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1 Center for Physical
Development Research, ABSTRACT Thomis, Martine A., Marc Van Leemputte, Hermine H. Maes,
Cameron J. R. Blimkie, Albrecht L. Claessens, Guy Marchal, Eustachius Willems, Robert F. Vlietinck, and Gaston P. Beunen. Multivariate genetic analysis of maximal isometric muscle force at different elbow
angles. J. Appl. Physiol. 82(3):
959-967, 1997.
heredity; genetic model-fitting analysis; twins; maximal voluntary
contraction; muscle cross-sectional area
INTRODUCTION THE GENETIC and environmental determinants of muscle
strength as measured by isometric arm pull or handgrip tests have been studied by several authors. Transmission coefficients for isometric strength (handgrip and arm pull), on the basis of parent-child and
sib-sib correlations from family studies, vary between 0.20 and 0.60 (12, 13, 18, 20-22, 25). Heritability estimates in twin studies
are higher and vary between 0.60 and 0.80 (10, 11, 23). Absence of any
genetic variation in isometric quadriceps strength is reported in one
study (7) on the basis of a nonsignificant intrapair variance ratio of
monozygotic (MZ) vs. dizygotic (DZ) twins. In 10-yr-old twins, 73% of
the variance in arm pull is determined by additive genes, whereas 27%
of the variance is explained by the unique environment (11). There is
no evidence for gender differences in relative genetic and
environmental contributions in the 10-yr-old subjects in this study.
However, including strength measurements of the parents reveals a
significant evidence for different genes acting in adults and in
10-year-old subjects.
Jones and Klissouras (6) demonstrate that individual differences in
maximal isometric elbow flexion force at 100° (180° = straight
arm) measured on a self-constructed ergometer in nine MZ and eight DZ
male twins (11-17 yr) are highly determined by genetic factors.
The within-pair variance F-ratio of MZ
and DZ twins is significant, and the heritability estimate, computed by
using the Holzinger index, is 83%.
Handgrip and arm pull are standardized and reliable tests for measuring
static or isometric strength in large population-based surveys.
However, from a biomechanical point of view, they provide only a crude
measurement of nondynamic force, produced by the combined action of
several muscles at the wrist, elbow, and shoulder.
Muscle force production is determined by general factors such as the
size, number, and type of muscle fibers, pennation of the fibers, and
type of contraction and activation level, which are independent of the
joint angle. From previous studies, it is known that variation in
physiological muscle cross-sectional area (MCSA; measured as limb
circumferences or muscle widths) is moderately to highly determined by
genetic factors (2, 4, 9, 11). Differences in limb-segment lengths have
their impact on the measured torque, and twin studies have shown that
individual differences in arm-segment length are largely explained by
genetic factors (2, 10, 11). Additionally, torque at specific joint angles (19) is influenced by the force-length relationship (8) and
moment arm with respect to the joint axis (lever arm) (1, 29). Muscle
force production is, therefore, possibly determined by the same genetic
factors that influence MCSA, arm-segment lengths, the force-length
relationship, and moment arm. The relative genetic and environmental
contributions of these factors to the resulting torque may vary
considerably across joint angles and remain to be determined.
The method of genetic model fitting used in this study has become a
standard in the analysis of twin data and been applied, in recent
years, to the study of individual differences in several somatic
characteristics (10, 11). Major advantages of this method over the
classical heritability estimations are that
1) assumptions are explicitly stated
in the model; 2) more than two groups of twins can be studied as well as extended family data; 3) a goodness-of-fit test of the
model is given; 4) quantitative genetic parameters are estimated and SE can be calculated;
5) maximum likelihood solutions are
obtained; 6) the fit of several alternative models can be compared; and
7) univariate and multivariate questions can be addressed. Basically, model fitting involves solving a
series of simultaneous structural equations to estimate genetic and
environmental parameters in such a way that the model predictions
closely match the observed twin correlations.
The primary purpose of the present study was to quantify the relative
genetic and environmental contributions to the observed variation in
maximal isometric elbow flexion torque and its key determinants, MCSA
and limb-segment lengths. Furthermore, it addressed the question of
whether the same genes and environmental factors contributed to the
variability in isometric torque at the different joint angles and the
MCSA. A third purpose was to determine the degree of shared genetic
variation among segment lengths, muscle size, and isometric torque.
METHODS Subjects
Measurement of Maximal Isometric Strength With Promett Evaluation
System
The maximal isometric moment at five different
elbow joint angles was measured in 25 monozygotic and 16 dizygotic male
adult twin pairs (22.4 ± 3.7 yr). Genetic model fitting
was used to quantify the genetic and environmental contributions to
individual differences in isometric strength. Additive genetic factors
explained 66-78% of the variance in maximal torque at
170-140-110 and 80° flexion (extension = 180°). At
50° flexion, common and subject-specific environmental factors
contributed equally to the variation. The contribution of unique
environmental factors concurs with the level of variability in muscle
activation and (dis)-comfort of torque production in the specific
angle. The relative contribution of lever arm and force-length
relationship in torque varies according to the angle. Because these
factors might be genetic, this variability is reflected in the genetic
contribution at the extreme angles of 170 and 50°. Multivariate
analyses suggested a general set of genes that control muscle area and
isometric strength, together with a more specific strength factor.
Genetic correlations were high (0.82-0.99). Genes responsible for
arm-segment lengths did not contribute to muscle area nor to isometric
strength.
Anthropometric and Midarm MCSA Measurement
Weight was recorded as a general body-size measurement, and more specific dimensions of the arm, including forearm length (FAL), upper-arm length (UAL), and midarm MCSA, were taken by computed tomography. All arm-segment lengths were measured by a trained observer, technical errors of measurement were small (0.28-0.31 cm), and reliability coefficients were high (>0.98). Computed tomography-imaging scans were done at three positions of the upper arm to measure the mean cross-sectional arm muscle area (26). Starting from the midhumerus position, three scans were done, with a 3-cm interval in the direction of the hand. A fourth scan was taken at the second position, with the relaxed arm in 150° flexion. Tissue within the limits of
50 and +200 Houndsfield units was defined as muscle
tissue. Both elbow flexors and extensors were included in this muscle
area. Technical error of measurement for muscle area was 0.16 cm2, with a coefficient of
reliability of 0.99. The mean MCSA over the four scans was used in the
further analyses.
Statistical Analysis
The distributions of the maximal isometric strength outcome at each angle were tested for Gaussian normality by using the Shapiro-Wilk test. Birth-order effects and differences in means or variances between MZ and DZ twins were tested with t-tests and F-tests, respectively. Pearson correlations between first- and second-born twins were computed for MZ and DZ twins. Results were considered statistically significant if P < 0.05. Univariate genetic analysis. The biometric approach using path-analytic models (14, 16) was applied to determine the relative genetic and environmental contributions to the observed variation in maximal isometric strength, MCSA, and arm lengths. Applied on a sample of MZ and DZ twins, the general quantitative genetic model decomposes the total observed phenotypic variance into genetic additive (A) and dominance (D) variances, environmental variation due to environmental factors shared by twins reared in the same family (C), and to non-shared environmental factors (E). The influence of these sources A-E on the phenotypic variation is given by parameters a-e, which are equivalent to the standardized regression coefficients of the phenotype on A-E, respectively. For a model including A, C, and E factors (Fig. 1), the phenotypic score is expressed as PT1 = aA1 + cC1 + eE1. In the twin model, subscript 1 is for the first-born twin and 2 is for the second-born twin. Squaring the factor loadings yields the variance (V) explained by each component (VA = a2, VD = d2, VC = c2, VE = e2). The contribution of genes and environment to the total variance is reported in the standardized form by dividing the specific variance component by the total phenotypic variance. In this model, it is also assumed that genetic and environmental factors do not correlate or interact and that there is no significant parental correlation for these characteristics.
Data on twin 1 and twin 2 were summarized in 2 × 2 variance-covariance matrixes. The maximum likelihood estimation of parameters a-e was done in Mx (15). The goodness-of-fit between the observed measurements and the expected values on the basis of the model was assessed by
2. Low
2 indicates consistency of the
model with the data, whereas high 2 values indicate poor fit.
Seven alternative hypotheses about the genetic and environmental
determinations of isometric strength were formulated. The simplest
model is one in which all variation is explained by unique
environmental factors that influence each individual separately, e.g.,
specific training status and unique lifetime events
(model E). The significance of
additional sources A and
D (or
C) was tested by likelihood-ratio
tests and Akaike's Information Criterion (AIC = 2 2 · degrees of
freedom) (30) by comparing the submodels to the full genetic model. The
AIC combines the goodness-of-fit of a model (the discrepancy of
expected to observed covariance matrixes) with its simplicity (the
degrees of freedom of the model), resulting in a measure of parsimony.
The reciprocal sibling interaction or phenotypic (P) interaction model
(APE) tested whether the performance of one twin influenced the
performance of his cotwin. An additional latent factor is only
significant if the fit of the submodel without the parameter is
significantly worse than the full genetic model. The maximum likelihood
estimates of the parameters of the most parsimonious model were
computed. These parameter estimates were expressed in percentages of
the total variance explained by genetic and environmental factors.
Multivariate genetic analyses.
To test whether the same genes influenced static strength at different
joint angles, the contribution of genetic and environmental factors to
the covariance between elbow flexion torques was estimated by using
multivariate models. Mean midarm MCSA was also included in this
multivariate analysis because this is a key physiological determinant
and one of the most important covariates of static strength (5).
Multivariate analyses of the isometric strength were performed only on
the three middle angles at 140, 110, and 80°. These phenotypes were
also modeled in this order because this was the test order. Strength
measurements at 170 and 50° were less reliable due to the
unfamiliar position in which the subjects were asked to perform a
flexing moment and were, therefore, not included in the analyses.
A first model included four distinct genetic effects,
A1-A4,
and four distinct environmental effects,
E1-E4
(Fig. 2). In a Cholesky or triangular
decomposition of latent factors, all the genetic variation in MCSA was
associated with factor
A1, whereas paths 2-4 indicated shared
genetic effects with all three strength measurements. Similarly, the
genetic effects of factor
A2 were associated with static
strength at 140° ( path 5),
and the other strength measurements ( paths
6 and 7) but not
with MCSA. In other words, these are residual genetic effects after
accounting for the first general genetic factor. The genetic effects of
A3 were shared only by strength
measurements at both 110 and 80° ( paths 8 and 9), whereas
A4 represented the genetic effects
that were unique for the variation in strength at 80°
( path 10). The same triangular
decomposition was modeled for environmental factors that were unique to
each individual but shared between characteristics. The model provided
an indication for the lower limit of
2 obtainable with the data.
This saturated model, however, did not provide a simple or biological
explanation of the data; therefore, submodels were tested. These
submodels had more restrictions on the number of genetic and
environmental parameters. The most parsimonious model was selected on
the basis of the lowest AIC and plausible biological interpretation.
The standardized genetic and environmental variance and covariance
components were computed as well as the standardized genetic and
environmental correlations (16).
To determine the degree of shared genetic and environmental influences, a second set of multivariate analyses, including static strength at 110°, FAL, UAL, and midarm MCSA, was studied. Analyses started with the Cholesky decomposition model (order of variables: FAL-UAL-MCSA-static torque at 110°), and, subsequently, submodels with more restrictions on genetic and environmental parameters were also tested. Again, the most parsimonious model was selected on the basis of the lowest AIC and biological interpretation.
RESULTS
Descriptive Statistics
Data showed a Gaussian distribution, and there were no significant birth-order effects. The group of DZ twins was, although not statistically significant, smaller and weaker overall than the MZ group of twins (twins taken as subjects) (Table 1). The mean MCSA was significantly greater in MZ than in DZ twins; however, no significant differences were found in the means or variances of maximal isometric moments between MZ and DZ twins. Highest maximal isometric moments were obtained at 80 and 110° for both MZ and DZ groups, with decreasing maximal moments at more extreme angles.
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Correlation Analysis
Except for strength at the 50° angle, the MZ twin phenotypic correlations (Table 2) were higher than the DZ twin correlations at all angles, which indicated the presence of additive genetic variation. The difference between the theoretical degree of genetic relatedness in MZ twins (r = 1.0) and the observed MZ correlation gives an indication of the importance of unique environmental factors: these values varied between 20 and 30% for all angles, except for the 50° angle. If the DZ correlation was lower than one-half of the MZ correlation, as was the case for the mean arm muscle area and all static moments except at the 50° angle, nonadditive genetic factors can be expected to contribute to the observed variance. At 50°, the DZ twin correlation was higher than the MZ twin correlation, which suggests that the similarity found at this angle was determined by common environmental factors and unique environmental factors. DZ correlations were also higher than one-half of the MZ twin correlations for height, FAL, and UAL, which also suggested shared environmental effects.
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Univariate Genetic Analysis
For all angles, except for the maximal isometric strength at the smallest angle (50°), the AE model was the most parsimonious model to explain the variance in maximal isometric strength. Individual differences in the somatic dimensions were also best explained by a model including additive genetic effects and unique environmental effects. The percentages of explained variance of the factors in the most parsimonious model are presented in Fig. 3.
Additive genetic factors (a2)
explained 66-78% of the variance in torque, whereas unique
environmental factors (e2)
accounted for 22-34% of the variance. From the MZ and DZ
correlations, nonadditive genetic factors were expected to contribute
to the total variance; they were, however, not significant. The lower 2 value of the ADE model for
angles 170-80° was not significantly lower than the
2 of the AE model; due to the
difference in one degree of freedom, this resulted in a lower AIC for
the AE model. To detect a rather small contribution of nonadditive
genetic factors, as could be the case in the present study, sample
sizes would need to be increased considerably (1,800 twin pairs are
needed to reject an AE model with a power of 80% when an ADE model is
the true model, with respective contributions of
a2 = 0.50, d2 = 0.30, e2 = 0.20). The upper and lower
95% confidence interval of the heritability estimates were computed by
maximum likelihood procedures (17). The lower confidence-interval limit
ranged from 0.40 (80° angle) to 0.56 (110° angle) and the upper
limit from 0.81 (80° angle) to 0.88 (110° angle).
Genetic factors seem to be absent in the determination of maximal
isometric strength at the smallest angle (50°). The ACE and APE
models, however, had the same 2
value as the CE model and fitted the data equally well, but the simpler
CE (more degrees of freedom) model was preferred because of its
parsimony. Common and unique environmental factors were of equal
importance at this angle.
Both height and weight are highly genetically determined
(a2 = 0.95 and 0.92, respectively). FAL and UAL also had high heritabilities (a2 = 0.84 and 0.86, respectively). The variation in mean MCSA was best explained by the APE
model, with a high genetic component (a2 = 0.92) and the indication of
a significant negative phenotypic interaction factor (0.24).
This small negative phenotypic interaction factor indicates that a
large arm muscle area in one twin goes together with a smaller arm
muscle area in the other twin.
Multivariate Genetic Analysis
MCSA-static torque at 140, 110, and 80°. A full Cholesky decomposition of both additive genetic and unique environmental factors of the covariance structure fit the data fairly well (252 = 56.72, P = 0.30, AIC = 47.28). Further
testing of more restricted models resulted in the model presented in
Fig. 4
(260 = 62.81, P = 0.34, AIC = 55.19). Genetic factor A1
represented a general genetic factor shared by all characteristics,
whereas A2 was a genetic factor
common to all torque measurements. There was only one environmental
factor common to all torque measurements
(E2), and additional
characteristic-specific environmental factors were also included in the
model. The loadings of these variable-specific environmental influences
could be equated between the strength measurements.
In model 1, the general genetic factor (A1) accounts for 41-83% of the variation in all characteristics (Table 3). The contribution of unique environmental factors to the variation of each trait was mostly explained by environmental factors that are unique to the specific trait and reached ~17-24% (paths 11, 15, 18, 20; Table 3). Very high genetic correlations were found among the three torque measurements (0.95-0.99), whereas there was a lower genetic relationship between MCSA and the torque measurements (0.76-0.90) (Table 3). The covariation among all traits was largely caused by genetic factors (86-97, Table 3), whereas environmental factors were only responsible for 3-14% of the covariation (Table 3).
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252 = 68.71, P = 0.06, AIC = 35.29). After
inspection of the path coefficients of this model, a more restricted
model was formulated as presented in Fig.
5. Genetic factor
A1 represented genetic factors
shared by both arm-length measurements, whereas
A3 was a genetic factor common to
both muscle area and static torque at 110°. A correlational path
between both genetic factors was included. Environmental contributions
to the characteristics seemed to be specific to each trait and were not
shared between traits (259 = 82.361, P = 0.024, AIC = 35.639).
Inspection of the standardized genetic paths in model 1 indicated that genetic factors shared by all traits (A1) as well as A2 did not contribute significantly to the variation in MCSA and torque at 110° flexion (paths 3, 4, 6, 7; Table 4). The genetic correlation between arm-segment lengths (FAL/UAL) was high (0.77), and the genetic predisposition was highly correlated between arm muscle area and static torque (0.71) (Table 4). Genetic correlations among arm-segment lengths and muscle area and torque were, however, low. The environmental contributions to arm lengths, MCSA, and torque at 110° were trait specific and explained ~11-17% of the variance in each trait (Table 4).
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DISCUSSION
Previous studies on the heritability of isometric strength differ from this study in strength evaluation, size, age, and gender of sample and use of heritability indexes. Heritability estimates in previous studies were calculated on the basis of correlations, intrapair variance ratios, and the Holzinger index, which fail to include estimates of the contribution of common environment, dominance, and so on, and may, therefore, be biased heritability estimations.
Maximal voluntary isometric torque of the elbow flexors at different angles was highly genetically determined in this group of adult men. Heritability estimates ranged from 66 to 78%, whereas unique environmental factors accounted for the rest of the variance. The confidence intervals around the heritability estimates were, however, rather large, probably due to the relatively small sample size of this study. Genetic effects seemed to be absent in the determination of maximal isometric strength at 50°, whereas common environmental effects explained one-half of the variance.
The heritability estimates in this study corresponded to those found in other twin studies measuring maximal static or dynamic strength by arm pull, handgrip, combined strength scores, or pull-ups (11, 23). These studies report heritability estimates ranging from 0.65 to 0.85. Jones and Klissouras (6) studied maximal isometric arm strength by a similar dynamometer in nine MZ and eight DZ male twins (11-17 yr). Using the Holzinger index, they estimated that genetic variation accounts for 83% of the variance in maximal arm flexor strength at 100°. This estimate is somewhat higher than the 78% genetic determination found for maximal isometric moment at 110° in this study. However, taking into consideration the confidence intervals around the heritability estimates associated with the sample size of this study, both estimates are quite similar.
Unique environmental effects, accounting for a part of the variance, can be interpreted as factors that contribute to the differences between members of a twin pair. Test-specific measurement error and motivational factors are included in this factor, although the latter could also be partly influenced by genes. Studies that demonstrate that the motivation or activation by electromyography is less stable at the 50 and 170° angles than at the middle angles is confirmed in our findings (28). Subjects also experience greater performance discomfort at 170 and 50° elbow flexion than at the middle angles of 140-80° flexion. We found that the degree of variability in muscle activation and performance discomfort was reflected by the general shape of unique environmental variation at the different angles (see Fig. 3), with the highest unique environmental impact at the extreme angles.
Although the factors mentioned above can explain some of the differences in unique environmental factors at different angles, the question remained as to why the genetic contribution was rather small or absent at the smallest angle (50°), whereas genetic factors were important (70%) at the 170° angle. In this regard, we can consider the dual origin of torque as a product of two factors: the moment lever arm and the force-length relationship (8, 19). Torque at 170° is relatively more influenced by the force-length factor, where the muscle is closer to its physiological resting length, than by the small moment arm. At 50° of flexion, the large moment arm has the greatest impact on the torque (1). Because genetic factors might be important in both the physiological resting length of the muscles and in the bone structure that largely determines the moment arm at 170° (2, 9-11), higher expression of genetic factors could be expected at this angle. The moment arm at 50°, however, is less dependent on bone structure, and individual variation in muscle origins and insertions will have smaller effects on the torque, resulting in lower expression of genetic factors.
Variation in physiological MCSA, univariately studied in families and twins by indicators of muscle mass (limb circumferences or muscle widths), is moderately to highly determined by genetic factors (2, 4, 9, 11), which was confirmed by the large genetic component (92%) for MCSA in this study. There was no clear biological explanation for the presence of a negative phenotypic interaction factor in MCSA in this study, and we mean that this factor rather reflects the significant difference in the mean and difference in variance in the MZ and DZ groups for this character.
In the multivariate analyses, the contribution of genetic and environmental factors to the observed covariation between isometric strength at different joint angles and MCSA was investigated and quantified. One common genetic factor explained the largest part of the covariation between MCSA and isometric torque at three elbow angles (genetic correlation 0.82-0.95). This suggested that, to a large extent, the same genes account for the variation in physiological cross-sectional area and isometric torque. These genetic effects could be the genes programming the total number of muscle fibers to develop and size of muscle fiber area, which, in turn, determine the individual differences in muscle mass (24), and, therefore, largely the variation in strength. A second common genetic factor explained a small part of the variation in all three torque measurements (6-24%). These genetic factors that were not shared with muscle mass could, in part, be genes coding for specific myofilament types and their proportion in a muscle or genetic factors regulating muscle innervation and coordination and energy supply and metabolism in the muscle during maximal contraction.
Unique environmental factors explained 12-14% of the observed covariation, and environmental correlations between the strength measurements ranged from 0.37 to 0.39. Unique environmental factors that affect the three strength measurements may reflect individual strength-training experience and Promett-related measurement errors.
The only study that reports genetic correlations between muscle area and strength was performed on 10-yr-old twins. A genetic correlation of 0.46 was found between an individual's factor score on a muscularity factor, on the basis of bone-width and extremity-circumference measurements and static strength measured by arm pull (10).
Our results suggested that genes played an important role in the variation of the FAL and UAL because estimated heritabilities were 84 and 86%, respectively. These heritabilities were higher than reported by Maes et. al. (10, 11), who found a significant influence of shared environmental factors in the variation of FAL in 10-yr-old twins. Because arm-segment lengths might influence absolute torque measurements at the elbow, both segment lengths and MCSA were included in a multivariate model to study the covariation with isometric torque. We found that subjects genetically predisposed to have longer arm segments did not seem to be predisposed to have a larger MCSA nor larger torque. Arm-segment lengths and muscle dimensions thus appear to be coded by a different set of genes. Subject-specific environmental factors, such as training status, had no general effect on the set of different length, muscle mass, and strength measurements but seem to be specific to arm-segment length, muscle mass, or strength.
In summary, we found that the variability in maximal isometric strength of the elbow flexors between 170 and 110° is highly determined by genetic factors. The contribution of unique environmental factors was in agreement with the level of variability in muscle activation and strength performance discomfort at specific angles. Furthermore, we found that the underlying relative contribution of lever arm and force-length relationship in the product of torque at different angles was reflected in the difference in genetic contribution at the extreme angles. With multivariate genetic model fitting, evidence was found for a general set of additive genetic factors that accounted for variation in muscle area and the covariation in isometric strength, together with a more specific strength factor. Specific environmental factors and measurement errors were shared among the strength measurements but not with muscle area. Furthermore, we found that genes coding for arm-segment lengths did not contribute to muscle area nor to isometric strength.
ACKNOWLEDGEMENTS
We thank I. Vallaey for assistance in Promett testing and training supervision, B. Staf for taking the blood samples, and D. Kellens for serological preparations. We also thank Dr. R. Andries for guidance during Promett evaluations and all the twins for their participation in the study.
FOOTNOTES
Address for reprint requests: M. Thomis, Faculty of Physical Education and Physiotherapy, Katholieke Universiteit Leuven, Tervuursevest 101, B-3001 Leuven, Belgium.
Received 3 September 1996; accepted in final form 22 October 1996.
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