTORS IN F10.1 FORMAT:MIN THEN MAX. These scaling factors are the minimum and maximum values to which a l l 104 records of displayed EMG data w i l l be scaled to on the screen. The operator w i l l then be asked to: ENTER RECORD NUMBER This allows the program to keep count of the number of records that have been displayed on the screen. The number should be entered in 14 format; for example, usually the f i r s t record in a f i l e w i l l be displayed and the operator w i l l enter 0001. C.3 Controls Fig. C l shows the layout, of the function button and their as-signments. Fig. C..2 shows the variable control dials. BUTTON 11 This w i l l terminate the program, returning the operator to MTS. Issuing the MTS command ^RESTART w i l l restart the program at the same point as i t was terminated. The input or output f i l e s may be redefined i f desired at this stage by the command $RESTART 1=NEW WAVEFORM and/or 2=NEW POTENTIALS. BUTTON 12 This button causes the Adage Computer to read the next sequen-t i a l record in the f i l e WAVEFORM into an input buffer. The entire record in the buffer i s then displayed on the screen. When an end of f i l e i s encountered, the program w i l l terminate. It should be noted that operations of the other function buttons are performed on the input buffer. BUTTON 13 - GROW This w i l l cause the points presently on the display screen to be rescaled and spread out; only about half of the original points (those points about the center), w i l l be 'grown'. This causes no permanent ( PULSE 1 ) o © © © © © © © © © : © © © FIG. C . l FUNCTION BUTTONS -LAYOUT AND ASSIGNMENT FIG. C.2 VARIABLE POTENTIOMETER CONTROL DIALS 106 changes in the values of the sample points in the record. BUTTON 14 - SHRINK This w i l l double the number of points on the screen or, i f a l l the points in a record are displayed, i t reduces the step size between the points. No permanent changes in the values of the parts are produced. BUTTON 15 - CENTER This together with the x cross-hair (see later) allows points to be scrolled onto the screen from the l e f t or right. It is normally used to center a selected motor unit potential on the screen (usually the peak of the potential i s chosen as the center) before enlargement. BUTTON 3 This enables the sample point nearest the x cross-hair to be chosen as the start of a range of points to be extracted and stored i n the f i l e POTENTIALS. BUTTON 7 This selects the point nearest the x cross-hair to be the end of a range of points. The program w i l l display on the terminal the number of sample points in the chosen range by THE NUMBER OF SAMPLE POINTS = XXXX The operator w i l l be prompted to respond by ENTER YOUR RESPONSE 1=YES, 2=N0. Entering 1 w i l l cause the chosen range of points to be extracted and stored in the next sequential record of f i l e 2. Entering 2 w i l l allow the operator to reselect BUTTON 7 or alternatively reselect BUTTON 3 and BUTTON 7. It should be noted that i f BUTTON 7 is depressed before BUTTON 3 the program w i l l respond MUST USE BUTTON 3 FIRST. 107 BUTTON 1 This changes a point on the screen identified by the x cross-hair to a new coordinate identified by the y cross-hair. This feature may be used to mark the beginning and end of a range of points. To do this i t must be used after BUTTON 3 and after BUTTON 7. The other func-tion buttons are not required by the program. C.4 Variable Control Dials In Fig. C.2 control potentiometer A controls the position of the y cross-hair on the screen while A controls the position of the x cross-hair. The control potentiometer labelled B i s used to control the brightness of the trace on the screen and E controls the aspect. C.5 Foot Switches There are 2 foot switch controls, one i s used to 'store' the trace currently displayed on the screen. This i s indicated by a propor-tionate increase of the trace brightness with each depression of the switch. This trace w i l l remain on the screen while further records are displayed and any number of traces may be stored on the screen. The other foot switch w i l l 'unfreeze' the trace and i f i t does not belong to the currently displayed record, i t w i l l disappear off the screen. C.6 Additional Features Once a motor unit potential has been identified, centered and 'stored' on the screen, the next selected potential may be matched to i t . During this matching process, the operator may move the x cross-hair to the marked beginning of the trace and depress BUTTON 3. On depression of BUTTON 7 the program automatically adds the previously defined number of sample points to the beginning. The operator i s s t i l l prompted for his 108 response; a 'No' means the number of sample points to be extracted to be redefined. The program also keeps count of the number of records that have been displayed. The record number w i l l appear on the terminal after the use of BUTTON 12. The number of motor unit potential that are stored in f i l e 2 i s also displayed after a new potential has been extracted. When a record i s displayed on the screen, 12 additional points are added to the display. The f i r s t two points represent the maximum and minimum scale factors while the last ten points are set to zero, thus defining a zero baselines APPENDIX D COMPUTER LISTING OF THE MOTOR UNIT POTENTIAL SIMULATION MODEL C_ •_ — _ . . __ c C * * T H I S PROGRAM R E P R E S E N T S A MODEL S I M U L A T I N G T H E HUMAN M U S C L E A C T I O N C P O T E N T I A L * * C c. C* D E F I N I T I O N OF I N P U T P A R A M E T E R S : C Z E E NUMBER OF S I N G L E .MOTOR U N I T P O T E N T I A L S TO B E FORMED C N F I B S NUMBER O F S I N G L E F I B E R S I N AN ARRAY C NO NUMBER OF P O I N T S ON T H E X C O O R D I N A T E C DEV S T A N D A R D D E V I A T I O N OF A G A U S S I A N D I S P E R S I O N OF F I B E R S C J I T T E R V A L U E OF J I T T E R I N M I C R O S E C O N D S ( S E T TO A G A U S S I A N D I S T R I B T I O N C •NOTE... J I T T E R I S T H R E E T I M E S T H E STANDARD D E V I A T I O N C A J I T T V A L U E OF J I T T E R A P P L I E D TO A M P L I T U D E C : F I R S T ~ ~ I N T I A . L P O I N T ON X C O O R D I N A T E FOR THE P O T E N T I A L C NCYN NUMBER OF C Y L I N D E R S I N T H E ARRAY C D ( I ) D I S T A N C E FROM E L E C T R O D E O f C Y L I N D E R I C N ( I ) _~_NUMBER OF F I B E R S I N C Y L I N D E R .1 C C* P A R A M E T E R S I N PROGRAM: C S C A L E =0.004 AS .1 MM I S EQUAL TO 25 MICROSECONDS C P A T H ( I ) A X I A L D I S P E R S I O N FOR' "ALL F I B E R S C S T A R T ( I ) _ J I T T E R V A L J E S FOP. S I N G L E F I B E R S C T H I ( I ) S I N G L E F I B E R P O T E N T I A L V E C T O R C V E C T [ i j SUMMED S I N G L E F I B E R S P O T E N T I A L S I N A MOTOR U N I T C C* O U T P U T C C U N I T 1 W I L L C O N T A I N ' Z E E ' MOTOR U N I T P O T E N T I A L S C * U P P S R L I M I T S 100 MUP'S „ 8 0 0 S I N G L E F I B E R S , 2 0 0 P O I N T S C C LAST U P D A T E 7 A P R I L 1 9 7 6 c . : : R E A L D I S { 8 0 0 ) , V E C T ( 2 0 0 ) , S T A R T ( 8 0 0 ) , P ATH ( 8 0 0 ) R E A L T H I ( 2 0 0 ) ,D ( 2 0 0 ) R E A L J I T T E R I N T E G E R Z E E , N ( 2 0 0 ) I N T E G E R * ? I. EN SCA'LE=0,00 4 C C R E A D I N T H E P A R A M E T E R S R E A D (5 R 6) Z E E , N F I B S , N U , D E V , J I T T E R , A J I T T , F I R S T 6 FORM AT ( I 3 / I 3 / I 3 / F 1 0 . 3 / F 1 0 . 3 / T T 0 . . 3 / F 1 0 . .3) W R I T E (6 , 4 0 1) Z E E 401- F O R M A T ( 2 X , ' T H E NUMBER OF MOTOR U N I T P O T E N T I A L S G E N E R A T E D — ' , 1 3 ) ' . WRITE ( 6 , 4 0 2) N F I B S U0.2 FORK AT ( 2 0 X NUMBER OF F I B E R S I.N T H E A R R A Y = V , I 3 ) . W R ITE (6 , a n 3 ) NU 4 0 3 FORMAT ( 2 0 X , • NUMBER OF P O I N T S CONS I DERE D.= ' , 13) 110 :WRITE ( 6 , 4 0 4) D.EV 4 0 4 FOR MAT.{20X,'THE A X I A L DT S P B R S 1 0 N - • , F 1 0 . 3 ) WRITE ( 5 , 4 0 5 ) J I T T E R 4 0 5 F O R M A T ( 2 0 X , 1 T H E J I T T E R I N MICROSECONDS^',F10.3) W R I T E ( 6 , 4 0 6 ) A J I T T '406 FORM AT (20X , ' T H E A M P L I T U D E J I T T E R I S S E T . AT ' ,.F10.3) WRITS (6 , 40 7) F I R S T 4 0 7 FORMAT ( 2 0 X , ' T H E . ' F I R S T P OINT C O N S I D E R E D I S V , F 1 0 . 3 ) I F (DEV. NE. 0. 0). GO TO 2 C ' C S E T PATH TO ZERO I F NO A X I A L D I S P E R S I O N OF F I B E R S DO 54 I - 1 . N F I B S 54 PATH (I) =0.0 GO TO 12 C C A P P L Y G A U S S I A N A X I A L D I S P E R S I O N ( I F DEV I S 0.0 NO D I S P E R S I O N ) 2 P = 1 2 3 . 4 5 6 7 Z=RANDN(P> DO 94 I = 1 , N F I B S F^FRANDN (D) 94 . PATH (I) =F#DEV 12 . C O N T I N U E C C D E F I N E T H E F I B E R A TIB A Y C READ (5,8) NCYN 8 FORMAT (13) DO 901 1=1,NCYN R E A D ( 5 , 1 9 1 ) N ( I ) ' 191 FOR HAT (13) R E A D ( 5 , 9 0 2 ) D (I) C C T E S T I F F I B E R I S TOO C L O S E TO P O I N T SOURCE E L E C T R O D E 901 I F ( D ( I ) . L S . 0.08) D (I) =D ('I) +0 . 08 9 0 2 F O R M A T ( F 1 0 . 3 ) INDEX=0 DO 3 0 0 ICYN=1 ,NCYN NEND= N (NCYN) I F { I C Y N . GT. 1) INDEX=INDEX+N ( I C Y N - 1) DO 200 I=1,NEND D I S ( I + INDEX) =D (ICY N ) -200 C O N T I N U E 300 C O N T I N U E . .121 C O N T I N U E C C I N T I A L I Z E T H E NUMBER OF MOTOR UNIT COMPUTATIONS NCOUNT=0 LEN=4*NU 39 C O N T I N U E . C C A P P L Y G A U S S I A N J I T T E R I F ( J I T T E R . NE. 0 . 0) GO TO 3 C 1 C I F NO J I T T E R THEN EACH P O T E N T I A L HAS S A Li 2 S T A R T I N G POINT DO 55 I = 1 , N F I B S I l l 5 5 S T A R T (I) = F I P. S T GO TO HH 3 T = S C L O C K (0.0) Z= R AMDN (T) DO M 1=1,NFIBS F = FRANDN (D) STAND=JITTFR./3. C C ASSUME J I T T E R L I E S WITHIN +/-3 STANDARD D E V I A T I O N S S T A R T (I) =F*STAND C C S C A L E TO M I L L I M E T E R S 1 S T A R T (I) - S T A R T (I) * S C A L E C C F I N D I N T I A L P O I N T OF COMPUTATION WITH R E S P E C T TO ' F I R S T ' 13 C O N T I N U E S T A R T (I) =START (I) +F.IRST 44 C O N T I N U E C C I N T I A L I Z E V E C T (I) TO ZERO C V E C T C O N T A I N S SUMMED C O N T R I B U T I O N S FROM S I N G L E F I B E R S DO 30 1=1,NO 30 V E C T (I) =0.0 C •C APPLY J I T T E R AND D I S P E R S I O N C NOTE. ONLY T H E J I T T E R WILL VARY I N EACH D I F F E R E N T MUP 112 DO 21 1=1,NFIBS S T A R T ( I ) = START ( I ) +PATH (I) C A L L F I B E R ( D I S (I) ,START ( I ) ,THI,NO, A J I T T ) C C SUM UP S I N G L E F I B E R C O N T R I B U T I O N S DO 2 9 J=1,NU 29 V E C T (J) = V E C T (J) +THI (J) 21 C O N T I N U E NCOUNT=NCOUNT+1 I F ( N C O U N T . GT. ZEE) GO TO 4 C C CHECK I F T H E D E S I R E D NUMBER OF MOP'S HAVE BEEN COMPUTED C S T O R E T H E P O T E N T I A L I N UNIT 1 C A L L W R I T E ( V E C T , L E N , 0 , L N R , 1 ) GO TO 3 9 4 C O N T I N U E S T O P END C S O B R O O T I N E F I B E R ( D I S , S T A R T , T H I , N U M B , A J I T T ) C T H I S S U B R O U T I N E COMPUTES T H E S I N G L E F I B E R P O T E N T I A L C T H I S S I N G L E F I B E R P O T E N T I A L I S BASED ON T H E D I P O L E MODEL C OF R O S E N F A L C K (1969) R E A L T H I (NUMB) R=DIS .S = 0.25 , C C D I S T A N C E BETWEEN THE P O L E S =2*S I F ( A J I T T . NE. 0.0) GO T 0 4 AMP=1.0 Z = EANDN (T) AMP=.F*AJ.ITT • 12 CONTINUE Z=STAST DO 15 1=1,NUMB A= AMP/ (SQET { (Z + S) #*2 + R**2) ) B=AMP/ (SQ3T (.(Z-S) **2+R**2) ) T H I ( I ) = A - B C C INVERT THE POTENTIAL (DOWNWARDS + VE) C THIS I S THE CONVENTION IN ELECTROMYOGRAPHY THT (I;) = -THI (I) 15 Z=Z+0.1 C GO TO 12 C C APPLY AMPLITUDE J I T T E R U T=SCLOCK (0.0) C INCREMENT BY .1 MM. RETURN END APPENDIX E COMPUTATION OF.THE AVERAGED. POTENTIAL, THE VARIANCE AND THE PLOTTING OF RESULTS c — • • • C** T H I S PROGRAM COMPOTES T H E AVERAGE S I M U L A T E D P O T E N T I A L , C T H E VARIANCE,AND PLOTS THE R E S U L T S ** C c C * I N P U T PARAMETERS C NAVG NUMBER OF P O T E N T I A L S C U N I T 1 C O N T A I N S T H E MOTOR UNIT P O T E N T I A L S •C* OUTPUT • C U N I T 6 V A R I A N C E V A L U E S ARE PRINTED ON T H I S U N I T ' r» C U N I T 7 WILL CONTAIN T H E AVERAGE P O T E N T I A L C C * UPPER L I M I T S 200 MOTOR ACTION P O T E N T I A L S C C L A S T UPDATE =5 A P R I L 1 9 7 6 . C c . . C T H I S PART OF T H E PROGRAM COMPUTES THE AVERAGE MOTOR. UNIT P O T E N T I A L C REAL Y ( 2 0 0 ) ,X (200) , AVG (200) , VECT (200) I N T E G E R * 2 T E N R E A D ( 5 , 2 9 0 ) NAVG 2 90 FORMAT ( I 3) C C I N T I A X I Z A T 1 0 N NCOUNT=1 DO 66 1 = 1 , 2 0 0 66 Y ( I ) =0. 0 C C READ I N T O ARRAY X T H E P O T E N T I A L S TO AVERAGED 11 C A L L READ (X , L E N, 0, L N R , 1 , £ 5 0 1 ) L= LEN/4 DO 4 1=1,1 C C SUM THE P O T E N T I A L S 4 Y ( I ) = X (I) +Y (I) NCOUNT=NCOUNT+1 I F (NCOUNT. L E . NAVG) GO TO 11 F=N AVG C F I N D AVERAGE BO 2 3 1=1,1. 23 Y ( I ) . = Y ( I ) / F C C SAVE THE AVERAGE DO 24 I = 1 , L 24 AVG (I) =Y ( I ) 114 C WRITE AVERAGED P O T E N T I A L . INTO U N I T 7 C A L L WRITE (AVG, L E N , 0 ,1 NR, 7) C C PLOT T H E AVERAGE . C A L L D I S P ( Y , L ) C C T H I S PART OF THE PROGRAM COMPUTES THE V A R I A N C E C C IN T I A L I Z A T I 0 N NCOUNT=0 DO 14 .1=1,200 1 4 V E C T (I) =0. 0 C , C COMPUTE T H E V A R I A N C E REWIND 1 C C READ I N T O ARRAY X T H E P O T E N T I A L S 3 C A L L R E A D { X , L E N , 0 , L N R , 1 , & 501) DO 5 1=1, L 5 V E C T ( I ) = V ECT (I) + (AVG ( I ) -X (I) ) **'2 NCOUNT=NCOUNT+1 I F ( N C O U N T . L T . N A V G ) GO TO 3 DO 2 9 1 = 1 , L 29 V E C T ( I ) = V E C T (I) / F C C WRITE V A R I A N C E ON UNIT 6 WP.ITS(6,99) ( V E C T ( I ) ,1=1 ,L) 99 . FORM AT (2X , 5G10.4) C C PLOT T H E V A R I A N C E C A L L D I S P ( V E C T , L ) C A L L, P.LOTND STOP . 501 STOP % 0 1 END S U B R O U T I N E D I S P ( Y , L ) C C T H I S S U B R O U T I N E CONTAINS T H E P L O T T I N G R O U T I N E S R E A L T I M E (200) ,Y (200) T I M E (1) =0.0 DO 25 1 = 2 , 1 25 T I M E (I) = T I M E ( I - 1 ) +0.. 1 C A L L S C A L E ( Y , L , 5 . ,XMIN,DX,1) C A L L S C A L E ( T I M E , L , 6 . , Y M I N , D Y , 1 ) C A L L A X I S ( 0 . , 0 . , ' A M P L I T U D E • , 9 , 5 . , 9 0 . , X M I N , D X ) C A L L A X I S ( 0 . ,0. , • D I S T ( M I L L I M E T E R S ) ' ,-1.7,6. ,0. , YMIN , D Y) C A L L P L O T ( T I M E ( T ) , Y (1) ,+3) C A L L L I N E ( T I M E , Y , L , 1 ) C A L L PLOT ( 1 2 . 0 , 0 . 0 , - 3 ) RE TURN END 115 REFERENCES [I] H. Piper, Electrophysiolbgie Menschlicher Mxiskeln. Berlin: Julius Springer, (1912). [2] E.D. Adrian and D.W. Bronk, The discharge of impulses in motor nerve fibers, II. 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