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Special Communications: Methods

Validity of an anthropometric estimate of thigh muscle cross-sectional area


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Medicine & Science in Sports & Exercise: December 1996 - Volume 28 - Issue 12 - p 1523-1530
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Knowledge of muscle cross-sectional area can be extremely useful in assessing nutritional status, determining basic factors involved in human performance, and providing insights into injury mechanisms. Inadequate caloric intake can result in depletion of body protein reserves(15) reflected in the loss of muscle cross-sectional area (8). Both muscle strength (17) and muscle power production (7) are strongly related to the cross-sectional area of muscle tissue. It is possible that muscle area is related to physical training injuries since subjects with low muscle mass may have inadequate strength (17) for particular types of physical activity and may be more susceptible to muscle strains and joint sprains (27).

Muscle cross-sectional area can be obtained from computed tomography(17), ultrasound (11), and magnetic resonance imaging (1), but these methods are time consuming, expensive, and require highly specialized equipment. Techniques have been developed to obtain anthropometric estimates of muscle cross-sectional area (4,8). These methods use limb circumference and skinfolds to estimate total limb area and fat-plus-skin thickness with bone-plus-muscle cross-sectional area obtained by subtraction. Anthropometric approximations have the advantages of being noninvasive, cost effective, simple to administer, and quick to complete, but they may be susceptible to large errors (4,6,8) depending on the assumptions made and accuracy of the measures.

The purpose of this study was to develop and validate an anthropometric estimate of thigh muscle cross-sectional area for young men and women. This study extended previous work(1,3,4,6,8,22) in two ways. First, one commonly cited source of error is compression of the skin-plus-fat by skinfold calipers (4,6). This investigation attempted to decrease this error by using a reduced caliper tension. Second, no previous study had attempted to estimate bone area; this investigation does so by using an anatomical association between femoral epicondyles and the diameter of the femoral shaft(20,29).



Subjects were nine young men and nine young women, all of whom were healthy as determined by physical examination, blood tests, and urinanalysis. Most subjects were U.S. Army soldiers who performed aerobic exercise (primarily running) about twice a week as part of their military training. Two subjects(one male and one female) who were not soldiers both exercised about three times per week. After a briefing on the purposes and risks of the study, the subjects gave their written, voluntary consent to participate in accordance with the U.S. Army Surgeon General's guidelines (Army Regulation 70-25) and the policy statements of the American College of Sports Medicine. The study was approved by the institutional Human Use Review Committee of the two institutions involved.


Subjects reported to the laboratory about 2 h after breakfast or lunch. Anthropometry and MRI were completed within about 3 h of each other, in either a morning or afternoon session.

Anthropometry. On the first day of the study, age, body mass, and height were determined. The subject's age was determined from date of birth. Total body mass and height were measured with a digital scale (Seca, Columbia, MD), and anthropometer (GPM, Seretex Inc., Carlstadt, NJ), respectively, with subjects in gym shorts, t-shirts, and stockinged feet.

Two investigators both took all measurements on all subjects on two occasions 2-3 d apart. On each occasion investigators obtained three values which were averaged for data analysis. With the subject standing, the midpoint of the right thigh was determined as the distance halfway between the greater trochanter and lateral epicondyle. An indelible pen was used to make marks 4 cm distal (toward the epicondyle) to the midpoint over the quadriceps muscle group. Circumference and skinfold measurements were made over these marks.

The remaining anthropometric measurements were made with the subject supine on a table, with the right foot on the table surface and the knee at about a 90° angle. Measurements required about 10 min to complete. Total thigh circumference was measured using a fiberglass tape (Gulick, Country Technology, Gay Mills, WI). The built-in tractor spring in the tape applied a standard force of 2 N. Skinfolds were measured with calipers (Harpenden, British Indicators, Ltd., West Sussex, England) using both a low spring tension (measured at 5 g at the opening of the caliper) and a normal spring tension (measured at 26 g at the opening of the caliper). To obtain the skinfold, the skin was grasped between the thumb and index finger above the marked location such that the fold was along the long axis of the leg. The calipers jaws were applied to the area marked about 1 cm distal to the fingers. The distance across the medial and lateral epicondyles of the femur was measured with a sliding vernier caliper (GPM, Seretex, Inc.).

Magnetic Resonance Imaging. Measurements of each subject's fat-plus-skin, muscle, and bone areas were obtained from magnetic resonance imaging (MRI). Measurements were made on two separate occasions 2-3 d apart. A radio frequency coil was placed over the right thigh of the subject who was supine on a sliding table. An MRI visible marker was placed at the location of the circumference and skinfold measurements so that the 1-cm deep image scan included the same site. The subject was placed in the static magnet, which had a field strength of 1.4 Tesla. Images were T1 weighted and repetition and echo times were 200 and 22 ms, respectively. Each image required about 5 min to obtain and subjects were supine for about 10 min. Cross-sectional areas of the total thigh, fat-plus-skin, muscle, and bone were obtained from each image using manual computerized planimetry.

Data analysis. To determine variability and reliability of the anthropometric and MRI measurements, coefficients of variation and intraclass correlation techniques were used. For anthropometric measures, variance due to subjects, days, and raters was determined; for the MRI measures variance due to subjects and days was calculated (24).

The anthropometric model assumes the thigh is circular and composed of concentric circular layers of fat-plus-skin, muscle, and bone tissue(Fig. 1). Anthropometric estimates of various cross-sectional measures were obtained using equations for the area, radius, and circumference of a circle. Total thigh cross-sectional area was calculated as follows: Equation

where C is the circumference; T, the entire thigh; r the radius; and A, the area. Fat-plus-skin cross-sectional area was calculated as follows:Equation

where S is the skinfold; Q, the quadriceps; L, the lean tissue, including only muscle and bone; and F, the fat-plus-skin.

Bone diameter near the center of the femur was assumed to be 0.3 the epicondyle width (20,29). Bone cross-sectional area was calculated as follows: Equation

where B is bone and dE is the distance across the lateral and medial epicondyle.

Muscle cross-sectional area was calculated as follows:Equation

where M is muscle.

By substitution and simplification, an equation was derived to directly calculate muscle cross-sectional area: Equation


Male subjects had a mean ±SD age, height, and body mass of 21.0± 2.3 yr, 178.4 ± 6.1 cm, and 81.6 ± 7.0 kg, respectively. These same measures for the females were 25.2 ± 5.5 yr, 164.2 ± 5.7 cm, and 59.6 ± 7.0 kg, respectively.

Table 1 shows the coefficients of variation, estimates of variance components, and reliability of the anthropometric measurements. Both the between-day coefficients of variance and proportion of total variance attributed to days were low, indicating that raters tended to obtain similar measurements on the two days. The between-raters variance was also low for thigh circumference and distance across epicondyles; however, variance was greater for the skinfolds. In all cases, the intraclass reliability coefficient was 0.90 for the four trials (two for raters and two for days). The average of the four trials was used in further anthropometric calculations.

Table 2 shows that the between-day variability in most of the MRI tissue measurements was small. Bone crosssectional area tended to have greater day-to-day variability, probably due to the narrow range of scores for this measure, which would tend to magnify measurement error. The two MRI values were averaged for further analysis.

Figure 2 shows magnetic resonance images of midthigh cross sections of a representative man and woman. Adipose, muscle, and bone tissue can be distinguished by their shading; bone is the darkest while muscle and adipose tissue are successively lighter shaded areas. The lighter-shaded circular region in the center of the bone tissue is bone marrow.

The relationship of midfemur diameter to the distance across the medial and lateral femoral epicondyles is shown in Table 3, with individual values depicted in Figure 3. The ratio of femur diameter to epicondyle distance was relatively consistent: the largest individual ratio was 0.35 and the smallest was 0.28.

Table 4 shows comparisons of MRI measurements with anthropometric estimates using the reduced caliper tension for the skinfolds. Total thigh and muscle cross-sectional areas were overestimated by the anthropometric approximations, while the fat-plus-skin area was underestimated. These relationships are shown graphically for individual subjects in Figure 4. Average muscle cross-sectional area from anthropometry was overestimated by 18% in the men, 30% in the women, and 22% overall. The average thickness of the fat-plus-skin was calculated by subtracting the average radius of the MRI derived muscle-plus-bone area from the radius of the entire thigh cross section. The anthropometric assessment of the fat-plus-skin thickness underestimated the MRI-derived values.

Table 5 shows the anthropometric estimates of cross-sectional areas using the normal skinfold caliper tension. In all cases, the average error was greater compared with the reduced caliper tension.

Figure 5 shows muscle-plus-bone cross-sectional area as a proportion of the total area. As the ratio decreases, the proportion of the fat-plus-skin area increases, suggesting greater adiposity. The figure shows that more obese subjects had a larger departure from the line of identity between the MRI and anthropometric estimate indicating a greater error of prediction. A test of parallelism of regression slopes(14) showed that there were no significant differences between the normal and reduced caliper tensions (t = 0.51,P > 0.10).


The methods and assumptions used here produced estimates of muscle cross-sectional area that correlated very well with the MRI determined muscle areas, but overestimated them. The overestimate of muscle area by anthropometry was similar to that of previous investigations in which arm, thigh, or leg cross-sectional muscle-plus-bone area was calculated from body measurements(1,3,4,6,8,22). The error was due to an overestimate of total thigh compartment and underestimate of the fat-plus-skin compartment.

The overestimate of total thigh area averaged 6% for men and 5% for women and was due primarily to the assumption that the thigh was a perfect circle. For any given circumference, a circle will have the largest area(4). The thigh is not a perfect circle(Fig. 2) and thus will have less area for the same circumference.

Using the distance across the femoral epicondyles to estimate midshaft femoral diameter has not been reported previously. The epicondyle distance obtained in the present study was about 10% larger than that reported by Yoshioka et al. (29) who measured this dimension on 37 pairs of cadaver bones. This difference is partially accounted for by the fat and skin tissue that overlay the epicondyles in vivo. Midfemoral shaft diameters found here by MRI are almost identical to those recorded by others in cadaver specimens(10,18,20,23). No single study has reported both shaft diameter and epicondyle width; however, pooled results from the above sutdies suggest a ratio of 0.33, which is similar to our MRI-derived ratio of 0.30.

Several investigators (1,4,6) have noted a progressive increase in the overestimate of the fat-plus-skin area with increasing adiposity. Forbes (6) attributed this to compressibility of the skinfold which has a larger absolute error in more obese subjects. In the present study reducing caliper tension had little influence on this phenomena since subjects with greater skinfolds still had greater error. However, the absolute error in determining the fat-plus-skin cross-sectional error decreased from 43% to 27% using the reduced caliper tension. Two other studies that estimated midthigh fat-plus-skin area reported underestimates of 35% (3) and 38%(1).

In this study we examined younger subjects, and age appears to have an influence on the errors associated with estimating muscle cross-sectional area. Baumgartner et al. (1) reported little association between MRI and anthropometric estimates of muscle cross-sectional area (r = 0.43) when they examined healthy, elderly subjects (68-92 yr). Rice(22) compared arm and leg computed tomography with anthropometric estimates in older (65-90 yr) and younger (25-35 yr) subjects and found less estimation error in younger subjects. Younger subjects have less cross-sectional fat-plus-skin (21) than older subjects and thus underestimates in this compartment will result in less overestimate in the muscle compartment. Further, there appears to be more fat infiltration within and between the muscles of older subjects(2,19,21); in younger subjects the fat-plus-skin compartment is more circular, symmetrical, and evenly distributed (19,30) so that the anthropometric assumption of circularity is less violated.

Beside age and adiposity, athletic status may influence the accuracy of anthropometric estimates of muscle cross-sectional area. When compared with unselected samples of similar age(12,13,28), athletes(25,26) have less total body fat and less subcutaneous fat as measured by skinfolds. Since the fat-plus-skin compartment accounts for the largest source of error in muscle area estimates, it is possible that the muscle cross-sectional area of certain athletic populations may be predicted with greater accuracy.

Despite the fact that the anthropometric method overestimated MRI-measured muscle cross-sectional area, the two sets of values were highly related in our subjects, indicating that a linear transformation of the anthropometrically predicted values could produced very acceptable population estimates of MRI-derived muscle cross-sectional area. The following adjustment was produced by linear regression: y = 0.99 x-25.5 (r = 0.96, SEE = 10.1) where y is the actual muscle cross-sectional area (cm2) from MRI and x is the muscle cross-sectional area (cm2) from anthropometry.

To cross validate this equation, predicted residual sums of squares (PRESS) techniques were used (5,9). PRESS statistics compute residual errors based on successive removal (and subsequent replacement) of cases. These “PRESS residuals” are summed and replace the residual sums of squares for the entire model to provide modified versions of R2 and SEE which can be used for cross validation purposes(9). PRESS estimates for and SEE were 0.94 and 10.9, respectively, similar to those of the complete data set. These results indicate the original equation is consistent and the anthropometric estimate provides an adequate predictor of thigh muscle cross-sectional area.

However, an adjustment based on zero-intercept regression may be considered preferential for at least two reasons. First, there is a factual basis for assuming that the error in anthropometrically estimated muscle cross-sectional area is largely a percentage error, and the zero intercept regression produces a multiplication factor which corrects for such an error. Second, while standard linear regression produces the best least squares fit of a line to the data, the particular combination of slope and intercept to the best fit data can be very specific to a test group. Slopes and intercepts can vary considerably, particularly when sample sizes are small. A correction factor produced by zero-intercept regression is more robust, being more likely to hold for populations outside the group upon which the adjustment was developed. Based on these considerations, the following correction factor was produced using zero-intercept linear regression: y = 0.826 x (r = 0.96, SEE 11.3) where x and y are as above.

The adjustment based on the zero-intercept fits the data virtually as well as standard linear regression and is more convenient. Therefore, it was incorporated into the following final equation for anthropometric estimation of muscle cross-sectional area: Equation

or, by multiplication: Equation

Because of the population specificity of anthropometric estimates(16), this equation is most appropriately used to obtain population estimates of thigh muscle cross-sectional areas of healthy, young, active individuals similar to those in this study. Also, this equation was developed using a lower caliper tension that reduced the error in the fat-plus-skin estimate. With these cautions in mind, the equation developed here can be useful as a research tool when MRI is either unavailable or prohibitively expensive.

Figure 1-Anthropometric model of the thigh.
Figure 2-Magnetic resonance images of cross sections of a male (top) and female (bottom) thigh. For both figures, top is anterior and right side is lateral.
Figure 3-Comparison of midshaft femoral diameter with distance across medial and lateral femoral epicondyles.
Figure 4-Relationship between anthropometric and MRI measurements. Solid line is the line of identity and dashed line is regression line. (a) Total thigh cross-sectional area. (b) Fat-plus-skin cross-sectional area. (c) Bone cross-sectional area. (d) Muscle cross-sectional area.
Figure 5-Ratio of muscle-plus-bone cross-sectional area (MBA) to total cross-sectional area comparing MRI and anthropometric estimates. The solid line is the line of identity; the dotted line, the regression from high(normal) caliper tension (HT); and the dashed line, the regression from reduced caliper tension (RT).


1. Baumgartner, R. N., R. L. Rhyne, C. Troup, S. Wayne, and P. L. Garry. Appendicular skeletal muscle areas assessed by magnetic resonance imaging in older persons. J. Gerontol. 47:67-72, 1992.
2. Borkan, G. A., D. E. Hults, S. G. Gerzof, A. H. Robbins, and C. K. Silbert. Age changes in body composition revealed by computed tomography. J. Gerontol. 38:673-677, 1983.
3. Buckley, D. C., K. A. Kudsk, B. S. Rose, P. Fatzinger, C. A. Koetting, and M. Schlatter. Anthropometric and computerized tomographic measurements of lower extremity lean body mass. J. Am. Diet. Assoc. 87:196-199, 1987.
4. Dekoning, F. L., R. A. Binkhorst, J. M. G. Kauer, and H. O. M. Thijssen. Accuracy of an anthropometric estimate of the muscle and bone area in a transversal cross section of the arm. Int. J. Sports Med. 7:246-249, 1986.
5. Draper, N. R. and H. Smith. Applied Regression Analysis, New York: John Wiley and Sons, 1981.
6. Forbes, G. B., M. R. Brown, and H. J. L. Griffiths. Arm plus bone area: anthropometry and CAT scan compared. Am. J. Clin. Nutr. 47:929-931, 1988.
7. Harman, E., P. Frykman, and W. Kraemer. Maximal cycling force and power at 40 and 100 RPM. Nat. Strength Cond. Assoc. J. 8:71, 1986.
8. Heymsfield, S. B., C. McManus, J. Smith, V. Stevens, and D. W. Nixon. Anthropometric measurement of muscle mass: revised equations for calculating bone-free arm muscle area. Am. J. Clin. Nutr. 36:680-690, 1982.
9. Holiday, D. B., J. E. Ballard, and B. C. McKeown. Press-related statistics: regression tools for cross-validation and case diagnostics. Med. Sci. Sports Exerc. 27:612-620, 1995.
10. Holtby, J. R. D. Some indices and measurements of the modern femur. J. Anat. 52:363-382, 1917.
11. Ikai, M. and T. Fukungaga. A study on training effect on strength per unit cross-sectional area of muscle by means of ultrasonic measurement. Int. Z. Angew Einschl. Arbietspsychol. 28:173-180, 1970.
12. Katch, F. I. and W. D. McArdle. Perdiction of body density from simple anthropometric measurements in college-age men and women.Hum. Beol. 45:445-454, 1973.
13. Katch, F. I. and E. D. Michael. Prediction of body density from skin-folds and girth measurements of college females. J. Appl. Physiol. 25:92-94, 1968.
14. Kleinbaum, D. G. and L. L. Kupper. Applied Regression Analysis and Other Multivariable Methods, Boston: Duxbury Press, 1978.
15. Knapik, J. J., C. Meredith, B. Jones, R. Fielding, V. Young, and W. Evans. Leucine metabolism during fasting and exercise. J. Appl. Physiol. 70:43-47, 1991.
16. Lohman, T. G. Anthropometry and body composition. In:Anthropometric Standardization Manual, T. G. Lohman, A. F. Roche, and R. Martorell (Eds.) Champaign, IL: Human Kinetics Publishers, 1988, pp. 125-129.
17. Maughan, R. J. Relationship between muscle strength and cross-sectional area. Sports Med. 1:263-269, 1984.
18. Noble, P. C., J. W. Alexander, L. J. Lindahl, D. T. Yew, W. M. Granberry, and H. S. Tullos. The anatomic basis of femoral compartment design. Clin. Orthop. 235:148-165, 1988.
19. Overend, T. J., D. A. Cunningham, J. F. Kramer, M. S. Lefcoe, and D. H. Paterson. Knee extensor and knee flexor strength: cross-sectional area ratios in young and elderly men. J. Gernotol. 47:204-210, 1992.
20. Parsons, F. G. The characters of the English thigh-bone. J. Anat. Physiol. 48:238-267, 1914.
21. Rice, C. L., D. A. Cunningham, D. H. Paterson, and M. S. Lefcoe. Arm and leg composition determined by computed tomography in young and elderly men. Clin. Physiol. 9:207-220, 1989.
22. Rice, C. L., D. A. Cunningham, D. H. Paterson, and M. S. Lefcoe. A comparison of anthropometry with computed tomography in limbs of young and aged men. J. Gerontol. 45:175-179, 1990.
23. Rubin, P. J., P. F. Leyvraz, J. M. Aubaniac, J. N. Argenson, P. Esteve, and B. deRoguin. The morphology of the proximal femur.J. Bone Joint Surg. 74:28-32, 1992.
24. Safrit, M. J. Reliability Theory. Washington, DC: AAHPERD Publications, 1976.
25. Sinning, W. E., D. G. Dolny, K. D. Little, et al. Validity of “generalized” equations for body composition analysis in male athletes. Med. Sci. Sports Exerc. 17:124-130, 1985.
26. Sinning, W. E. and J. R. Wilson. Validity of“generalized” equations for body composition analysis in women athletes. Res. Q. Exerc. Sport 55:153-160, 1984.
27. Stone, M. H. Muscle conditioning and muscle injuries.Med. Sci. Sports Exerc. 22:457-462, 1990.
28. Wilmore, J. H. and A. R. Behnke. An anthropometric estimate of body density and lean body weight in young men. J. Appl. Physiol. 27:25-31, 1969.
29. Yoshioka, Y., D. Siu, and T. D. V. Cooke. The anatomy and functional axes of the femur. J. Bone Joint. Surg. 69:873-880, 1987.
30. Young, A., M. Stokes, and M. Crowe. Size and strength of the quadriceps muscles of old and young women. Eur. J. Clin. Invest. 14:282-287, 1984.


©1996The American College of Sports Medicine