When strength is assessed as the muscle torque recorded with a standard isokinetic apparatus (Figure 2), the torque T changes with body size not only due to the change in muscle cross-sectional area (proportional to m2/3), but also due to the lever arm a of the muscle. As with other linear dimensions, the lever arm changes proportionally to m1/3, which gives the product m2/3·m1/3 = m1. Consequently, the allometric parameter to normalize strength relative to body mass when it is measured as muscle torque should be q = 1.
Although the concept of distinguishing between tests of muscle force and muscle torque has only recently been suggested (8,15), previous experimental findings underscore this distinction. For example, the literature (7,8) suggests that the allometric parameters for various measurements of muscle force have been q = 0.45–0.87, whereas those for muscle torque have been within the range q = 0.74–1.31. These results indicate that the allometric parameter is generally greater for torque compared with force. However, even some extensive reviews on the methodology of muscle-strength testing neglect this distinction (14).
NORMALIZATION OF MOVEMENT PERFORMANCE
Although various features of movement performance are related to body size (for review, see (1) and (10)), normalization for body size has been rarely applied when presenting results of routine tests of movement performance (7). What could add to the complexity of this problem is that the outcome of different movement performance tests can be related in different ways to body size, as described subsequently.
A number of performance tasks are based on exerting the maximum force against external objects. Examples include determining the maximum load that can be lifted in a standard lifting task, assessing the maximum force that can be exerted during a handgrip task, and evaluating performance on manual material-handling task in ergonomics. Both everyday experience and experimental results (3,4,12,15) suggest that the observed index of performance (i.e., the maximum force exerted, or the maximum load lifted) increases with body size. Accordingly, this force should be related to body size in the same manner as the tested muscle force discussed within the previous section. Therefore, the allometric parameter (see equation 3) used to normalize performance of functional movement tasks based on exertion of external force could be close to q = 2/3. It should be noted that the standard tests of muscle power could also belong to this group (1), although more complex scaling methods suggest somewhat higher values (10).
An important group of functional movement tests is based on performing rapid movements of either body limbs (e.g., kicking, throwing) or the entire body (such as jumping and sprinting). The literature suggests that there is a weak relation, if any, between movement velocity and body size within a wide range of body sizes across species (10); this relation becomes negligible within the relatively narrow range of sizes for the human body (1). Furthermore, performance in athletics is generally consistent with this conclusion because the fastest sprint times, the longest jumps, and the longest ball kicks are not expected from either the largest or the smallest athletes. Therefore, the allometric parameter used to normalize performance of functional tasks involving rapid movements should be close to q = 0, because no normalization is required.
Finally, a number of functional tests are based on muscle actions intended to support body weight under strength-demanding conditions. Examples include actions to move the body (e.g., sit-ups, pull-ups, chin-ups, one-leg raises) and to sustain particular postures (e.g., keep the back extended in a horizontal position, hold a pose in yoga, maintain a balance position in gymnastics). Because the capacity to exert muscle force increases at a lesser rate than body weight, these types of tests should be negatively related to body size. This relation is readily apparent when the effect of body dimensions is examined across species (see (10) for review), and by the experiential observation that gymnasts and acrobats tend to have a smaller stature compared with their peers. Because the allometric coefficients for muscle force (q = 2/3) and body weight (increases proportionally to m1, hence q = 1) are different, the allometric parameter used to normalize performance on tasks based on overcoming body weight should be q = −1/3.
A number of studies underscore the dissociation in the relation between body size and performance on various movements. For example, lighter subjects have lesser capabilities in functional tests based on overcoming an external load (e.g., bench-press, hip-sled, medicine-ball throw, two-hand lift), whereas they are more successful when supporting their own weight (e.g., pull-ups, sit-ups, maintaining a posture) (2,11). A simple scaling approach suggests similar results (1). The correlation analysis of ergonomics tests based on exerting forces against external objects (push, pulls, manual material handling) and those based on lifting one’s own body (squats, lift-ups, one-leg lifts) suggests that they belong to different “movement abilities” (6). The same result was reported in the classical studies of Fleishman (see (5) for review) for the tests of “static strength” (exerting external forces), “dynamic strength” (push-ups, chin-ups), and “explosive strength” (running, jumping). It seems, therefore, that some elements of Fleishman’s “structure of movement abilities” (5) represent an artifact of inappropriately applied normalization for body size.
MUSCLE STRENGTH AND MOVEMENT PERFORMANCE
The normalization methods (Table 1) are expected to present the body-size–independent indices of muscle strength and movement performance. These standardized procedures will facilitate the comparison of data obtained in different studies.
The most important point of the review, however, concerns the strength-performance relation. As stated previously, a frequent reason for testing muscle strength is to assess functional capabilities with various movements, and the converse is also a common experimental strategy. As depicted in Figure 3, both muscle strength and movement performance tests could be related to body size. Moreover, this relation could be based on different values of the allometric parameter q. As a consequence, the selection of appropriate normalization methods is required for both muscle strength and movement performance. The normalization of various indices of muscle strength and movement performance for body size was discussed separately in the preceding sections and is summarized in Table 1. Therefore, this section examines how these separate normalizations can be reduced to a single factor when assessing the strength-performance relation.
For example, let us assume that the maximum voluntary forces of the elbow flexor muscles and shoulder extensor muscles are measured to assess the ability of a particular subject population to perform the chin-up exercise. These tests correspond to “muscle force” and “supporting body weight” groups of tests depicted in Table 1. To relate body-size–independent measures of the tested strength and performance (Pn ∼ Sn), equations 4 and 8 (see Table 1) must be used:MATHwhich reduces to:MATHThis result suggests that the recorded maximum voluntary forces should be divided by body mass to estimate the number of chin-ups that subjects of different size can perform.
This approach also applies in the converse direction. For example, let us assume that the muscle torques acting about the shoulder and elbow joints are assessed from a functional test of pushing an implement under standardized working conditions. To relate the muscle torque to the tested performance (i.e., Sn ∼ Pn),equations 5 and 6 (see Table 1) should be applied. The relation between normalized strength and normalized performance provides:MATHwhich reduces to:MATHThis result suggests that the estimated torque for subjects of different size is approximately equal to the performance on the test multiplied by body mass raised to the 1/3rd power.
This approach can also be applied to relate two different strength or movement performance tests. For example, let us assume that the ability for manual material handling (e.g., pushing, pulling, and lifting various objects) is assessed from results of push-ups, squats, and chin-ups. Because these tests respectively correspond to “exertion of external force” (P1) and “supporting body weight” (P2) groups of movement performance tests (Table 1), equations 6 and 8 provide:MATHwhich reduces to:MATHThis result suggests that the recorded number of push-ups, squats, and chin-ups should be multiplied by body mass to estimate the ability of manual material handling in subjects of different size.
Despite a number of limitations with this approach (see next section), these examples illustrate how the normalization of body size should be applied when assessing the relations between muscle strength and movement performance. However, these examples also illustrate what happens when the appropriate normalization procedures are not applied to both the tests of muscle strength and muscle performance. In short, the obtained relations remain confounded with the body size effect. Interestingly, none of the studies cited within a recent literature review (7) considered the role of body size in both muscle strength and movement performance tests, whereas other reviews on the same topic do not mention the effect of body size at all (e.g., (14)).
Most of the normalization methods for body size proposed in the literature have been based on the aforementioned presumption of geometric similarity (1,8,10). The same approach has been used for assessment of the allometric parameters presented in Table 1. However, it is well known that human bodies are not geometrically similar because there are some prominent systematic differences in either body shape or body composition when different groups of subjects are compared (1). Among the well-known examples are prominent differences in body shape between men and women and among children of different ages, and significant differences in both body shape and body composition among some athletic groups (e.g., basketball players, gymnasts, and swimmers). Processes of maturation and aging are associated with different rates of change in body size, muscle strength, and movement performance, whereas both sport selection and athletic training could also affect muscle strength and body size in particular groups of subjects. Finally, the tests of the rate of force development could be more important than tests of maximal muscle force or torque when assessing ability for performing rapid body movements (12,14). Therefore, one could conclude that the relations between muscle strength, movement performance, and body size could be both complex and specific to the subject group. This conclusion implies that different subject populations tested on the same tasks could require different values for the allometric parameters. This conclusion has been supported by a number of studies (1,9). Because routine tests do not provide conditions for assessment of optimal allometric parameters for each particular subject group, muscle strength test, or movement performance tests, the standardized methods, such as those depicted in Table 1, should be used.
Although the relations between body size and some standard tests of muscle strength and movement performance represent a well-documented phenomenon in the literature, the normalization for body size has been used both inconsistently and arbitrarily. This problem is exacerbated when muscle strength is tested to assess functional capabilities or when movement performance is tested to estimate muscle strength. The reason is that both muscle strength and movement performance can be influenced by body size. Moreover, these relations can differ for the particular muscle strength and movement performance tests.
This review proposes a more systematic approach for normalizing the effect of body size on the outcomes of both muscle strength and movement performance tests. This approach is expected to provide indices of muscle strength and movement performance that are independent of the body size and to facilitate the assessment of functional performance based on the tests of muscle strength. Moreover, these normalizations can be reduced to a single procedure for particular groups of the related tests. However, further research is needed to determine the exact effect of body size on the various tests of muscle strength and movement performance, as well as to reveal the role of some potentially confounding factors (e.g., body shape and body composition) that could influence the allometric parameters in specific subject populations.
The study was supported in part by grants from The Swedish Sport Research Council (Centrum for Idrottsforskning), the Swedish Council for Work Life Research, and the Serbian Research Council.
1. Astrand, P.-O., and K. Rodahl. Textbook of Work Physiology. 3rd edition. New York: McGraw-Hill, 1986.
2. Barnekow-Bergkvist, M., G. Hedberg, U. Janlert, and E. Jansson. Development of muscular endurance and strength from adolescence to adulthood and level of physical capacity in men and women at age of 34 years. Scand. J. Med. Sci. Sports. 6: 145–155, 1996.
3. Batterham, A.M., and K.P. George. Allometric modelling does not determine a dimensionless power function ratio for maximal muscular function. J. Appl. Physiol. 83: 2158–2166, 1997.
4. Challis, J.H. Methodological report: the appropriate scaling of weightlifting performance. J. Strength Cond. Res. 13: 367–371, 1999.
5. Fleishman, E.A. The Structure and Measurement of Physical Fitness. Englewood Cliffs, NJ: Prentice-Hall, 1964.
6. Hogan, J. Structure of physical performance in occupational tasks. J. Appl. Physiol. 76: 495–507, 1991.
7. Jaric, S. Muscle strength testing: the use of normalization for body size. Sports Med.
(in press, 2002).
8. Jaric, S., S. Radosavljevic-Jaric, and H. Johansson. Muscle force
and muscle torque
may require different methods when adjusting for body size. Eur. J. Appl. Physiol.
(in press, 2002).
9. Jaric, S., D. Ugarkovic, and M. Kukolj. Evaluation of methods for normalizing strength in elite and young athletes. J. Sports Med. Phys. Fitness.
(in press, 2002).
10. McMahon, T.A. Muscles, Reflexes and Locomotion. Princeton, NJ: Princeton Press, 1984.
11. Schmidt, W.D. Strength and physiological characteristics of NCAA division III American football players. J. Strength Cond. Res. 13: 210–213, 1999.
12. Vanderburgh, P.M., M.T. Mahar, and C.H. Chou. Allometric scaling
of grip strength by body mass
in college-age men and women. Res. Quart. Exerc. Sport. 66: 80–84, 1995.
13. Weir, J.P., T.J. Housh, G.O. Johnson, D.J. Housh, and K.T. Ebersole. Allometric scaling
of isokinetic peak torque
: the Nebraska Wrestling Study. Eur. J. Appl. Physiol. 80: 240–248, 1999.
14. Wilson, G.J., and A.J. Murphy. The use of isometric tests of muscular function in athletic assessment. Sports Med. 22: 19–37, 1996.
15. Wisloff, U., J. Helgrund, and J. Hoff. Strength and endurance of elite soccer players. Med. Sci. Sports Exerc. 30: 462–467, 1998.
Keywords:©2003 The American College of Sports Medicine
force; torque; allometric scaling; functional test; mass