Pergamon

J. Biomechmdcs,

Vol. 28, No. 7, pp. 191-199, 199s Copyright 0 1995 Ekvier Science Ltd Printed in Great Britain. AU rights reserved 0021-9290/95 $9.50 + .oo

0021-9290(94)00137-5

TENDON BIOMECHANICAL PROPERTIES ENHANCE HUMAN WRIST MUSCLE SPECIALIZATION Gregory J. Loren and Richard L. Lieber Department of Orthopaedics and AMES/Bioengineering, University of California and Veterans Administration

Biomedical Sciences Graduate Group, Medical Centers, San Diego, U.S.A.

Abstract-Biomechanical properties of human wrist tendons were measured under loads predicted to be experienced by those tendons under physiological conditions. This was accomplished by measuring the architectural properties of the five prime wrist movers-extensors carpi radialis brevis (ECRB), extensor carpi radialis longus (ECRL), extensor .carpi ulnaris (ECU), flexor carpi radials (FCR), flexor carpi ulnaris (FCU)-and predicting their maximum tension (P,) using a specific tension value of 22.5 N cm- *. Loading the corresponding tendons to PO resulted in significantly different strain among tendons (p < 0.01) with the largest strain observed in the FCU (3.68 + 0.31%) and the smallest strain observed in the ECRL (1.78 + 0.14%). Further, strain magnitude was significantly positively correlated with the tendon lengthto-fiber length ratio of the muscle-tendon unit, a measure of the intrinsic compliance of the muscle-tendon unit. Theoretical modeling of the magnitude of muscle sarcomere shortening expected based on the measured biomechanical properties revealed a maximum sarcomere length decrease of about 0.6 nm for the FCU to a minimum of about 0.2 nm for the ECRB at PO. Thus, tendon compliance may, but does not necessarily, result in significant modification of muscle force generation. The significant variation in tendon biomechanical properties was not observed using traditional elongation-to-failure methods on the same specimens. Thus, the use of elongation-to-failure experiments for determination of tendon properties may not be reasonable when the purpose of such studies is to infer physiological function. These data indicate that muscle-tendon units show remarkable specialization and that tendon intrinsic properties accentuate the muscle architectural specialization already present. Keywords: Tendons; Biomechanics; Muscle architecture; Motor control.

nificantly different maximum tensions and act

INTRODUCTION

through

Skeletalmusclesexert their actionson bonesvia tendons.While the biomechanicalpropertiesof isolated tendonshavebeenstudiedin detail (Butler et al., 1979, for review),only recently havemuscle-tendoninteractions been characterized.

Hoffer et al. (1989) demon-

stratedin cats,during normal gait, asthe paw contacted the ground and the muscle-tendonunit was forcedto lengthen(i.e. during the yield phaseof the step cycle),the tendon lengthened,while the musclefibers actually shortened.Thus,muscle-tendoninteractions may convey distinct functional properties on the muscle-tendonunit that may not be predictedbased on knowledgeof isolatedmuscleor tendon attributes. In a theoretical model, Zajac (1989)demonstrated tendon complianceincreasesthe operating range of a muscle,suggesting that tendon isnot merelyan inert link between musclesand bones,and further that tendon complianceimparts specificpropertiesto the muscle-tendonunit. Skeletalmusclesare highly specializedwith regard to force generatingproperties.Musclesgeneratesig-

Received in final form 5 September 1994. Address for correspondence: Richard L. Lieber, Ph.D., Department of Orthopaedics, U.C. San Diego School of Medicine and V.A. Medical Center, 3350 La Jolla Village Drive, La Jolla, CA 92093-9151, U.S.A.

significantly

different ranges based primarily

on different architectural design(Lieber et al., 1990; Powellet al., 1984;Sacksand Roy, 1982;Zajac, 1989). Given, then, that tendonscan modify musclecharacteristics beyond architecture alone, the extent to which contractile propertiesof skeletalmusclesare modified by tendon complianceis unclear. Furthermore, whether architectural specializationis correlatedin someway with tendon biomechanicalproperties is unknown. It is not possibleto addressthis questionby simply applying publishedmodulousand strain valuesobtained from traditional elongation-to-failureexperiments.This is becausetendonshave a safetyfactor of from 5 to 30(Ker et al., 1988)andare highly nonlinear in their biomechanicalbehavior (Butler et al., 1979). Extrapolation from such published ultimate stress and modulousvaluesis thus not feasible. In this report, we have studied the relationship betweenmusclearchitectural designand tendon biomechanicalpropertiesby loadingthe tendonsover the range of physiologicalforces predicted to be generated by the muscles. METHODS

Skeletal muscle architecture

Muscle architecture was determinedaccording to the methodsdevelopedby Sacksand Roy (1982)as 791

G. J. Loren and R. L. Lieber

192

previously implemented (Lieber et al., 1990).Five cadaveric specimenswere used, intact from the midhumeral level and free of obvious musculoskeletal defects. The prime wrist movers-extensors carpi radialisbrevis (ECRB),extensorcarpi radialislongus (ECRL), extensor carpi ulnaris (ECU), flexor carpi radials(FCR), flexor cat-piulnaris (FCUtwere isolated by dissectionof the forearm.The muscle-tendon units (n = 25) were removed and weighed. Muscle length (L,) was measuredas the distancefrom the origin of the mostproximal musclefibersto the insertion of the most distal musclefibers. Then, utilizing the Lr :L, ratios previously measuredin our laboratory, we calculated musclefiber length (&). Surface pennationangle (0) with the muscleunder zero tension wasalsotaken from the previousstudy. Muscle length and fiber length were normalized to a sarcomerelength of 2.5pm usinglaserdiffraction of fiber specimensin order to compensatefor variations in limb position during fixation. Muscle physiologicalcross-sectionalarea (PCSA) was determinedaccording to the following equation (Sacksand Roy, 1982):

0.05 to 0.14% s-i. Simultaneousforce-time records were obtained at 0.1s intervals via the’servo-motor interfaced with a Macintosh 11x computer (Apple Computer, Inc., Cupertino, CA) using SuperScope software(version 1.0, GW Instruments,Inc., Somerville, MA). The experiment was video-recordedfor subsequentstrain analysis. Becauseof the 1OON mechanicalload limitation of the motor, the FCU of arm specimen5 with a predicted maximum force of 120N wasexcludedfrom biomechanicalexamination. The fourth force-deformationcycle wasutilized for strain analysis using a video dimension analyzer (VDA; Model 303,PIM, Inc., SanDiego, CA; Woo et al., 1980).The VDA signalwasamplifiedby a factor of 100and low-passfiltered at 10Hz (Universal Amplifier 13-4615-58,Gould, Inc., Cleveland,OH) prior to computer acquisition. Each specimenwas straintrackedthree timesfrom parallelregionsof the tendon specimenwith correspondingrecordsaveragedover time. From correspondingpoints on the load-time relationship and strain-time relationship, the load-strain curve wasconstructed(Woo et al., 1980). Tensile failure of tendons

Muscle mass(g) cosfl After physiological testing, the tendon specimen p(gcmm3) Fiber length (cm)’ (1) wasmounted on a MMED systemsapparatuswith wherep = muscledensity(1.056g cm- 3, Mendez and a 3000lb load cell (Materials Technology CorporaKeys, 1960)and 0 = surfacepennation angle. Based tion, La Canada, CA) and securedto a stationary on the fact that musclePCSA is correlated with platform usingmodifiedCryo-Jawclampfixation and musclemaximum tetanic tension (P,), P,, for each liquid carbon dioxide (Riermersaand Schamhardt, muscle was predicted by multiplying PCSA by 1982);the interface strength was further augmented a musclespecifictensionof 22.5Ncm-’ (Close,1972; with cyanoacrylate adhesive.The tendonswere preconditioned by cyclical deformation, 10 timesat 3% Powell et al., 1974) strain as describedby Woo et al. (1980;note that this wasgenerallyoutsideof the physiologicalrange)and Physiologicaltendon loading deformedto failure at a strain rate of about 0.5% s-i. Muscle-tendon units werestoredfresh-frozen.The muscle-tendonunit wasdivided at thejunction of the Tendon cross-sectional area determination aponeurosisand external tendon and the respective Tendon area dimensionwas assessed using three lengthsmeasuredwith digital calipersto the nearest methods:manualdigital micrometry, salinedisplace0.1mm. A 40 mm segmentof external tendon was ment, and computedmicroscopicanalysisfollowing sectionedbeginning10mm from the distal insertion. standardhistologicalpreparation.First, prior to speciCarewastaken to keepthe specimenmoistby bathing menbiomechanicaltesting,a digital caliper wasused it in salineat all times.Usingelastinstain,transverse to determine the major (a) and minor (b) tendon dyelineswereappliedto the unloadedcentral tendon diametersin three distinct and representativeregions. region at a 10mm gaugelength after cautious re- Tendon cross-sectionalarea(CSA) wascalculatedas moval of the peritenon. The tendon was placed in the averagearea of the three regionsusing the equaa 37“C salinebath, and clampedto the arm of a dual- tion: modeservo-motor(Model 310B,CambridgeTechnoCSA = nab, (2) logy, Inc., Watertown, MA) permitting controlled loading. The free end of tendon wassecuredto a sta- where a and b representthe major and minor radii tionary clamp yielding about 30 mm of exposedten- respectively.Tendon CSA wascalculatedagainusing dons betweenclamps. approximately 3 ml of 0.9% NaCl solution at room A digital function generator(Model 3314A, Hew- temperature placed in a 5 ml graduated cylinder lett-Packard Co., Everett, WA) was programmedto etched at 0.1 ml increments.Initial volume was redrive the motor in five linear load-unload cyclesto corded at the baseof the meniscusto the nearest the P, of the musculotendinousactuator tested.To 0.05ml. The tendon specimenwassubmergedin the minimize strain rate effects,load was imparted over cylinder after gentleblotting with gauzeand the final a 30-s interval (0.017Hz) and releasedover a con- volume recorded.Three displacementmeasurements secutiveperiod, with actual strain ratesrangingfrom weremade,divided by specimenlength, and averaged PCSA(cm’) =

Physiological behavior of human wrist tendons to yield mean tendon CSA. Lastly, after transection of the tendon to experimental length, the distal fragment was fixed in 10% buffered formalin for 24-48 h at room temperature, serially dehydrated in alcohols, cleared, and infiltrated with paraffin under vacuum. The specimen was subsequently embedded in SurgiPath medium and sectioned to 6 pm perpendicular to the longitudinal axis. Three representative sections were selected for microscopic analysis using image 1 software (Universal Imaging Corporation, West Chester, PA) to calculate average tendon CSA. Pilot studies on fixed vs. frozen human wrist tendons documented an approximate 30% area shrinkage with histological preparation. Thus tendon microscopic CSA calculations were corrected by this factor. The three procedures yielded comparable results. Variability was noted, however, in interval micrometry measurements likely reflecting the inherent variability of the biological tissue. Moreover, although image analysis was repeated in three histological sections, such sections only represented the region adjacent to the specimen to undergo biomechanical examination and thus may not have accurately represented the variability along the entire tendon length. Consequently, tendon CSA determined by saline displacement normalized to specimen length was used for stress calculations. Biochemical

assay

Followingfailure testing,the fracturedtendonspecimenwasrehydratedin saline.Threerepeatwet masseswereobtainedon an analytical balanceafter gentle blotting of the specimenand the meanhydrated mass for each tendon calculated. Specimenswere subsequentlyquenchedin isopentanecooled in liquid nitrogen and lyophilized at - 20°C for 24 h. Three repeat dry weightswere similarly obtained and the meanpercent hydration determined. A central 1cm fragment was sectionedfrom the tendon specimenand then divided longitudinally for duplicatepercentcollagenassaysby a modificationof the automatedmethod of Blumenkrantz and AsboeHanson(1974). Muscle-tendon

193

in humanwrist muscles(Lieber et al., 1994).Average myosin filament length was 1.66pm while average actin filament length was 1.30pm. Using thesefilament lengthsto construct a hypothetical length-tension curve yielded an optimal sarcomerelength of 2.80pm and a maximumsarcomerelength for active tensiondevelopmentof 4.26pm. (2) The sarcomerelength-passivetensionrelationshipwasmodified from the relationshipobtained by Lieber et al. (1991)for frog muscleby shifting the sarcomerelength at which tensionis zero from 2.2 to 2.8pm soasto align sarcomerelength at zero tension with optimal sarcomerelength (seealsoZajac, 1989). (3) Muscle fiber length, tendon and aponeurosis lengths(externaland internal tendonin Zajac’s(1989) terminology) for eachmuscle(Table 1) aswell as the specificcompliancefunction for each muscle(Fig. 1) weresubstitutedfor the analogousvaluesin the frog model. The logical program flow proceededas follows: Following initialization of experimentalparameters such as connective tissue material properties, sarcomere length and muscle-dimensionalquantities, resting tendon and musclefiber lengths were calculated using experimentally obtained load-strain values(Fig. 1). The musclewas then “activated” according to the data of Huxley (1957).As the muscle developed tension appropriate to the sarcomere length specified,a certain amount of tendon tension resistedsarcomereshorteningaccordingto the measured load-strain values.This tensionwascompared to the isometrictensionfor that sarcomerelength and level of activation to determinethe relative isometric tension.Using the force-velocity relationship(Katz, 1939),sarcomereshortening velocity was then calculated and the new sarcomerelength calculated EC\RB

modeling

To predict the magnitudeof wrist musclesarcomere shorteningat the expenseof tendon lengtheningfor a maximal musclecontraction, the theoretical model describedby Lieberet al. (1992)wasused.This model assumes that sarcomerelength-tensionand force-velocity properties are identical betweenmusclesand uniform acrossthe entire muscle.The model also assumesa finite time-courseof cross-bridgeattachment (Huxley, 1957),an ideal sarcomerelength-tension relationship(Gordon et al., 1966)and an ideal force-velocity relationship(Edmanet al., 1979;Katz, 1939)and was implementedas previously described with the following modifications: (1) The isometric sarcomerelength-tension relationship wasscaledto the filament lengthsmeasured

Strain

(Percent)

Fig. 1. Averaged load-strainrelationships for thefiveprime moversof thewrist.Eachcurverepresents theaverageoffive differentspecimens. Notethateachtendonstrainsto a different magnitudewith a varying shapein the physiological forcerange.Normalizationof loadto stressdoesnot appreciablydiminishthe variabilityamongtendons.

77.0 * 1.5 77.0 f. 2.0

0.29 0.20 73.5 6.4 161.2 1.7 74.4 f 2.9 78.4 + 2.1

f 15.2 k 5.1 &- 15.7 0.18 f 0.5 f 2.30 f 0.27 1.78 + 0.14 438.1 f 93.7 4.4 67.9 ++ 113.6 604.1 31.8 f 4.4

f 6.0 f 1.7 f 14.1 f 3.4

80.3 f 79.6 f

21.4 f

2.0 1.0

0.6

f 7.6 f 8.7 f 4.9 f 0.13 * 1.4 3.36 f 0.25 2.35 f 0.30 721.6 + 167.3 70.8 ff 131.9 3.4 1021

153.7 61.4 215.1 3.67 15.7

209.9 58.8 210.0 51.5

ECU + + k f

79.3 f 74.0 f

126.5 f 103.8 f 230.3 f 3.86 f 17.7 + 3.06 k 2.48 k 595.4 f 74.0 ff 857.5 23.7 +

192.8 59.8 211.9 51.9

1.8 5.1

5.8 7.4 5.6 0.12 1.6 0.32 0.45 93.0 13.5 142.1 2.7

4.8 1.5 15.4 3.7

FCR k k + +

10.3 4.7 9.1 0.18 3.6 0.66 0.31t 95.7t 9.37 152.67 5.2t

8.6 1.6 34.3 8.4

83.6 + 2.0 69.4 + 5.4

160.6 + 47.0 f 207.6 + 4.96 f 27.4 + 3.54 + 3.68 f 448.0 f 51.6 + 540.6 f 16.8 *

220.6 41.9 363.6 89.0

FCU

p > 0.2 p >> 0.4 0.1

= 0.06 pp > 0.3

3.

g

p = 0.06 ***

*

P r

**** **** **** **** **

p

P s s aCI 5a

** **** **** ****

One-way ANOVA significance level +

*Values shown are mean f standard error of n = 5 independent measurements; +significance level from one-way ANOVA. $Qprifies n = 4. Abbreviations: ECRB, extensor carpi radialis brevis; ECRL, extensor carpi radialis longus; ECU, extensor carpi ulnaris; FCR, flexor carpi radialis; FCU, flexor carpi ulnaris; CSA, cross-sectional area; P,, muscle maximum tetanic tension. *p < 0.05; **p < 0.01; ***p i 0.005; ****p < 0.0001.

Biochemical properties Hydration (% dry mass) Collagen (% dry mass)

Tendon stress at PO (MPa) Tendon strain at PO (%) Modulus at PO (MPa) Ultimate stress (MPa) Tangent modulus (MPa) Safety factor ( x PO)

2.1 4.6 4.4 0.11 0.7

81.9 182.1 264.1 2.10 14.2

* f f f + 4.06 & 1.99 f 726.1 + 71.3 +k 904.7 18.0 f

Tendon properties Aponeurosis length (mm) External tendon length (mm) Total tendon length (mm) Tendon length(mm*) : fiber length ratio Tendon CSA

101.3 102.7 204.0 2.89 14.6

6.9 5.6 11.1 2.7

155.3 127.3 130.0 31.9

Muscle properties 186.4 f 4.5 Muscle length (mm) 70.8 f 1.7 Fiber length (mm) 240.1 f 20.5 Physiological CSA (mm2) Predicted maximum tetanic tension (N) 58.8 + 5.0 f + f k

ECRL

ECRB

Parameter

Table 1. Measured properties of muscles and tendons*

Physiological behavior of human wrist tendons (based on the sarcomere shortening velocity and time interval of 0.01 ms). This process was repeated in 0.01 ms increments and sarcomeres continued to shorten until muscle contractile force was equivalent to the resistive force of the connective tissue. This program was written in FORTRAN in the Macintosh Programming Workshop (MPW) programming environment using the MPW SADE symbolic debugger program. (MPW 3.2.3, Apple Computer, Inc., Cupertino, CA.) Statistical

analysis

Biomechanicalparametersfor individual tendon sampleswere analyzed by one-way analysisof variance (ANOVA). Multiple paired comparisonsbetweentendonswereperformedpost-hoc usingFisher’s protected least-squaresdifferencemethod. In addition, tendonswere groupedasflexor or extensorand asradial deviator or ulnar deviator; suchgroupswere compared by two-way ANOVA. Simple regression was usedto determinethe significant interrelationshipsbetweenmorphologicaland functional characteristics.Stepwiseregressionwas usedto distinguish which of the many independentvariablesmeasured (Table 1) had the greatest influence on sarcomere shortening (the dependentvariable). F-to-enter was set to 4.000 and F-to-remove 3.996.Data were analyzed usingStatView 4.0 software(AbacusConcepts, Inc., Berkeley,CA). Significancelevel (a) wasselected as 0.05; statistical power (l-j?) exceeded65% for all parameters evaluated. Data are expressed as mean+ SE unlessotherwisenoted. Exponential curves for the individual load-strain and stress-strainrelationshipswere obtained in the form y = a? with correlation coefficientsexceeding 0.76for all data sets.

RESULTS

Muscle architecture

and actuator morphology

Musculotendinousactuator propertiesweresimilar to thosereportedpreviously(Lieberet al., 1990,Table 1). Maximum tetanic tensionfor all muscleswaspredicted basedon the relationshipestablishedbetween PSCA and PO (Powell et al., 1984).Predicted maximumtetanic tension(P,) of FCU (89.1f 8.4N) was significantly greater than PO of other wrist muscles (p < 0.0005)while that of ECRL (31.9+ 2.7N) was significantly less(p < 0.05).Moreover, the FCU tendon CSA was significantly larger (27.4& 3.6mm2) than other wrist tendons (range 14.2f 0.5-17.7 &- 1.6mmz), in effect normalizing the maximum physiologicalstressimposedon tendon groups(wrist flexors 3.31f 0.40MPa, extensors3.24+ 0.24MPa). Wrist extensormusclefibersweresignificantly longer than the fibers of flexors (p < O.OOOS), while the radial muscleshad significantly longerfibersthan the ulnar deviators (p < 0.0005)as previously reported (Lieber et al., 1990).Total tendon length (L,) was

195

comparable among tendon groups, though ECRL had a significantly longer tendon than others (p < 0.05;Table 1).Given the inherent tendon material compliance,both the relative tendon stiffnessand the tendon 1ength:fiber length ratio (L,: &) of a muscle-tendon unit influence the complianceof a musculotendinousactuator. A greater L,: Lf ratio results in an increasedintrinsic compliance of the system.Wrist flexor units and ulnar deviator units werenoted to havea greaterintrinsic compliancethan the extensor and radial groups basedon this ratio (p < 0.0001). Physiological load-strain of prime wrist movers

relationships

Under physiological loads, the relationship between load and strain was characterizedby a curve with progressivelyincreasingslopeand no clear demarcationbetweentoe andlinear regionsasis evident in deformation-to-failureexperiments(Fig. 1). At P,,, wrist flexor tendonsstrainedsignificantly more than extensortendons(p < 0.005)while tendonsacting to deviate the wrist ulnarly strained more than those acting radially (p < 0.01; Fig. 2). Specifically, FCU strained 3.68_+0.31% at P,,, more than any other wrist tendon (p < 0.05). Normalization of load to stressand determination of tendon tangent modulus at PO from individual exponential curve fits revealedno significant differenceamongtendons(p > 0.2).Thus,the slopesof the stress-strainrelationshipsof the tendonswere comparable at maximum tetanic tensions,yet notable variability wasapparentat tensionslessthan PO (Fig. 1). Normalization of the load-strain relationshipto tendon CSA did not appreciablydiminishthe variability noted in physiologicaltendonbehavior, suggesting materialsdissimilaritiesbetweentendonsat low forces. Physiological strain was significantly positively correlated with tendon CSA (p < 0.01, r2 = 0.3).

FleXOr

EXt0lWX

Fig. 2. Averagestrainat muscle POfor tendons groupedby function.Openbarsrepresent radialmuscles whilefilledbars representulnar muscles.Data were obtained from load-strainrelationships similarto thoseshownin Fig. 2. Two-wayANOVA revealed a significant difference between strainin flexorsvsextensors fp < 0.005)andulnar-vsradial deviators(p < 0.01)withno significant interaction(p > 0.2).

796

G. J. Loren and R. L. Lieber

Thesedata indicate that the larger tendonsstrain to variations in tendon hydration or possibly matrix a greater extent in uivo and are in contrast to the composition may contribute to the individual biopremiseof Ker et al. (1988)that increasedtendonCSA mechanicalbehaviors of tendons at physiological protectsagainstincreasedstrain in musculotendinous loads. actuators which generatehigh forces. As previously model simulation noted by An et al. (1991),musclePCSA correlated Muscle-tendon significantlywith tendonCSA (p < 0.0005, rz = 0.46). The variable considered to have the greatest physiologicalimportanceresultingfrom tendoncomTensile failure relationships pliancewasmaximumsarcomereshortening.Because No significant differences were noted in bio- of the differing biomechanicalpropertiesand tendon mechanicalproperties of human wrist tendons de- and fiber lengths, the magnitude of sarcomere formed to failure. Ultimate stress (range 51.6- shorteningpermitted was significantly different be+ 9.3-74.0 f 13.5MPa, p > 0.4), ultimate deforma- tweenmuscle-tendonunits (p < 0.0001;Fig. 3). Sartion (range 11.4f 1.0-16.6f 1.7%, p > 0.3), and comereshorteningbetweenall pairs of muscle-tentangent modulus in the linear region (i.e. forces don units was significantly different (p < 0.05) with greater than P,, and lessthan ultimate force; range the exception of the ECRB and ECRL (p > 0.4) and 540.6+ 152.6-1020.6+ 131.9MPa, p > 0.1) did not the ECU and FCR (p > 0.1). Sarcomereshortening vary significantlybetweentendons.Suchfindingssup- magnituderangedfrom about 0.2 pm for the ECRL to port a common structure-function relationship of about 0.6 pm for the FCU. Given sarcomerelengths tendonsat supramaximalmuscleforces. of myosin and actin filaments of 1.66 and 1.3pm The fact that physiologicalstrain averagedapprox- respectively(Lieber et al., 1994),this magnitude of imately 2.5% for the different tendonsbut ultimate sarcomereshortening could result in muscleforce deformationscorrespondedto strainsof about 14% changesof lo-50% P,, dependingon the rangeover indicatesthat, at in oivo loads,tendonsof the human which the sarcomereshortened. wrist operate within the toe region of this curve. The best predictor of sarcomereshortening was Indeed, the tangent moduli of individual tendonsat tendon strain at P,, (F-to-enter = 100.7)which acP0 were significantly less than the moduli in the countedfor 81% of the experimentaldata variability. linear regionof the stress-straincurve (at higher for- The only other variable to enter the stepwiseregresces;p > O.OOS), lending further support to this con- sion equation was L,: Lr ratio (initial F-to-enterclusion.In addition, the safety factors did not vary = 44.7; F-to-enter after step 1 = 24.3) which then significantly among flexors and extensorsor radial accountedfor an additional 11% of the experimental and ulnar groups;ECRL, though, wasnoted to have variability. Thus, the multiple regressionequation rea greater safety factor (31.8f 4.4 x PO) than other sulting from statisticalanalysiswas tendons(range 16.8f 5.2x PO-23.7f 2.7x P,), likeMaximum sarcomereshortening(pm) = ly due to the relatively low maximummuscletension. - 0.149(% strain at PO) Biochemical composit;‘on of tendons + O.O88(L,:L,) + - 0.182, Wrist flexor tendonswere composedof a significantly lower percentageof collagenthan wrist exten- which had a multiple correlation coefficient of 0.92 sors(p < 0.05;Table l), while no appreciablediffer- (p < 0.0001). encewas noted among radial and ulnar deviators. This finding was anticipated basedon the higher strain in flexor comparedto extensor tendons.The significantly greater tendon CSA of wrist flexor tendons(p < 0.0005)thus cannot be attributed solelyto an augmentedcollagencomponent.In fact, collagen I percentagenegatively correlated with tendon CSA (p < 0.01,rz = 0.28).Furthermore,no correlation between percent collagen and strain was evident (p > 0.9, r2 < 0.0001).Sincein vivo tendonsoperatein the toe region of the stress-strainrelationship,presumably the geometrical configuration of collagen fibrils rather than the relative collagencontent deters E minestendon behavior at physiologicalloads. ‘Z 00 _,n Tendon hydration may be useful as an index of ECRB ECRL ECU FCR FCU r” Muscle groundsubstancegiven the hydrophilic nature of proteoglycan.FCU had a significantlygreaterwater conFig. 3. Average sarcomere shortening predicted given tent than both radial extensor tendons (p c 0.05), muscle-tendon unit architectural properties and tendon Physiologicalstrain, moreover,varied significantlyas biomechanical properties. The best predictor of sarcomere percenthydration (p < 0.05, r2 = 0.2).Consequently, shortening was tendon strain at PO. T

II

Physiological behavior of human wrist tendons DISCUSSION

The purpose of this investigation was to define the biomechanical properties of the prime wrist tendons under physiological loads predicted based on muscle architectural properties and a theoretical model of muscle-tendon activation (see methods). Our goal was to extend our previous study of muscle architecture to an understanding of muscle-tendon interaction in the wrist. The advantages of tendon straining under physiological loads are not intuitively apparent. Indeed, tendon deformation may impair the ability of a muscle-tendon unit to displace a joint, theoretically requiring an increased muscle fiber length to restore mechanical capability. However, by incorporating tendon compliance, the operating range of the system may be increased if that muscle is operating on its ascending limb. Conversely, if the muscle operates on its descending limb, tendon compliance will decrease its operating range. Currently, there are no data available which describe the normal operating range of the human wrist muscles and thus the underlying consequences of tendon compliance cannot be unambigously determined. Tendon serves as an elastic component in series with a contractile component or muscle fiber. As a muscle develops force, then, a segment of length change may be taken up by the tendon rather than the muscle fiber. This in effect skews the sarcomere-length tension relationship, allowing sarcomeres on the descending limb to shorten onto the plateau of the curve; we predict muscle force changes of up to 50% PO depending on the range over which the sarcomeres shorten. Tendon strain as well as the relative tendon length determines the magnitude of increase in the operating range of the muscle-tendon unit. A second consequence of tendon compliance is to act as a length buffer-preventing joint rotations imposed on the muscle-tendon unit from being directly transduced as length changes by the skeletal muscle. The FCU tendon, for example, when subjected to a load equivalent to its maximum isometric tension (9 kg; Table 1) will extend 7.4 mm which corresponds to a wrist rotation of 29” (Jacobson et al., 1993). Similarly, FCR tendon stretch at peak isometric tension accounts for a 20” joint rotation, while equivalent deformations of ECRB, ECRL, and ECU tendons correspond to ll”, 16”, and 36” of wrist rotation, respectively. This buffering effect is emphasized in compliant actuators, improving the neuromuscular system’s ability to maintain constant force despite external length perturbations, as discussed by Rack and Ross (1984). In contrast, relatively stiff actuators have improved sensitivity to extrinsic joint rotations providing precise control of joint position. We found that tendon properties do not simply scale with muscle architectural properties. Rather, they act to add further specialization to the

197

muscle-tendon unit. For example, the FCU muscle, with its short fibers (L, = 41.9 mm) is arranged in series with a long length of tendon and aponeurosis (L, = 207.6 mm) which renders it the most compliant of the wrist joint actuators (L, : Lr = 4.96; Table 1). The FCU tendon is also the most materially compliant (strain at PO = 3.68%) which indicates that the biomechanical properties of the tendon accentuate the already compliant nature of the musculotendinous actuator. In contrast, ECRL has long fibers (& = 127.3 mm) and, though in series with a long tendon and aponeurosis (L, = 264.1 mm), is the most intrinsically noncompliant of the wrist muscle-tendon units (L,: Lr = 2.10; Table 1). Under physiological loads, however, the ECRL tendon is quite stiff (strain at P, = 1.78%); thus the intrinsic noncompliance of the musculotendinous actuator is enhanced by the incorporation of a stiff tendon. Such findings were unexpected based either on our previous frog studies (Lieber et al., 1991;Trestik and Lieber, 1993) or basedon reviewsby Zajac (1989)and Ker et al. (1988).This generalrelationship is the rule for the wrist actuatorssinceL*: Lf ratio waspositively correlated with tendon strain at PO(Fig. 4). The best predictor of sarcomereshortening was tendon strain at PO(Fig. 2). We initially expectedthat L,: Lf ratio would be the best predictor since the relative amount of tendon in serieswith a given number of sarcomeresis directly related to the absolute sarcomereshortening magnitude. However, in this study, becausetendon complianceaccentuatesthe intrinsic muscle-tendonactuator properties,strain at POis actually a better predictor of sarcomereshortening. It shouldbe noted,aspointed out by Zajac(1989), that L,: Lr ratio is a good predictor of sarcomere shortening,but not the best. In musclessuchasFCU with short fibers and thus low amplitude contractions and a limited active range,augmentingthe intrinsic complianceby incorporation of a compliant tendon servesto maximize

.s 2

6

I

2

Swint3~

PO (“$2)

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Fig. 4. Relationship betweenstrainat muscleP, (abscissa) and L,:L, ratio (ordinate).Note the significantpositive correlation(r’ = 0.44,p < 0.001)suggesting that material propertiesaccentuate structuraldesign.Note alsothat the flexors(0) strainto a greaterextentthantheextensors (0).

198

G. J. Loren and R. L. Lieber

the operating range. In contrast, muscleswith long fiberslike ECRB andECRL maintainan ampleactive contractile range and thus may not benefit from a compliant tendon. Most power activities of the humanwrist are performedin the flexed and ulnar position; by design,then, muscleforce and operating rangeappearto be emphasized. Precisionand control of motion are accentuatedin the radial extensors perhapsfor manipulative tasks. Interestingly,physiologicalstrainsdid not correlate with collagenpercentagewhich may indicatethat the structural basisfor the increasedcomplianceis the geometrical configuration of collagen fibrils. The wavy nature of collagenfibersat low tensionand the alignment of fibers at greater force have been described(seeViidik, 1973,for review). Consequently, the toe regionrelevant to physiologicalforcescorresponds to the gradual straighteningof the collagen fibers and thus is influencedby fiber shapeand surrounding matrix. Conversely,at higher loads,the linear region of the stress-strainrelationshipand ultimate tensilestrength reflect the number of collagen fibers and are thus influenced by relative collagen content. Lanir (1978)modeledfiber-matrix interactionsaffecting tendon behavior at low tensions.Such relations are dominatedby the bulk tissuepropertiesof the matrix and the amplitudeand periodicity of collagenfibers.With considerationof our data, specifically the variability in load-strain relationshipsat submaximaltensions,it is likely that suchparameters have a greater influence on physiological behavior than relative collagenconcentration. Thesedata also argueagainstthe notion that the connectivetissuecomplex remodelsitself like bone, which regulatestrabecular orientation and densityto maintain constantstrain despiteforce variation. Ker et al. (1988)proposed that increasedtendon crosssectional area protects against increasedstrain in musculotendinousactuators which generate high forces;we, however,have demonstratedthe converse with increasedphysiological strain noted in larger tendons.Tendon cross-sectionalarea was found to vary with musclephysiologicalcross-sectional areaas demonstratedby An et al. (1991).This relationship may be inherentto efficient force coupling with each contractile unit connectedto one tendon fiber. Finally, the varying biomechanicalbehavior of the primehumanwrist tendonswereapparentonly under physiologicalloadsand were not manifestat supramaximal muscleforces.Therefore, the use of traditional deformation-to-failure experimentsfor determination of tendon propertiesmay not be appropriate whenthe purposeof suchstudiesis to infer physiological function.

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