muscle, the motor of movement: properties in function, · pdf filejournal of electromyography...

Journal of Electromyography and Kinesiology 8 (1998) 61–77

Muscle, the motor of movement: properties in function, experimentand modelling

Peter A. Huijinga,b,*

a Instituut voor Fundamentele en Klinische Bewegingswetenschappen, Faculteit Bewegingswetenschappen, Vrije Universiteit, Amsterdam, TheNetherlands

b Integrated Biomedical Engineering for Restoration of Human Function, Biomedisch Technologisch Instituut, Department of BiomedicalMechanical Engineering, Universiteit Twente, Enschede, The Netherlands

Abstract

The purpose of this paper is to review exemplary aspects of different views of skeletal muscle characteristics. A classical viewof muscle characteristics plays a very important role in modelling of muscles and movement. However, it often also pervadesconcepts on which our understanding of muscle function is based. In this view length effects, velocity effects and effects of degreesof activation and recruitment are distinguished and, often implicitly, assumed to be independent effects. It will be illustrated thatusing the classical approach many valuable things may be learned about muscle function and adaptation. At the same time weshould realize that such a classical approach is too limited for use in generating knowledge about properties of muscles duringdaily use. The use of scaling of force to estimate muscular properties during submaximal activity on the basis of properties duringmaximal activation is shown to be very inadequate. An alternative view is described and particular examples are provided of changesin length–force characteristics as a consequence of submaximal activation, previous length change, as well as the effect of short-term histories of these variables. In addition, effects of inhomogeneities of muscle in morphology as well as physiological propertiesare considered. It is concluded that length–velocity–force characteristics are not unique properties of a muscle, and that thesecharacteristics are not only strongly influenced by actual effects of recruitment, firing frequency, shortening performed and actualvelocity of shortening but also by the short time history of these factors. Therefore, length, velocity and activation cannot beconsidered as independent determinants of muscle functioning. It is also shown that we are confronted with many indications ofphysiological individuality regarding these phenomena. 1998 Elsevier Science Ltd. All rights reserved.

Keywords:Skeletal muscle; Modelling; Length force characteristics; Stimulation frequency; Potentiation; Fatigue; Muscle architecture; Immobiliz-ation; Sustained contraction; Sarcomere length; Concentric shortening

1. Introduction

Muscular properties can be classified into two categor-ies: intrinsic properties and contextual properties. Themost general statement of function of muscle is that ithas to contract. In more physical terms this means thatthe muscle has to deliver work to its outside world byexerting force while changing length. Work deliveredwill be determined by the properties that are related tothe muscle material and architectural properties. Contex-tual properties, which are determined not by specific

* Corresponding author. Tel.: 31 20 548 6260/6261; fax: 31 206462228.

1050-6411/98/$19.00 1998 Elsevier Science Ltd. All rights reserved.PII: S1050-6411 (97)00023-0

properties of the muscle itself but by the way it is built,are very important because they determine the specificfunction of a particular muscle. For instance, a particularmuscle is a flexor of a joint because of a positivemoment arm with respect to the flexion–extension axisof that joint. Another example of a very important con-textual property of muscle is the number of joints itspans. By being biarticular a muscle may play the veryimportant role of transporting power or energy from jointto joint (e.g. [9]), which plays a major role by(inter)muscular coordination (of movement) [41,42,74].

Intrinsic properties of muscle determine the functionalcapabilities of muscle to deliver external work. Theseproperties are usually defined exclusively at the molecu-lar, sub-sarcomeric or sarcomere level of intracellular

62 P.A. Huijing /Journal of Electromyography and Kinesiology 8 (1998) 61–77

mechanisms of the muscle fiber. However, if understand-ing of movement of humans or other animals is the aim itis essential that intrinsic properties should also describecontributions at the level of the muscle and muscle ten-don complex.

The aim of the present work is to review a selectionof intrinsic muscular properties at these different levelsof organization and discuss consequences for our insightinto muscle functioning as well as for modelling ofmuscles and movement.

First, a classical way of looking at intrinsic muscularproperties will be discussed and confronted with experi-mental results to asses its advantages and limitations.Subsequently, an alternative approach will be presented.

2. Intrinsic muscular properties: a classicalapproach

In addition to experimentation, modelling of muscleallows manipulation of parameters to asses their impor-tance for muscular properties. It also contributes to for-ming simplified images of reality that is so important forhuman understanding. Much scientific effort has beendevoted towards modelling of skeletal muscle and ofmovement. This effort started in the seventeenth centuryand is continued in the present at an enormous volumedue to the development of easily accessible compu-tational facilities.

2.1. Geometric models

In seventeenth century myology a controversy raged[43] between proponents of the idea that muscle couldcontract because of an increase in volume that flowedfrom the brain to the muscles [10,50] and those that wereconvinced that the volume of muscle is constant duringcontraction. Niels Stensen [62] made geometric modelsof muscle, which indicated that the fiber angle of pennatemuscle has to change in order to accommodate increasedfiber cross-sectional area. He was aware of the constancyof muscle volume because he came into contact with JanSwammerdam who had performed experiments showingthat fact (Fig. 1). This happened during his travelsthroughout Western Europe as Stensen visited LeidenUniversity. Swammerdam’s results were not publisheduntil 1737 [68]. Due to strong opposition from the scien-tific community, the insights of Stensen and Swammer-dam disappeared from the current body of knowledge ofmyology until the twentieth century. This paragraph mayserve as a warning to all of us that particularly inmyology there is a tendency for this to happen regularly(e.g. [40]), with sometimes disastrous consequences[30]. Predominantly in the second half of this centurythe basic ideas on muscle geometry have been redisco-vered (e.g. [5,18,35,36,55,60,61,81–83]). Fig. 2 shows

Fig. 1. Swammerdam’s experiment showing constancy of musclevolume during contraction and shortening. The isolated muscle wasplaced in a fluid filled tube with a very narrow tip (e). When the nervewas pulled against a piece of metal the nerve was excited and themuscle contracted without a load. If any change in muscle volumewould have occurred the fluid level at (e) would have indicated achange. This was never found.

the basics of these principles. These angular changes arefunctionally important, particularly in very pennate mus-cle because they contribute to muscular length changeat lower muscle lengths. This occurs at the expense ofdelivering force at these lengths [55], as is apparent fromEq. (1):

Fma = Ffa·cos(a + b)

cos(b)(1)

whereFma andFfa indicate muscle and total fiber forcerespectively. The anglea represents the fiber angle andb the aponeurosis angle with respect to the muscle’s lineof pull respectively.

It should be realized that these geometric models arenot mechanical models but simply link fiber length toforce exerted by the fibers by the definition of fiberlength force characteristics. In other words mechanical

63P.A. Huijing /Journal of Electromyography and Kinesiology 8 (1998) 61–77

Fig. 2. Slanted cylinder model of increase in fiber angle as a conse-quence of shortening. Due to the constancy of volume(Vf = Afl f = Aa 2 flf sin g) it can be shown that the fiber angle with theaponeurosis increases such that the increased fiber cross-sectional areaAf can be accommodated on an unchanged area of attachment on theaponeurosis (Aa-f). If the aponeurosis has elastic properties it mayshorten as force exerted on it is decreased (Dla). In order to still accom-modateAf, the fiber angle will have to increase even more. Theseprocesses are governed by the following equation:

sin g(short)Ysin g(long) = S√l f(long)Y√lf(short)D(lA2f(long)

YlA2f(short))

where l f represents fiber length andlA-f the length of the attachmentarea on the aponeurosis. If the fiber is allowed to bulge, a much largerfiber cross-sectional area can be accommodated.

interactions between fibers themselves and other con-stituent parts of muscle are neglected.

2.2. Phenomenological Hill models

Another important example of the effects of imageforming on understanding of muscle is provided by themechanical models of A. V. Hill [29]. These modelspool all elastic properties of muscle, regardless of theiranatomical location or level of muscular organization,in either series elastic or parallel elastic elements. Allcontractile properties not involving elasticity are concen-trated in a contractile element, to which length–force andforce–velocity characteristics are assigned. The modelhas been very successful by allowing a very muchenhanced understanding of elastic contributions to thedelivery of work by the muscle.

Geometric and Hill-type models have in common thatmuscle is modelled as being homogeneous with respectto fiber properties and/or muscle geometry (e.g.[5,7,9,18,22,23,35,36,45,46,55,60,79,81–83]).Therefore, they are to be considered as so-called lumpedfiber models. Hill-type models are the most applied typeof model but often the geometric effects described aboveare neglected.

2.3. Combination of geometric and elastic effects

Recently it has been shown that elastic properties ofaponeuroses (to which muscle fibers attach) can beincorporated in geometric models according to Eq. (2)derived by Zuurbier and Huijing [84]:

dlma = dl fa·cos(b)

cos(a + b)+ dlaa·

cos(a)cos(a + b)

(2)

where dl indicates instantaneous length change,a andbfiber angle and aponeurosis angle, respectively, andlma,l fa andlaa represent muscle, fiber and aponeurosis lengthof the active muscle, respectively.

2.4. Other effects of muscle geometry

Muscle geometry also affects adaptation of pennatemuscle to altered conditions. These altered conditionsmay be growth, immobilization, etc. These conditionsmay cause the muscle to hypertrophy or atrophy (i.e.change its physiological cross-sectional area) or adaptthe number of sarcomeres in series.

It is a well-known experimental result, particularly forlower leg muscles exposed to immobilization andgrowth, that muscle will adapt its optimum length to thelength that is imposed [27,70,80]. Fig. 3 illustrates thisconcept for rat medial gastrocnemius muscle. The usualexplanation for this phenomenon is that the number ofsarcomeres is controlled in such a way that optimal over-lap of myofilaments is made to coincide with the

Fig. 3. Length force characteristics of young adult rat medial gastro-cnemius muscle as affected by growth and immobilization. Animalsat 10 weeks of age are taken as reference. Nest mates were allowedto grow for 4 and 6 weeks or exposed to short length immobilizationof the muscle for the same time period. Note the increased force, theshift of optimum and active slack lengths to higher muscle lengthsaccompanying growth. A large decrease of force and a shortening ofthe muscle belly was seen after immobilization.


imposed length of the muscle [70,80]. This idea wasincorporated in a theory of control regarding number ofsarcomeres in series [28]. Based on geometric models,an alternative idea was tested. The idea is that in pennatemuscle changes of optimum length could also be broughtabout by length changes of the muscle as a consequenceof contributions of increased or decreased fiber cross-sectional area [26]. In such a case there would be nonecessity of changing number of sarcomeres in serieswithin fibers. Experimental results show that at least forimmobilization at short length [27] such ideas are ten-able. It was estimated that fibers of very pennate medialgastrocnemius muscle were immobilized at short lengthscomparable to those of less pennate soleus muscle.Despite that situation, the number of sarcomeres in serieswas not altered substantially in gastrocnemius butdecreased very significantly (by more than 20%, Fig. 4a)in soleus [28]. In addition, during growth from young toyoung adult age, the number of sarcomeres in serieswithin fibers increased by approximately 10% in soleusmuscle. In contrast, no changes at all were found for thenumber of sarcomeres in series in gastrocnemius muscle[28]. These effects were attributed to the fact that, inless pennate muscle, adaptation of the number of sar-comeres in series is the only major mechanism for adap-tation of muscle optimum length. In contrast, in verypennate muscle adaptation of optimum length hasalready occurred at the extracellular (organ) level:changing fiber diameter will have an effect on musclelength (Fig. 4b). In very pennate muscle, hypertrophyper sewill increase muscle optimum length and atrophywill decrease it. As a consequence of atrophy-relatedchanges in muscle optimum length, the followingchanges take place: during short length immobilizationof pennate muscle sarcomeres, which initially were atlow lengths, are returned towards their length of opti-mum overlap at the new muscle length, and the signalto change the number of sarcomeres is turned off. Thefact that for gastrocnemius muscle (GM) the lengthrange between optimum and active slack lengths wasunchanged [27] (see also Fig. 3) is in accordance withthis view.

2.4.1. Conclusions on geometric andphenomenological models

It is concluded that muscle geometry is functionallyof very high importance, both for acute muscular proper-ties and adaptation of these properties to altered con-ditions.

Clearly, simple models may contribute substantiallyto understanding of aspects of muscle function. It shouldbe pointed out, however, that major limitations of thesemodels also affect their application for other than heuris-tic purposes. One of these limitations is the assumptionof homogeneity already indicated. Most definitely, themost limiting factor is not considering the degree of acti-

Fig. 4. (a) Number of sarcomeres in series within fibers of rat medialgastrocnemius (GM) and soleus (SOL) muscles after growth andimmobilization. Animals at 10 weeks of age are taken as reference(line indicating 100%). Nest mates were allowed to grow for 4 and 6weeks or exposed to short length immobilization of the muscle for thesame time period. For both muscles results for distal (dist) and proxi-mal (prox) fibers are shown. Significant (arrows) changes of numberof sarcomeres are limited almost exclusively to soleus muscle for bothgrowth and immobilization effects. For GM this means that any adap-tation of length (see Fig. 3) was not performed by alteration of numberof sarcomeres in series. It was concluded that atrophy or hypertrophyof this very pennate muscle caused length changes due to immobiliz-ation and atrophy respectively. (b) Schematic illustration of the effectsof altered fiber diameter on muscle length.

vation or designing models to describe effects in maxi-mally activated muscle only. The wide use of such mod-els is enhanced by the fact that most experimentsdescribing physiological properties of whole muscle areperformed under conditions of supramaximal stimulationof the peripheral nerve. As during in vivo activity muscleis not likely to be maximally active very often, modellersmust deal with this problem in some way. Below wewill consider the way this is usually done and contrastits effects with experimental results.

2.5. Modelling submaximal activation by scaling ofmuscular properties

A very practical way of dealing with situations of sub-maximally activated muscle is to assume that muscular


length–velocity–force properties are identical to those ofmaximally activated muscle apart from the fact that theforce has to be scaled down. This means that propertiesnormalized for force are identical for maximally andsubmaximally activated muscle. Usually, linear scalingis applied (Fig. 5). This approach is well known eventhough it is not always described explicitly whenapplied. A less well known but more confronting wayof describing this approach is described below. As thephysiological mechanism of submaximal activation of afully recruited muscle is manipulation of firing fre-quency of muscle fibers, linear scaling of force can beperformed by assuming that a linear force–firing fre-quency curve is applicable. In contrast, experimentalforce–stimulation frequency curves have a more sig-moidal shape. To fully describe the practice of linearscaling of force one should realize that a second andmaybe more important assumption is made implicitly toobtain identical length–velocity–normalized forcecharacteristics. The force–frequency characteristics haveto be independent of muscle length. Fig. 6 shows a three-dimensional representation of normalized force as afunction of firing frequency and length, as applied forrat GM on the basis of properties of maximally activatedmuscle. In the frequency–force planes linear relations areclearly visible. In the length–force planes clearly lengthrange of active force generation is independent of degreeof activation.

In skinned fiber the sarcolemma of muscle fibers is

Fig. 5. Three-dimensional representation of the effect of linear scaling of force on length–velocity–force curves. The top left panel shows assumedproperties under conditions of maximal activation. The bottom left panel shows a 50% scaled version of these characteristics. Note that afternormalizing for optimum force, one curve (left panel) describes both 100 and 50% activation conditions. This indicates that the material propertiesof the muscle were unaltered.

Fig. 6. Linear scaling of force, as often applied in muscle modelling,represented as a function of muscle tendon complex length and firingfrequency. The surface represents conditions of both maximal and sub-maximal activation. Force is normalized for optimum force at 100 Hzand length is expressed relative to optimum length. For a given lengththe firing frequency–force curve can be discerned. Note the linearcharacter of this relation. Also note that if normalized for maximalforce at each muscle length one linear curve would be obtaineddescribing frequency force characteristics at all lengths. For a givenfrequency, length–force curves can be discerned. Note that if forcewould be normalized for optimum force of each length–force curve,one curve would be obtained describing length normalized force curvesfor all frequencies. As a consequence, optimum (arrows) and activeslack length are unchanged at different frequencies.


removed by chemical treatment or mechanical pro-cedures. In such preparations it is possible to manipulatethe intracellular conditions by superfusion, using sol-utions containing different concentrations of calciumions. This allows the study of the effects of calciumperseon exerted muscle force. Results are usually publishedas pCa–force curves for one or at best a few fiberlengths. These curves are the intracellular equivalent forsteady state force–firing frequency curves. Results showthat pCa-normalized force curves are sigmoidal in shape.The details of the sigmoid curve are very dependent onmuscle length (e.g. [64–66]). This feature is referred toas a length-dependent calcium sensitivity of myofila-ments. Calcium sensitivity is defined here operationallyin terms of normalized force. This means that for a givencalcium concentration a higher force, normalized for itsvalue at maximal activation at that length, is obtainedthan at a lower length. To keep this definition explicitand clear it may be wise to refer to this phenomenonas “calcium sensitivity of (normalized) force” until themechanism is more clearly understood.

Only Stephenson and Wendt [65] presented such fin-dings also in terms of (partial) sarcomere length–forcecurves of skinned fibers (Fig. 7). This figure shows thatwith decreasing activation optimum length shifts tohigher fiber lengths, whereas maximal sarcomere lengthof active force generation is unchanged. Recent experi-ments [3] on intact muscle fibers in which calcium con-centration was measured as well as force also showedsuch effects for partial fiber length–force curves nearoptimum length. This study also showed that altered cal-cium concentrations were not found at different lengths,so that the effects must be related to the actual mech-anisms of contraction. It has been suggested that alength-dependent affinity of troponin C may be involvedin this phenomenon [3,65].

In their classic study Rack and Westbury [57] reportedsimilar results for whole cat soleus muscle. Shortly

Fig. 7. Sarcomere length-dependent sensitivity of force as found inskinned fibers of rat muscle. Drawn lines indicate experimentaldata[64] and dashed lines extrapolations to active slack lengths. Asactivation is decreased ([Ca] decreases), optimum and active slacklengths shift to higher sarcomere lengths as force is lowered.

thereafter, Close [11] reported that length normalizedforce curves for twitches are different than the curvefor tetani.

When activated at fairly low frequencies, force is notconstant in time but significant force ripples are present.This is caused by synchrony of recruitment of motorunits in such experiments. For simplicity, representationof length force results in this article will be made forpeak forces only. Fig. 8 gives such a representation forthe results of Rack and Westbury [57]. This may be oneof the most neglected results in twentieth centurymyology and biomechanics. Therefore, we conclude thatan alternative approach of describing properties of sub-maximally active muscle is needed badly, and modellersshould be encouraged to use it. At present, this authorknows only one study in which it is unequivocally evi-dent that attempts were made to incorporate sucheffects [22].

2.5.1. Conclusions on the classical approachDespite the limitations of the classical approach

described above, clearly much has been learned fromusing it. In particular, this is the case for mechanismsactive in muscle that determine both acute and long-termproperties. At the same time we should realize that sucha classical approach is too limited for use in generatingknowledge about properties of muscles during daily use.

3. Alternative approach

3.1. Effects of firing frequency and its history

We repeated the experiment of Rack and Westbury[57] for rat GM [59,60] and small bundles of its fibers[86]. Fig. 9a shows the principle of the protocol used inthose studies for constant stimulation frequencies and an

Fig. 8. Effects of constant stimulation frequency on length forcecurves of cat soleus muscle. Experimental data were derived from theclassic study of Rack and Westbury[57]. Note the similarity of resultsregarding muscle optimum and active slack lengths with Fig. 7.


Fig. 9. Frequency protocols and examples of muscle force as a function of time. (a) Frequency protocol for constant stimulation frequencies(CSFs). These frequencies are imposed in separate contractions of the muscle for each frequency studied. The protocol was repeated at each ofthe lengths studied. (b) Frequency protocol for a decreasing staircase stimulation frequency (DSF). The stimulation frequency staircase was imposedduring one contraction. The protocol was repeated at each of the lengths studied. (c) Superimposed force records for one muscle length belowoptimum length. Arrows indicate points of comparison with results of the DSF protocol.

example of force exerted in time as obtained at one mus-cle length. Fig. 10 shows the results of such experimentsrepresented as a three-dimensional representation of nor-malized force as a function of firing frequency andlength. Note the following features:

(a) Sigmoidal shapes of the curves in the frequency–force planes. The shape of these curves is verydependent on muscle length.(b) With lower constant frequencies, optimum lengthis encountered at muscle lengths progressivelyhigher than in maximally activated muscle.(c) With lower constant frequencies active slacklength moves substantially and progressively tohigher muscle length. This shift tends to be some-what smaller than the shift of optimum length, there-fore length range between optimum and active slacklength increases at lower constant frequencies.

It should be pointed out that the length force charac-teristics may no longer be what their name indicates butmay also contain some velocity effects. This will happen[32] if a phase delay of sufficient magnitude is foundbetween varying muscle force and consequent lengthchanges due to viscoelastic properties of tendon and ten-don plate. This may be true for the experimental datashown here. If it is, it is also likely to be the case forin vivo conditions.

Hatze [22] attempted to incorporate effects of firingfrequency in his model by altering the slope of the force–frequency curve as a function of muscle length. How-ever, it should be realized that such an action will notbe fully successful as it has the effect of taking intoaccount shifts of optimum length but not of active slacklength. In such models, overestimation of force at lowerlengths is a direct consequence. Recently, van Zandwijket al. [76] were fairly successful in modelling submaxi-


Fig. 10. Three-dimensional representation of effects of constantstimulation frequency (CSF) and muscle tendon complex length onforce of rat medial gastrocnemius muscle. Force is normalized for opti-mum force at 100 Hz stimulation and length is expressed relative tooptimum length as encountered at this stimulation frequency. In thefrequency–force planes the change of shape of the stimulation fre-quency–force curves can be clearly seen. Note the progressive shift ofoptimum length to higher lengths at lower stimulation frequencies(white arrows). At the lowest frequencies, which are physiologicallymost important, active slack length also shifts to higher lengths.

mal force exerted by fully recruited rat GM during con-stant frequency stimulation (CSF) on the basis of twitchcharacteristics. It should be noted, however, that successwas dependent on the model being optimized for individ-ual variables of twitches and used to predict force of GMfrom individuals.

A different type of stimulation frequency experimentwas also performed [58,59,86] in which stimulation fre-quency was decreased in a stepwise fashion during eachisometric contraction (for the decreasing stimulation fre-quency (DSF) protocol, see Fig. 9b). Normalized forceas a function of actual firing frequency and length isshown in Fig. 11. Note the following features:

(a) Sigmoidal shapes of the curves in the force fre-quency plane differ substantially with respect tothose of constant stimulation frequencies.(b) Shifts of optimum lengths to higher lengths withlower stimulation frequencies still occur albeit to asmaller extent. Therefore, the history of stimulationfrequency of this particular protocol has the neteffect of shifting optimum length back to somewhatlower lengths.(c) The shift of active slack length to higher lengthswith lower frequencies is only minimally present. Itseems as if a memory persists of muscle being pre-viously stimulated at high frequencies and almostmaintaining active slack length accordingly.(d) These changes cause force to be potentiated sub-stantially at many lengths (Fig. 5 in [59]). In thatstudy the authors normalized force for its value dur-ing maximal stimulation at each length, therebydrawing attention to extremely high normalized lev-

Fig. 11. Three-dimensional representation of effects of decreasingstimulation frequency (DSF) and muscle tendon complex length onthe force of rat medial gastrocnemius muscle. Force is normalized foroptimum force at 100 Hz stimulation and length is expressed relativeto optimum length as encountered at this stimulation frequency. In thefrequency–force planes the change of shape of the stimulation fre-quency–force curves can be clearly seen. Note the progressive shift ofoptimum length to higher lengths at lower stimulation frequencies(white arrows), but this shift is smaller than during CSF stimulation.At only the very lowest frequencies, active slack length also shifts avery limited amount to higher lengths.

els of potentiation at low muscle lengths that may bevery important functionally because it allows forceexertion many times higher than during constant fir-ing frequencies. However, when these results areplotted as absolute force or normalized for force atthe original (i.e. 100 Hz) optimum length (as is donein Fig. 12), clearly at higher lengths substantialpotentiation occurs.

Initially, potentiation was defined operationally, i.e. interms of increased force. However, more recently it hasbeen described in terms of effects of phosphorylation ofthe myosin light chain (see review in [69]). The myosinlight chain is an integral part of the cross bridge and itextends from the tip of the head to the neck region closerto the thick filament. Donation of a phosphate groupfrom ATP is intimately related to the process of contrac-tion. Considerably different ideas about the moleculareffects of phosphorylation exist (e.g. [56]), but not aboutits increasing effects on force. Force increases arereported [54] to be linearly related to the amount ofphosphorylation of the myosin light chain.

A more detailed analysis of these interesting phenom-ena is beyond the scope of the present paper. A morepractical question that remains to be answered is howdo these results of stimulation frequency experimentscompare to those predicted by linear scaling of force forthis muscle. Fig. 12 shows errors of linear scaling offorce with respect to CSF and DSF results. The errorcurves are obtained by subtracting the curve of Fig. 6from those of Figs 10 and 11 respectively. The resultsof this operation speak for themselves: very substantial


Fig. 12. Three-dimensional representation of differences in rat GM isometric force as obtained from linear scaling of force, constant (CSF) ordecreasing (DSF) stimulation frequencies. Differences in force are normalized for optimum force at 100 Hz stimulation and length is expressedrelative to optimum length as encountered at this stimulation frequency. The two figures on the left show the errors that would be made if linearscaling of force rather than experimental data of protocols regarding CSF (top panel) or DSF (bottom panel) would be used. At low lengths andfrequencies negative errors of linear scaling compared to CSF and DSF protocols were not plotted. The figure on the right shows the difference inforce between the DSF and CSF experimental data. In all three figures very substantial differences are encountered at many lengths and frequencies.

errors (up to 50% at some lengths in the lower frequencyranges) result for both conditions.

As indicated above Fig. 12 also shows differences inforce between the particular DSF and CSF protocolsused. Preliminary results (Bosch, Roszek and Huijing,unpublished observations) indicate that these effects maybe quite specific for the particular protocols. A majorchallenge is found here for experimental physiologistsand biomechanists alike to attempt to describe the effectsof history of activation in such a general way that it canbe applied for modelling of muscle and movement.

3.1.1. Conclusions on firing frequency and historyDue to the interaction between level of activation as

well as its short time history and length force character-istics, linear scaling of force is not an adequate way ofdealing with the problem of modelling submaximal acti-vation if the model has to incorporate features of realmuscle on this point. There is some hope that taking intoaccount adequate features of excitation dynamics mayallow incorporation of CSF effects. However, individualproperties seem to play an important role in these effects

and have to be taken into account. The effects of potenti-ation will further complicate such attempts. Describingsuch complicated effects as a function of muscle lengthseems to be indicated.

3.2. Effects of sustained isometric contraction (atconstant stimulation frequency)

Many people are aware that, during sustained contrac-tion, fatigue (e.g. [1,15]) will play a major role indetermining how much force the muscle exerts at anypoint in time. It is common practice to define suchfatigue operationally as the decrease in force seen in timeduring a contraction. Recently, Huijing and Baan [33]reported effects of fatigue on isometric length forcecharacteristics during tetanic contraction, at almostmaximal activation (100 Hz). Because of the finding ofsmall shifts of optimum length but not of active slacklength, we hypothesized these effects to be related tointracellular inhomogeneities of calcium concentration[31,32] and thus inhomogeneities of activation [1]. Itshould be noted that alternative hypotheses may have to


be considered as well. In any case these results indicatethat, during sustained maximal contraction, isometricmuscle length force characteristics are changing as afunction of time. Few people realize that very compli-cated interactions between fatigue [1] and potentiation[69] are observed during sustained submaximal iso-metric contraction. It is argued [34] that the mechanismsof fatigue may even lead to an increase of force at highermuscle lengths (Fig. 13). Crucial to these arguments isthat the maximal length of force exertion is considereda fixed property of muscle regardless of its degree ofactivation and potentiation. In the work on skinned fibers(see also Fig. 7) experimental evidence for this assump-tion is found, but the point requires further attention alsofor intact fibers and whole muscle. In any case, the netchanges in force during an isometric contraction, evenunder conditions of constant firing rate, cannot beadequately assigned to be the consequence of fatigue[33,34]. Following similar arguments it is feasible thatthe effects of myosin light chain (MLC) phosphorylation(Fig. 13) may lead to a decrease of force [34] at certainlengths. Therefore, the use of operational definitions for

Fig. 13. Schematic representation of alterations of isometric length–force curves as a consequence of two different mechanisms active duringconditions of local muscle fatigue, potentiation by myosin light chain phosphorylation and distribution of sarcomere length in series within fibers.The alterations indicated are deduced from experimental data[32,57] on rat GM during sustained contraction. The magnitude of effects is verylength dependent and may change to a direction that is in contradiction with operational definitions commonly used for fatigue (decrease of forcein time) and potentiation (increase of force in time). Even during a sustained isometric contraction at constant firing frequency (CSF) the actuallength–force properties would change dynamically in time and would at any time be determined by the net effect of the mechanisms illustratedhere and most likely others as well.

these phenomena is likely to interfere with enhancedunderstanding rather than to facilitate it.

It should be noted that in vivo the central nervoussystem responds to short term sustained submaximal iso-metric contractions by lowering firing rates [6]. In sucha case effects of potentiation, such as described fordecreasing stimulation frequency protocols, should alsobe taken into account.

3.2.1. Conclusions on sustained contractionFrom the results described in this section it becomes

clear that what may seem to be a simple isometric con-traction is already a very complex phenomenon duringwhich length force properties alter in time by effects offatigue and potentiation of force. We should consider itlikely that dynamic muscular properties will also changewith time. It should be noted, however, that in theseexperiments the relatively long duration of contractionwas used compared to in vivo intermittent contractionsthat are encountered in cyclic movements. Therefore,one has to be careful with extrapolating the magnitudeof these effects to the in vivo situation. Instead, this work


should be used as an indication of mechanisms possiblyactive during in vivo movement.

3.3. Inhomogeneous fiber properties within a muscle

The problem of assumed homogeneity of fiber proper-ties within a muscle is indicated above as one of thelimiting factors playing a role in muscle modelling. Itshould be realized that this factor may also play a rolein the interpretation of experimental results. For humanmuscles, joint angle moment characteristics were hardto explain on the basis of fiber lengths or number ofsarcomeres in series within fibers (e.g. [25,37,39]). Inaddition, we know surprisingly little about which part ofthe length range of the length force curve is actuallyused by humans in vivo. Recently, Lieber, Friden andco-workers extended their previous experimental animalwork dealing with the relationship of joint angle and sar-comere length [45,46,49] to architecture studies ofhuman muscles [47] as well as invasive experiments onhumans [48] (see also this issue).

The importance of knowledge about the joint angle–sarcomere length is evident. Many patients are hamperedseverely by limitations of joint excursion, which may becaused by consequences of faulty regulation of optimumlength and/or length range of active force exertion.Therefore, it is very important to be aware of factors thatshould be taken into account in interpreting joint angle–sarcomere length data. Only fairly recently, some model-lers interested in morphological details of active musclehave tried to study aspects of functional consequencesof inhomogeneities in muscle (e.g. [8,16,24,76]) or applyfinite element models to skeletal muscle [71–73,75].Recent results presented by van der Linden et al.[21,72,73] will be discussed here. Fig. 14 shows animportant feature of the model: initially, the muscle ismodelled in the passive state with homogeneous proper-ties just as in the geometric modelling. In similarity withgeometric models, muscle fibers are represented bystraight lines, but only for the initial passive state. Asthe muscle is activated a distribution of fiber lengthdevelops. The assumed homogeneity of the model mus-cle means that the muscle fibers contain the same num-ber of sarcomeres in series. Therefore, fiber mean sarco-mere length becomes distributed as well: different fiberswithin the active muscle have different mean sarcomerelengths. Such a distribution has been referred to as asecondary distribution of fiber mean sarcomere length[31,32]. Contraction also introduces curved fibers andaponeuroses. For the fibers the amount of curvature isdependent on the location within the muscle. We mustconclude that mechanical interaction between theelements of the model makes the continued presence ofhomogeneous characteristics within the muscle imposs-ible. Despite this added feature it was concluded [72,73]that muscle length force characteristics were not

adequately described by the model: substantial differ-ences for length force data remained. Clearly, factors ofmajor importance are not included in the models used.

3.4. Primary inhomogeneities of fiber mean sarcomerelength

For rat muscle circumstantial evidence regarding theexistence of a distribution of fiber mean sarcomerelength is available (e.g. [16,20,27,39,79,85,86]). Themajority of this indirect evidence is based on the follow-ing finding. At muscle optimum length the mean sarco-mere length of certain (groups) of fibers is not equal tosarcomere optimum length as expected from a simplehomogeneous muscle. For example, GM active distalfibers reach optimum sarcomere length at muscle lengths1.27 mm over optimum length [38]. This amounts tomore than 10% of the length range between optimumand active slack lengths. For GM inhomogeneous withrespect to mean sarcomere length of different fibers,models have been made to assess effects on length forcecharacteristics [16]. For EDL muscle [8] a first effectwas modelled in 1990.

Particularly for cat muscle, direct evidence has beenaccumulating in the last two decades that, at any musclelength, sarcomere length may be distributed [44,63]).This evidence is obtained from studying length forcecharacteristics of whole muscle and single motor unitsstimulated through their isolated ventral roots. In somecat muscles (flexor digitorum longus muscle) the distri-bution is systematic for motor unit size (Fig. 15). How-ever, for another cat muscle this could not be shown[44]. Note that if the distribution is regulated by motorunit size, muscle length force characteristics will be verymuch dependent on the degree of recruitment of motorunits. More recently, direct evidence for distribution oflength force characteristics of (groups) of motor unitswas also encountered for rat GM [12,13]: for that musclebigger motor units tended to have their optimum lengthat higher muscle lengths than whole muscle optimumlength. This means that to obtain total fiber force for amuscle its fiber length force curves do not add “in phase”with respect to fiber or sarcomere length. Instead, theaddition should take place with the curves shifted a cer-tain amount along the length axis with respect to eachother (see also [32,34]). In such a muscle at muscle opti-mum length the grand mean of the sarcomere lengthsshould be equal to sarcomere optimum length. In a pen-nate muscle the situation is complicated by fiber lengthdependent angular effects described above.

3.5. Individual variation

In an experiment the functionally parallel-fiberedsemi-membranosus lateralis muscle (SMl) of the rat wasexamined [79]. Individual SMl muscles may show con-


Fig. 14. Changes of muscle geometry as modelled by a Finite Element Model of rat medial gastrocnemius muscle (GM). The top panel showslinearized geometry of the muscle as assumed to occur at optimum length in the passive state. The values for fiber as well as aponeurosis lengthsand angles were experimentally determined for the most distal fiber and proximal aponeurosis of GM. The muscle is assumed to be fully homo-geneous and muscle volume is constant. As the model muscle is activated a distribution of fiber lengths develops due to interactions between fibersas well as between fibers and aponeuroses. As this distribution was not present initially but developed as the muscle was activated, it is referredto as “secondary”.

siderable differences in length range between optimumlength and active slack length: ascending limb of thelength force curve of maximally activated muscle (Fig.16). Surprisingly, the mean number of sarcomeres in ser-ies showed no correlation (r = 20.14) with these individ-ual length ranges. In contrast, the coefficient of variationof fiber mean sarcomere length at optimum musclelength correlated significantly (r = 0.88) with the lengthrange. Some of these individual muscles showed no evi-dence of distributed sarcomere length. Therefore, weconclude that most of this variation of sarcomere lengthis most likely not due to secondary effects but is causedby a primary distribution of sarcomere length. This con-cept was reviewed in detail [32,34].

3.5.1. Conclusions on inhomogeneous propertiesInhomogeneous properties, particularly those related

to primary and secondary distributions of fiber mean sar-comere length, have a sizable effect on length forcecharacteristics of maximally active muscle but moreimportantly on not fully recruited muscle. Some evi-

dence is available that such properties may be influencedby exposing the muscle to different conditions. In anycase it is clear that a physiological individuality causesconsiderable variation between individuals in thesephenomena. This will be very difficult to deal with inmodelling unless model variables can be based on indi-vidual data.

3.6. Effects of previous shortening

It has been known for quite some time (e.g. [14]) thatprevious shortening leads to what is called a deficit inisometric force (Fig. 17). This means that, after shorten-ing, the redeveloped isometric force does not attainvalues that are as high as that of a comparable isometriccontraction at the target length. These effects may, forthe major part, be ascribed to inhomogeneities of lengthsof sarcomeres that are in series within one fiber [14].However, some differences in force were also encoun-tered in conditions in which no changes of such distri-bution could be shown [67]. On the basis of that finding


Fig. 15. Example of a distribution of motor unit optimum length withrespect to whole muscle optimum length as found in cat flexor digito-rum longus muscle[2]. Isolated motor units were stimulated supramax-imally through their axons made accessible at the ventral roots of seg-ments of the spinal cord. Length–force curves thus obtained werecompared to those obtained under supramaximal stimulation of thewhole peripheral nerve. Motor unit optimum lengths are distributedand in this case the distribution is systematic with respect to motorunit fiber type and thus size.

Fig. 16. Length–force characteristics of individual lateral semi-mem-branosus muscle of six rats. Force is normalized for optimum force ofeach individual muscle and length expressed relative to its optimumlength. Substantial differences are found regarding length rangebetween optimum and active slack lengths. These differences did notcorrelate with the number of sarcomeres in series within fibers. How-ever, they did correlate highly and significantly with the amount ofdistribution of fiber mean sarcomere length (r = 0.88). The muscleswith the smallest length range showed no evidence of such a distri-bution, whereas those with the highest length range also showed evi-dence of the highest amount of distribution. It is evident that, regardingprimary distribution of fiber mean sarcomere length, individual vari-ation may have a sizable influence on length–force characteristics.

Fig. 17. Effects of previous shortening on length–force character-istics of rat medial gastrocnemius muscle (GM). The top panel showslength changes imposed on an individual GM muscle tendon complexas a function of time. Superimposed are length time trajectories ofcontractions that start at different lengths but end after isokinetic short-ening at the identical target length. Note that shortening speed is ident-ical regardless of initial length but range of shortening is varied (from1 to 4 mm). One contraction, which remained isometric throughoutactivation, is used a reference (isom 0–0). The middle panel shows anexample of force exerted as a function of time. After redevelopmentof isometric force, a “force deficit”, relative to the fully isometric con-traction, is seen in contractions that actually involved a concentricphase. The magnitude of the force deficit is also dependent on theamount of shortening that was imposed. Such experiments were perfor-med for many target lengths. The bottom panel shows mean length–force curves for six muscles. Active muscle force and muscle lengthare plotted. Individual curves represent these characteristics for GMwith equal previous shortening history. Clearly, force deficit is encoun-tered at all target lengths but its magnitude is very much dependenton muscle length. Small differences in optimum length are found.


as well as other work [19] it is concluded that this effectis also likely to be caused by more than one mechanism,the relative importance of which should be a matter ofdiscussion.

The existence of distributions of sarcomere length inseries within fibers and their effects may be anotherexample in recent myology in which the debate is notfully executed. The major part of the physiological com-munity that is involved in fundamental research on mus-cular mechanism seems convinced that this distributionis present and has substantial effects on muscular proper-ties. Nevertheless there are indications that the debateon alternative explanations is somewhat suppressed. Acomplicating factor may be that if such distributionswould not exist, the sliding filament theory proponentswould have difficulty explaining fiber characteristics, forfixed end isometric contractions rather than those underservo-length control, without major adaptation oraddition to the theory. On the other hand, proponents ofalternative theories or hypotheses (e.g. [56]) are verymuch dependent on the absence of in series distributionsof sarcomere length.

It is clear that the phenomenon of force deficit afterprevious shortening exists and we have to deal with itseffects. There are also indications that an opposite effectmay be found after previous lengthening of the activemuscle: “force surplus for at least some muscle lengths”(e.g. [17]). The effects of previous lengthening of theactive muscle on muscle length force curves has not beenstudied systematically.

Until recently, only very little attention was paid topossible changes in length force curves due to previousshortening [77]. Meijer et al. [51–53] showed that iso-metric length force characteristics are influenced system-atically by previous shortening (Figs 17 and 18). Notethat the force deficit is very much length dependent: atrather small lengths the differences with the fully iso-metric curve are much smaller than at lengths over opti-mum length. Note also that the force deficit is alsodependent on the amount the muscle shortened. If con-tractions were sustained longer until a full force plateauwas reached in time, length force results were qualitat-ively similar [53]. Their results also indicate that theeffects on length force characteristics are smaller forcontractions at higher velocity of shortening [52]. Thesame authors [55] realized that the isometric length forcecurve of a muscle would not be equivalent to followingthe curve for one shortening condition. They pointed outthat this curve should be constructed from points ofcurves of different shortening history (Fig. 18). Note theabsence of negative slopes in the curves that take theeffects of previous shortening into account even athigh lengths.

Classically, muscle force–velocity characteristics aredetermined in isotonic or isokinetic contractions. Gener-ally, force–velocity curves based on isotonic contrac-

Fig. 18. Construction of isometric length–force curves of a progress-ively shortening rat GM muscle. Curves of Fig. 17 are shown alsoin this figure. However, the isometric properties of an active muscleshortening progressively will not be described by any of these curves.As the curves drawn describe properties for equal amounts of shorten-ing (0 to 4 mm), the curves for isometric properties of a shorteningmuscle (effects of velocity are not considered) should connect aftereach millimeter of shortening a point of appropriate length on the sub-sequent curve. The polylines drawn in the figure represent such curves.Even at high lengths, that correspond to the original descending limbof the isometric length–force curve, no negative force–length slopesare encountered. At low lengths the polylines seem to converge.

tions are considered more advantageous, as theoreticallythey do not contain effects of series elastic elements.However, the above indicates that force–velocity charac-teristics both for isotonic and concentric contractions arecontaminated by length-history and or velocity-historyeffects in a way that seldom will reflect in vivo charac-teristics. This effect may very well be larger for isotoniccontractions. Experimentally, such contractions have theadded disadvantage that the history of shortening is notunder the control of the experimenter, as it is determinedby interaction of muscular length–force properties andimposed load.

The recent model reported by Barrata et al. [4,78] isa new effort to take such effects into account. However,this model is also based on experimental results involv-ing isotonic contractions and is therefore likely to sufferfrom the lack of control of the determining factor: short-ening history.

3.6.1. Conclusions on effects of previous shorteningand its history

Previous shortening affects length force characteristicssubstantially. Its short-term history is also an importantfactor. The concepts of length–force and force–velocitycharacteristics need to be reconsidered in view of whatis needed to understand performance in daily movement.


4. Summarized overall conclusions

The major conclusions are:

I Length–velocity–force characteristics are not uniqueproperties of a muscle.

I These characteristics are not only strongly influencedby actual effects of recruitment, firing frequency,amount of shortening performed and velocity of short-ening but also by the short time history of these fac-tors.

I Therefore, length, velocity and activation cannot beconsidered as independent determinants of musclefunctioning.

I For experimenters it is crucial to study muscularproperties not just at one length but effects should beconsidered over the whole length range relevant foractual function.

I We are confronted with many indications of physio-logical individuality regarding these phenomena.

The effects for modelling are summarized below:

I Depending on their purpose, modellers should stillselect relatively simple models of muscle.

I However, chosen limitations should be madeexplicitly.

I Comparisons with experimental results are crucial forvalidation, but more so for generation of new ideas.

I As a consequence we should be focusing much moreon differences rather than agreements between modeland experimental results.

Acknowledgements

Continuing discussions with my co-workers and closecolleagues on the topics described in this article havecontributed substantially to views described here. There-fore, I would like to acknowledge such contributions ofHenk Grootenboer, Bart Koopman, Kenneth Meijer, Bartvan der Linden at the Universiteit Twente and those ofGuus Baan, Peter Bosch, Gertjan Ettema, Hans Heslinga,Boris Roszek, Mark Willems and Coert Zuurbierpresently or formerly at the Vrije Universiteit, Amster-dam. Several of those mentioned prepared figures relatedto their work for use in the present article. I would alsolike to thank the Canadian Society of Biomechanics andtheir Organizing Committee of the 9th Biennal Confer-ence at Vancouver B.C., in particular Andy Hoffer andWalter Herzog, for the invitation to present the keynotelecture on which this article is based.

References

[1] Allen DG, Westerblad H, Lee JA, Lannergren J. Role of exci-tation contraction coupling in muscle fatigue. Sports Med1992;13–:116–26.

[2] Bagust J, Knott S, Lewis DM, Luck JC, Westerman RA. Iso-metric contractions of motor units in a fast twitch muscle of thecat. Journal of Physiology 1973;231–:87–104.

[3] Balnave CD, Allen DG. The effect of muscle length on intracellu-lar calcium and force in single fibres from mouse skeletal muscle.Journal of Physiology 1996;492–:705–13.

[4] Barrata RV, Solomonow M, Nguyen G, D’Ambrosia R. Load,length and velocity of load-moving tibialis anterior muscle of thecat. Journal of Applied Physiology 1996;80–:2243–9.

[5] Benninghoff A, Rollhauser H. Zur inneren Mechaniek des gefie-derte Muskels. Pfluegers Archiv fuer die Gesamte Physiologie1952;254–:527–48.

[6] Bigland-Ritchie B, Dawson N, Johansson R, Lippold O. Reflexorigin for the slowing of moto-neurone firing rates in fatigue ofhuman voluntary contractions. Journal of Physiology 1986;379–:451–9.

[7] Bobbert MF, Van Zantwijk JP. Dependence of human maximaljump height on moment arms of the biarticular m. gastrocnemius;a simulation study. Human Movement Science 1994;13–:696–716.

[8] Bobbert MF, Ettema GJ, Huijing PA. Force length relationshipof a muscle tendon complex: experimental results and model cal-culations. European Journal of Applied Physiology 1990;61–:323–9.

[9] Bobbert MF, Huijing PA, Van Ingen Schenau GJ. A model ofhuman triceps surae muscle-tendon complex applied to jumping.Journal of Biomechanics 1986;19–:887–98.

[10] Borelli, G. A., De motu animalium, Bernabo, Roma, 1680, trans.P. Maquet as On the Movement of Animals, Springer Verlag,Heidelberg, 1989.

[11] Close RI. The relations between sarcomere length and character-istics of isometric twitch contractions of frog sartorius muscle.Journal of Physiology 1972;220–:745–62.

[12] de Ruiter, C. J., Physiological properties of skeletal muscle unitsvary with intra-muscular location of their fibres. Doctoral disser-tation, Vrije Universiteit, Amsterdam, 1996.

[13] De Ruiter CJ, De Haan A, Sargeant AJ. Physiological character-istics of two extreme muscle compartments in gastrocnemiusmedialis of the anaesthetized rat. Acta Physiologica Scandinavica1995;153–:313–24.

[14] Edman KAP, Caputo C, Lou F. Depression of tetanic forceinduced by loaded shortening of frog muscle fibers. Journal ofPhysiology 1993;466–:535–52.

[15] Enoka RM, Stuart DG. The neurobiology of muscle fatigue. Jour-nal of Applied Physiology 1992;72–:1631–48.

[16] Ettema GJC, Huijing PA. Effects of distribution of fiber length onactive length force characteristics of rat gastrocnemius medialis.Anatomical Record 1994;239–:414–20.

[17] Ettema GJC, Van Soest A, Huijing PA. The role of series elasticstructures in prestretch-induced work enhancement during iso-tonic and isokinetic contractions. Journal of ExperimentalBiology 1990;154–:121–36.

[18] Gans C, Bock WJ. The functional significance of muscle architec-ture: a functional analysis. Ergebnisse der Anatomie undEntwicklungsgeschichte 1965;38–:115–42.

[19] Granzier HLM, Pollack GH. Effect of active pre-shortening onisometric and isotonic performance of single frog muscle fibres.Journal of Physiology 1989;415–:299–327.

[20] Grottel K, Celowski J. Division of motor units of medial gastro-cnemius of the rat in the light of variability of their principalproperties. Acta Neurobiologiae Experimentalis 1990;50–:571–88.

[21] Hakkinen, K., Keskinen, K. L., Komi, P. V. and Mero A. (ed.),Proceedings of 15th Congress of the International Society ofBiomechanics. University of Jyvaskyla, Finland, 1995.

[22] Hatze, H., Myocybernetic Control Models of Skeletal Muscle.University of South Africa Press, Pretoria, 1981.


[23] Hawkins DA, Hull ML. A computer simulation of muscle mech-anics. Computers in Biology and Medicine 1991;21–:369–82.

[24] Hawkins DA, Hull ML. An activation recruitment scheme for usein muscle modelling. Journal of Biomechanics 1993;26–:1117–28.

[25] Herzog W, Ter Keurs HEDJ. A method for determination offorce–length relation. Pfluegers Archiv 1988;411–:637–41.

[26] Heslinga JW, Huijing PA. Effects of growth on architecture andfunctional characteristics of adult rat gastrocnemius muscle. Jour-nal of Morphology 1990;206–:119–32.

[27] Heslinga JW, Huijing PA. Muscle length force characteristics inrelation to muscle architecture: a bilateral study of gastrocnemiusmedialis muscles of unilaterally immobilized rats. European Jour-nal of Applied Physiology 1993;66–:289–98.

[28] Heslinga HE, Te Kronnie G, Huijing PA. Growth and immobiliz-ation effects of sarcomeres: a comparison between gastrocnemiusand soleus muscles of the adult rat. European Journal of AppliedPhysiology 1995;70–:49–57.

[29] Hill, A. V., First and Last Experiments in Muscle Mechanics.Cambridge University Press, Cambridge, 1970.

[30] Hoyle, G., Muscles and their Neural Control. Wiley, NewYork, 1983.

[31] Huijing PA. Parameter interdependence and success of skeletalmuscle modelling. Human Movement Science 1995;14–:443–86.

[32] Huijing PA. Important experimental factors for skeletal musclemodelling: non-linear changes of muscle length force character-istics as a function of degree of activity. European Journal ofMorphology 1996;34–:47–54.

[33] Huijing, P. A. and Baan, G. C., Fatigability and length forcecharacteristics of rat gastrocnemius muscle during sustained tet-anic contraction. In Proceedings of 15th Congress of the Inter-national Society of Biomechanics, ed. K. Hakkinen, K. L. Kes-kinen, P. V. Komi and A. Mero. University of Jyvaskyla, Finland,1995, pp. 408–409.

[34] Huijing, P. A. and Roszek, B., Length–force characteristics of ratmuscle during isometric contraction are determined by inde-pendent and cumulative effects of fatigue and potentiation. InProceedings 18th Conference of IEEE Engineering in Medicineand Biology Society, ed. H. B. K. Boom. IEEE Publishing Ser-vice, New York, 1996, pp. 215–216.

[35] Huijing PA, Woittiez RD. The effect of architecture on skeletalmuscle performance: a simple planimetric model. NetherlandsJournal of Zoology 1984;34–:21–32.

[36] Huijing PA, Woittiez RD. Notes on planimetric and three-dimen-sional muscle models. Netherlands Journal of Zoology 1985;35–:521–5.

[37] Huijing, P. A., Greuell, A. E., Wajon, M. H. and Woittiez, R.D., An analysis of human isometric voluntary plantar flexion asa function of knee and ankle angle. In Biomechanics: Basic andApplied Research, ed. G. Bergman, R. Kolbel and R. A. Rohl-man. Nijhoff, Dordrecht, 1987, pp. 662–667.

[38] Huijing PA, Nieberg SM, Van De Veen EA, Ettema GJC. A com-parison of rat extensor digitorum longus and gastrocnemiusmedialis muscle architecture and length force characteristics.Acta Anatomica 1994;149–:111–20.

[39] Huijing, P. A., Wajon, M. H., Greuell, A. E. and Woittiez, R.D., Muscle excitation during voluntary maximal plantar flexion:a mechanical and electromyographic analysis. In Proceedings of8th Conference of I.E.E.E. Engineering in Medicine and BiologySociety, Vol. 1, ed. G. V. Kondraske and C. J. Robinson. I.E.E.E.Publishing Service, Piscataway, 1986, pp. 637–639.

[40] Huxley AF. Muscle structure and theories of contraction. Pro-gress in Biophysics and Biophysical Chemistry 1955;7–:255–318.

[41] Jacobs R, Van Ingen Schenau GJ. Control of an external forcein leg extensions in humans. Journal of Physiology 1992;457–:611–26.

[42] Jacobs R, Van Ingen Schenau GJ. Intermuscular coordination ina sprint push-off. Journal of Biomechanics 1992;25–:953–65.

[43] Kardel T. Steno on muscles. Introductions, texts, translations.Transactions of the American Philosophical Society 1994;84–:1–252.

[44] Lewis DM, Luck JC, Knott S. A comparison of isometric contrac-tions of the whole muscle with those of motor units in a fasttwitch muscle of the cat. Experimental Neurology 1972;37–:68–85.

[45] Lieber RL, Boakes JL. Sarcomere length and joint kinematicsduring torque production in frog hindlimb. American Journal ofPhysiology 1988;254–:C759–68.

[46] Lieber RL, Brown CG. Sarcomere length–joint angle relationshipof seven frog hindlimb muscles. Acta Anatomica 1992;145–:289–95.

[47] Lieber RL, Fazeli BM, Botte MJ. Architecture of selected wristflexor and extensor muscles. Journal of Hand Surgery 1990;15–:244–50.

[48] Lieber RL, Loren GJ, Friden J.In vivo measurement of humanwrist extensor muscle sarcomere length changes. Journal of Neur-ophysiology 1994;71–:874–81.

[49] Lieber RL, Raab R, Kashin S, Edgerton VR. Short communi-cation sarcomere length changes during fish swimming. Journalof Experimental Biology 1992;169–:251–4.

[50] Maquet, P. (trans.), On the Movement of Animals (translation ofBorelli’s De motu animalium, 1680). Springer Verlag, Heidel-berg, 1989.

[51] Meijer, K., Grootenboer, H. J., Koopman, H. F. J. M. and Huij-ing, P. A., The isometric length force relationship during concen-tric contractions of the rat medial gastrocnemius muscle. In Inte-grated Biomedical Engineering for Restoration of HumanFunction, ed. J. Feijen. Institute for Biomedical Engineering,Universiteit Twente, Enschede, 1995, pp. 73–76.

[52] Meijer, K., Koopman, H. F. J. M., Grootenboer, H. J. and Huij-ing, P. A., The effect of shortening history on the length forcerelationship of the muscle. In Proceedings of 15th Congress ofthe International Society of Biomechanics, ed. K. Hakkinen, K.L. Keskinen, P. V. Komi and A. Mero. University of Jyvaskyla,Finland, 1995, pp. 618–619.

[53] Meijer K, Grootenboer HJ, Koopman HFJM, Huijing PA. Fullyisometric length force curves of rat muscle differ from those dur-ing and after concentric contraction. Journal of Applied Biomech-anics 1997;13–:164–81.

[54] Moore RL, Persechini A. Length dependent isometric twitch ten-sion potentiation and myosin phosporylation in mouse skeletalmuscle. Journal of Cellular Physiology 1990;143–:257–62.

[55] Otten E. Concepts and models of functional architecture in skel-etal muscle. Exercise and Sport Sciences Reviews 1988;16–:89–139.

[56] Pollack, G. H., Muscles and Molecules. Uncovering the Prin-ciples of Biological Motion. Ebner and Sons, Seattle, 1990.

[57] Rack PMH, Westbury DR. The effects of length and stimulusrate on tension in the isometric cat soleus muscle. Journal ofPhysiology 1969;204–:443–60.

[58] Roszek, B. and Huijing, P. A., Stimulation frequency historyalters length force characteristics of fully recruited rat muscle.Journal of Electromyography and Kinesiology, in press.

[59] Roszek B, Baan GC, Huijing PA. Decreasing stimulation fre-quency dependent length force characteristics of rat muscle. Jour-nal of Applied Physiology 1994;77–:2115–24.

[60] Scott SH, Winter DA. A comparison of three muscle pennationassumptions and their effect on isometric and isotonic force. Jour-nal of Biomechanics 1991;24–:163–7.

[61] Spoor CW, Van Leeuwen JL, Van Der Meulen WJTM, HusonA. Active force length relationship of human lower leg musclesestimated from morphological data: a comparison of geometric


muscle models. European Journal of Morphology 1991;29–:137–60.

[62] Stensen, N. (N. Stenonis), Elementorum Myologiæ Specimen sevMusculi Descriptio Geometrica, Florence, 1667, cited by T. Kar-del, Transactions of the American Philosophical Society, 1994,84, 1–252.

[63] Stephens JA, Reinking RM, Stuart DG. The motor units of catmedial gastrocnemius: electrical and mechanical properties as afunction of muscle length. Journal of Morphology 1978;146–:495–512.

[64] Stephenson DG, Wendt DA. Effects of sarcomere length on theforce–pCa relation in fast- and slow-twitch skinned muscle fibresfrom the rat. Journal of Physiology 1981;333–:637–53.

[65] Stephenson DG, Wendt IR. Length dependence of changes insarcoplasmatic calcium concentration and myofibrillar calciumsensitivity in striated muscle fibres. Journal of Muscle Researchand Cell Motility 1984;5–:243–72.

[66] Stienen GJM, Blange´ T, Treijtel BW. Tension development andcalcium sensitivity in skinned muscle fibres of the frog. PfluegersArchiv 1985;405–:19–23.

[67] Sugi H, Tsuchiya T. Stiffness changes during enhancement anddeficit of isometric force by slow length changes in frog skeletalmuscle fibers. Journal of Physiology 1988;407–:215–29.

[68] Swammerdam, J., Biblia Naturae, Leiden, 1737, cited by T. Kar-del, Transactions of the American Philosophical Society, 1994,84, 1–252.

[69] Sweeney HL, Bowman BF, Stull J. Myosin light chain phos-phorylation in vertebrate striated muscle: regulation and function.American Journal of Physiology 1993;264–:C1085–95.

[70] Tabary JC, Tabary C, Tardieu C, Tardieu G, Goldspink G.Physiological and structural changes in cat’s soleus muscle dueto immobilization at different lengths by plaster casts. Journal ofPhysiology 1972;224–:231–44.

[71] Van Den Donkelaar CC, Drost MR, Van Mameren H, TuinenburgCF, Janssen JD, Huson HA. Three dimensional reconstruction ofthe rat triceps surae muscle and finite element mesh generationof the gastrocnemius medialis muscle. European Journal of Mor-phology 1996;34–:31–7.

[72] van der Linden, B. J. J. J., Huijing, P. A., Meijer, K., Koopman,H. F. J. M. and Grootenboer, H. J., In Integrated BiomedicalEngineering for Restoration of Human Function, ed. J. Feijen.Institute for Biomedical Engineering, Universiteit Twente,Enschede, 1995, pp. 53–57.

[73] van der Linden, B. J. J. J., Meijer, K., Huijing, P. A., Koopman,F. F. J. M. and Grootenboer, H. J., Finite element model of aniso-tropic muscle: effects of curvature on fibre length distribution.In Proceedings of 15th Congress of the International Society ofBiomechanics, ed. K. Hakkinen, K. L. Keskinen, P. V. Komi andA. Mero. University of Jyvaskyla, Finland, 1995, pp. 956–957.

[74] Van Ingen Schenau GJ, Van Soest AJ, Gabriels FJM, HorstinkMWIM. The control of multi-joint movement relies on detailedinternal representations. Human Movement Science 1995;14–:511–38.

[75] Van Kan WJ, Huyghe JM, Jansen JD, Huson A. A 3D finiteelement model of blood perfused rat gastrocnemius muscle. Euro-pean Journal of Morphology 1996;34–:19–24.

[76] Van Leeuwen JL, Spoor CW. A two dimensional model for theprediction of muscle shape and intramuscular pressure. EuropeanJournal of Morphology 1996;34–:25–30.

[77] van Zandwijk, J. P., Bobbert, M. F., Baan, G. C. and Huijing, P.

A., From twitch to tetanus: performance of excitation dynamicsoptimized for a twitch in predicting tetanic muscle forces. Bio-logical Cybernetics, in press.

[78] Vance T, Solomonow M, Barrata RV, Best R. Comparison ofisometric and isotonic length tension models in two skeletalmuscles. IEEE Transactions on Biomedical Engineering1994;41–:771–81.

[79] Willems MET, Huijing PA. Heterogeneity of mean sarcomerelength in different fibres: effects on length range of active forceproduction in rat muscle. European Journal of Applied Physi-ology 1994;68–:489–96.

[80] Williams PE, Goldspink G. Changes in sarcomere length andphysiological properties in immobilized muscle. Journal of Anat-omy 1978;127–:459–68.

[81] Woittiez RD, Huijing PA, Boom HBK, Rozendal RH. A threedimensional muscle model: a quantified relation between formand function of skeletal muscles. Journal of Morphology1984;182–:95–113.

[82] Zajac FE. Muscle and tendon: properties, models scaling andapplication to biomechanics and motor control. CRC CriticalReviews in Biomedical Engineering 1989;17–:359–411.

[83] Zajac, F. E. and Winters, J. M., Modeling musculoskeletal move-ment systems: joint and body segmental dynamics; musculoskele-tal actuation, and neuromuscular control. In Multiple Muscle Sys-tems, ed. J. M. Winters and Woo. 1990, pp. 121–164.

[84] Zuurbier CJ, Huijing PA. Influence of muscle geometry on short-ening speed of fibre, aponeurosis and muscle. Journal of Biome-chanics 1992;25–:1017–26.

[85] Zuurbier CJ, Heslinga JW, Lee-De Groot MBE, Van Der LaarseWJ. Mean sarcomere length–force relationship of rat muscle fibrebundles. Journal of Biomechanics 1995;28–:83–7.

[86] Zuurbier CJ, Lee-De Groot MBE, Van Der Laarse WJ. Effectsof in vivo fibre activation frequency on length dependent forcegeneration of skeletal muscle fibre bundles. European Journal ofApplied Physiology, in press.

Dr Peter A. Huijing received his undergraduatetraining in Physical Education at the AmsterdamAcademy of Physical Education and a Ph.D. inPhysiology from the University of Minnesota.He is a member of the Faculty of Human Move-ment Sciences at the Vrije Universiteit inAmsterdam and its Research Institute: Funda-mental and Clinical Movement Sciences. He isalso affiliated with the Institute for BiomedicalTechnology at the University of Twente and itsresearch institute: integrated Biomedical Engin-eering for restoration of human function

(iBME). He holds the chair in Functionality of the Locomotor Apparatus.His major research interest is in myology with a focus on physiology,biomechanics and functional anatomy of muscle.

muscle, the motor of movement: properties in function, · pdf filejournal of electromyography...

Documents