Muscle force and moment arm contributions to torque production in frog hindlimb

RICHARD L. LIEBER AND JENNETTE L. BOAKES Division of Orthopedics and Rehabilitation, Department of Surgery, Veterans Administration Medical Center and University of California, San Diego, California 92161

LIEBER, RICHARD L., AND JENNETTE L. BOAKES. iWuxZe force and moment arm contributions to torque production in frog hindlimb. Am. J. Physiol. 254 (Cell Physiol. 23): C769-C772, 1988.-The relative contribution of maximum muscle tetanic tension (PO) and muscle moment arm to maximum knee flexion torque was investigated in the frog hindlimb. Isometric torque was measured in frog semitendinosus muscle-bone complexes throughout the range of O-160” of flexion. Optimal joint angle (the angle at which isometric torque was maximum) was ob- served at 140” of flexion. After torque measurements, the muscle was excised and the muscle length-tension relationship measured for determination of P, and optimal muscle length. In addition, the kinematics of the knee joint and therefore, the muscle moment arm was measured as a function of joint angle using principles of rigid body kinematics. Stepwise linear regression indicated that maximum torque was most highly correlated with P, (r = +0.77, P < 0.01) and accounted for -75% of the measured torque. In addition, there was no signif- icant correlation between maximum torque and maximum mus- cle moment arm (r = +O.ll, P > 0.7) suggesting that muscle force, not musculoskeletal anatomy, represents the major de- terminant of maximum torque production in the frog hindlimb.

joint torque; joint kinematics; muscle contraction; knee joint; semitendinosus muscle; Rana pipiens

DETERMINATION OF THE FACTORS that limit perform- ance is of interest in sports and medicine. A common method used to investigate these factors is to measure the extension torque of the quadriceps musculature (5, 18, 21, 22). Studies that implement isometric and isoki- netic testing of the quadriceps muscles have also docu- mented the nature of muscle adaptation to exercise train- ing (5, 18, 27) and have elucidated the relationship be- tween muscle structure and human performance (1, 4, 13-1521-2527-29). Generally, investigators agree that maximum extension torque is correlated with quadriceps cross-sectional area (CSA) as measured by ultrasound (8) or computed tomography (13-15), although these correlations are relatively low, ranging from 0.4 to 0.6 (8, 13-15). In addition, differences exist as to whether iso- metric or isokinetic extension torque are correlated with the percentage of fast twitch (%FT) muscle fibers or the area of FT fibers in the muscle [as estimated from vastus lateralis biopsies (6, 13, 15, 20-22, 27, 28)].

In spite of the information gained from these studies, several difficulties arise when investigating the human quadriceps musculature. First, accurate determination of

muscle fiber CSA is difficult through use of current technology, especially in light of the complex fiber ar- rangement that exists in the quadriceps (26). Second, it is difficult to precisely determine the fiber type distri- bution of the quadriceps muscles based on a single vastus lateralis needle biopsy, not only due to fiber type differ- ences between muscles (3) but also due to such differ- ences within a muscle (7,9). Third, it is not clear to what extent the motor unit population is activated during a maximal voluntary contraction.

Thus the complexity of the human neuromuscular system precludes detailed elucidation of the factors that contribute to maximum isometric torque. The purpose of this study, therefore, was to investigate these factors in one system in which muscle and joint properties can be precisely measured, the frog hindlimb. A portion of this work has been previously presented (11).

METHODS

The dorsal head of the semitendinosus muscle from the grassfrog (Rana pipiens) was chosen because of its well-established sarcomere length-tension relationship (6) and longitudinal fiber architecture. The semitendi- nosus is a biarticular muscle, functioning primarily in the frontal plane as both a hip extensor and a knee flexor. Frogs [mass = 25.9 t 4.5 (k SD) g (n = 9)] were killed by double pithing.

In nine animals, immediately after death, the thighs were exposed bilaterally and all of the thigh musculature and skin were removed except the dorsal head of the semitendinosus muscle. The muscle-bone complex, con- sisting of the pelvis, femura, tibiae, and semitendinosus muscles, was secured to the horizontal arm of a specially designed jig using 3-O stainless steel suture for measure- ment of joint torque as described in the previous paper (12). The force generated at the distal tibia, muscle moment arm, and resulting torque were determined at 10” increments over the range of O-180” of knee flexion as previously described (12).

Measurement of maximum tetanic tension. After torque measurements, the semitendinosus origin and insertion tendons were cut free from the pelvis and tibia, respec- tively, and secured with 4-O silk suture. One suture was attached to a force transducer (Entran model ELF-TSOO- 2, Entran Devices, Fairfield, NJ) driven by a strain- gauge conditioner (Daytronic model 3270, Daytronic, Miamisburg, OH), and the other tendon was secured to

0363-6143/B $1.50 Copyright 0 1988 the American Physiological Society C769

c770 DETERMINANTS OF MAXIMUM JOINT TORQUE

a micromanipulator. The muscle was stimulated in 0.6 mm increments in length through use of the above pa- rameters. This provided a muscle length-tension curve from which maximum tetanic tension (PO) and optimal muscle length (L,) were obtained. The muscles were then dissected free of the bones, muscle mass was determined, and the tibiae and femura were stored with the joint capsule intact at -10°C for future measurement of joint kinematics.

Muscle CSA was calculated using

CSA (cm2) = mass k) density (g/cm3) l fiber length (cm)

where muscle density is 1.056 g/cm3 (17). Determination of muscle architecture. Muscle architec-

ture was determined according to a modification of the methods of Sacks and Roy (2). Briefly, muscles were fixed in 10% buffered Formalin (formaldehyde solution) for 24-72 h, rinsed in 0.4 M phosphate buffer at pH of 7.2, and placed in 15% H2S04 for 24 h. Muscle length was measured with dial calipers as the distance from the origin of the most proximal muscle fibers to the insertion of the most distal fibers. Bundles consisting of lo-15 muscle fibers were then dissected from the muscle for bundle length measurement. Bundle lengths were nor- malized to a sarcomere length of 2.2 pm (6) to correct for variability caused by differences in muscle fixation lengths. Sarcomere length was measured along the length of the fiber bundles using laser diffraction (10). Pinna- tion angle, as measured using a dissecting microscope and goniometer, was not measurably different from 0’.

Statistical analysis. Variables measured for each ani- mal included P, (g), muscle moment arm (cm), maximum torque (g/cm), frog mass (g), muscle mass (mg), L, (cm), and CSA (cm2). To determine the relative contribution of each variable to maximum torque, stepwise linear regression was implemented (BMDP program P2R; 2). In the preliminary analysis, F-to-enter and F-to-remove were set to 3.000 and 2.996, respectively. Next, each variable was forced to enter the regression equation to quantify the proportion of maximum torque, which was accounted for by each variable. The relationship between P, and maximum joint torque and maximum muscle moment arm and maximum joint torque were analyzed by linear regression (BMDP program PlR; 2). All results were considered significant for P < 0.05.

RESULTS

Experimental torque measurements. For each muscle studied, the force measured at the distal tibia during semitendinosus contraction and the measured moment arms were combined to yield the relationship between torque and joint angle (compare Figs. 4 and 5 of Ref. 12). Isometric torque demonstrated a linear increase from 0 to 140" and a sharp drop in torque from 140 to 160'. Architectural analysis yielded a bundle length-to-muscle length ratio of 0.70 that was used to calculate the bundle length (from muscle length), which was then used for CSA calculations. The average calculated CSA for the muscles was 0.23 t 0.18 (&SE) cm2 (n = 9).

Of the seven variables investigated. onlv two were

significantly correlated with maximum torque (Table 1). These were P, (r = +0.77, P c 0.01) and frog mass (r = +0.67, P < 0.05). Muscle mass was nearly significantly correlated with maximum torque (r = +0.59, P = 0.09). Stepwise linear regression revealed that the variables most highly correlated with maximum joint torque were in the following order (F value from step 1 ANOVA): P, (10.35); frog mass (5.69); muscle mass (3.77); CSA (2.25); and L, (1.35). Thus, in the first step of the stepwise regression, P, was entered in the equation. In the second step, based on the high covariance between P, and the other variables, F values dropped significantly with the highest correlations seen in the following order: L, (1.17); frog mass (0.58), muscle mass (0.25); moment arm (O.lO), and CSA (0.02). Thus the remainder of the variables contained no significantly unique information relative to that contained by P,.

When forcing the variables into the regression equa- tion in a stepwise fashion, it was observed that the serial correlation coefficient increased slightly as variables were added (Table 2). The variables and the associated correlation coefficients were P, (0.772), P, -t moment arm (0.776), P, + moment arm + frog mass (0.808), P, + moment arm + frog mass + muscle mass (0.809), P, + moment arm + frog mass + muscle mass + CSA (0.855). These correlation coefficients (Table 2) indicate that P, accounted for the greatest proportion of maximum torque (77%, Fig. 1), whereas moment arm accounted for a much lower proportion (0.4%, Fig. 1).

Linear regression demonstrated that there was a sig- nificant relationship between P, and maximum torque (Fig. 2A, r = +0.77, P < 0.01) but no significant relation- ship between maximum torque and maximum muscle

TABLE 1. Correlation matrix for measured variables

Maxi-

PO Moment mum Frog

Arm Tor- Mass Muscle L

Mass O CSA

we

PO 1.00 Moment 0.24 1.00

arm Maximum 0.77” 0.11 1.00

torque Frog mass 0.69” 0.38 0.67* 1.00 Muscle 0.64" 0.10 0.59 0.79” 1.00

mass LO 0.19 0.04 0.40 0.24 0.23 1.00 CSA 0.60 0.07 0.49 0.74' 0.97' 0.00 1.00

P,, maximum muscle tetanic tension; Lo, optimal length; CSA, cross- sectional area. * Significant correlation between variables (P < 0.05).

TABLE 2. Correlation between maximum torque and parameters forced into multiple regression equation

Serial Parameter Correlation % Maximum

Coefficient Torque Explained

Maximum tetanic tension 0.772 77.2 Moment arm 0.776 0.4 Frog mass 0.808 3.2 Muscle mass 0.809 0.1 CSA 0.855 4.6

DETERMINANTS OF MAXIMUM JOINT TORQUE c771

Max Tensiol

p, ,Unknow In

Moment Arm H Frog Mass

- Cross-Section

FIG. 1. Pie graph of proportion of maximum torque that is ac- counted for by measured variables. These percentages are based on multiple regression coefficients presented in Table 2. Max Tension: maximum muscle tetanic tension. Cross-Section: physiological cross- sectional area as calculated in Methods. Unknown: remainder of torque not explained by measured variables (includes experimental error).

- -25 30 35 40 45 50 Maximum Tetanic Tension (g)

g 20 !F I-

g 15 .-

: l l

l

n m I l

8 ‘: =E l lO* ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ I ’ PB ’ ’ ’ ’ ’ I

0.30 0.35 0.40 0.45 0.50 Maximum Moment km (cm)

FIG. 2. A: relationship between maximum tetanic tension (PO) and maximum tetanic torque. Linear regression yielded a significant rela- tionship between 2 variables (r = +0.77, P < 0.01, n = 9). B: maximum moment arm vs. maximum torque. Linear regression yielded no signif- icant relationship between 2 variables ( r = +O.ll, P > 0.7, n = 9).

moment arm (Fig. 2B, r = +O.ll, P > 0.7). These results suggest that muscle force, not musculoskeletal anatomy, significantly contributed to torque production in frog hindlimb.

DISCUSSION

The main result of this study was that maximum isometric torque was most significantly correlated with the maximum tetanic tension of the muscle involved. Frog mass was also significantly correlated but covaried with P, and thus was not entered into the regression equation without forcing.

The result is in agreement with the numerous human studies that demonstrate statistically significant corre-

lations between maximum isometric torque and muscle cross-sectional area (8,13,X, 21,22) and body mass and maximum isometric torque (21, 22). It was interesting that moment arm and maximum tetanic torque were not significantly correlated. Several investigations of knee mechanics have alluded to the importance of the knee moment arm acting at the patellar tendon in determining maximum torque (15, 21). However, the data from the present study indicate that, for the frog semitendinosus, moment arm is not a major determinant of torque mag- nitude. It thus appears that moment arm is more closely correlated with muscle fiber length than muscle cross- sectional area (16) and that moment arm variations are not used in the frog system as a mechanism for increasing joint torque. Moment arm magnitude might be more closely linked to muscle fiber length (number of sarco- meres in series) to match sarcomere shortening to joint rotation. Whether such a hypothesis applies only to the semitendinosus-knee system, or whether it is a general strategy applied to other joints and muscles, requires further investigation.

The correlation coefficient between P, and maximum torque was 0.77. In human studies, lower correlations have been reported and thought to be caused by varia- bility associated with muscle cross-sectional area meas- urement techniques, uncertainties associated with esti- mating pinnation angle, and motivational differences of human subjects. Such limitations were not part of the present study. In the present study, >85% of the varia- bility in maximum torque was accounted for by all of the measured parameters (multiple correlation coefficient > 0.85, Fig. 1, Table 2).

We thank Profs. D. H. Sutherland and R. M. Braun for their many helpful suggestions offered during the course of this work and Eric Reindel and Thalia McKee-Woodburn for their excellent technical assistance in the kinematics experiments.

This work was supported by the Veterans Administration Rehabil- itation Research and Development program and National Institutes of Health Grants AM-25501 and AM-266344 (to Prof. Alan R. Hargens) and AR-35192 (to R. L. Lieber).

Received 13 August 1987; accepted in final form 13 January 1988.

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