In Vivo Measurement of Human Wrist Extensor

ECRB tendons were dissected free of the muscle and transverse dye lines were placed at a IO-mm spacing along the tendon length for measurement of strain as ...
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JOURNALOFNEUROPHYSIOLOGY Vol. 7 1, No. 3, March 1994. Printed

in U.S.A.

In Vivo Measurement of Human Wrist Extensor Muscle Sarcomere Length Changes RICHARD







Department of Orthopaedics and Biomedical Sciences Graduate Group, University of California and Veterans Administration Medical Centers, San Diego, California 92161; and Departments of Anatomy and Hand Surgery, University of Umed, S-90185 Umeb, Sweden SUMMARY


Sosnicki 199 1 ), and the descending limb (Herzog et al. 199 1; Lieber and Brown 1992; Lieber and Boakes 1988; Mai and Lieber 1990). There is, therefore, no general agreement regarding the physiological operating range of sarcomeres. Understanding this range is important for a complete understanding of the physiological basis of neuromotor control. Although muscle force can be altered by the number and frequency of activated motor units, force can also be altered by sarcomere length changes that are effective and predictable. Understanding these relationships in the human upper extremity may provide unique insights into the design of the musculoskeletal system because hand and wrist function are highly specialized to perform manipulative tasks. Thus, the purpose of this study was to measure the sarcomere length-wrist joint angle relationship in patients undergoing surgical release of the extensor carpi radialis brevis muscle (ECRB).


1. Human extensor carpi radialis brevis (ECRB) sarcomere length wasmeasuredintraoperatively in five subjectsusinglaser diffraction. 2. In a separatecadavericstudy, ECRB tendonswereloadedto the muscle’spredicted maximum tetanic tension, and tendon strain wasmeasuredto estimateactive sarcomereshorteningat the expenseof tendon lengthening. 3. As the wristjoint waspassivelyflexed from full extensionto full flexion, ECRB sarcomerelength increasedfrom 2.6 to 3.4 pm at a rate of 7.6 nm/degjoint anglerotation. Correcting for tendon elongationduring muscleactivation yielded an active sarcomere length range of 2.44 to 3.33 ,um. Maximal predicted sarcomere shortening accompanyingmuscle activation was dependent on initial sarcomerelength and wasalways co.15 pm, suggestinga minimal effect of tendon compliance. 4. Thin filament lengthsmeasuredfrom electron micrographs of musclebiopsiesobtained from the sameregion of the ECRB muscleswere 1.30 * .027 (SE) ,ccrnwhereasthick filamentswere 1.66 t .027 pm long, suggestingan optimal sarcomerelength of 2.80 pm and a maximum sarcomerelengthfor active force genera- METHODS tion of 4.26 pm. 5. Theseexperimentsdemonstratethat human skeletalmus- Patient inclusion criteria cles can function on the descendinglimb of their sarcomere The five patientsincluded in the study wereundergoingsurgical length-tensionrelationshipunder physiologicalconditions. Thus, lengthening of the ECRB tendon for treatment of chronic lateral muscleforce changesduring joint rotation arean important comepicondylitis (tennis elbow). Patientsrangedfrom 35 to 50 years ponent of the motor control system. of ageand included three men and two women (Table 1). All proceduresperformed were approved by the Committee on the Useof Human Subjectsat the University of Umea and University INTRODUCTION of California, San Diego.

The sarcomere represents the fundamental unit of force generation in skeletal muscle. Elucidation of the relationship between sarcomere length and isometric tension represents one of the great accomplishments in muscle biophysics (Gordon et al. 1966). Less-well understood, however, are sarcomere length changes that occur during normal movement. Attempts to define such changes have involved sarcomere length measurements from fixed tissues (Rack and Westbury 1969; Rome et al. 1988; Rome and Sosnicki 199 1; Weijs and van der Wielen-Drent 1982), theoretical modeling based on geometric relationships (Delp et al. 1990; Herzog and ter Keurs 1988; Hoy et al. 1990), laser diffraction of isolated muscle-joint specimens (Lieber and Boakes 1988; Lieber and Brown 1993; Mai and Lieber 1990), and laser diffraction of intact muscles (Fleeter et al. 1985; Lieber et al. 1992b). Sarcomere lengths so obtained fall on all portions of the length-tension relationship: the ascending limb (Rack and Westbury 1969), the plateau region (Lieber et al. 1992b; Rome et al. 1988; Rome and 874


laser device

The device usedwasa modification of that originally described by Lieber and Baskin ( 1985) and Fleeter et al. ( 1985). A 5-mW helium-neonlaserbeam ( Melles-Griot, model LHR-007, Irvine, CA) was aligned with a specially designedprism such that the beam projected normal to one prism face and wasreflected90”, exiting the other prism face (Fig. 1). The prism reflective surface wasaluminum coated( Melles-Griot, model 001PRA/OO 1) to direct all availablelaserpower through the muscle. The device wascalibratedusingdiffraction gratingsof 2.50 and 3.33 pm grating spacingsplacedat the location of the musclefiber bundle (seebelow) directly on the prism. Diffraction order spacingsfrom the t 1st order and the t2nd order weremeasuredto the nearest0.1 mm usingdial calipersthat correspondedto a spatial resolution of ~0.02 pm. In practice, repeatedmeasurementof diffraction order spacingresultedin a sarcomerelength variability ofO.lO+0.21(SE)~m(n= 12measurements from two separate orderson three musclebiopsy samplesby a singleobserver). Repeatability of sarcomerelength measurements betweenobservers

0022-3077/94 $3.00 Copyright 0 1994 The American Physiological Society






Characteristicsof experimentalsubjects



Age, yr


Flexed angle, O

Neutral angle, O

Extended angle, O

UF TL IS LA IA4 Average + SD

50 36 35 43 41 40.5 I!I 5.3


-27 -19 -72 -73 -41 -46.4 + 22.5

15 0 7 * -8 3.5 + 8.5

49 36 33 18”f 57 51.0 L 16.9



value not obtained. t-Patient with wrist arthrosis.

was determined by sequential blinded measurement of diffraction patterns obtained from muscle biopsies. Average between-observer variability was 0.16 t 0.29 pm.



Immediately after administration of regional anesthesia, an electrogoniometer (Penny and Giles, model 2 110, Blackwood, Gwent, UK) was placed on the palmar surface of the subject’s wrist and hand. The electrogoniometer was contained within a sterile plastic wrap and secured to the palmar skin using sterile tape. The wrist was allowed to assume its neutral position [a radiocarpal angle of 10 t 2’ (mean t SD) of flexion] and this was defined as 0”. The small radiocarpal angle variability between subjects was considered negligible ( see below). The distal musculotendinous junction of the ECRB was exposed via a dorsoradial incision - 10 cm proximal to the radiocarpal joint. The overlying fascia was removed exposing the underlying ECRB muscle fibers. A small fiber bundle was isolated at the insertion site using delicate blunt dissection, with care not to overstretch muscle fibers. The illuminating prism was inserted beneath the fiber bundle (Fig. 1) and approximated into the normal plane of the muscle.

We made every effort to measure sarcomere length in the in vivo position of the fibers and not to elongate them artificially by elevation of the fiber bundle. Estimation of error due to fiber elevation was obtained in pilot experiments and never exceeded 0.2 pm. Only the distal 2 cm of muscle fibers were exposed, and thus sarcomere lengths reported represent these distal fiber regions. Currently we do not know the extent to which these are representative of the entire fiber length or of different fibers along the muscle length. All sarcomere lengths were calculated using the +2 to -2 diffraction order spacing. Redundant measurements of + 1 to - 1 and +3 to -3 were also made to ensure calculation accuracy. The 2nd order was chosen because the larger order spacing made small absolute spacing measurement errors proportionately less than for the 1st order and the intensity was usually greater than that of the 3rd order. Diffraction angle (8) was calculated using the grating equation, y1X = dsin0, where X is the laser wavelength (0.632 pm), d is sarcomere length, and y2is diffraction order (2nd in all cases) and assuming that the 0th order bisected the orders on either side. Sarcomere length was measured with the wrist placed in each of three positions: full flexion, neutral, and full extension. The actual angular value corresponding to each position was noted from the electrogoniometer’s digital display (Table 1). It was not technically possible to place the wrist in the same extreme angular posi-










FIG. 1. Device used for intraoperative sarcomere length measurement. The He-Ne laser is aligned normal to the transmitting face of the prism for optimal transmission of laser power into the muscle. Second-order diffraction spacing was measured manually using calipers. Inset, a transverse view of the illuminating prism placed beneath a muscle fiber bundle.







ECRB muscleand tendonproperties

Muscle Mass, g

Muscle Length, mm

Fiber Length, mm

Estimated Muscle PO,kg

Muscle Cross-Sectional Area, mm2

11.8 IL 1.09

176 + 4.4

70.8 IL 1.7

6.0 I!I 0.5 1

240 I!I 21

Tendon Length, mm 204.0

AI 4.4

Tendon Strain at PO, % 2.0 IL 0.2

Values are means rfrSE for n = 5 samples. ECRB, extensor car-pi radialis brevis; PO, maximum tetanic tension. tions for each subject due to physiological variations in patient range of motion and, in one case (subjectLA ), wrist arthrosis.

Sarcomere length measurement from biopsies and micrographs After sarcomere length measurements, muscle biopsies ( - 15 mm long) were taken from the same region by isolating a small fiber bundle as in the diffraction experiment and securing it to a wooden stick using two silk sutures. Wrist angle at which the biopsy was obtained was noted. Extreme care was used to maintain the muscle biopsy in its in vivo configuration by suturing the biopsy to a stick before cutting the fibers. In two subjects ( UFand LA), two biopsies were obtained with the wrist joint in different configurations yielding a total of 7 biopsies. Biopsies were obtained to corroborate sarcomere length values obtained by laser diffraction and were immediately passed to the operating room technician and immersed in 2.5% phosphate-buffered glutaraldehyde (0.1 M buffer adjusted to pH 7.4) for fixation. One to two days after immersion in fixative, biopsies were rinsed in buffer and trimmed to remove obviously damaged muscle fibers, and sarcomere length was again measured using the identical laser diffraction device. In all cases, the presence of three to five diffraction orders suggested preservation of muscle structural integrity. The mechanically undamaged portion of the biopsy was transversely cut into slices - 1 mm thick. From these slices, 8- 10 tissue blocks were postfixed for 2 h in 1% osmium tetroxide, dehydrated in graded alcohols, and infiltrated with Spurr embedding resin (Polysciences, Warrington, PA). Blocks were oriented so that the muscle fibers could be sectioned either longitudinally or transversely. Survey sections of 1 ,ccrnwere stained with toluidine blue, and a region was selected, trimmed, and sectioned for electron microscopy. Section thickness was kept as close to 60 nm as possible. Five micrographs were printed from each biopsy at approximately X30,000 magnification. An image analysis system (IBAS, Zeiss, New York, NY) was used to measure A-band length (corresponding to the myosin filament length), actin filament length, and sarcomere length. Micrograph magnifications were calculated using the M-line repeat distance of 220 A within the M-band (Thornell et al. 1987) as well as the 385-A troponin repeat distance along the actin filament (Huxley and Brown 1967). Actin filament length was measured as the distance from the center of the Z-line to the end of the filament projecting into the A-I overlap region. Six measurements of each structure from each print were averaged to yield a single value for that specimen.

ECRB tendon biomechanical


Muscle-tendon units from five fresh-frozen cadaveric specimens were removed and muscle architectural properties measured as previously described (Lieber et al. 1990). ECRB fiber length-tomuscle length ratio was -0.4 with a cross-sectional area of 2.4 cm2, in agreement with our previous study. ECRB maximum tetanic tension (P,) was then predicted for each specimen by multiplying the calculated physiological cross-sectional area by a specific tension of 2.5 kg/ cm2, which yielded an average P, of 6 kg (Table 2). This procedure has been shown to predict muscle tetanic tension accurately (Powell et al. 1984).

ECRB tendons were dissected free of the muscle and transverse dye lines were placed at a IO-mm spacing along the tendon length for measurement of strain as previously described (Lieber et al. 199 1). The marked ECRB tendon was then placed in a bath of normal saline at a temperature of 37OC and slowly loaded (over a 30-s interval) to P, during which time surface strain was recorded. This relatively slow strain rate (0.1 %/s) was chosen to permit maximum tendon strain and permit calculation of maximum sarcomere shortening. Because tendons are somewhat viscoelastic (Herrick et al. 1978)) demonstrating increased stiffness with increasing strain rate, it is likely that sarcomere shortening during physiological contraction rates would be slightly less. Load-strain relationships were calculated for each tendon and averaged across tendons to yield a single load-strain equation in the form Load (“/,p,> = a + 10” - c where E represents tendon strain and a, b, and c are regression constants. This relationship was then used with muscle architectural properties to predict sarcomere shortening at the expense of tendon lengthening during muscle activation by using the computer model previously described (Lieber et al. 1992a).



Comparison between wrist angles and sarcomere lengths in the different wrist configurations was made using one-way analysis of variance with repeated measures and multiple paired comparisons performed using Fischer’s least significant difference test (Statview 4.0, Abacus Concepts, Berkeley, CA). Differences between sarcomere lengths measured in vivo were compared with those measured from biopsies and electron micrographs by calculating the root mean square (RMS) difference between the data sets and using a one-sample t test to determine whether the RMS difference was significantly different from zero. Significance level was set to CY = 0.05. Based on the experimental coefficient of variation of 2 I%, statistical power ( 1 - ,Q was calculated as 8 1% (Sokal and Rohlf 1981). RESULTS

DiJfiiaction pattern characteristics In all cases, multiple diffraction orders were observed on either side of the 0th order with approximately equal intensities. Typically, three diffraction orders were seen, but in several cases, up to five diffraction orders were observed implying excellent preservation of the normal sarcomere lattice. In two specific cases, intensity fluctuation of even and odd orders was seen as would be expected from thick grating effects ( Magnusson and Gaylord 1977) . It was easy to see that wrist flexion caused diffraction orders to come closer together, and wrist extension caused diffraction orders to spread apart as expected. Sarcomere length change with joint rotation Despite of the difficulty in achieving uniform joint angles for the flexed, neutral, and extended positions, there was a significant difference (P < 0.00 1) between joint angles in

MAN IN WV0 E 2 /4 c


4.0 3.5



0 n


F a I a, k E

1 3.0






2 a











SL (pm) = -0.0076 pm/O* Joint Angle (“) + 3.01 pm


(I? = .68, P < 0.001) 2.0 -100

I -50

1 0

I 50

1 100 0 .

c 'i, 5 I


cantly different from that observed in the flexed (P < 0.05) but not the extended position. There was a significant correlation between sarcomere length and wrist joint angle (Fig. 2A) with the slope of the sarcomere length-joint angle curve being 7.6 nm/ deg wrist joint rotation. This relationship was well approximated by the linear function

Flexed Neutral Extended





3.2 0 q


In one subject, due to the more extensive exposure, it was possible to determine the sarcomere length-wrist joint relationship of both the ECRB and the extensor carpi radialis longus (ECRL) muscles (Fig. 2B). The slopes of the two relationships were significantly different (P < 0.05) with ECRB changing sarcomere length more for a given joint rotation (7.4 nm/deg) compared with the ECRL (5.2 nm/ deg)-


Biopsy sarcomere lengths 0 q

2.6 ! -100

c 5 Iti

i!? a, E 0 2 ctl


I -50

I 0



50 0 + 0


100 In Vivo Biopsy Microg raph 0

3.0 0

2.5 2.0 -100


I -50

1 0



1 50



Wrist Joint Angle (“) 2. A : sarcomere length vs. wrist joint angle relationship determined for the 5 experimental subjects. Negative angles represent wrist flexion relative to neutral whereas positive angles represent wrist extension. One-way analysis of variance revealed a significant difference between wrist joint angles and sarcomere lengths in the three positions. o, flexed angles; n , neutral angles; A, extended angles. Note that one point is missing from subject LA at a neutral joint angle (Table 1) . B: comparison of the sarcomere length vs. wrist joint angle relationship in one subject for which both the human extensor carpi radialis (ECRB) and extensor carpi radialis longus (ECRL) were exposed. Slope of sarcomere length-joint angle curve for ECRB was 7.4 nm/deg whereas that for the ECRL was only 5.2 nm/deg. C: comparison between sarcomere lengths measured in vivo ( l ) , those measured from muscle biopsies ( + ), and those measured from electron micrographs prepared from muscle biopsies (o ) .

Laser diffraction of muscle biopsy specimens obtained revealed differences between in vivo muscle sarcomere lengths and those measured by laser diffraction in the biopsy at the corresponding joint angle (Fig. 2C). Biopsy sarcomere lengths were found to be both shorter and longer than corresponding sarcomere lengths obtained intraoperatively. Average root mean squared difference between biopsy sarcomere length and the expected in vivo sarcomere length calculated using the regression relationship (because biopsies could not always be obtained at wrist angles identical to those used in sarcomere length measurements) was 0.48 t 0.16 pLm (mean t SD; n = 7 biopsies from 5 individuals), which was significantly different from zero (P < 0.05). This suggests that sarcomere lengths obtained from fixed biopsies may not accurately reflect the sarcomere length in the fresh tissue. ECRB tendon biomechanical



the three positions (Table 1). The average flexed joint angle was approximately -50’ whereas average extension angle was approximately + 50 O. Therefore, sarcomere lengths were measured over a 100’ range of wrist motion. With the wrist in full extension, sarcomere length was -2.6 pm (Fig. 2A), which was significantly shorter (and thus would develop - 50% of the tension) than the 3.4-pm sarcomere length measured in the flexed position (P < 0.005 ). Sarcomere length with the joint in the neutral position was intermediate between these two values ( 3.0 pm) and signifi-

Load-strain relationships within each of five samples were highly reproducible and consistent between specimens. All correlation coefficients obtained from curve-fit of the raw data exceeded 0.7, suggesting that the exponential fit was appropriate. The averaged load-strain relationship (Fig. 3A) was described by the equation: Load (% P,) = 2.415. 10°.818c- 2.4 15. Using this relationship along with muscle architectural properties and tendon dimensions (Table 2), the computer model predicted slight sarcomere shortening at the expense of tendon lengthening (Fig. 3 B). Maximum sarcomere shortening was 0.15 pm at intermediate sarcomere lengths ranging from - 1.8 to 2.7 pm with less shortening at longer and shorter sarcomere lengths. At the measured sarcomere length extremes, passive sarcomere length of 2.6 pm shortened to 2.44 pm and passive sarcomere length of 3.4 pm shortened to 3.33 pm ( Fig. 3 B) . Electron microscopic sarcomere andfilament


Sarcomere lengths measured directly from micrographs were found to be both shorter and longer than those measured by laser diffraction from biopsies (Fig. 2C). The aver-




0 0 n E






Strain (%)

B 0.15-




00 0

3 5 m ii I



.-P 2


00 O.lO-

0 0

00 0a 0 00 00


00 0

00 a, 00 E 000 0 z z 0.00 I ’ I ’ I ’ I ’ I 00 TV m 1.0 1.5 2.0 2.5 3.0 3.5 4.0 2




Length (pm)

FIG. 3. n : average load-strain relationship for five human ECRB tendons. Solid line represents exponential curve fit described by the equation: Load (%P,) = 2.415 10°~818c - 2.4 15. B : predicted sarcomere shortening as a function of passive sarcomere length. Note that the maximum shortening magnitude is -0.15 pm, which occurs at intermediate sarcomere lengths. l

age root mean squared difference between biopsy sarcomere lengths and micrograph sarcomere lengths was 0.39 t 0.16 ,um, which was significantly different from zero (P < 0.05) while the difference between micrograph sarcomere lengths and the in vivo sarcomere lengths was 0.33 t 0.24 and not significantly different (P > 0.25 ). Average myosin filament length was 1.66 t 0.027 pm while average actin filament length was 1.30 t 0.027 pm (Fig. 4) using the 435-A troponin repeat distance and - 13% shorter using the M-line repeat distance. To facilitate comparison with other data, only the troponin-calibrated data are presented. Using actin and myosin filament lengths to construct a hypothetical length-tension curve yielded an optimal sarcomere length of 2.80 ,urn and maximum length for active tension development at a sarcomere length of 4.26 pm (Fig. 5). DISCUSSION

ECRB sarcomere length range The main result of this study was that human passive ECRB sarcomere lengths varied from 2.6 to 3.4 pm throughout the full range of wrist joint motion whereas active sarcomere lengths ranged from 2.44 pm to 3.33 pm.



Given the measured actin filament length of 1.30 pm and myosin filament length of 1.66 pm, these data suggest that the muscle operates primarily on the plateau and descending limb of its sarcomere length-tension curve (Fig. 5 ). Assuming that human muscles generate force as do frog skeletal muscles (for which the sarcomere length-tension relationship has been elucidated; Gordon et al. 1966 ), optimal sarcomere length would occur between 2.60 and 2.80 pm, which agrees well with the optimal sarcomere length of 2.64 to 2.8 1 pm predicted by Walker and Schrodt ( 1973) on the basis of filament length measurements. These data suggest that the ECRB muscle would develop near-maximal isometric force at full wrist extension, force would remain relatively constant as the sarcomeres lengthened “over” the plateau region, and then force would decrease to -50% maximum at full wrist flexion. This result contrasts with the generally accepted notion that skeletal muscles generate maximum forces with the joint in a neutral position. We conclude, therefore, that muscle force change due to sarcomere length changes during joint rotation is “built-in” as part of the control in the musculoskeletal system and not simply a consequence of muscle microanatomy. Of course, the actual muscle force generated at a given angle depends not only on sarcomere length, but also on the number and firing frequency of motor units. Thus, the change in sarcomere length might be viewed as setting the “upper limit” for force production at a given joint angle.

Muscle sarcomere lengths in vivo Previous studies relating sarcomere length to in vivo movement have produced a variety of results. In part this may be due to the variety of methods used, including fixation and manual sarcomere counting (Rack and Westbury 1969; Rome et al. 1988; Weijs and van der Wielen-Drent 1982 ) , theoretical modeling based on geometric considerations (Delp et al. 1990; Herzog et al. 199 1; Hoy et al. 1990), and direct laser diffraction (Lieber and Boakes 1988; Lieber et al. 1992b; Mai and Lieber 1990). Studies of mammalian muscle have suggested that the muscles operate both on the ascending and descending limb of their length-tension curve. In the cat soleus muscle, this corresponded to a predicted sarcomere length range of 2.1-3.2 pm [cf. Fig. 2 of Rack and Westbury ( 1969)]. In the human rectus femoris, sarcomere lengths were not calculated, but it was suggested that fibers operated at lengths corresponding to the descending limb (Herzog et al. 199 1). In contrast to mammalian muscle, studies of swimming fish have suggested that active physiological sarcomere lengths lie almost exclusively on the plateau of their sarcomere length-tension relationships, resulting in maximum efficiency and muscle power output (Lieber et al. 1992’0; Rome et al. 1988; Rome and Sosnicki 199 1). This concept was supported experimentally by Rome and Sosnicki ( 199 1)) who compared in vitro contractile properties to predicted in vivo velocities and claimed that sarcomere velocity corresponded to 0.3 Vmax, the peak power and efficiency point of these muscles. In contrast with fish locomotion studies, in situ optical diffraction studies of frog semitendinosis muscle demonstrated that sarcomere lengths well onto the descending limb of the length-tension curve






FIG. 4. Electron micrograph of human ECRB muscle. Lines in the inset indicate M-line repeat distance (spacing = 220 A) on the myosin filament. A, A band; I, I band; act, actin filament. Calibration bar, 5 wrn in main figure and 220 nm in inset.

occur in normal joint configurations (Lieber and Boakes 1988; Lieber and Brown 1993; Mai and Lieber 1990). It thus appears that various muscle-joint systems operate with sarcomeres on different portions of the isometric lengthtension curve. This could be a result of the different types of movements initiated by these muscles: oscillatory for the fish, propulsive for the frog, and manipulative for the human ECRB. It is possible, that operating on the descending limb allows the ECRB to “automatically” decrease the muscle’s maximum force in the configuration where it is less often used (i.e. llexion). However, the data may also suggest that the most important design constraint of the musculoskeletal system is not to simply maintain constant sarcomere length. As more data are acquired, the underlying design constraints for determination of sarcomere length range will undoubtedly be better understood. It is interesting to note, however, that the slope of the ECRB sarcomere length-joint angle relationship (7.6 nm/deg) is completely within the range of similar values measured in a variety of frog muscle-joint combinations (Lieber and Brown 1993). ECRB/ECRL comparison Although we acknowledge the paucity of data available for ECRB/ECRL comparison, it is interesting to note that, in the one subject for whom ECRB and ECRL sarcomere lengths were measured, there was a significant difference

between the slopes of the sarcomere length-joint angle relationships (Fig. 2 B). The slope for the ECRB relationship was -40% greater than that of the ECRL, which is about the same proportion as the ratio between fiber lengths: ECRL fibers (76 mm) are -50% longer than the ECRB fibers (48 mm; Lieber et al. 1990). Because the ratio of sarcomere length change is nearly the same as the fiber length ratio, these data suggest that the moment arm of the two muscles at the wrist joint are approximately equivalent. Experimental data from Brand ( 1992) and Buchannan et al. ( 1993 ), however, suggest that the ECRL moment arm is -50% larger in flexion-extension than the ECRB. It is not clear why our sarcomere length-joint angle data do not reflect the combination of anatomical muscle differences (ECRL fibers 50% longer than ECRB fibers) with moment arm differences (ECRL moment arm 50% greater than ECRB moment arm). Using the anatomic and moment arm data from the literature, we would predict that the ECRL sarcomere length-joint angle relationship would actually have a smaller slope than that of the ECRB. Nevertheless, based on our measured sarcomere lengthjoint angle data, we would predict that the ECRL would generate greater active force over a greater range of motion than would the ECRB. This type of fiber length disparity between synergists is not unprecedented. For example, the rabbit tibialis anterior (TA) and extensor digitorum longus (EDL) have approximately the same moment arm at the




a, I-

2.80 FIG. 5. Hypothetical length-tension curve obtained using measured filament lengths and assuming the sliding filament mechanism proposed by Gordon et al. ( 1966). Shaded area represents sarcomere length change during wrist flexion (causing sarcomere length increase) and wrist extension (causing sarcomere length decrease). Top : schematic of filament lengths measured in the current study. Numbers over graph represent calculated inflection points based on filament lengths measured and a Z-disk width of 1,000 A.


E .-z



a 2



0 1.5








Length (pm)

ankle joint but have muscle fibers that are significantly different in length (Lieber and Blevins 1989). We thus speculate that the musculoskeletal system may be designed such that “high gear” and “low gear” muscles are juxtaposed in order to permit generation of a significant joint moment at a variety of angular velocities (Gans and deVree 1987). Such a m usculoskeletal interacti .on could control joint stiffness and improve control. This type of muscle-joint interaction might be a parameter defining the properties of a muscle-joint combination in the same way that muscle architecture defines a muscle’s contractile properties (Walmsley and Proske 198 1). Additional studies of this sort in a variety of muscle-joint systems may a more clear understanding of the rationale for the design of musclejoint combinations. The authors thank the many individuals whose support made this project possible: L. Bergfors ( OR nurse), B. Bush ( machine shop foreman), U. Ranggard (electronics technician), M. Jacobson, and S. Shoemaker (UCSD), E. Mjorndal (head nurse), B. Chamberlain (medical illustratar), U. Hedlund (electron microscope technician), and M. Schmitz (micrograph analysis). This work was supported by the Veterans Administration and National Institute of Arthritis and Musculoskeletal and Skin Diseases. Grant AR35 192. Address for reprint requests: R. L. Lieber, Dept. of Orthopaedics, U.C. San Diego School of Medicine and V.A. Medical Center, 3350 La Jolla Village Drive, La Jolla, CA 92093-9 15 1. Received 10 August 1993; accepted in final form 5 November 1993. REFERENCES BRAND, P. W. AND HOLLISTER, A. Clinical Mechanics of the Hand, 2nd ed., Mosby, St. Louis, MO: 1992. BUCHANAN, T. S., MONIZ, M. J., DEWALD, J. P., AND ZEV RYMER, W. Estimation of muscle forces about the wrist joint during isometric tasks using an EMG coefficient method. J. Biomech. 26: 547-60, 1993.


L., LOAN, J. P., HOY, M. G., ZAJAC, F. E., TOPP, E. L., AND J. M. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans. Biomed. Eng. 37: 757-767, 1990. FLEETER, T. B., ADAMS, J. P., BRENNER, B., AND PODOLSKY, R. J. A laser diffraction method for measuring muscle sarcomere length in vivo for application to tendon transfers. J. Hand Surg. 1OA: 542-546, 1985. GANS, C. AND DE VREE, F. Functional bases of fiber length and angulation in muscle. J. Morphol. 192: 63-85, 1987. GORDON, A. M., HUXLEY, A. F., AND JULIAN, F. J. The variation in isometric tension with sarcomere length in vertebrate muscle fibers. J. Physiol. Lond. 184: 170-192, 1966. HERRICK, W. C., KINGSBURY, H. B., AND Lou, D. Y. S. A study of the normal range of strain, strain rate, and stiffness of tendon. J. Biomed. Mater. Res. 12: 877-894, 1978. HERZOG, W., GUIMARAES, A. C., ANTON, M. G., AND CARTER-ERDMAN, K. A. Moment-length relations of rectus femoris muscles of speed skaters/cyclists and runners. Med. Sci. Sports Exercise 23: 1289- 1296, 1991. HERZOG, W. AND TER KEURS, H. E. D. J. A method for the determination of the force-length relation of selected in-vivo human skeletal muscles. Pfluegers Arch. 4 11: 637-64 1, 1988. HOY, M. G., ZAJAC, F. E., AND GORDON, M. E. A musculoskeletal model of the human lower extremity: the effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle. J. Biomech. 23: 157-169, 1990. HUXLEY, H. E. AND BROWN, W. The low angle x-ray diagram of vertebrate striated muscle and its behavior during contraction and rigor. J. Mol. Biol. 6: 46-60, 1967. LIEBER, R. L. AND BASKIN, R. J. Surgical myometer method. U.S. Patent Number: 4,570,64 1, 1985. LIEBER, R. L. AND BLEVINS, F. T. Skeletal muscle architecture of the rabbit hindlimb: functional implications of muscle design. J. Morphol. 199: 93-101, 1989. LIEBER, R. L. AND BOAKES, J. L. Sarcomere length and joint kinematics during torque production in the frog hindlimb. Am. J. Physiology 254: C759-C768, 1988. LIEBER, R. L. AND BROWN, C. G. Sarcomere length-joint angle relationships of seven frog hindlimb muscles. Acta Anat. 145: 289-295, 1993. LIEBER, R. L., BROWN, C. G., AND TRESTIK, C. L. Model of muscle-tendon



interaction during frog semitendinosis fixed-end contractions. J. Biomech. 25: 42 l-428, 1992a. LIEBER, R. L., FAZELI, B. M., AND BOTTE, M. J. Architecture of selected wrist flexor and extensor muscles. J. Hand Surg. 15: 244-250, 1990. LIEBER, R.L., LEONARD, M.E., BROWN,C.G.,ANDTRESTIK,C. L.Frog semitendinosis tendon load-strain and stress-strain properties during passive loading. Am. J. Physiol. 26 1 ( Cell Physiol. 30): C86-C92, 199 1. LIEBER, R. L., RAAB, R., KASHIN, S., AND EDGERTON, V. R. Sarcomere length changes during fish swimming. J. Experimental Biol. 169: 25 l254, 1992b. MAGNUSSON, R. AND GAYLORD, T. K. Analysis of multiwave diffraction of thick gratings. J. Opt. Sot. Am. 67: 1165-l 170, 1977. MAI, M. T. AND LIEBER, R. L. Model of semitendinosus muscle sarcomere length, knee and hip joint interaction in the frog hindlimb. J. Biomech. 23: 27 l-279, 1990. POWELL, P.L., ROY, R.R., KANIM, P., BELLO, M., ANDEDGERTON, V.R. Predictability of skeletal muscle tension from architectural determinations in guinea pig hindlimbs. J. Appl. Physiol. 57: 17 15- 172 1, 1984. RACK, P. M. H. AND WESTBURY, D. R. The effects of length and stimulus rate on tension in the isometric cat soleus muscle. J. Physiol. Lond. 204: 443-460, 1969. ROME, L.C., FUNKE, R.P., ALEXANDER, R.McN., LUTZ,G.,ALDRIDGE,




H., SCOTT, F., AND FREADMAN, M. Why animals have different muscle fiber types. Nature Lond. 335: 824-827, 1988. ROME, L. C. AND SOSNICKI,A. A. Myofilament overlap in swimming carp II. Sarcomere length changes during swimming. Am. J. Physiol. 260 ( Cell Physiol. 29) : C289-C296, 199 1. SOKAL, R. R. AND ROHLF, F. J. Biometry, 2nd ed., San Francisco, CA: W. H. Freeman and Company, 198 1. THORNELL, L.-E., CARLSSON, E., KUGELBERG, E., AND GROVE, B. K. Myofibrillar M-band structure and composition in physiologically defined rat motor units. Am. J. Physiol. 253 (Cell Physiol. 22): C456C468, 1987. WALKER, S. M. AND SCHRODT, G. R. I Segment lengths and thin filament periods in skeletal muscle fibers of the rhesus monkey and humans. Anat. Rec. 178: 63-82, 1973. WALMSLEY, B., AND PROSKE, U. Comparison of stiffness of soleus and medial gastrocnemius muscles in cats. J. Neurophysiol. 46: 250-259, 1981. WEIJS, W. A. ANDVANDER~IELEN-DRENT, T.K.Sarcomerelengthand EMG activity in some jaw muscles of the rabbit. Acta Anat. 113: 178188, 1982. WILLIAMS, P. AND GOLDSPINK, G. Changes in sarcomere length and physiological properties in immobilized muscle. J. Anat. 127: 459-468, 1978.