J. Anat. (1989), 166, pp. 77-84 77With 3 figures

Printed in Great Britain

Sarcomere length changes in muscles of the human thighduring walking

ALISON CUTTS

Rheumatism Research Unit, University of Leeds, 36 Clarendon Road,Leeds LS2 9NZ

(Accepted 31 January 1989)

INTRODUCTION

Knowledge of changes in sarcomere length during locomotion enables us toestimate the part of the length tension curve over which muscles are operating. Onewould expect the sarcomere lengths to be indicative of maximal or near maximal forceproduction capacity but it has been suggested (Edman, Elzinga & Noble, 1978) thatthe descending limb of the length tension curve may be unstable. Although a numberof studies have investigated the sarcomere length changes during jaw movements ofvertebrates (Nordstrom & Yemm, 1972; Nordstrom, Bishop & Yemm, 1974;Hertzberg, Muhl & Begole, 1980; Weijs & Van der Weilen-Drent, 1982), relatively fewstudies have been carried out to determine the working range of sarcomere lengthsduring locomotion. Dimery (1984, 1985) investigated the sarcomere length changes inthe muscles of the hind limb during galloping, Cutts (1986) investigated sarcomerelength changes in the flight muscles of birds during a wing beat cycle, and Rome et al.(1988) considered the range of sarcomere length in the red swimming muscles of thecarp. The results from the first investigation suggested that the operational range ofsarcomere length covered the plateau of the length tension curve and the upper partsof both ascending and descending limbs (Dimery, 1984). The investigations of birdmuscle (Cutts, 1986) and red fish muscle (Rome et al. 1988) indicate that the range ofsarcomere length covers only the upper part of the ascending limb and the plateau.

There is relatively little knowledge regarding sarcomere lengths in human muscle;sarcomere lengths have been measured from cadavers in the anatomical position forthe lower limb (Cutts, 1987, 1988 a) and the upper limb and parts of the trunk (Cutts,1988 b). The range of sarcomere lengths from theoretical minimum to theoreticalmaximum muscle lengths has been considered (Cutts, 1988 a). The minimal andmaximal muscle lengths were determined from bone models arranged in extreme jointangles. In the present work, this concept is extended into an investigation of thechanges in sarcomere lengths during walking. There are inherent difficulties ininvestigation of the working range of sarcomere length in human muscle asexperimental material is available only when already fixed in the anatomical positionand sarcomere lengths for other positions must be predicted mathematically. Thederivation of formulae for the prediction of sarcomere length based on changes inoverall muscle length, muscle fibre length and angle of pennation has been describedpreviously (Cutts, 1988 a). In the present investigation sarcomere lengths have beenpredicted using this information, and the sarcomere lengths measured in theanatomical position, to build a picture of sarcomere length changes, and hencevariations in force production capacities, of the muscles of the thigh during normal,level walking.

ALISON CUTTS

MATERIALS AND METHODS

Sarcomere lengths for the muscles of the thigh in the anatomical position and amethod for the prediction of sarcomere lengths at other limb positions have alreadybeen determined (Cutts, 1988a). These data were used in the present investigation.Two normal male volunteers aged 27 and 33 were studied. The experimental

procedure was fully explained to them, including the possible risks of the X-rayinvestigation, and their consent obtained before experiments were embarked upon. Asthe investigation required the overall muscle lengths over a range of experimentalpositions, a life size bone model for each subject was constructed. Lateral X-rays ofthe leg were taken from a distance of 2 metres to give a life size image. It is not ethicallypermissible to take X-rays of the pelvic region in subjects of reproductive age, so thecentre of rotation of the hip had to be determined by an alternative method. TheMoire fringe technique was used. In this technique, two grids of parallel lines at rightangles to each other were attached to the leg. A double exposure photograph wastaken with the leg at slightly different angles and interference fringes were formed. Thetwo sets of fringes intersected at the centre of rotation of the hip. The procedure forthe Moire fringe technique is explained fully by Shoupe & Steffen (1974).The outlines of the X-rays were traced onto stiff card, onto which the centre of

rotation of the hip as determined by the Moire fringe technique was marked. Theshape of the outline of the pelvic girdle and the points of muscle attachment wereobtained from an anatomical text (Williams & Warwick, 1980). The models were cutout, the areas of attachment of the muscles marked and the articulations of the jointssimulated with pins. The model made was necessarily in two dimensions and it ispossible that some movement in the lateral plane may have occurred, introducingerror into the calculations. Observation of the films taken, however, has shown thatany lateral movements of the legs during walking are minimal, so it is unlikely thatlarge errors will be introduced because of this simplification.Cine film was taken of both subjects walking normally along a walkway. This was

projected to life size, with the aid of a small plastic marker attached to the surface ofthe skin. Positions were chosen to represent the following stages in each cycle ofnormal walking: (1) Heel contact.

(2) Foot flat.(3) Heel off.(4) Toe off.(5) Heel contact.

The positions were chosen on the basis of the work of Radcliffe (1962). He showed thepositions along a time scale where one unit represented an entire step. This timingcorresponded well with the observed timings from the cine film.At each of the five positions, the overall muscle lengths were determined. The bone

models were arranged within the outlines of the film, using anatomical landmarks asguides, the lines of action of the following muscles were marked onto them and theoverall lengths measured:

Vastus medialisVastus lateralisRectus femorisSemitendinosusSemimembranosusBiceps femoris

78

Sarcomere lengths during locomotionTable 1. Contractile proportions of the muscles of the thigh

Mean contractile proportionsMuscle (%) + 95% confidence limits

Rectus femoris 71 1 + 1-14Vastus lateralis 94 8 + 7 49Vastus medialis 96-9 + -Semimembranosus 67 7 + 8 66Semitendinosus 46-6 +4-72Biceps femoris (long head) 69 3 +0 94

To convert the overall muscle lengths to lengths of contractile tissue, the contractileproportions of the muscles had to be determined. This information was obtaineddirectly from a series of cadavers; the overall length, including the tendons, and thelength of the contractile portion were measured. The contractile proportions were thencalculated; Table 1 shows the mean contractile proportions with 95% confidencelimits from 3 cadavers. These values were then used as conversion factors to determinecontractile lengths. The length of tendon and contractile tissue was determined for themuscles of each individual in the anatomical position and, assuming the tendon lengthremained constant in all positions, the tendon length was subtracted from the overalllength in the experimental positions to yield the contractile lengths.The following formulae were used to calculate the sarcomere lengths in the required

positions:

(a) Pennate type-muscles:

S2 =S s(. LI-L2)2 1 111 'COSwhere S1 is sarcomere length in anatomical position, S2 is new sarcomere length, L,is the contractile length in the anatomical position, L2 is the new contractile length, 11,is the fibre length in the anatomical position, , is the angle of pennation of the fibres.

(b) Muscles with parallelfibres:

2 Si.LThe derivations of these formulae have been dealt with fully elsewhere (Cutts, 1988 a).

To use these formulae, the sarcomere lengths in the anatomical position, angles ofpennation and the fibre lengths were required. This information has been documentedpreviously (Cutts, 1988 a).The sarcomere lengths were calculated for the muscles mentioned at each stage of

the walking cycle. The corresponding force production capacity was then determinedby comparison with a length tension curve for human muscle (Walker & Schrodt,1973).

RESULTS

Figures 1 and 2 show the sarcomere lengths in the three hamstrings and threecomponents of the quadriceps respectively. These data are the means of the twosubjects over several steps. The sarcomere lengths are presented as graphs covering therange of movement; the regions where the sarcomere length indicates that the muscle

79

ALISON CUTTS

3.5- T T T

80%MFPC

3.0 +

E

cm

c

00

U,

2.5 -+-

100%MFPC

100%MFPC

80%MFPC

2.0 +

1.5 -l

Fig. 1. Sarcomere length changes in the hamstring muscles during walking. MFCP, Maximum forceproduction capacity. +, Semimembranosus. *, Semitendinosus. o, Biceps femoris. -, Muscleinactive. -, Muscle active.

can produce up to 80% maximum tension are indicated by a light stipple and theregions where 100 % maximum tension could be generated are indicated by a heavierstipple.EMG data were consulted to give an indication of where in the walking cycle the

muscles were active. In Figures 1 and 2, the lines joining the sarcomere length datapoints for the different positions are thickened where Paul (1971) indicated the musclesto be active.

DISCUSSION

Some possible sources of error must be recognised; most importantly that themathematical prediction of sarcomere lengths can never yield such an accurate valueas could a direct measurement method (e.g. Dimery, 1984, 1985; Cutts, 1986), but thiswould be impractical with human material. The use of pre-fixed cadavers for thedetermination of the sarcomere lengths in the anatomical position has its own sources

80

Sarcomere lengths during locomotion

35 -r- T T T

3 0 -

2.0 -1-

i/I

80%MFPC

100%MFPC

100%MFPC

80%MFPC

1-5

Fig. 2. Sarcomere length changes in the quadriceps muscles during walking. MFCP, Maximum forceproduction capacity. +, Rectus femoris. *, Vastus medialis. o, Vastus lateralis. -, Muscle inactive.-, Muscle active.

of error which have been discussed in detail previously (Cutts, 1987, 1988 a). Tosummarise them briefly, the most serious possible source of error is that the cadavermay have passed out of rigor mortis before fixation and then would have been prone

to passive stretch, with erroneously long sarcomere lengths. A less likely source oferror with this material would occur if the tissue has been subjected to rough handling;again muscles could stretch and excessively long sarcomere lengths would bemeasured. Another source of error is the production of the bone models from X-raysand Moire fringe photographs. These may not represent the structures of the bodyaccurately, and to use a two dimensional model of the leg may be an oversimplification,although lateral movements of the leg during walking appear to be minimal.

During one step of the walking cycle, most of the sarcomere lengths seem to liewithin the range where at least 80% of the maximum force production capacitycan be realised. The observed sarcomere lengths are shown on the length tensioncurve for human muscle in Figure 3. From this it is clear that the operational

-

4-

c

wj 2-5 -

E00

(n

81

T

ALISON CUTTS

C) 100

80

0 E 60

400ao20

CD)

L_ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5Sarcomere length (,im)

Fig. 3. Sarcomere length range during walking (Subjects A and B) in comparison with the range fortheoretical minimum and maximum muscle lengths. 1E, Sarcomere length range during walking.n, Sarcomere length range from theoretical minimum to theoretical maximum muscle lengths.(Length tension curve for human muscle prepared from the data of Walker & Schrodt, 1973.)

sarcomere lengths cover the top parts of both the ascending and descending limbs ofthe curve as well as the plateau. Although it has been suggested that the descendinglimb may be unstable (Edman et al. 1978), these results are in agreement with thefindings of Dimery (1984, 1985), working on another mammalian species.The results of the investigation of sarcomere lengths in the range from minimum to

maximum theoretical muscle lengths are also summarised in Figure 3. The range ofsarcomere lengths calculated for walking is considerably narrower than this, indicatingthat the muscles are not operating at lengths approaching the predicted extremes.The observations of a working range of sarcomere length which did not cover the

descending limb were made on birds and fish, and it is possible that there are somedifferent adaptations in the functional range of muscles in the different vertebrategroups. Morgan (1985) has disputed the interpretation of Edman et al. (1978) andsuggested that the supposed instability is functionally unimportant. The shape of thelength tension curve for human muscle (Walker & Schrodt, 1973), compared with thatof frog muscle (Gordon, Huxley & Julian, 1966), suggests that human muscle isspecifically adapted to work at longer sarcomere lengths as the plateau is displaced tothe right and extended. This is due to the length of the actin filaments; in man theyare 2 64 ,um long, but in the frog they reach only 2 05 ,um.The range of sarcomere length in the individual muscles is not the same, although

there is reasonable agreement between the two subjects. Whilst there are some minorvariations between the two in the pattern of calculated sarcomere length changesduring walking, this is only to be expected as two individuals would be unlikely to haveidentical gaits. In both subjects the maximum calculated sarcomere length of the rectusfemoris is about 3 4 ,um, occurring in the toe-off position. The EMG data presentedby Paul (1971) indicate that the rectus femoris is active at this point in the step cycle.This muscle has two actions - to extend the knee and to flex the hip. At the toe-offposition the knee was in flexion and the hip in extension in both subjects and it waspossible that this combination of joint angles had led to a passive stretching of themuscle with resulting long sarcomere lengths. The calculated sarcomere lengths for thetwo vasti all fall within the 80 % of maximum force production capacity range.

Considering the knee flexors, at the toe-off position in Subject A, both the bicepsfemoris and the semimembranosus have calculated sarcomere lengths suggestive of aforce production capacity less than 80% of maximum. In Subject B, the calculatedsarcomere lengths indicate that the semimembranosus is not capable of producing

82

Sarcomere lengths during locomotion 8380 % maximum tension whilst the biceps femoris may just be able to do so. Paul's data(1971) suggests that these muscles are active in this position. In the positionimmediately preceding this (heel off), again the calculated sarcomere lengths are short,but in this position the EMG data indicate that the muscle is not active (Paul, 1971).The calculated range of sarcomere length in the semitendinosus is much smaller thanthose of the other two hamstrings.

SUMMARY

In a previous investigation (Cutts, 1988a) sarcomere lengths were determined formuscles of the thigh in the anatomical position, and a method devised for theprediction of sarcomere lengths at other positions.

In the present investigation, this information was used to predict the sarcomerelength changes in the muscles of the thigh during walking, in conjunction with cinefilm and bone models of experimental subjects. When compared with the lengthtension curve for human muscle (Walker & Schrodt, 1973), the results indicate thatduring walking the muscles operate at sarcomere lengths near the plateau of the curve,where maximum tension can be realised.

I would like to thank Professors R. McNeill Alexander and V. Wright and DrB. B. Seedhom for their advice and support. I must also thank the experimentalsubjects for their willingness to participate in the experiments. Financial support wasprovided by the Arthritis and Rheumatism Council for Research.

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