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 observed 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 significant correlation between maximum torque and maximum muscle moment arm (r = +O.ll, P > 0.7) suggesting that muscle
force, not musculoskeletal anatomy, represents the major determinant 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 performance 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 isokinetic testing of the quadriceps muscles have also documented the nature of muscle adaptation to exercise training (5, 18, 27) and have elucidated the relationship between 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 isometric 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
0363-6143/B
$1.50 Copyright
0
muscle fiber CSA is difficult through use of current
technology, especially in light of the complex fiber arrangement that exists in the quadriceps (26). Second, it
is difficult to precisely determine the fiber type distribution of the quadriceps muscles based on a single vastus
lateralis needle biopsy, not only due to fiber type differences between muscles (3) but also due to such differences 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 semitendinosus 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, consisting 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 measurement 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, respectively, and secured with 4-O silk suture. One suture was
attached to a force transducer (Entran model ELF-TSOO2, Entran Devices, Fairfield, NJ) driven by a straingauge conditioner
(Daytronic model 3270, Daytronic,
Miamisburg, OH), and the other tendon was secured to
1988 the American
Physiological
Society
C769
c770
DETERMINANTS
OF
MAXIMUM
a micromanipulator.
The muscle was stimulated in 0.6
mm increments in length through use of the above parameters. 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) fiber length (cm)
l
where muscle density is 1.056 g/cm3 (17).
Determination
of muscle architecture. Muscle architecture 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 normalized 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). Pinnation angle, as measured using a dissecting microscope
and goniometer, was not measurably different from 0’.
Statistical analysis. Variables measured for each animal 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
JOINT
TORQUE
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 equation 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 significant relationship between P, and maximum torque
(Fig. 2A, r = +0.77, P < 0.01) but no significant relationship between maximum torque and maximum muscle
TABLE
1. Correlation matrix for measured variables
PO
Moment
Arm
PO
1.00
Moment
arm
Maximum
torque
Frog mass
Muscle
mass
LO
CSA
0.24
1.00
0.77”
0.11
P,, maximum
Maximum
Torwe
0.69”
0.38
0.67*
0.10
0.59
0.19
0.04
0.07
0.40
0.49
muscle
tetanic
Muscle
Mass
L
O
CSA
1.00
0.64"
0.60
Frog
Mass
tension;
1.00
0.79”
1.00
0.24
0.23
1.00
0.74'
0.97' 0.00 1.00
Lo, optimal length; CSA, cross-
sectional
area. * Significant
correlation
between
variables
(P < 0.05).
For each muscle
studied, the force measured at the distal tibia during
TABLE 2. Correlation between maximum torque and
semitendinosus contraction and the measured moment
parameters forced into multiple regression equation
arms were combined to yield the relationship between
torque and joint angle (compare Figs. 4 and 5 of Ref. 12).
Serial
Isometric torque demonstrated a linear increase from 0
% Maximum
Parameter
Correlation
Torque Explained
to 140" and a sharp drop in torque from 140 to 160'.
Coefficient
Architectural analysis yielded a bundle length-to-muscle
Maximum
tetanic
tension
0.772
77.2
length ratio of 0.70that was used to calculate the bundle
Moment
arm
0.776
0.4
length (from muscle length), which was then used for
Frog mass
0.808
3.2
CSA calculations. The average calculated CSA for the
Muscle
mass
0.809
0.1
CSA
0.855
4.6
muscles was 0.23 t 0.18 (&SE) cm2 (n = 9).
Of the seven variables investigated. onlv two were
Experimental
torque measurements.
DETERMINANTS
p,
OF
MAXIMUM
,Unknow In
Moment Arm
H Frog Mass
- Cross-Section
Max Tensiol
FIG. 1. Pie graph of proportion
of maximum
torque
that is accounted
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
crosssectional
area as calculated
in Methods.
Unknown:
remainder
of torque
not explained
by measured
variables
(includes
experimental
error).
- -25
:
g
!F
20
g
.8
=E
15 I
‘:
30
35
40
Maximum Tetanic Tension (g)
45
50
l
l
l
I-
lO* ’
0.30
n
m
l
l
’
’
’
’ ’ ’ ’ ’ ’ I ’ PB ’ ’
0.40
0.45
0.35
Maximum Moment km (cm)
’
’
’
I
0.50
FIG. 2. A: relationship
between
maximum
tetanic
tension
(PO) and
maximum
tetanic
torque.
Linear
regression
yielded
a significant
relationship
between
2 variables
(r = +0.77, P < 0.01, n = 9). B: maximum
moment
arm vs. maximum
torque.
Linear
regression
yielded no significant 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-
JOINT
c771
TORQUE
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 magnitude. It thus appears that moment arm is more closely
correlated with muscle fiber length than muscle crosssectional 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 sarcomeres 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 variability associated with muscle cross-sectional area measurement techniques, uncertainties associated with estimating pinnation angle, and motivational differences of
human subjects. Such limitations were not part of the
present study. In the present study, >85% of the variability 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
Rehabilitation 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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