The Torque-Angular Velocity Relationship in Human Muscular

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

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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 experiraents exaatine the dependaacy of the torque-angular velocity curve for huloan ltrusclufar contraction on the technique used to derive that curve- The charactefistics of the CC depend upon whether the experimental conditions required isometric contractiosjls or uhether the conditio~srequired dynamic contractions (ParlrtJeg, Yeatman and

Sonnenblick, 1970)- If the behaviour of an isolated muscle depends upon the type of resistance encauntered then one can only wonder at what constitutes the real characteristics of each co~ponent, Isonietric and dynamic contractions will be etllployed in this study to derive the tofqne-angular velocity curve which should provide a weans of cofpariny the characteristics of the nauscle under different axp~riritental conditions,

The follouing section outlines sonm of the historical devefop~entof research in this area, This section is followed by the description 02 an experinent designed to investigate sortie of the areas associated with human muscuXar contraction-

The implications of these findings are discussed in the final sections, HPLWTED LITEXRTUW E

Historical Development

In an atte~ptto understand the mechanis~sof gross muscular aclxvity investigators have used mechanical analogues. They attempted to design ~echanicalmodels that adequately described the many characteristics of this physiological activity, Early studies ref icd upn observatious on the mechanical oukput of a ruuscie, later, measures od the heat released during a contraction &ere used as iudicators of any internal changes ~esuftingin that aechanical autput,

The observation that a muscle moved fighter loads at a higher velocity than it aoved heavier faads initiated considerable research into the subject of the aechanical features of muscular contraction, Early investigators

(f ick,lY82; Blix, 1893) represented the ~luscfeas a spring moving through a visccus aedium and they observed that a tetanized muscle did less work if allowed to shorten quickly against a small mass, This observation %asconsidered indicative of the su~positionthat vhen shortening much of the muscular energy was degsaded into heat vhen overcoming the internal or viscous resfstance, This internal resistance was greater the more rapid the movement [Fick, 7893)-

Lanlaine (3905) was arrtong the first to recognize explicitly that in human muscular movement the efficiency

(work/total energy used) varied with the speed of contraction. The existence of such a rflationshi~invited studies into the possibiiitj uf a rziati6aski.p between sho~teflingspeed and force exerted, Surprisingly, this line of investigation was not undertaken until Hill (1922) reintroduced the idea of 3muscle viscosity8 to account *or the decrease in force uith an increase in th~spea of shortening observed during experimeats on the elbow flexors, He showed that the work done increased rapidly at first during a single contraction and then Bore slowly beconing asymptotic with time reaching a theoretical maximum, This observation identified the amount of energy degraded to heat uith viscous resistance vithin the muscle, The amount of energy dissipated in overcoming the f rictionaf resistance was psoporticnal to the speed cf the contraction

(Lupton, 1922)-

Gasser and Hill (1924) repeated Hillis earlier work Iro examine whether there could have been any reciprocal innervation that wouPa have distorted HillSs studies (i-e, the results might have been the consequence of nervous activity rather than muscle activity alone), They were able to confirm

E[ii19sconciusicns, however, using isolated Irag muscles, They concluded that ,, the ~hencmenainvestigated are not due primarily to an inkervention of the nervous system, but to some fundamental character ot the auscle fibre itself-8*{Gasser and

Hi11, ?92q), The question ok whether the relationship was the consequence of a viscosity tactor remainea to be determined,

In 1327 Eevin and Wyman studiea quick stretches and releases in contracting muscle, They cbserved that the tension never responded instantaneous1y to the stretch or felease, secondly, the classicaliy proposed linear relationship between force and velocity of the theoretical viscous model was found instead to be a non-finear one, To account for these differences Levin and Pyman suggested solncz nttodifications to the single spring rsodel prexiously postulated, They proposed adding an undamped spring in series with the damped spring. This latter mdel satisfactosilg described their data, The investigations of Boukeart, Capelfen and de Blende

(1930) also confiraed the modifications of Levin and gyman- The coaclusions they reached fsoa stndies on isolated Erog muscle, were that H,,, there was no doubt that the auscfe behaves as a viscous elastic systeln of the darttped undamped two spring type, '*(Mukea-ft et al,, l93Q), The investigations during this era supported the viscous hypothesis which was considered applicable to a wide variety of muscfes from dogfish

{Bursh, 1938) to tortoises (kyraan, 3926), Houever, Fenn in cooperation with Harsh produced soae cantravgrsial findings that demanded lnodification of the viscous node1 IPenn and Barsh,

1935) ,

Fenn and Harsh 11935) exa~inedthe rauscular force at different speeds of shortening usinq isolated frog and cat

Bustles by studying the mechanical properties of muscle deprived of any participation By possible &on-viscous elastic elements, This was done by observing the speed of shortening Under different isotonic loads varying froftl zero to the ~laxiretuoa which could be Lifted.

They found that the force-velocity characteristics of the

isolated contractile element did not follow the equation

derived by Hill (l922), They re-expressed the relationship

referring to a coefficient cf tension loss, rather than a coefficient 02 viscosity, as being a major factor in deter~iningthe force-velocity characteristics of a muscle,

This claim was supported by the observation of the non-lineasity of the force-velocity relationship, "--*this

exponential relation was concerned iq solne way with the process

of developing extra energy for the work of shortening and that

a muscle cannot properly be treated as a simple mechanical

systen,**,

Three years later Hill (1938) developed the force-velocity relationship in the course of experiments examining the heat

I production of isolated frog auscle, This curve was siailar to that of Pan and Barsh (7935) but obeyed a siaapler and more

I convenient relationship: [ j (P +a)V= {Po-P)b 1 1 i iorce, and ", where P is the V the velocity of shortening, Po the 1 1 isoaetric maximum force devefo~ed, The values for a and b were I t 1 chosen to give the best fit of the equation to a series of i E observed values of V and P and the constants *bf and *ag have I 6 I the diiaensions of velocity and Eo rce respectively,

This study uealt the final blcv to the viscosity

hypothesis which had held scientists captive for so long, "The

fact that a ~uscleshortens mote slowly under greater force was due, not to a~

The ~usclewas still described as a two-co~ponent system with an undamped elastic element and a contractile elemnt in series, The characteristic equation 2or the force-velocity relationship described the activity of the contractile element.

The characteristic equation 11) and ntodel suffered some limitations in thak they were essentially empirical arad aade no statements ahout the mechanisas underlyiag the properties of the contractile componsu t, They did describe accurate1y the phenomenological relationships and ia doing so provided a convenient mechanism by which one could study muscle action,

There have been other equations derived to describe the force-velocity reiationsbi~[Fenn and Harsh,1935; Polissar,l9!iL;

Bbbott and %ilkie,1953) but they were in no funda~aentalconflict with Hill's derivation, Later studies confirmed the appiicability 02 Hif 1's characteristic 2orce-veloci ty relationship to several muscle types without excluding the other possikle equations (Katz, 1939; Abbott and Lowy, 1952;

Ritchie, 1954) ,

Characteristics of isolated muscle

The force-velocity relationship adequately describes the activity of the contractile component (CG) of skeletal muscle,

Nabtever, there are &her structures uhicft also contribute to the ~echanicaEoutput of the ~uscle, fnvestigations into the properties of length and tension of a nuscle began as early as

1893 (Blix), Studies conducted through the fslloning years psoduced some conflicting results concerning the length-tension relatioraship and its anatcraical basis, gamey and Street (7940) ateri buted these conflicts primarily to differences in experimental technique and, as a consequence, to the magnitude of the resting tension,

To settle these differences RaBsey and Street f1940) examined the isoaetric length-tension diagram of isof aeed frog semi- tendonous muscle fibres, The length-tension curve that they developed comprised three subco~psnents,one being the sum of the other %no- The curve r in figure 1 reprgsented the passive length-tension relationship developed for isolated muscle, The muscle was stretched in stages and tension recorded at each increment of stretch, Having noted this curve the next step was to identify the anatoaical co~refates,The investigators developed a technique that allowed them to destroy the muscle fibtares alone without altering the external sascotrilarnma, f solated sarcclemma from such a p~eparation possessed a carve for the passive stretch identical to intact auscfe indicating that the safcolem~agas responsible far the passive length-tension curve for whcle muscle while the contractile material contributed nothing to this tension,

The active tension curve a in figure 1 was obtained by setting the initial muscle length and stinulating the muscle tetanicalfy, The relationship between force and length in this FIGURE 1 : The length-tension curve far isolated frog muscle w he~e: curve XI-- passive stretch of the ~uscle curve a - maximally activated muscle curve d - the difference between curves p. )r and a adapted from WiPkie, 1958,

case appeared independeat of the sarcolema tension and seemed

to act in parallel to the passive tension, This active curve

was actually the consequence al the interaction of t~o

components, the active contractif e co~poaent{CG) and the

passive parallel elastic component [PECf , X t is evident

froa figure 1 that the PEC contributes to the overafl tension only after a specific length has been obtained, This 'thfeshofd

length* is a characteristic of each individual muscle- If the passive contribution fcurve r) was sabtracted fro& the active curve (a) there renraiaed a bell shaped curve, Xt was thought

that this curve represented the true fength-tension carve for

the contractile cornponeat [curve d),

B wide variety of muscles have been investigated in this

Banner {see Ciose,1972), Technical limitations delayed the deter~inationoE the real length-tension curve of the

contractile coapsnent, These liaitations sere overcome ia 3366

I I when Gordon, Huxley and JuLiaa 11966f elrarained the effect of changes in length of a single sarcomere on the force developed

over a range of lengths of 130% of the resting length Lo- The

f nvestigators found a length-tension relationship that Mas

siailar to that of Ramsep et al, ff940)-

The eontractife coaponent has two characteristics that

describe its activityt These are the force-velocity

relationship and the isctw tric length-tension relationship, It

gas pertinent, therefose, to observe vbether there was any

interplay between these which would affect the develop~entof

force or tbe shortening of the auscle- Hill (1950) stated that ,_,?he experimental relatim between speed of shortering and load could be expressed by a family of curves, each for a given rnuscle length over a

considerakfe range ,,, it was given mathematically by the single characteristic equation,., ",

r3sing frog sartorious utuscPe Abbott and Wilkie j1953)

examined the selationship between the velocity of shortening

and muscle length to verify whether Rill's charackeristic

equation fitted at other wuscle lengkhs, They found that if the

isometric maximum force far that muscle length aas used as Po

then the equation fitted very well, In othes words, there was a

range of force-velocity curves each a charackeristic of soBe

~alueof Po which could be attributed to the resting auscle

length,

Bahler, Fales and Zierler 11 968) exa~inedthe

interrelationship of force, velocity and muscle length $',-,of

the contractile coiriponent of tetanicallp stimulated intact

mannaliaa skeletal muscle, the rat gracilis antic~s,~. The

results were displayed as a three dimeosicnal representation of

the family or force-velocity curves with respect to muscle

length [figure 2). It may ke seen that the instantaneous length

through uhich the muscle shortened a•’fected both the vef ocity

o•’shortening and the force developed,

The development of the length-tension relationship, the

force-velocity relationship and the interrelationship of all these factors on isolated preparations has been considered, The

next issue requir Zng investigation was whether the same ref ationships held for intact hunan ~uscfes- FIGURE 2 : The force-velocity-length curve for isolated rat gracilus anticus muscle adapted fro^ Bahler, %ales and Zierler, 6958

Character istics of intact nuscle

The problems of determining the characteristics of intact

human muscles are nunerous due to the concern for the well

being of the subject, Rafston, Znrrtan, Strait, and Shaffratlh

17947) attempted to find the length-tension relatioraship for

intact human muscles, Their subjects were veterans with

ampukated forearms, Expri~entalPythey were fitted cinepfastic

tunnels connect& to a tension recording device so that the

muscle tension at different lengths could be exaained.

These data showed a relationship sinilar tc that proposed

by Ramsey and Street [l940), However, there were some problems

in correlating the two studies because in the study oZ RaSston

g& al, 11947) tho muscles were not *normala muscles in the

ordinary sense, They oere nct attached to the forearia as they

would be in the intact subject and it was not clear vhere these

data of Ralston g&&, 37947) Lay on the total length-tension

curve of normal subjects. hlso, the aaximula .tensions recorded

were y uite low %hen compared to other studies pdilkie, IgSO).

That there gas at feast a similarity in the two curves

{isolated and intact) was encouraging since it iladicated a

possibility of conpasable length-tension refatiunships for intact human ~uscles, I I 1 Anather approach to studying the applicability of the a length-tension curve derived by Walston et a& (1940) to intact human muscles has been outlined by Stolcv and Weilepp (1965) - They cited six anatomical dements possibly contsibutiny to the pas~ivelenijth-tension curve, These were; 1, the outer

tissue sheath; 2, the perlirttysiutr! an3 endontysiu~;

3. the sarcofemaa; 4, the individual fibre contents; 5, the tendons at origin and insertion; and 5, adhesions to neighboaring structures, Although the exact contribution of each of these factoss remained unknown the autaors suggested that each &ust be taken into consideration when exaaining the

PEC and its contribution to the tension developed,

Dern, Levine and Slair (1947) atte~lptedto define the force-velocity relationship in human ~usclesabout the elbog joint, Bouever, thei~results were not described by the characteristic equation, The authozs documented sowe antagonistic muscular activity and suggested that this was one source ol discrepancy, Lack of consideration far the accef@ration of the arm vould have led to further error. The authors did not suggest that the characteristic equation was in fundamental error, only that f ufther study of its general applicability was required,

Wiifrie 11 950) propcsed the first signiflcant atte~plto apply the model to intact human muscles, He developed a force-velocity relationship for a tau-co~ponent XCC plus SEG) single equivalent ~uscle,parallel to the upper arm, acting at the hand (figure 3)- This model represented the combined effect of all the elbow flexor muscies, Its force-velocity relationship was accurately described by the characteristic equation, after justifiable corrections for the acceleratioa of the inertia of the forearn, PIGUSE 3 : The linear horizontal equivalent BO&?~ used by Hiikie (1950) to describe ef bow flexion f - horizontal force recorded L - torque produced 8 - efbow angle CC - contractile coaponent SEC - series elastic component adapted fssm iiilkie, 1950,

Aovever, attempts to generalize from gilkia+s model to thc range of movenent from a horizontal position to coraplete flexion of the e.fbors raet with difficulty, Chapman 11973) has shown wide variation ia horizontal force devefopeci through a ranqe of flexion of the elbow (30 of the greatest isoaetric force), Bilkie showed a 20% variation over 90 degrees of flexion, On the basis of these observations, it wuld seem that the single equivalent horizontal usa ale way be a fair representation of a ~uscleover a small range of lengths only,

Between elbow-angles of 0 degrees and 20 degrees [long muscle

Penqths), changes in force take place vhich are Ear too great to be compatible with those predicted from the relationship between isometric tension and length of a *realgmuscle,

Chapman I1 973) suqgested that a geometrical. correction may have to be applied as the tendons of the biceps brachii and brachialis pass over the capitulum and trachlea of the humerous respectively, This factor would alter the aagfe of pull of the tendons and in doing so alter the torque developed about the ef bow- joint,

The examination presented thus far has centered on the CC=

There is also a SEC which affects the transmission of the force developed by the CC to the insertion of the muscle, The presence of such a component has been evident from some of the earliest studies (Levin and Wyrnan, 1927)- These authors considered the SEC as an undamped spring in series with the contractife component and as such the SEC modified the rate of change of the external tension recorded as sell as the velocity of movement, Shiie the SEC has been shewn to be a passive eleaent throuqhout contraction Inilkie, 7 956) it does introduce peaking and ~scillationin the velocity-time curve during flexion of the forearm fPilkie, 1950)- Accurate determinatian of the velocity ot shortening of the CC is dependant upon the determination of tne velocity of move~entat the hand as a function of bath the changing fengthe of the SEC and the velocity of aovement of the CC, If the velocity of shortening of the CC is rapid then the velocity of flexion of the hand will be different by an amount equi~salentto the velocity of movement of the SEC,

The location OF the SEC has not been conclusively determined, It seems likely that some resides in the tendons 7950) tissue, has (Wilkie, and connective It also bean I suggested that some can be attributed to the contractile f material itself, In any case, it is not possible to remove the

SEC from intact musches and therefore some vigilance will have to be maintained on the effect of the changing length of the

SEC,

One factor which affects studies of intact huaan auscles is the degree of voluntary muscular activation, This probiem was most troublesome when repeatable maximal voluntary contractions are required, In isolated ~uscfepreparations the activation of the muscle would be very carefully regulated, In human muscles this regulation is not quite as simple, Factors I such as frequency of stimulation and the number of active motor units affect the rise of force (Bahler et at,1968), There is also the possibility of inkcrackion cf antagoaistic units resultinq in reflex control @ern et a,,1947)- In studies dealing with intact human muscles these factors raust be taken into account and corrected for where possible, Hew investigators have matie repetitive studies to confirm the achievement 02 repeated ~aximalactivation or whether it has been achieved even once,

Electro~yography(ERG), as a technique to explore the events ocurring within a muscf e, has received much attention.

Use of surface electrodes provides a simple non-invasive technique for aonitoring internal electrical activity*

However, there are a number of problems associated with the quantif icatioa of the EEG signal [Balston, 1967) and consequently there has not been any snccessfuf attenpt at refatiny the EaG sigaal, be it unprocessed os quantified in soae fashion, to the events leading to activation of the auscle. The purpose of this thesis is not in any way to attempt to devise such a relationship nor will any attempt be made to use E%G,

The problems of determining the effect of active state on the rise in force cannot be ignored, Jevell and Wilkie (1958) have shown that the theoretical rise in force derived frog isotonic force velocity relationships @as quicker than recorded experirsentaf iy, Parmiey, Yeatmasl and Sonraenblick (7 970) have derived force-velocity elations ships from isotonic and isometric contractions, Their results show that there was a consistent difference in the two curves, Both groups 02 iavestiyatars argued that this azcmaly csuld Se attcibuted to

differences in the active state of the muscle,

Pringle (1859) postulated a diEferent vie% of the active

state to explain these observations. Rather than hypothesize an

active state as being unaffected by guick stretches or guick

releases '*,,,oue might pcstulaee a property called, say

activation, which was increased by tension and which controls velocity of shortening at a given tension,", Using this

definition Pringfe was able to desccibe the origin of the \ differences between isotcnhc and isometric derivations of the \ force-velocity relationship, The force-velocity relationship

now represented the combined action of tension and activation

and the observations of Jewfl. a, (1958) aad Parntley at AS

(1970) could be explaised, Whether this vLew is in greater

harmony vith the underlying mechano-elecitrical-chemical events

than the traditional view, postulated by Hill (3949), remains presently undeterained,

Since this thesis is ccncerned vith the rate of rise ia

force measured under isoirietric conditions the above co~mentsof

Jewel1 & a, (3958) and Parmley et af- g1970) are i~portant- -7- If such dramatic differences were shoan in isolaked

prepa~atians,equally prcnounced variations Bay well be

observed in intact preparations, Obviously, extreme vigilance

%illhave to be aaiutained on ail factors affecting the rise in

force, Paraley ~t d, (1970) have shown that the force-velocity curve calculated from iscmetric contractions of isolated preparations uas different from that derived •’son the same preparations using dynamic contractions. Tt would be interesting to see whether the same observations would be made on intact human muscles. To cotaplete this task required the development of two techniques, one using isowetric contractions and one using dynataic contractioas, While these techniques are discussed extensively in the section titled Eethod of Analysis they will be outlined briefly here,

To derive a force-velccity curve from isometric contractions BacPherson (1953) devised a techaigue that relied on the development cf farce under two conditions, In the first condition the muscle contracted isometrically against a force transducer and the rise in force was recorded, A compliant structure fa spring) was then fixed between the muscle and the transducer and the muscle was sti~ulatedagain- In both conditious the stimulaticn ~roduceda maximal isometric contraction but the rise in force in the second instance was sloves than in the first instance, The magnitude of the compliance had to be farge enough to permit the separation of the tuo force-time curves but not sa farge as to permit gross changes of the rnuscle length, MacPherson assunted only that the velocity of shortening was a function of the force developed,

With this assumption he was able to use the differeatial of the ~isein farce in the +uo ccntractions and throagh a series of mathematical manipulaticns determine the velocity of shortening

05 the coutractile component, This method is very aesirabfe as it permits the determination of the force-velocity curve of the contractile cowponent fro^ tuo contractions usnaffected by the sex ies elastic component. The SEC modifies the velocity of shortening of the CC as it transmits that velocity to the insertion of the muscfe, If this effect caa be bypassed then the determination of the force-velocity curve of the CC is very mch simplified,

The method of uevefoping a force-velocity curve for hu~an muscles from dynamic contractions is not quite as straight forvard as when it is developed isontetrically. The rotation of the elbow, the interaction of the series elastic cowponent in the modification of the velocity of shortening of ad joining structures and the interaction of the subjectJs conscious awareness of the required muscular activity all affect the fofce recorded, Bezore one can isolate the force developed and velocity of shortening produced by the contractile component alone, the magnitude uf the iuvolveaent of the interfering factors must he assessed and subsequentf y reatoved, f deal1y, for the determination of the velocity of shortening of the CC the rate of change nZ torque must be zero. At this point the veZocity of the hand is the sam as the velocity of shortening of the CC, However, this restricts the selectiam of points for the dsveiopment of a torque-angular velocity curve and it Bay be desirable to select a range of torques where the change is small ~nnughto Fntmducc a negligible error in the calculation of the velocity of shortening of the CC. This possibility will be explored in the section titled 'Hethod of Analysis*, Once the two methods Tor development of the torque-a~gular velocity curve are devehuged the study proposes to exa~inzthe f ollowiny;

1, Is there a difference in the torque-angular velocity curve derived from iso~etriccontractions when co~pared

to a torque-angular velocity curve derived from dynamic

contractions?

2, Through the range of excursion of the elbow-joint is

these suff icieat lengthening of the Ct to change the force produced by the muscle? 1 3, Do the properties of the series elastic coapanent is change durinq a maximal contraction at different joint

posit ions?

4, Does Wlfkiegs single equivalent model adequately

describe the characteristics of human muscular

contraction? These were two grouFs of subjects in this study, The

embers of each group were healthy male university personelf and their aqes, weights and statures were listed in Appendix I,

All subjects were right handed and although some exercised

reqularily none were engaged in progressive resistance

exercises, In group one there were niue subjects and in g~oup

two there vers two subjects, a) The apparatus used for the ncasurement of torque, displacemsnt and acceieration

The apparatus [figure 4) essenltially comprised the rear axle of an automobile which %as supported with its outer casing rigidly fixed in a wooden tressle and aligned parallel to the sagittal axis of -the subject, The two half-shafts, coraplete

! with hearings, remained within the casing of the axle and as the differential had been removed, the tuo opposinq eads of the ha12 sha%&s%ere joined with a mila steel collar, To the collar was attached a spring which could be so arranged to provide a

~ornpfiant connection betreen the tuo half shafts [f icjurs, 5)-

At one end of this apparatus were located the torque, 11 111 acceleration and dispfacemeat transducers and the aechanism for aligning the subject with the apparatus, The subject was seated in an adjustable chair with the right arm elevated so that the upper arm was horizontal in the coronal plane, There was a vcrtical suppcrt for the elkow as well as a chest support to stabilize the subjectrs position, To maintain this position safety belts were passed around tbe subjects chest and thighs and attached to the apparatus,

At the other end of the apparatus was located a board that was used to fix the position of the axles for the isometric pulls as well as provide a convenient place to hang the weights for the dynamic pulls, FIGURE 4 : The apparatus used in the present study, (see text for a complete description)

FIGURE 5 : This spring provided a coapliaat connection between the two half shafts,

FIGUXE 6 : This shows the two halves oP the cast used to present vsist flexion during cantractiora-

FfCUBE 7 : This illustrates a schematic of the dynamometer used in the experiment, The various transducers were attached to this dynamolrte ter, The ditnensions of the beam {in cms) are as follows;

Tc li~ittbe flexion cf tZz forzarm 2 fibreglass cast was taped to the su~jectsfoream, This cast consisted of tso sides and extended from the fingertips to the elbow, It did not iirait elbow flexion but it did prevent wrist flexion, On the pafwer side awl located in the centre of the palm a block of %~00dwas fixed with a thxeaded bolt which could be attached to the beam

[figure 6)-

b] The dynaraoraeter for the transduction of torque,

displacement and acceleration

The dyn~rnometer (figure 7) was required to register torque, displacement and acceleration with ref ererice ko the axis af rotation of the efbcer joint, Xn order to keep compliartt connections to a miniaum, a beam, to which the forearia cast could be bolted, was chosen as the basic unit of the dynanometer, This beam or lever had to be constructed in such a manner that it allowed the individual transducers to operate without interference, While rigidity was important a certain amount of bend was necessary to ensure an output from the strain guage transducers, This criterion was determined by the characteristics of the strain guages which had a linear range of resistance in response to strain between zero and 1/1000 of their unstraineii length, Tc meet these specifications a beaw was chosen that would bend 20 more than ,00125 radians at its outer end (40cn from the axis of rotation), This transauction was coapleted by four strain gauges

(type MA-0b-250BG- 120, manufacused by Eicro Ceasurernents,

~ich,) attached to the beam, their long axes coincideatal to the long axis of the beam, 10 cns from the centre of the axle,

The four strain gauges were wired together as the active arBs of a Wheatstone bridge {figure 8)- The use of four gauges minimized the eifect of temperature [all four uould be affected thereby increasing the stability) and allowed for greater resolution of the applied torque as two of the gauges wers subject to strain while the other two were subject to compression.

ii) Transduction of displaceaent

The transducer for recording displacement was a wire wound potentiometer with a resistance which varied from O ohms to 10 kilohrns (type 153-585313, manufactured by TRC, St, Petersburg),

The axle of this potentiometer was fixed to the oentre of the half shaft closest to the subject, The transduction of the angular displacement of the Dea~from the horizontal iiepended upon the f inear relatienship between angular displace~entof the shaft and the electrical resistance of the potentiometer- FIGURE 8 : The circuit of the Wheatstone Bridge fR1 to 8G) along with the power supply (2-5v) and the balancing resistor {Rd) used for the transducers of tafque and angular acceleration, The bridye used for the transduction of torque invovled R3 and R3 in compression and $2 and BY in tension or vice versa depending upon the direction of the torque, The bridge used for the transduction of acceleration involved R2 in conpression and B& in tension or vice versa depending upon the direction of the acceleration while El and R3 remained fixed in value, The nominal values for the resistors fin ohms) ace as follows:

Torque acceleration both 31-R4 = 120 variable El and 23 = 320 fixed R6 = 10K R5 = O •’32 an4 R4 = 320 variable X7 = 10R 25 = 1K R8 = IDK H9 = 1M

FIGUBE 9 : This shows the main amplifying unito

iii j Thc fransducticn of accefcration

This was performed by a miniature accefer~~eter{type i3LA2, manufactured by Pye Dyn., London) mounted on a rigid clip fixed to the outer end of the beam, The sensitive axis of the acceleroaeter was oriented with the sensitive axis of the beare,

A small inertia affected the output of the strain gauges vithin the accelerometer when the transducer was subject to acceleration, These two strain gauges were coupled with two fixed resistors within the amplifier tc form a Wheatstone bridge circuit,

The power suppiy tc each transducer and a~piificationof its output voltage was centrolled by separate strain gauge amplifiers {type AD6) mounted in a single inteqfated unit [type

TE4, manufactured by Teca, Ghite Plains, N, ]I,), See figure 9-

c) Calibration of the traasducers

i) Static properties

To assess the hidirectionalitg of the torque transducer a series of weights were hung from the slot when the lever was horizontal on either side of the vertical, A plot of the relationship between the known applied torques and the calculated torques, based cn the output of this transducer, showed that the torque transducer exhibited a linear response bidirectionaUy, There was no measureable variation from this expected for even the strongest ctf subjects.

Since the accelerometer and torque transducer weEe subject

to the effects of qravity the output for the full range of

positions was expected to be proportional to the cosine of the

angle of the beam, This angle was determined by aligning the

displacerttent transducer so that at angle 0 (fever horizontal)

i: p the output voltage was 0 and the output voltage was fullscale (1.25 V) at the anqle 180 degrees, By knowing the angle and

recording the cutput from the other two transducers a plot of

and torque transducers followed a cosine curve,

iif ~ynamicproperties k h The dynamic properties 0% the transducers were assessed as 5 f ollorsrs: t

1, The angle measured from the output voltage of 'the

displacement transducer was compared with i he angle determined

ky rapidly mtatiny the lever as it was illuminated with a

strobosc~piclight and photographed, There was no detectable

difference between the results obtained from the two ~ethodsof

determination of the anqle,

2, The frequency respcnse of the torque transducer was

determined by examining its output fo-llowing a step input- The

output of the transducer was exponential in form with a

time-constant of 10 msecs indicating that it would faithfully repr35uce the sisnals slcgfr than this, Thc time constant for an isometric pull has been estimated to be near 50 msec which is well within the capabilities of the apparatus,

3, The response of the accelerometer was assessed by oscillating the lever from the opposite end of the apparatus, A bolt was fixed to the slot in the beam so that a larger output from the torque transducer could be achieved, Because the inertia of &he bolt and beam was constant the ratio of the torque to the acceleration should also have been constant, A variation of 2% was observed in the response of these transducers, This variation was attributed to the frequency response of each transducer, This was not a ssrious defficiency since the signals sere filtered prior to analysis or storage as described below, Hence, the signals were attenuated to the same level,

d) Filtering the oatput of the transducers

Electronic filtering of the output from each transducer permitted the removal of nonphysiological disturbances, such as the natural frequency of the bean (36fia,), and matchinq the Sreyuerxq response of the acceleroneter and torque tsansducer . The output from the accelerometer contained the highest

frequency components anrd hence, the unfiltered outpuz from this

transducer was recorded and subsequently played back through an

ad justabhe analogue filter, The band uidth or frequency response was deterained by narrowing the width until the signal. was attenuated 3db, The recordings demonstrated that the signal became attenuated below freguencies of f 2Hz f-3db), The cutoff frequency was chosen to be 35Hz 4-3db) to raaintain a aargin of safety.

ef Permanent recording of the output f ro~tt the transducers

i) The fregueaep aodulated (FE4) tape-recorder I$+ An f tape recorder {type 309Q&, nanufactured by Hevieit Packard, Colorado USA) was used to store the outpnk frortl the transducers, This recorder has Eouf separate channels each with an input and output amplifier, Each ainplifier has a gain control which afLoued the nser to maintain the input and output f~ltagesvithin the iifiear response range of the amplifiers

{f u3.f scale 0-2.5 8)- The tape used was low noise Phiflips Xnstruaentation tape {aanufactured in Vancouver Canada) - 535 ca in width, The record and playback speed gas 38- 1 can/sec, The centre frequency of wodufation was 27KHz and the signal to noise ratio was 48db-

The input signals sere filtered to and froa the tape recorder through the saw filters, This served to reaove any high frequency noise generated by the tape-recorder during either the recording or retrieval process, . XL) Anal o~uctc digital conversion

In o~derto use a computer for the computatioa it was necessary to transfer the analogue signal on the F2 tape recorder to the computer, Phis was completed by transfering the data through a 10 bit, 10000 samples per second aaalogue to digital converter {type BDC, manufactured by Digital Equipment

Corp,, sass. USA) which was a peripheral unit to a minicomputer with 12K locations of 12 bits each (type PDP-8e, aaufactured by

Digital Eguip, Corp,, Bass, USA), All signals were converted at a sampling rate of 200 samples per second, This was chosen as the minimum rate which would accurately reproduce the inptrL signal, A cornprornise between the ideal saatple rate and available storage space vithin the coiaputer was necessary and therefore a higher sampling rate could not be used as it vould result in an overfilling of the storage,

Tha process of conversion was controlled by machine language (BAT, 111) while the initialization was controll*d by the operator through a conversational language FOCAL, A control switch was used to initiate the acquisition and to reset after

completion of one pass, PC acquire +he data the operator played

the output from the tape recorder to an oscilloscope with storage facility (type 1201 A, ~anufacturedby Heslett Packard,

Colorado USA) and then replayed th~output with the iraage remaining on the screen, As the image moved across the screen a second time the uperatcr initiated the A-D with the control switch at the appropriate time, Storage of LX+= data was conrpli;ted in Giyitiaed fora ou

~agnetictape (type DECTAPE, ztanufactured by Digital Equip,

Corp- Eass USA) through a tape drive systertl interzaced with the computer.

iiif Recording Oscillograph

A inufti-channel oscillcgraph {type 5-127, manufactured by

Bell and Howell, Basingstoke, Eng,) was used to record the rise in torque in a series of of isometric contractions, These data were used in the determination of the compliance of the SEC as well as in the determination of the time-constants of the rise in torque, This oscillcgraph was connected on-line with the transducers elirninat.inq int~rlmstoritqe or! F%e ??PI tape-recorder. PROCEDURES

This study comprised two segaf ate experiments, The eguipaent used was the salne but the procedures for each

experiment differed greatly ant3 sill be itiscussed separately, i be aim of the first experinent uas to obtain a torque-angular velocity relationship f roa isometric contractions while

that of the second experi~entras determination of the same relationship from dynamic contractions,

A) Procedures - Experimenk 1

Subjects attended experimental sessions at their convenience, 811 subjects attended three such sessions each session being separated from the others By no less than one

week, These sessions will be termed uork-session 1, 2 and 3-

The purposes of this session were to locate accurately the subject within the apparatus, to determine the maent sf inertia of the forearm and to familiarize the subject with the

expari~entalprocedu~es of the study-

The first step was to attach the cast to the forear% A

light uadeswrap was used to ease the coatact bstween fibreglass and skin when the cast was attached to the foream, The wrap was tightly compressed and contributed a negligable amunt to the compliancc2 of the forearm. The cast was placed on +Ee forearm, sdjusted to its most comfortable position and secaroly wrapped with tape in order to prevent wrist flexion without restricti nq bloc4 flow,

The subject was then placed in the cxperimentaf posj +.;on and the apparatus adjusted to ~akethe axis nf the qik~%-inin+ coincidental with the axle and +o position the uppnr arm horizontally, A safety strap fro3 an ai~tomrtbiln was placzd around the chest and another around the +kiqhs to elimina*~ gross changes in the ex~erimentalposition, To check tht? location of tho elbcw-joint a pencil was attached to the cay+ and the suhject was instructed to flex the elbcu-joint s? th?* an arc was drawn on paper placed verAically in the frontal plane of th~sukiect,

This procedure was repeated several times and the pespendicular tisectors nf two chords drawn on these arcs intersected at the locaticn of the axis of rotation of the efkoa-jaint, Any necessary adjustaent was made to the el5nw and chest suppnrts to aljgn the axis c-E rotation of the elbow with tha axle, The individual p~sitioncf suppcrts for th~ chest and elbow were noted so that they could be replicated in all further experiments.

With +he subject fixed in the angaratus the next step ~35 to determine the moment cf inertia of the li~h.The mi?thod described in Chap, IV, a (iifwas used, Yhen this was complete the subject practiced some trial ccntracti3ns with careful obssrvation by the investiqator and suksequen t 50

suggestions for improve~entshoald they be required, The

subject gas not informed about the aim of the stud?, However,

the i~portanceoE ~aximalactivation was stressed,

ii) VJork-Session 2

3n this session data needed to derive the torque-anyulax

velocity relationshi F %ascollected, Upon arri oaf the subject was placed in the apparatus accordigg to previous measureaents

taken du~ing~iork-session 7, On all occasions the subject was instructed to produce maxi~alvoluntary contractions about the elbow joint as rapidly as possible, The verbal stimulus fro& the isrrestigatof was the comaand *pull@, Five starting posit ions were chosen for the devefaprwnt of

the torque-angular veic;cii;g curve, These Here 0-5, 0-8, 1-0, 5 -5, and 2-0 radians where 0-0 radians regresenqed full exteasion of

the elbow, The beam was set at the required position by a

- chain attached at the other ernd of the axle, At each position

the subject aade eight separate pufls, The first, third, fifth an8 seventh pulls were coapleteky iss~etric,There was no added

co~plianceand the investigator ensured that the resisting

chain had no slack, The second, fourth, sixth and eighth pulls

were not coapletefy isoaetric in that they were made agaiast the spring, wkich was naw part of the system- The spsing

uncoiled by aa a~ountrefated to the tension exerted and the coiapfiance of the spring,

The data were collected on an FR tape-recorder, The subject raz alPc~sdtit rctate his ara frzbiy tetueen each conttackioit to ease any stress lnd~cedby the contraction, Each pull lasted no nore than 1-5 seconds,

Upon completion of all the pulls the calibration for the effect of gravity {Chap, IV, a (iii))was coltlpleted, The subject was removed fro^ the apparatus and the calibration [Chap, IV, ali)) of the transducers was co~~leted-

iii) Work-Session 3

This session was a repeat of work-session 2 and served to provide a check on the repeatability of the previously collectea data, The intersessional time-interval was no less than one week,

After all the data from each vork-session bad been collected on a tape-recorder it was transferred to a conputer

DECTBPE in prepdration for analysis, Analysis of the original data showed that it did not exhibit the expected form* The rise of torqne duriag a co~piiaatpull was faster than in a non-conpliant pull, As the converse of this observation was a necessary condition of the analysis an usidentieied phenomenon was judged to have been ccntributing to the difference between rise-time of the compliant and non-compliant pulls,

Consequently, a new approach to the deduction of the torque-angular velocity carve was required,

wilkie 11950) was able to elicit a response front intdct human muscles siaiilar tc that reported by MacPherson (1953), wilkie's siltjtxt~&ere presented uith Bare coatractiotts to complete than in the present study. Therefore the unusual

sesults obtained here may have been due to a lack of practice

or skiff in recruiting ~uscularactivity as rapidly as possible

on all occasions, It was 'thought that perhaps a period of

training nas required, Consequently two subjects were chosen

and performed a series of experimental sessions from which

their data was analysed progressively, There was no trend in

the data that indicated an effect which could be associated

with practise, The subjects did make soBe coraments on how they

felt during each type of contraction, Both said that they felt

more satisfied with the compliant pull than with the

non-compliant pull and a ttsibuted this feeling to the fact that

they had accoaplished something hy making the hea~move a

considerable amount. In the case of the non-compliant pull the

extent of movement was so small that there was little feedbsck

to the subject in terms cf how that person had done,

On the basis of these comments it seemed that there was

perhaps some form of physiological feedback that affected the

performance sf the subjects, With this in mind it seemed

reasonable to try a session during which the subjects uould not

be informed of the nature of the contraction that would be

required, The motions the investigator went through during a

recording session were standardized so as not to provide any

hints, The only coiiiment during this session was the command to

pull,. Zn spite 02 tts atteapts to aask the appdratus the data were at variance with the intention of the study, It was decided at this stage to abandon this approach and concentrate on the second part of the study,

It should be noted that the response of the apparatus was checked to ensure that the problem was not a function of she apparatus, Po do this the investigator attached a weight [32,15

Kg) by a rope to the lever in the horizontaf position,

Initially the invesigato~supported the weight so the rope was slack but released the weight applyibg a sudden input to the lever, This procedure was compf eted under bokb experiments l conditious, The rise 02 torque in the contraction with the added compliance was slower than without the added compliance,

The apparatus gas not the source of %he variation in the data with that reported elsewhere,

B) Procedures-Experiment 2

As before this qroup came at their convenience and since the dynamic contractions were not as demanding as isometric cane as freguently as orice a day, One subjerk canie only six ti~esbut the other subject was able to attend seven sessions,

A session similar to work-session 1 in experi~ent1 was completed before %he actual data collection began, The subject was carefully fitted intc the apparatus and the ao~entof inertia of the liab was determined, . . TCe method of dctcrmlnng the torque-auyu2ar veloci%j curve froin dyuainic contractions required the subject to contract against a variety of opposing loads, The opposing loads were a series of weights that could be fixed to any one of three positioas on the hard at the end of the apparatus opposite the subject, The bard was fixed off centre to the axle, Two of the holes in the board were on one side of the

1 axle and one on the other side, Using different weights and hole position produced a range of torques that the subject had to overcome, To enable achievement of high velocities of

~ovementthe the investigator aided iaoveaent by rapidly rotating the the board in the direction of flexion,

It was decided to deter~ine torque-any ular ve_locity curves for five elbow positions, 0-5, 0-8, 3-0, 1-5, and 2-0 radians, where 0,0 radians represents full extension of the elbow-joint,

To complete the torque-aagular velocity curves it was necessary to record the isometric torques for each of these positions. A torque-angle curve was developed by requesting the subject to contract isometrically four times during each experi~ental session. To maintain the position of the beam during an isometric contraction a chain was used to fix the board to the floor, The investigator ensured that there was no slack in %he chain during the contraction,

The experiaental situations were the same for the kirst four sessions for subject one ana first three for subject tuo-

Upon arrival the subject was fixed within the apparatus in accordance with the measures noted during the trial session- During thcsc axpzriifiertal ssssions tiid first and last two contractions were isometric while the re~ainingeighteen were dynamic, B dynamic contraction required that the investigator fully extend the relaxed right arm cf the subject, At the command *PULLq the subject maximally activated the flexors of the elbow and flexed his am as quickly as possible, The f lexica was arrested by a mechanism of rope that prevmtea the subject hitting himself, For each weight and hole position two puf ls were conpieled, The ether four pulls were completed, two of uhich were done when there %as no load on the board and the other two were done while the investigator assisted the rotation, The latter four provide& torques that sere low with high velocities,

In the remaining three sessions the contractions were isometric only, This data was used in the deteraination of the compliance of the SEC during an isonetfic contraction and in

.the calculation of the, time-constant of the rise in torque. In the first tvo of these sessions the subject pulled once at each of the five elbow positicns described above, A third session was completed during which the subjects completed three pulls at each of these elbow positions,

The data to be used in the determination of the torque-angular velocity curve were collected on the Ff!i tape-recorder, The data to be used for the calculation of the conpliance of the SEC and the ti~e-constantof the rise in torque during an isometric contraction were collected onto the recording oscilloyraph, The prigaary aim of this study was to derive a torque-angular velocity relationship for huaan ~uscufar contraction, Two different etethods have been developed to achieve this aim, Since joint-angle ref Zeets auscfe-length then the interrelationship of three variabf es could be studied, During the experi~ontal process ealibratioe ua s perf orated to facilitate quantification of the ref a tionships in absolute uni is, a) Calibmtion during the experi~ents

i) Calibratioa constants

410 determine absolute units for the data it was necessary to use a calibratioa procedure that vould canvert the output voltage from the transducers to absolute units. The procedure was as foliaws (see DBCAL-SV in Appendix 2). The lever was placed in five different positions, In the first position the lever was placed vertical and in the other positions the lever was placed horizontal alternating from side to side of the sertical, These positiorns were nuxibered sequentiaily froia one to five,

In position one the lever was vertical and there was no torque recorded by the strain gauges, The output fro& this position was oiased to 50% oaf full scale to facilitate rec~rdin?bipkasic sigrtals, To cafcuLate the torque factor a known torque was applied in positions four and five, The torque

*seeng by the transducer when the fever was horizontal %ith no load, positions 2 and 3, was that torque attributable to the effect of gravity on the lever, The difference in output between position four and two and position five and three uas the consequence of the known applied torques, Calculation of two torque factors served to check the linearity of the response of the transducer in the early stages of the experiment,

Once the invesigator %as satisfied with the response characteristics of the torque transducer the bias level was shifted to a value slightly higher than zero volts, This shift, concomitant with an increase in the gain of the the amplifier, permitted an increase in the resolution of the data collected from this transducer,

To calculate the accelerometer factors (in radians per sec, per sec,) the differences in output betueen position two and one and position three and one were determined, The accelerometer recorded zero acceleration when the lever was vertical, At each of the hcrizontal positions the accelerometer recorded one g or 9-8 1 m Jsec/sec of tangential acceleration,

The relatioriship between tangential acceleration "FAa and angular acceleration &AA* is;

TB = AA * B 2

Mhere *Kg was the distance ketween the axis of rotation and the acceierorrletrtr, This equation was solved for the angular accel~zation~Aich %as tZen Givlded by tb~output froa positions 1 and 2, A second accelercmeter factor was deternined using the output from positions one and three, The effect of gravity on the accelerometer was assessed by calculating the digference between the output fro@ position twc and three and dividing by 2,

The displacenent or position of the lever was considered in radians, Full extension of the elbow was considered to occur at 0-0 radians, The relationship between radians an3 degrees was described as 1.90 degrees being equivalent to 3,1&15 radians, From this relationship the radian factor was determined, The difference in the output frcm gositions tuo and three (lever horizontal on opposite sides of the vertical) was equivalent to a displacement of 3,3416 radians or 180 degrees,

The radian factor [radiaas/unit) was determine4 by dividing

3,1416 radians by the differences in the output from the lever when horizontal oa opposite sides,

To maintain a safety margin in case of drift uithin the amplifiers a small voltage above zero was included in the determination of the radian factor, To aajust the levels to absolute zero a radian remainder (units) was determined by caLcuPatiny the differences between the output when the lever was horizontal for full extension and real zero volts- This radian- remainder was subtracted fro@ the calculated positions to assure the calculation of angle in absolute units- 59

iif Deteraioation of thc moment of inertia of the Emeara

The strain gauges were fixed to the lever between the axle and the slot where the cast was attached, A consequence of this arrangement vas that the torque recorded by the strain gauges only reproduced the torque developed by the ~usclewhen the mass lying between the elbow-joint and strain gauges was not accelerating, Under conditicns of acceleration of this mass the torque recorded vas less than the torque developed by an amount equal to the torque required to accelesate the mass,The torque record~dwas that torque available to bend the fever and the added coatpliance,

If an iapulse was applied to the axles fra~the opposite end of the apparatus then the torque recorded is that torzue uhich accelerates the the Bass distal to the strain gauges,

Consequently, this torque can be used to determine the insrtia of the forearm dnd casts, This recorded torque is equal to the acceleration of the inertia of the forearm and cast multiplied by the inertia,

The technique develcped required the investigator ta apply a rapid positive and negative torque to the subject*^ forearm via the axles linking each end of the apparatus while the subject uas at rest, The applied i~pufsewas of short duration in order to exclude involuntary activity by the subject and of small displacement to exclude the effects of gravity, The accuracy of this technique was deterained by fixing known ine~tiasto the beam and performing the experiment. There was littlc 5ifZercnce between thc camputcd vafues dfiJ the kno~n values of inertia,

four trials were used and the mean of value of these four estimations was chosen as the final value. Tis data and the calibration data vas acquired directly by the computer- A program [see 3EWflfS,SV in Appendix 2) deterlained the absolute vafues of torque and acceleration frcm which the value of inertia %as determined, The final values were typed oa paper and the Bean value calculated,

iii) Estimatic-n of the gravitational effects on the lever with the subjects arm and cast attached

The efteet of gravity on the lever was seen to modify the output of the transducess with respect to angular: positiort, Kt

was necessary to remove this effect when determining the absolute values of torgue, For this reason, hhe output of the torque transduce~was measured for eighteen different angular

positions with the subject in the experimental position, B

program (see GBAV.SV in appendix 2) printed out the associated

positions and torques and then sub~ittedthe eighteea pairs to

a polynomial curve-•’it ting prograa {see CURFIT, SV in appendix

2) whica predicted torque at any given axlgle by a polynomial

equation, This equation could then be subtracted from the

obtained values of torque to reiuove the effect due to gravity, bj Expcrincct 1 - Detcminaticn of the tocyue-angular velocity relationship from two isometric contractions

ItiacPherson (9953) devised a technique which allowed the derivation of the force-velocity relationship of the CC

unaffected by the SEC, The method essentially comprised the

mnscfe contracting iso~etricalPyat one time and then contracting again vith a compliant connection b~tweeathe

~uscfeand the recording transducers, By examining the

differences betueen the force-time curves in the two conditions

he was able to derive the force-velocity refathoaship- This method is outlined below as %elf as the modifications necessary for a situation with intact human muscle,

In developing this method of analysis Mac Pherson assu@ed

that the force developed by the CC varied only with the velocity of shortening. Given two conditions of force vhich rose to the same isoaetric level vith little or no change in

length, any point of force on these curves indicated equal

velocities of shorteniaq of the cC, To create tuo different conditions EacPherson inserted a coinpliance betueen the nuscfe and the recording transducers, This compliant connection could

be either isolated from the experiment, allowing for an

isometric contraction, or included, which produced a slower

rate of rise of force, From the two different rates of rise of FfGUBE 10 : This is a drawing oE the system described by EacPherson, a) this describes the situation without the added compliance, b) this respreserits the situation with the added as a paht of the total system

P = the force developed by the CC F = the force rfcordad by the transducers x = the lengthening of the SEC y = the lengthening of the added compliance SEC \. \ CC P

\ \ SEC added compliance CC . force he CC~SSqus1 values of force and, therefore, equal calculated vetoci ties, Figure 10a illustrates the experimental conditions and the f aliouiny is the mathematiczil manipulation required to achieve the drinal results- When the contraction is total1 y isometric,

and

where (iitr/d%) o is the velocity of the CC, The subscript loi denokes the coolidition without: the addzd compliance, Figut's 10b shows the situation with the added compliance, Now,

This reduces to

Now velocity of the CC is fd[x+y)/dt)c whefe the subscript 'ci denotes the condition with the added compliance, Since, at any instaat velocity depends upcn force then for any equal values of P the velocities could he equated, Thus, equating equations 4 and 6; The value of dx/dP is the compliance of the SEC and can be

substituted into equation 4 which is solved for the velocity of shortening 0% the CC,

ii) fladifications tc fit rotational system

This above analysis uas developed f cr linear systems and

befare it was used cat rctational systems (human movement) some

modifications were aade, Tbs measurements were made in an~ular terms, such as moment of inertia, angular velocity etc-

Secondly, it was not possible to couple an added compliance

directly to the SEC of intact human muscles, There was an

inertia between the SEC and the added compliance, namely the arm, casts and beaai, During contraction with the added

compfiance this inertia gas accelerated and, hence, the torque

recorded was less than the torque developed by an amount equal

to that required to accelerate the arm, casts and beam* If P

was the torque developed by the CC and T was the torque

recorded then;

P=T+f6

where 10 was the torque required to accelerate the inertia-

This manipulation vas completed prior to the application of MacPhersonss analysis, Once T was corrected very little FEGUXE 11 : This is a drawing of the system described in figure 10 as modified to suit the needs of the present study, a) this describes the situation without the aaded compliance, b) this respresents the situation with the added as a part of the total system

P = the torque developed by the CC T = the torque recorded by the transducer i3, = the angular displacement of the SEC 8, = the angular displacement of the added ccmpliance T = the inertia of the forearm, cast and outer portion of the lever Lnadded ,.'f?fl compliance f ollowirlq presents the modified analysis (see figure 11).

and

With the added co~pliaace

and

Equation of the angular velocities and reduction gives;

The value for the corngfiance of the SEC, de, /d~,was

substituted into equation fl which was solved for the velocity

of shortening of the CC, This technique allowed one to arrive at a torque-angular velocity refatioaship for the contractile

component as well as check on changes in the compliance of the

SEC, When the analysis was done at a series of different muscle

lengths one was able examine the effect of changes in length on

I the torque-angular velocity relationship for intact human auscfe. iii) Data manipu~atioa

When the operator was ready to begin the final computation the data set %as transferred from the DECTAPE to core meaory,

The psograa used to wanipulate the data gas catalogued as

DAVEP2,SB and a listing and typical printout is shown in Appendix 2,

The prograa initialfly required the operatof to enter the calibration constants, coefficients for the correction of torque due to gravity and the momeat of inertia of the torearm and cast, These values were used in the computation of absolute units from arbitrary computer units, To make use of the full capabilities of the computer the calculated values were scaled by the use of multiplicatioa constants, Uhen data was digitized the range in values was O to 102Y units but the computer nas the capacity to deal with numbers ranging from 0 to 4095 units-

In the case of displacement, the largest possible value gas

3,142 radians, Hence, this number was multiplied by 1000 to increase the resolution, When the results were printed out the aultiplyer becaw the divisor and 3142 was returned to 3.142.

Additive constants were also used to aake all nu~berspositive.

Because of the discrete increments in the aata resulting from the digital. conversioa a method of digital smoothing was employed to smooth these increments, A utethod describetl by

Lanczos f1956) was errrpfoyed, This method entailed thd aves-aginj of five successive points and depositing thein here the? third point in the array gas located, The next series of points to be averaged Fccluded this third, now szoothed, poicr, The process of smoothing included three points that had been smoothed and two, as yet, unprocessed ~cints,

Upon completion of these steps a subroutine within the program displayed the data on an oscilloscope interfaced with the computer, In this fashion a visual check was r~aintainedon the proyraB as it processed the data, %hen this step was complete the actual analysis was begun, The prograia determined the numefatctr for equaticn 14, This reduced to the velocity at the hand and its determination was dons by differentiating the array of displacement, This step was completed and the array of velocity was stored in the iocation previously held by acceleration, "fe array of acceleration was not required after the array of torque had been corrected for acceleration of the mass discussed above, The velocity %as scaled but not smoothed as one had no weans of assesing what was signal aad what zaay have been aoise. Xt should be pointed out that there were kwo methods egployed to calculate the velocity of wovement of the hand during the compliant pull. One method assuned that there was no wovement during the isometric contract ion and therefore any aovement in the compliant contraction was attributed to the spring, The other method was not to assuae zero movment in the first pukl aud to calculate the difference in velocities as a result of moyemect in both pulls, In this fashion the velocity that arose strictly frcm the added com~liaucewas determined-

Using two methods provided soae further information that Bay have been useful, rrrin2 l next step st;.qsir&d the iie.t+raination 5LZ the denominator in equation 14, The denominator coasisted of two components, the aifferentiafs of the rise in torque from two contractions, The values for these differentiaf s were determiued, their differen~ecalculated and divided into the nuaerator, The value was deposited in care for later acquisition, This step was completed for the array of torque values already processed and stored in core, ff the difference between the differentials was zero or negative execution of the program was stopped.

Havinq cafcufated the solution to equation 14 and the values stored as an array in the Deuiory the prograa initiated the calcufation of the vvelccity fro& equation 9, These values were also deposited for l ater acquisition, The plotting subroutine was employed uFcn completion to permit visual inspection of the results,

A separate prograa, PLOTDB-SV, was loaded to plot the final results on hard copy, This progrant picked up the arrays oE velocity, torque, and compliance and plotted thea on a plotter which was a peripheral. device to the PBP-8e-

c) Sxperimenk-2 The determination of the torque-angular velocity relationship Ercw dynamic contractions

The data required for this analysis was the torque developed at any tiae during a dynamic contraction and the 72

velocity at that same icstmt in tiae, lo detsraine the velocity it was necessary to differentiate the output froin the displacemant transducer, This was the velocity at the hand and how accurately it was a measure of the velocity of the contractile component depended upon how quickly the torque nas changing, Under coaditicns of high rate of change of torque the

5EC was either lengtheuing or shortening and this change in length in the SEC affected the velocity recorded at the hand,

When the rate of caange of torque was low then the SEC was stable and the velocity at the hand accurately reproduced the velocity of shortening of the contractile component,

An attempt was inade to assess the afkects of the rate of change of torque on the stretch of the SXC, Subject 2 had been a subject in another experiment the aim of which was to estimate a linear coapfiance for the SEC, That experimeat had determined this value to be ,004 Nw/radian. With this estimate it nas possible to correct the observed velocities to take into account changes in length of the SEC, However, this method of correction produced an overcorrection when the torques were low and an undercorrection when the torques were high. Xt was decided not to persue this thought as those points vhich rere affected, and consequently fufther displaced from the bulk of the data, could be ignored,

The analysis program printed the values of torque, angle, and angular velocity for the whole contraction, Since five positions %erechosen as suitable for the develcpment of the torque-angular velocity curve the operator had to select the points from the printout, ijsata manipulation

This proqrdm was catalogued as DFV-SV and a listing is contained in Appendix 2, The progrsia i~iitially required the operator to load the calibration factors, moment of inertia and coefficients for the correction of gravity prior to beginning the analysis, With these constants the pzograa determined\ the absolute values for each of acceleration, torque and displacement, smoothed these by the 5 point moving average technique and stored the%, The array of torque was corrected last because the array of acceleration was required to correct for acceleration of the limb, Velocity was calculated from the array of displacement and then stored in the location previously held by acceleration, Wben +he prcgxam gas finished the analysis and it punched the data on hard copy for the operator, A dxsplay program was built into the overall prograw and all the values were displayed for visual examination as the program progressed,

ii) Determination of the tirne constant of the rise in torque

Houk (19b3f linearized the relationships of f orce-velocity for the CC and the length-tension for the SEC and developed a transfer function that described the rate of rise in force,

This description was exponential in nature and followed closely the rise in force determined experinentally, Chap~an33973) 3lso used this detzrainaticn sf finear pr~pertiesof conpancnts of the model to examine some effects of length on the aodel,

Since the rate of rise in force could be described as an exponential it was possible to deterlnine the time constant of the rise in force, This determination ~ermittedthe examination sf the rate of activation of the muscle,

This rise in torque in the present study was considered to be nearly expc6ential in nature and the following analysis applied to dekesmine the tiw-constant of the r ise in torque,

The intial slow rising portion of the curve was ignored as being due to the compression of the soft tissue (Chapman,

1973), The curve was; extrapolated to the zero level, The time constant of an exponential curve was defined as that time required to attain 63% of the iaaximu~value, The maximum value for the isoaetric contractions obtained in this study were determined and then the time required to attain 53% of this value, These data were examined to see whether the change in elbow-position affected the rise in torque,

iii) Deteraination of the compliance of the SEC

The rate of rise in tcrque during an isometric contraction is dependent upon the torque-angular velocity relationship of the CC and length-tension curve of the SEC, Knowing the force-velocity curve and the rate of change of force during an iso~etriccontraction one nas able to determine the co~pliance of the sec. dynamic contractions, To facilitate the derivation of the compliance of the 5EC a smooth line was dram through the middle of the points on a torque-angular velocity curve, The calculation of the compliance was done bp hand and therefore an equation defining the torque-angula~ velocity curve was considered unnecessary,

The datddollected f roiu the isoaetric con tractions were displayed on the paper recording oscilloscope at a paper speed of 16 cm/sec, The calibration data was displayed in the same fashion, The investiqator sefecked points on the rise in torque curve on this recording and determined the absolute torque, A geometrical tangent was dram to the curve at these points and the value of rate of zise in torque determined in tlm/sec, The relationship between rise in torque and velocity of shortening is dependant upon the extension of the SEC [determined by its stiffness) and the velocity of shortening of the CC (see equation

3)- This relationship was used to calculate the com~lianceof the SEC (the inverse ot the stiffness of the SEC)

The points on the rise in torque curve were transferred to the torque-angular velocity curve determined in experiment 2 and the velacities for that torque recorded, Sultiplying the velocity by the inverse of the rate of rise in torque produced the compliance at that point during the contraction, The compliance data gas displayed as a function of torque- These were a number of factors which could have affected the outcome of the experimental results, A primary source arises from the conscious awareness of the subject,

The method of aligning the subject with the apparatus was made carefully consistent with each session, As was stated earlier the pc6ition of each support was recorded and the supports returned to that saae position each tim the subject was in the experiment, The application of the casts was also kept exactly the same so that the necessary consistency of fit was maintained, During She experiment the subject was instructed to look straight ahead at a blank wall and not to move during the contractions, The chest and thigh supports and safety straps maintained the experimental psi tion throughout the experiment,

With these precautions the investigator was assured that the subject was in the same position each time he was aligned with the apparatus, The oniy area where the investigator had no control #as the area of activation of the muscle, Repeatable

~tlaximum a.ctivation was a necessity of the experiaental technique, These has not been a methcd designed that will permit the estimation of activation in intact auscles, The investigator bad to rely on the subject appreciating the importance of consistent activation and atte~ptingto respond appropriately, It was possibly this item which fed to the discrepancies observea during experiment 1, Thc responsz characteristics of the transducers has been describes fully elsewhere and it was evident that they were nithin the requirements of this study, No detectable difference could be assesed in the static or dynamic response over a number of trials, Filtering to 15 Hz provided a wide aargin for response of each transducer as well as aatching the upper liait of the frequency response cf each transducer,

The filkering of the signal from the tape recorder removed aost of the noise inherent in that form of recording, Further digital smoothing renoved any noise resulting from the diyitizatioa of the a~alogueinput signal from the tape-recorder,

On this basis, then, there does not appear to be any ~ajor source of error In the experimental procedure, This section presents the data as they %ere collected

during the study, These data are presented priaarily in

graphical. form, The implications of the data will be discussed

in the following section,

As described in the section titled 'Bethod of Analysis1

the success&- MacPherscn9s technique relied on the rise of

torque in the non-compliant pull being quicker than the rise in

torque in the compliant pull, However, in this study this

condition %as not me%, Figure 12 illustrates the rise in torque

for a typical pair of contractions, It is evident that the rise

in torque in the non-co~plint pull is slower through a large

range of the contraction, This pair were chosen as they were a

typical example of the data observed during the experiment

regardless of attempts to gather data similar to that repurted

by HacPherson (l953), On the basis of this inability to obtain

appropriate data this experiment was abandoned, The re~ainder

of the data presented here was derived from experiment 2 using

dynamic ~ontractions,

Figures 13 and 14 present the points describing the

relationship for each of the subjects in group 2.

The variation in isometric torque with elbow position indicate

that at least one point an the toxgue-angular velocity curve is

dependant upon joint position, To determine the isometric / torque for each of the experimental positions a smooth line was 'drawn through the points in figures 13 and 74, The value of torque was determined at tho intersecti.cn of this line with a line cirdwn rrom the dpproprlate elbow position,

figures 15a to 15c and 17a to 17e present the intersessional data describing the relationship between torque developed and anquiar veiccity for each subject at each of the \ five experiaental positions, It is evident from the scatter of the points that the data froa each session overlaps the cthers,

The overiapping of the intersessional data permitted the drawing of a linz thfouyh these points that would permit coniparison ot a mean 02 each curve for each eibcw position

(Figures 16 and 18)- Aii assessment of the compliance cf the SEC and the use of that assessment to correct the torque-angular velocity curves did nct dlter the curves to any extent fsee

Betbod of Analysis),

The compfiance oi the SEC was determined from the rise in isometric torque and is presented as a functi.cn of torque in figures 1Ya-e and 20a-e for each elbow position, Trials 1 and 2 were obtainea on aifferent days while trial 3 was conpleted at one session, Trial 3 contains 3 contractions for each position of the elbow-joint,

Table 1 presents tte time-ccnstants for the rise in torque during an isometric contraction, These data were couiputed Lrom the data cullecteu as described in Chap, IV, cfii), FIGURE 12 : The rise in torque in two contractions, one with the added conapfiance and one without the added compliance,

FIGURE 13 : The torque-angle curve for subject BC, 0 I SPLRCEMENT (RFIOI FINS) FIGURE 34 2 The torque-angle curve for subject HV,

PIGUEE 15 : The koryue-angular velocity curve for different sessions and at different joint angles for subject AC, a) torque-angular veiocity curve at 0- 5 radians b) torque-angular velocity curve at 0-8 radians c) torque-angular velocity curve at 1-0 radians d) torque-angular velocity curve at 1-5 radians e) torque-aagulas velocity curve at 2-0 radians x T/RV 8CO fl1 .5 RRDS 0 T/flV 8Cl RT .5 RRDS X T/8V HC2 fiT .5 flHOS # T/BV flCU 81 .S RflDS x T/RV SMOOTH .5 AflDS.

I I I I I0 3.00 61 4-30 12.00I 15.00 VELOC I TO U?ADS. SEC. I I I I I 8 00 3.00 6.00 9.00 12.00 15.00 VELOC 1 TY ~6RDS. / SEC. 1 x T/RV FICO FIT 1.0 AFlOS + T/WFlClFIT 1.0RFIOS x T/AV BC2 FIT 1.0 RflOS x T/FIV flcu flT 1.0 RFIOS T/FIV SnOOTH FIC T/RV SMOOTH RC

%%y %%y 3.00 6.00 9.00 12.00 15.00 VELOC I TY (RFIDS. / SEC. 1 X T/RV flCO flT 2.0 RflOS 0 T/RV RCl FIT 2.0 RRDS x T/RV RC2 BT 2.0 RBOS # T/RV BCY RT 2.0 RROS T/RV SHCJCJTH 2.0 AROS

0 0 0 ' o* .-I

Q 0. 0- rC) 18 4f m -0Om t& LT-n- W z m Y m )It '% f 30 m m f Q m 6 f- *e" 0 0. Q, CV X W %m rn 0 0 I I(c %?OO 3.00I 6.001 9.00I 12.00 15.00 VELOCITY (RRDS. / SEC. 1 FIGURZ 16 : The torque-angular velocity curves determined ky drawing a smooth line through the pciuts displayed in figure 15, 93 x T/aV HC F1T .S RROS 0 T/FIV i92 FIT .8 RHOS x T/FIV FIC RT 1.0 HflUS T/gV 41: FIT 1.5 ,911OS T/CI'J 112 FIT 2.0 RRDS FIGURE 17 : The torque-angular veJ_ocitycurve for differnnt sessions and at different joint angles for subject HH, a) torque-angular velocity curve at 0-5 radians b) torque-angular velocity curve at 0-8 radians c) torque-angular velocity curve at 1-0 radians d) torque-angular velocity curve at 1-5 radians e) torque-angular velocity curve at 2.0 radians

x T/flV HW3 flT .8 RROS T/FIV HW4 FIT .B AFIOS x T/RV HU5 flT .8 RflOS # T/FIV SHOOTH -8 AflOS

0 I I I 1 9 3.00 6.00 9.00 12.00 15.00 VELOCITY IRRDS. / SEC. 1 9 7 x T/CIV Hh3 flT 1.0 flR0S 0 T/W Hull AT 1.0 RADS x T/@V HW5 fl7 1.0 RRDS # T/FIV HU SHOOTH flT 1.0

I 1 I I 00 3.00 6.00 9.00 12.00 l$.OO VELOCITY [RFIDS. / SEC.1 I 1 I f ,00 3: 00 6.00 9: 00 12.00 15.00 VELBC; I TY (RFIQS. / SEC. I

FIGURE 18 : The torque-angular velocity curve determined by drawing a saooth fine through the points displayed in figure 17- 3 r3 c

w c.3 m x % I-- 3€ X w f x Is o m 36 t) x )(li W '3, m N 31C W m IY

-2 0 , 0 1 I I I .OO 3.00 6.00 9.00 12.00 15.00 VELOCITY (RHOS. / SEC, I FIGUBE 19 : The compliance-torque curve for different sessions and at different joint angles for subject AC, a) compliance- torque curve at 0.5 radians b) co~pliance-torquecarve at 0-8 radians c) cqmpliance-tcrque curve at 1-0 radians d) compliance- torque curve at 1-5 radians e) compliance-torque curve at 2-0 radians I I I 1 4t 20.00 iSO.00 60.00 60.00 1QO.OO TORQUE iNM1 0 1 V 400 20.00I qo.I 00 60.00I BU, 00 100 TORQUE INM) TORQUE [NMI x RC11.5RflOS RC2 1.5 RROS x RC3 1.5 RRDS

FIGURE 20 : The compliance-torque curve for different sessions and at different joint angles for subject BW,

a) colrrpliance- torque curve at 0-5 radians b) compliance-torque curve at 0-8 radians < -, c) cotapfiance-torque curve a& 9.0 radians d) ~ora~liance-torquecurve at 1-5 radians e) compliance-torque curve at 2-0 radians

I I I I P 20.00 110.00 60.00 80.Orl ld3.00 TORQUE INM) I I I I V 00 20.00 40.00 60.00 80.00 100.00 TORQUE INM) position -5 - 3 1-0 1-5 2-0 trial

Table la: tirae-constants for rise in isoaetric torque subject AC (in ntlsecs,) position -5 - 8 1-0 1-5 2- 0 trial

fable Ib: the-constants for rise in isoaetric torque subject Hi4 (in Rtsecs,) One of the initial aims of this project was to- adapt aacPherson *s method for determination of the f orce-velocity curve oE the CC to intact human muscles, The ~ethodoutliued by EacPhesson (1953) was developed oa isoia ted preparations and its simplicity aade it a desirable method for use in other types of preparations, However, the method was found to be inadequate for use in intact huaan muscles in that it produced results that were inconsistent with those derived fron isolated pseparat ions,

Torque developed by tho CC is a function of at least three factors; the veiocity of shortening (Bill, 1938) , the activation of the CC (Yahler eS 3868) aaii the initial length of the

LnC (Bahler et a&, 153683, To examine the relationship between torque developed and velocity of shortening extraneous factors must be held constant, Failure to maintain the@ constant presents problems in the interpretation of the effect of velocity of shortening alone on force developed by the CC- In expqriments on isolated preparations, such as BacPherson's, the length of the inuscle can be maintained fairly easily as can the activation, In human pre~arationsthese factors are more difficult to control and it is likely that at least one of these variables, velocity of shortening, activation or initial length, was not slayiag constant in the present study- Durinq the presenk experiment t5c subjects x@re inforaed of the importance of activation and vere requested to activate maxiraafiy each time as fast as they could, Blthough the subjects reported that they felt that they had done so throughout the experiment, activation was not well controlled as is evident from Table 1, Because of this difficulty examination was made of the possibility that variations in activation were the source of the problem,

WiPkie (1950) eras able to obtain results similar to those described by PIacPherson ('1953) and did so on intact Buoaan iauscles, Wilkie's data was obtained after a number of trials and it seemed possible that there was a training effect, To examine this hypothesis two subjects were chosen to perf or^ a number of contractions, The subjects vere aware of the need for consistent activation and tried very hard to achieve that,

However, there was no change in the data that would support the clain that a period of training was beneficial, The later results were as variable as those produced earlier in this s%udy,

To explore further the possible sources of variation in activation it was thought that pre-knowledge of the type of

required affected the ability of the subject to contract maximally, This hypothesis was based on the cam@ents of the subjects who reported that they felt better after completing a compliaut pull rakher that a non-compliaat pull* Hhile these feelings of accomplishment could on1y be realized after the contraction was well underway there may have been some for the nsn-c~~pliantpull was then mkntsined at 1-0 radians,

The starting position of the non-compliant pull was set at one of three locations, For example, with a developed torque of 80

Bm the starting position of one of the compliant pulls was set

-15 radians before the starting position of the non-compliant pull, In this contraction the tuo pulls finished at the sane position, Another pair of c~ntractionswere obtained by starting the compliant pull -08 radians before the non-compliant pull. The third pair were obtained rhea the starting positions were the same, However, the procedure described did not produce data which differed fro& that described initially, It seems that the range of length of the

CG in these contractions was insufficient to affect the rate 02 development of torque,

As the present data are not substantially iafluenced by either changes in activatisn or changes in elbow-angle, the inconsistencg with the data of 'Miilkie (1950) is even Bore inexplicable- His study examined the f orce-velccity curve of a single eguivaf ent horizontal muscle in linear terms, The added compliance he used was almost 3 times as large as that used in the present study, Gjilkie justified this selection on the grounds that the horiacntal force developed by his single equivalent model was fairly constant over a vide range of elbow flexion, The use of a highly compliaslt stxucture as the added compliance ensured that his results ZolZowed a format similar to MacPhersonas data, The present study has shown ho% large is the variation in torque with respect to joint-angle so that cjross cbanges in length of the mnscle nay render the use of iYacPhersont s technique invalid.

It is evident that the variation of the data presented here froa the expected for^ arises frog the subject rather than from the apparatus, The origin of the rnechanisg of response is not obvious, A possible candidate is the central nervous system, Feelings of satisfaction reported by the subjects arise from higher orders of the CNS which enhances the possibility thaS this system is somehow involved, However, response from the CNS requires ti~eand the contraction voufd most likely be over by the time the GNS had responded, In cther words, the contraction would nave to be complete before oae could feel satisfied with it, Even if satisfaction was based ou prior experience the contraction would be well on the way before the subject could be aware of how he naiqht feel about it, This possibility is ruled out, of course, because of the time iactor

involved, Also, when the subjects were unaware of what type of contraction was to be required they reacted ia the same manner as when they were aware of what was coming next, Activation of lower orders of the nervous system (e,g- the spinal reflex Poop) also require time and consideration of these mechanisms sill not be of import here, It seems highly likely that some reflex activity resulted in the sharp change in the rate of rise in tcrque part nay throuyk the contraction with the added compliance (figure 121,

Thefe is an interaction between the muscles and the tendoa and muscle receptoss, Guyton (1971) stated that the muscle spindles cac reqond in a fractioc of a miliisecond, if their response Has quick enough this organ may have had au effect on the rise in torque, The selection of the starting pink for the analysis was done by searching for a change in the resting torque that was larger than the noise, Iftlben the change was larger than this level the program initiated and began the analysis, f f this point vas poorly chosen then ~erhapssome reflex activity aight have been missed, This is unlikely because before the spindles can react there has to be tension developed and once there was teasion it would be recorded by the transducer, The kbrcshold level in output for the torque transducer was quite small and the likelyhood of missing some activity is very small,

Similar considerations exclude explanations based on the studies of Gollnick, Pieti1 and Saltin (l974), They have suggested that there is scme selective recuit~entof different fibre types depending npon the type of contraczion. While this is interesting the ~echanismof selection of fibre types

undoubtedly relies on activation of some reflex system. There may be a new factor, as yet unknown, that is having a significank effect nn the rise in tcrque during iscmetric contractions.

This factor is neither neuro~uscufarnor mechanical in origin but rather muscular only* Speculation regarding a feedback system involving the gaigi tendcn organ, the muscle spindles and the muscle itself which bypasses the CNS are im~fausabfasince they uould imply an intramuscular synapse which would permit almost instataneous reaction between the effectors and af fectors- B nuzber of authors have susgested that these is soac other factor which affects the tensi.cn produced in contracting

muscle (Pringle, 1959; Hill, 1970)- These authors suggest that the presence of tension augments the active state, It Bay be

possible, then, for the type of resistance to affect the rise of active state, This sort of mechanism would ex~lainthe

findings here although the reason for such a raecbanism is not clear,

3) Experilneat 2

The initial aim sf the whole study was to investigate the dependence of the torque-angular velocity curve on its ~ethod of determination, The first experiment did not produce the expected resuits, the second experiment assumed the task of the determination of the torque-angular velocity relationship at different joint-angles,

There are some noticable defficiencies in the data as

exeaplified in figures 15a, 15e, 17a and 17e, Xn figures 1% and 17e these is a definite absence of points in some postions of the torque-angular velccity curves, This lack of points was the result of soae inadequacies in the experimenaal design,

Consequently, a line drawn through these points, including the

isoxtric point, passes through an area ufiere there are no

guidelines for the selection of its path, The smooth fines were

drawn on the basis of observations made in other studies and on

the assumption that human striated muscle acts in a similar fashio3, This stsp is, perhaps, of questionabl2 validity Lor as was pointed out earlies there are differences in the force-velocity curves whfn determined by different techniques,

fa fiqures 15a and 17a the s~oothcurve rises almost too sharply to be consistent vith other data, The poiat where vef ocity of shorkening was zero was determined from isometric contractions whereas the ether points on the torque-aaqular velocity curve were deterwined Exom dynamic contractions, One is led to speculate that there may he totally different responses o•’ the tauscfe to different types of loading (Pringle,

IgTO), that is, a diffe~entforce-velocity curve for dynaiaic contractions and a different curve for isoaetric contractions.

These curves my have the same shape but will vary in absolute value,

The determination of the velocity of shortening of the CO fro@data collected at the elbow-joint is subject to error when the rate of change of torque is not zero, This is because the

SEC also changes length during an isomtric contraction- The velocity of iiiovement at the elbow-joint is the sum of the velocity of shortening of the CC and the rate of change of length of the SEC, A method for: estimating the error in velocity 02 shortening had to be devised, If the rate of change of force is gultiplied by the coiripliance of the SEC then the result is the velocity of cnange in length of the SEC. This figure can then be added to or subtracted from the velocity recorded at the hand thereby correcting the angular vefocity at the hand to piefd the velocity of shortening of tbe CC- To ~erformthis cosrectioc an estiination of the compliance

of the SEC was required. Gilkie 41950) determined the compliance of the sEC for a number of subjects, The most

coapfiant of those provided by Wilkie gas approximately 0-03

fadians/Nm, This value was aultiplied by the rate of change in

torque to give a value of velocity, The range of correction

yalues determined in this manner was fro@ ,001 rad./sec- to -19 rad./sec. These values %ere not sufficient to alter the shape

of the curves presented in figures 16 and 18 and so it is

assumed that the curves do represent the relationship between torque and angular velocity,

There are some differences in the torgue-angular velocity

curve vith elbow angfe that indicate similar characteristics to

isolated muscles as reported by Bahler et af, {l968), The

differences in the toque-angular velocity curves with joint

angfe are most obvious upGn comparison of data collected at Oaf

radians with that collected at 1-5 radians, There seem to be

tuo possible explanations for these differences, There may be a

lengthening of the CC to an extent where the torque generated

was less at the Bore acute angles. This effect has been

reported on isolated preparations by Bahler et ua(1968) and the exteat of the effect of lengthening the auscle on the

production of torque by the CC depends upon the force-length

curve of the CC, A second expfanation nay be found in the

structure of the el bow- joint, Chapman (1973) reported that the

shape a•’ the articular surface of the humerus affects the angle

of pull of the tendoas of the flexors in a fashion that increased the +orque at longer muscle lenc;ths, Ecth of -these possibilities will be discussed here,

To examine the extension oE the flexor muscles over a range of joint augles used in this study, weasurements were made on a skeleton of the distance between the short bead of biceps brachii and its insertion in the radius- An excursion of

he elbow joint ffom 0-5 radians to 1.5 radians represents a variation in the iength of 21%. During passive extension this stretch would be absorbed primarily by the contractile ntatefial for it would not resist stretch, as would the tendons and thus, the figure of 21% is small, Noble (personal contmunication) has conducted some measurements on a single cadaver and reported a change in length of the muscle Bass of the biceps of up to 60% of the resting length, This range was evident on flexion of the el bow from full extension to flexion of 2-4 radians, While this range is larger than the range used in the present study it illustrates the range of change in l~ngthacheived by flexion of the elbow, These measureaents suggest that there is a sufficient range of move~entin elbow flexion to induce changes in the output of torque by the CC, The magnitude of this change depends upon the shape of the force-length curve of the GC for intact hu@an muzzles which has yet to be defined,

GJifisie (1950) conducted a study to develop a force-velocity curve for a horizontally equivalent muscle acting at the hand parallol to the upper ar@= He reported that the horizontai force at, the hand was relatively constant over a. range of elbow flexion, Chapman (1973) reported that the horizontal force rnmaincd constact over a s~allcrrange of

flexion and that as the ar@became more extended the force rose

in a fashion unlike a real muscle- The fcrce rose as a function

of the sine of the angle of flexion of the elbow (figure 3)-

Wilkie assumed that the flexors af the elbow acted parallel to

the upper arm and, hence, was appropriate over a small range of

elbow flexion only, Chapman ( 1973) suggested that to calculate 'the correct horizontal force one had to take into account a geoaetrical factor, This factor resulted from the tendons of

the flexors curling over the humerus when the elbow was

extended passed a certain angle, As a result of this the angle of pull of the tendon remained constant for continued extension

of the elbow,

Conversion of the data presented in the present study

if lustrated si~ilafresults. The horizontal force

gt the hand at 0-5 radians was 97 Neutons whereas it was only 84

M at 1-5 fads fqr subject BC, for subject HW the differences

were larger, 750 N at 0-5 rads and 96 N at 1-5 radians,

It is fair to assume that when the elbow is near 90

degrees of flexion that the muscle is near its resting length

and the number of cross bridges formed during contraction at

this length would be the greatest (Gordon &* 1966) Idhen

the arm is extended then the number of cross bridges formed may

be less as the ~uscleis lengthened, Hence, the torque produced

at the extended positi.cn should be less than at the ideal

flexed positioa, Uhile it Is likely that this occurs the

presence of such high horizontal components, as noted here, i~dicatethat there is snae other factcr 3ffecting the torque recorded at the hand, The most likely explanatio~is that the transmission of torque to the hand is azfected by the structure of the joint itself (Chapman, 1973)- The overall effect is to perait the deveiopment of considerable torques at a position which is mechanically inefficient and when there are changes in

he ability of the CC to develop torques,

The structure of the jcint affects the transxi.ssion of the torque produced by the CC to the hand, Chapman (1973) has suggested that the ends of the hu~eruseffectively fix the angle of insestion of the tendoa thus gaintaining a constant moment arm at that point, This action produces apparent1y high torques when the elbou is extended, This also explaias why the horizontal Eosce is so high, An overall effect would be to ensure that there is substansiaf torque available ts lift loads when the efbcw is extended,

B prel,j.minary study by this author showed that the torques developed by the arm actually increased when the arm was extendsd fully, This has been supported recently by the preliminary studies of Noble [unpublished data) and lends further support to the clainr of Chapman (3973) that the elbow-joint ~odifiesthe torques recorded at the hand, Such a

~odificationis handy, of course, for it pernits a pefson to develop a torque about the elbou- joint at any angle even wher the elbow-joint is fully extended, Without this effect the lever arm permitted by the space between the tendon and the point of rotation of the elbow-joint would he so small that the toraues ;t this positicc aould be smaP1,

A common method for determining the compliance of the SEC is to calculate the force-velocity relationship from isotonic

contractions, record the rate of rise in torque during an

isometric contraction and, finally, solve equation 3 above, The recent obseris;,a tion of Parmley aJ, (IgTO), however, has shom an error id this technique, There are different force-velocity curves derivable for different types of con tractions, Hence, it is not really correct to use the different contractions during

the process of calculating the co~plianceof the SEC,

The error that is introduced, however, is not one of shape

but rather one of ~agnitude, With the exception of the higher

velocities of contractiora the two f orce-velocity curves are of

the same shape, As loag as the detefmination of the compliance

of the SEC is confined to the middle and end areas of the

isornetsic contraction then one can see the changes undergone

during that coratraction, The estimations for the actual value

of the compliance is, of course, subject to the error,

Because of the curious events noted during experiment 1

the compliance of the 3EC was determined in the Banner just

described, The torque-angular velocity curves were determined

f son dynaaic contractions and the torque-time curve recordea

during an isometric contraction, The coiapliance-torque curves

sere determined from these data,

The data shown here are similar to that reported by Wilkie

(1950)- The sharp swing upwards is due using the wrong i torque-angular velocity curve, ft is also noted that the shape 2, 2, of the ciirves does not vary with joint ?aqfe+ 'This implies that the characteristics of the SEC do not change with joint position, The intersessional variation is most likely due to the varaition in activation noted in Table 1, / &he charateristics of the SEC are uuite important in the deter~inationof the charactesistics of intact muscle, There has been some suggestion that the SEC cannot be represeated as a siaple aon-linear spring because its characteristics raay change at very high tensions (Hill, 1970). This issue needs

~uchmore examination before the SEC is completely understood,

A complete picture of the charateristics of huitian muscle viU have to wait until this is complete, This study embarked upon an investigation of five areas of

human ~uscuParcontraction, These areas were described by

quedioo io chapter 1. The conclusicns of the iavestigation are pfesented here.

1. The question of whether there are differences in the

torque-angular velocity curve of the CC that are ascribable to

the method of determination seaains unanswered, This was the

consequence of the kailure to adapt BacPherson3s technique to

intact human muscular contraction.

2. There was little doubt that the joint-angle affected

the prouuction of torque about the elbov-joint, It was not

clear whether the differences in the torque-angular velocity

curve with respect to elbow position were due to the anatomy of

the elbow- joiot per se or uhether the excursion of angle was

sufficiently large to provoke a lenqthening of the @C- If this

coraponent was lengthened then it gas likely that the torque

produced would decrease with lengthening in a fashion similar

to that described by Bahler &, (1968). It was concf uded

that there is an interaction of the aenatomy of the elbowjoint

with the torque-angular velocity curve obscuriag any

lengthening of the CC, It was not possible to assess the effect

of lengthening of the CC as that lengthening would depend upon

IUthe torque-angle curve of the CC which has yet to be described, regardlesy of the position of the elbow- joint, This is evident

from the figures that show little change in the shape of the curves with joint position, It is not possible to calculate the

actual co~plianreof the SEC because of the error introduced by

the method used to deterwine that value, The similarity of the

curves presented here with those presented elseuhere verify the

characteristics as reported by Wilkie (1950)-

4, #ilkie*s single equivalent horizontal model is not applicable to muscular contraction over the full range of joint

excursion, The effect of the anatomy of the joint i~pliesthe inclusion of another factor in his model, This factor would

take into account the changes in the angle of pull of the

tendon as the joint angle became more acute,

While not an original question the problems associated

sit h the application of BacPherson3s aethod to iatact muscles

presented some curious information, The use of MacPherson8s

technique in the present study did not produce results silnilar

to that reported elsewhere, This inability appeafed to be the

consequence of some factcr hitherto unrevealed, A number of attempts to obtain results sirnilas to other studies were

completed but these did not produce results that were any

different from those ohtained in the first instance-

),\) ,,

This study beqan with the aim of exploring a number of proble~sassociated with human muscular contraction,

Historically the basis of an understanding of muscular ccntraction has cowe from experiments dealing with isolated muscles, These preparations permitted control of variables that affected the output of the muscfss, The aia of the experimentation was to develop a conceptual model that described the observed characteristics oE striated musc2e* By

1938 the conceptual model comprised three components that coula to some degree be associated with anatomical parts of the

~uscle,These co~ponentswere the coatractile coaponent, a series elastic co~ponentthat transnitted the force to its attachments with bones, and a parallel elastic co~ponentthat prvviaed some resistance to stretch at longer lengths, This model adequately describes the observed characteristics of isolated muscles,

The next task facing researchers was the adaptation of this

~udelto intact human muscular contraction, There is no reason to suspect that huaan striated ~usclehas any different characteristics than other muscles, However, there are a numbes of variablj6 that are more difficult to control in intact wuscles than in isolated muscles, Key examples are activation, relationship of the muscle to the joint about which it is acting, ana the nature of voluntary control, Since the investigator has to rely on the subject maintaining conscious co2troL t~cinvcstigatcr has to be aware of the ~oodsof the subject and the possde effects of that mod on the outcome of the experiment,

It was thought that for the present study these factors could be sufficientfg ccatrolled to per~itthe collection of the information desirea, Apparatus was designed and built to permit the investigation of the properties of the CC and the

SEC, These properties were to be explored under conditions of iso~etriccontrackion and dynamic contractioa, Two techniques were devised for the experiment, The technique devised for isometric contractions was a modified version of oae descf ibed by MacPherson (l953), To explore tbe ntuscfe under dynamic contractions a new technique was developed,

with these techniques the investigator proposed exagioation of the characteristics of the CC and the SEC of human intact human musc2es, Some of the data c~hiectedprovided startling information, Xt seemed apparent that &he ~usclecould react instantaneously to subtle variations in the resistance lo contraction, studies dealing with isolated muscles do not show this response primrily because they are isofdted from the whole system, rThe phenomenon appears to occur in intact muscfes only. In spite of atte~ptstc produce data that did not exhibit these anaoaalies, The data remained the sa@e as it was u hen init ialf y cof lec ted,

The use of uynamic contractions alone in the determination of the characteristics of intact human @uscLes presents a limited view, In spite of the limitations the data was in+,-3res?ringSThere v3s an effect af -jcink position on the production of force by the CC, This effect was seen as a decrease in the farce produced as the angle of the joint became smaller i,e, with further extension of the ~uscla, The question of majcr concern here was whether the decrement in force uas due to chanqes in length of the CC or to the interaction of the muscles with the bones of the joint. It was concluded that the joint anatomy plays a large role in deteraining the output of the iauscle, ft was difficult to assess the exteat of change in length of the CC because is not easy or painless to measure this length. Measurements taken from a skeleton showed that for the range of joint excursion in this study there was a change in the distance between origin and insertion of the biceps in exess of 21%- The actual change in length of the muscle bundle as sepafate from the tendcns would be substantially larger-

This range of length implies some changes in the length of the

CC but #ðer the changes were sufficient to provoke a decrease in torque simifas: to that reported by Bahler st a1-

(1968) rcxiains undetermined,

The corupliance of the SEC was determined Eron isometric contractio@. The relationship of compliance, torque and elbow posit iort imply that the cfiaracterisZrics of the SEC are unnaffected by elbow position, Bo absolute values for caitipliance %ere determined because of the problems associdted with the use of a dynamic torque-angular velocity curve and an isometric torque time curve, The error is one 05 magnitude only in the middle portions of the compliance-torque curve, This portion in the prxsent data was very similar t3 that reporte2

by Wilkie (1950),

This study has shown that the three co~poneatmodel can be applied to intact human muscle only when some modifications arc made, There is a geometrical factor which must be taken into account as this factor can affect the force that is recorded at the hand, Such a correcticn, of course, uouhd depend on the muscle group being examined, Activation appeared to vary quite substantially froin contraction to con traction in spite of assurances by the subject that he was contracting consistently.

The area of activation requires much work, The development of a

technique of aonitoring and quantifying activation would be a great boon in achievinq a complete understanding of nusculaf contraction, Perhaps further study on the EHG vilf provide a solution, The problem that arose using aacPherson's technique

is, perhaps, the ~ostinteresting, There do not seem ti> be any

available mechanisms that describe why the ano~alyoccurred,

The area oT study dealing ~ithintra-ausculas receptors and response 02 muscle to different loads will obviously have to he examined further, 3 Abbott, LC, and Lowy ,J. (19521, Wechanical properties of Hytilus muscle, J, ~hysiol, 120, SOP,

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Chapman,A, E, (l373), The relation between length and the force-velocity curve of a single equivalent linear musctc at the hand during elbow flexion, Proc, Qth Ink. Seal, Biomech, in press,

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Derla, H-J, Leiline, Js E, and ftfair,H, A, (1967). Forces exerted at different velocities of shortening* Amer,. J, Phsiol- 151, 415-437,

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Fick, A, (1882) -iYiech. WrLei t u, Warraeenti~ickelungb, d, Buskelthatigkeit- Leipaig: Brockhaus, cited in Hill, 1938, p, 181,

Gasser,c S. and Hil1,A.V. (1921)). The dynamics of auscular contraction, Proc, Roy, Soc, B96, 398-437,

Golfnick, !?,a,, Piehf ,Kg and Sultin,B, (1971)- 3efective glycogen depletion pattern in human muscle fibres after exercise of varying intensity and at varying pedal1ing rates. J, Physiol, 243, 45-57,

Gordon,A. 3, Huxley, A,P, and Juiiaa,F, J, (1966)- The variation in ismetric tension with sarcomere length in vertebrate muscle fibres, 3, Physiol, 184, 176-182-

Guytsn,A,C, (1971). Textbook of Bedical Physiology, W- 3- Sdundefs Co, , Toronto, if,A,, [3922), The maximum work and mechanical efficiency of human muscles and their most economical speed, J, ~hysiof,5G, 19-41,

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------(1949), The abrupt transition from rest to full activity in rauscle, Proc, Roy* Soc, BY 36, 399-426,

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------(1970)- first and Last Experiments in Euscle Yechanics, University Printing House, London,

HouF,,J,C, [1963), A wathe~ltaticalmodel of the stretch reflex in the human muscle systea, cited in Plilhorn, 1966,

Hursb, JOB, j1938), The force exerted by dogfish phascolosoma at different vefocities of shorteningl 3, Cell, Camp Physiof- 11, 333-

JeweZP,B.R, and Kifkie, LH, (1958), An analysis of the mechanikal components in f rocj's striated muscle- J, Phgsiol, 143, 515-540,

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Noble, B- (1975)- Personal communication-

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Pringle,J, tu', S, .fl959), Eodels of muscle, Sac, Exper, Biol, 14, 41-68,

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Wyman,J, j1926)- Studies on the relation of work and heat in tortoise muscle. 2, Physiol. 61, 337-352, APPENDIX 1

Table 1: The ages, weights and statures of the subjects in groups one and too.

SUBJECT AGE WEIGHT HEX GNT Y EAXS KG, Cu4,

79-5 177,5 YO. 9 178.0 APPEMDIX 2

The prograa ADFOCA-SV was used to acquire the data into the cosputer nemory, The operator respo~dedto each question with a response appropriate to the needs of each particular acquisition, DACAL .SV

G=ls5;D % HF( 1)=3.1416/(H(3)-kt(2))iS HF(2)=3.1416/(R(5)-H(4>) Mi( l)=iI<2)*HF( 1 ); S HR<2)=H(4)*HF(2) "TOHQ APPL V[UI"TAj !;S TF( 1 )=TA/(T<5)-T(3) )iS TF(2)=TA/

5~0;8 H=8092+ l00~QIS T=9092+ 100*G: S A=8592+ 100tGJS E=959e* i@0*Q I=lr100iD 3 H(G)*S/100IS S=0IS h=TJF I=lr l00fD 3 T(G)=b/l00IS S=0f S R=AlF I=lr l00;D 3 A

S*S+FCOR

"EMG MILLIVOLT IVPUT IS";T XlrJJA EA/(E< J)-EtZ1;T " EF("rX1r JB") "~XlSr06rEF(J)r" MV/U"f 3 NEWMIS. SV GRAV .SV PLOTDA. SV

25.50 S Cz03F I=lrNID 27 25.53 S L=Yl;S YlsY1+400iF IllrN3D 27 25.56 S P=3000/Cf T "MAX ABCISSAoerX8. 048 C0 ! 25.58 S Cm0IS YlsTliF IPLIN~D27 25.60 T "MAX TORQUE'@C/40r! i S C=2000/CJ S Y lrL 25.65 D 26 25.70 I (3-1)25*8r25*8~25.85 25.80 T "RESET PLOTTER G 24. 55'@3SYlmYl-200iQ 25.05 T "RESET PLOTTER G 23.lne3Q 05. kl5 3 V=SIIW; A "I HI-L1;S LiTlJS Tl=AliF I=3,V-61D 25 05.62 5 Tl=LlS B=A2iTU D A2"rIfF V=lrViD 4 05.64 F I=5rV-4;D 23 05.66 F 1*5rN-BiD 25 85.68 5 B=TlIT "D T1";F VnlrYlD 4 05.70 5 LnTllS Tl=T2fS Ll=AllS AlfAZi5 L2tHl:S HbH2IF 1=5rM-4iD 23 05.72 S AlnLli5 HlnL2)F Ix5rN-BiD 25 05-74 S BnT2;S rlaL;T " D T2"r liF V=lrY;D 4 05.75 S +O;F 1=8,N-81D 24 05.76 b UmA115 LaIIlIS Ll=AliT "D V1"iF V=lrNlD 4 05.77 S Hl=H2i5 Al=ADlF I=B,N-BSD 24 05.78 S BzA2IT " D V2"r!iF U=lrY;D 4 85-79 5 HlnLJS AliLl 05.83 S SQ=0iD 20 05.84 T " P'dWPlr!fS P2.P1;5 Tl=LIT "6 5.87 FOk SECO'VD PASS", !iQ 05.87 5 til=8791;5 1<2=83Yl:b A1=959IIS A2a91911S rl=l0391jS T2~9391 05.86 S Y15694315 El*l0991I5 E2511191iG 5.2 ADFOCA .SV 02.&+8 E k32. la T " ANALOGUE ACQUI51IOV PtlOGHAMWr! ! ! 89-18 A "IYTEtlilUPT PEHIOD IN MSEC IS t "CPa I1 02.14 A "COYTHOL 'FUitN ON DELAY IV MbEC IS 8 "DEJ !! 02-16 A "MIY ON LEVEL (VOLTS) 8 "LO, !;S LO~FITR(LO*l02*4) 02.17 A "MAX ON LEbE!, (VOLTS) : "HII!~S HI=FITH(iiI*102.4) 02-16 R "TOTAL ACQUIbTIOV TIME IV MbEC IS 8 "TMI! 1 02.20 A "NO OF CHANNELS ACTIVATED r "NCJ!! 02.22 A "NO OF PASSES FOR THIS INITIALISATIOY : "NGI ! 1 02.24 S Tlm3967iS T!i?=7934iS X=T2+3839 02.26 A "AilE TOTAL DATA AHHAYS* 3839 r "AVbr! 02.28 1 (AVS-OYES)2.3012.32,2.30 02.30 5 TE=T2+lib Mn0iS JFn23G 3.10 02.32 S TE=0;5 M=4;5 JF=0

03.18 F ~~137;~"COLLECTING FROM CHWJT X1,A ;A "8" Sk(A)r ! 03.11 1' I!! 03.12 F Ae1~7;D 4 03.14 T "THIS IS ALL THE DATA HEQUIHED TO IYITIALISE"r!! 03.16 F Atl~71D5 03.18 F Anl17lD 6 03-19 b AA=AA*NG 03.20 1 (AA-X)3.2413.24,3.22 03- 82 T "TOO MUCH DATA 03.84 T "AMOUNT OF DATA1*IT X~IAAJ! ! 03-26 T "CHANNEL START ADDRESS FIELD ARhAY SIZE". ! 1 83.28 F A11~71D8 03.30 S TE=DE/CP;S DE=FITR(TE)t I (DE-TE)3.3213.3413.32 03.32 T "TURIV OhJ DELAY PERIOD NOT COMPATIBLE WITH IhJTEHFilJPT PEkIOD"r! 03.34 S DE=-(DE+l) 03.36 F Aslr71D 9 03.37 A "IS THIS A GOOD IVITIALISATIOY t "AVSI !; I

04. 10 1 (Sk

DFV .SV

(%',, .I , 1- I=(.lrcl.r lrc~);sI.=I.CC~I (1,~) 147 I: . 1 u=:'(!(>;b ijfisij 1,) 1;~AC=r(S+l; s lO=~k>2 1;b b..q=).r+ I;!- r8=lr~J3;5 Pb=t.l4:i 1:' 5 I5=6543iS r,k.=6443;A "At lo'c\b( l)#" PhP"fik(T)rm 1b"'1h~" t ke'k tr" bk R P?. 1 L, A WqI "MI *I Ij-L,, " fiAelMA, AZj"Atir I "k.Te'hT, " th"P.tqr I ; k I = 18 Y 3 fi "Cl "C( 1 P:'. ll 5 <=CI:X[(-5/ET);C I=lr'J; S L=bC('k(IA+Ir(Cl;C~F(I>P+l )*FC->F)* 1PC"V) @Pa 19 h I=lrV-4;D P9 P2.PP b I=3rV-?ill PH C"?.T3 5 L=bA;S hp=AC; C I=3raJ-bib 23 F?.PS S FP=L:E I=SrN-4;D ?I p?.?7 S L=hP;S FA=TO;t I=Srhl-H;l~ 29 r?.?a s r-P=r;b I=S,N-H;LI ~3 (*:'.3C S f?fi.;L;b I,=tCC'h(bl44r D);S Y=@; k I=?rN;L, P4 CP.32 S Y=@;F I=Sr14;S X=X+ECWi(AC+I) @Po33 F 1=7rN-4iD 23 02.34 5 L=ftPiS HA=fiS;t 1~7rd-Y;D 29 OP.35 S FA=VE;b 1=7riV-~:%l 29 @?.BY T " POINT TOLOUL AIQG bOL A.'JULL"r ! fiPr4C S f1A=L;A "SP"SPr !l fi V=SFrN-12: L, 8 flP.42 (3iT " FOI NT E WCE V CL LLI'JU'IY GW(8 03.44 F V=SPrN-IPID 9 PP.5F S Xt13257;S Z=ECCIR(X-~JAE(I)*~P~~);SZ=tCOh(X-lr(AE( 1)*1Pt6)-FCORI 02.52 S Z=FCO~(X-~JAF(~)*1Pt3)iS Z=CCOh(X-3r(Al.(P)* l@tb)-hCOh(X-4)* 1iWO) fiP.53 S Z=FCOFi(X+81rl3) f'+R*hl S Z=FCOR(X+P?.Ati)iS B=(Aci-bCOh(X+??))+ 1@t3;S Z=hCOH

PR.32 T XY .P5rV+lrFCOhlTO+V+1)/?8iS )!=A;1. JoV-ID V+R;S XmX+( CCCbh(RS*J)-1II m.35 T " "X/l6*" "FCOH(HA+V+I)/l~1@Or!

C"9*RI, T V+lrbCOH(O+V+ 1)/51S X=@iF J=U-7,b+H;b X=X+(ECPfi< VL+J)-lP)P)PI/?13P P9.35 T " "X/l hr" "FCOS< ECDH

?3*@5 S P=FCOE*1fii b I.*SCOh(Hb+I-lrX+ 1C4P)EJ 23.891 S Z=kCCIH