THE TORQUE- BNGTJIAB VELCCITY RELATXONSHIP IW HUMAN PUSCULBR GOl?TRBCTZON by David Jchn Sanderson B.Sc, [Kirtesiofoqy) Simon Prasef University, 1972 @ DAVID JOHB SANDERSON 1975 SLHQW PRASER UWPVEBSITY AUGDST 1935 All riqfits sesesv'ed, This thesis my not be reproduced in whole or in part, by vhotoccpy or other means without per~issionof the authcr, APPROV WI, NAME: David John Sanderson DEGREE : qast er of Science (Kinesioloqy) TITLE OP THESIS: The torque-anqulas velocf ky relatkonshi~in human muscalar contraction Dr, N,M,G, Bhakthan Dlcl A, E. Chapraant Senior Supervisor Dr- J,B, Wsrrison Externaf Examiner Associate P rofessos Kiaesiol oqy Depar taent Siaen Fsaser University PARTIAL COPYRIGHT LICENSE I hereby grant to Simon Fraser University the right to lend my thesis or dissertation (the title of which is shown below) to users of the Simon Fraser University Library, and to make partial or single copies only for-such users or in response to a request from the library of any other university, or other educational institution, on its 'own behalf or for one of its users. I further agree that permission for multiple copying of this thesis for scholarly purposes may be granted by me or the Dean of Graduate Studies. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission, Title of Thesis /~issertation: I -Author : (signature ) (date) iii This study proposed exa~inationof the characteristics of an assumed model of muscular contraction for intact human t~usclcs, This model co~prisesthree components; a contractile component (CC) , an elastic component in series with the contractile component. fSEC) and an elastic component in parallel with the other tua components [PEC), It has been shown on isolated muscle preparations that there is a difference ia the force-velocity curve ascribable to the method used in the deterwination of that curve, This observation sti~ulatedthe present invesigation. The saae apparatus %as used for two separate experintents to determine the torque-angular velocity relatianship of tbe elboa flexors over a range of excursion of the elbow-joint- Experiment 1 used the method described by fllacPhsrson 11953) for isolated muscles and adapted it to intact human ~uscular contraction, This method, based on non-linear differentiaf equations, was successfully adapted to the present experimental situation, However, the experimental results exposed sum curious events, A necessary condition for the completion of the analysis was that the rise in tcrque in an isometric contraction be quicker than when there was an added series co~pliance. While other research has shown that this condition can be satisfied on isclated psepara tions the exact opposite event was recorded repeatedly here, Possible anatoaicaf and physioPoyical explanations were discussed but it was concluded that further research was required, Kxyeciment, 2 deal* with the develop~entof the torque-angul ar vcf ocitp curve from dynamic con tractions, To obtain points on the torque-angular velocity curve when the velocity was zero some isometric contractions were co~pletedat five elbow positions from 0-5 radians to 2-0 radiaras where 0-0 radians was full extensio~,There appeared to be a variation in the torque-angular velccity curve as a consequence of the position of the elbow-joint, This variation arose out of the interaction of two co~~cnents;the effect of the change in length of the muscle in reducing the production of torque at long lengths, and the mdifications to the angle of pull of the tendon on the radius as a consequence of the joint anatmy. The compliance of the SEC was determined froin the torque-angular velocity curve derived from dynaaic contractions and the rise of torque during an isometric contraction, The compliance- torque curve appeared si~llar4x1 curves shown in other studies, The shape cf the compPia~ce-torque curve was similar regardless of the angle of the elbow--joint, This implied that the chaxacteristics of the SEC did not change with elbow position, TABLE CF CONTENTS PAGE ABSTRACT iii EfST OF TABLES vii LIST OF FEGUPES vii f IN TWO DUCT ION 11 RELATED LITEXATUHE Bistorical development Characteristics of isolated muscle Characteristics of intact muscle Statement of Problem 111 &ATERIALS, SETHODS and PRQCEDUBES Raterials ?jethais a) The apparatus used for the measufentent of torque, displacement, ana acceleration b) The dynamometer used for the transduction of torque, dispfacement, aad acceleration i) Transduction of torgue iif Transduction of displaceneat iii) Transduction of acceferation c) Calibratian of transducers i) Static properties ii) Dynarilic properties d) Filtering the output from the transducers e) Permanent recording of the output from the transducers i) The frequency modulated (FB) tape- recorder ii) Analogue to digital conversion iii) Becording oscilloyraph Procedures a) Proceuures-Experiment 1 i) h'ork-session 1 ii) Work-session 2 iii) Ktsr k-session 3 tt) Pcacedures - Experi~lent2 IV EETtiOU Cf AMALYSIS a) Calibration during the experiment i) Calibration constants ii) Determinalion cf the inornent of inertia of the foreata iii) Est iatation of the gravitational effect on the lever with the cast and forearm attached b) Experiment 1 - Deteraination of the torque- auaular velocity relationship from two isometric contrac tioris i) RacPhersonss method ii) ~odification to fit rotational systea iii) Data manipulation c) Experiment 2 - Determination of the torque- angular velocity relaticnship fro^ dyna~ic con tractions i) Data manipulation ii) ~eterlftinationof the time-constant ol the rise in torque iii) Determination of the compliance of the SEC V ACCUXACY OF RESGLTS 76 Vlt RESULTS 78 YXI DISCUSSION a) Experiment 1 b) Experiment 2 VIII CONCLUSIONS 729 IX SUBMARY 13 1 APPEW DIXES 138 vii LIST OF TABLES TABLE 1: Time constants for the rise in torque during isometric contractions for subjects AC and BW, FIGURE 1 : The length-tension curve for iscfated frog muscle, FfGUWE 2 : The force-velocity-length curve for isolated rat yraciius anticus ~uscfe, FIGURE 3 : 'The finear horizontal eguivafelnt @ode1 used to describe elbow flexion $or intact human muscle, FIGURE 4 2 The a-pparatus used in the present study, FIGURE 5 : This sprinq ~rovideda coapliant connection between the two half shafts, FIGURE 6 : This shows the tuo halves of the cast used to prevent grist Elexicn d uriny coa traction, FIGURE 7 : This is a schematic of the dynamometer used in the experiment, f IGUBE 8 : This 3s the circuit diagram for each of the transducers, FIGURE 9 : This is the main amplifying unit, FIGURE 10 : This is a drawing of the systeu described by BacPherson (1953)- PXGUBE 11 : This is a drawing of the system described in figure 10 as modified to suit the present study, BIGfJSE 12 : The rise in torque in two contractions, one with the added compliance and the other without the added compliance, FIGURE 13 : The torque-angle curve for subject AC, PIGUXE 14 : The Sorque-angle curve for subject, fly. PIGURE 95 : The torque-angular velocity curves for different sessions and at different joint angles for subject AC, iZ FIGURE 16 : The torque-angular velocity curves deter~ined by drawing a smooth line through the points displayed in figure 15. FIGURE 17 : The torque-angular velocity curves for differeat sessions and at different joint angfcs for subject H&, FIGURE 18 : The torque-angular velocity curves determined by drawing a smooth line through the paints diplayed in figure 17, PfGfJRE 19 : The compliance-torque curves for different sessions and at different joint angles for subject AC, FIGURE 20 : The compliance-torque curves for different sessions and at different joint angles for subject HW, I NTROD KTION A great deal of the knowledge concerning muscular contraction Bas been deterntined irom experintents with isolated muscl e preparations. These preparations were desirable becanse variables such as ~usclelength and activation conld be carefully controiled, Bhile these studies were used to examine the tnechanisrrrs of contraction in frog ntuscles the results could be applied to intact huaan ~uscles, In this manner a composite picture of muscular activity could be obtained, Hany investigators have used conceptual ntodels to describe the ph ysiaf ogical events snsrounding muscular contraction* A c~nceptuaPsodel has been devised which describes quite satisfactorily the phenoaena associated with @uscufar contraction, ~igorousapplication of this @&el to describe more coapfex systems, e,g, intact humn auscufar contraction, has pfosented so&@problleas, For exarttple, WiLkie (1950) used a conceptual mdef to describe flexor activity in human subjects- Chap~aa (1973) has shown that Wilkiets conclusions were particular to one elbou position only and that there were changes ia some other factors vhich prevented the sxtrapola tion from WilkieJs data to other elbow positions, B rstodel which is applicable to one set of conditions only is not as useful as one vhich describes activity uader a wiae range of conditiaas. B major problem associated with precise determination of -the characteristics o+ intact muscle is attributable to the complerit'y introduced by considering the ~nscleas part of a such larger corapfex system, It is difficult to quantify, and ia sofae cases qualify, the invo1vttrrteu-t of extraneous factors so as to take their affect into account, This is especially evidest when one has to consider the conscions subjective control of the human subject over his actions, The present