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Original Research

Establishing a New Index of Muscle Cross-Sectional Area and its Relationship With Isometric Muscle Strength

Akagi, Ryota1; Kanehisa, Hiroaki2; Kawakami, Yasuo3; Fukunaga, Tetsuo3

Author Information
Journal of Strength and Conditioning Research: January 2008 - Volume 22 - Issue 1 - p 82-87
doi: 10.1519/JSC.0b013e31815ef675
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The force generation capability of a muscle is related to its cross-sectional area (CSA) (13). Many studies have examined this subject through CSA measurements and/or estimates using imaging techniques such as computerized tomography (CT) (17,18,22), ultrasonography (13) and magnetic resonance imaging (MRI) (3,8,21), or using anthropometry (7). Among these techniques, MRI and CT provide precise muscle dimensions, but have poor applicability to practical use in filed studies. On the other hand, ultrasonography and anthropometry are more easily applicable in field studies on a large number of subjects. In particular, ultrasonography has the same merit as those of MRI or CT in directly visualizing fat and muscle tissues, but the major drawback of this technique is the limitation to image size which in many cases cannot cover the whole section of the muscle of interest. Anthropometry overcomes the latter concern, but it cannot evaluate distributions of tissues under the skin.

The forte of ultrasonography and anthropometry is that they make it possible to evaluate muscle dimensional changes during contraction owing to their real-time measurement. Hodges et al. (12) reported that an isometric contraction resulted in an increase in muscle thickness of parallel-fibered muscles such as the biceps brachii and brachialis. This implies that the CSA of parallel-fibered muscles increases during contraction and that it might affect muscle force production. One would therefore expect that if proper methodology is developed by combining ultrasonography and anthropometry to estimate muscle dimensions, it is valuable for not only quantitative assessment of muscle size in field studies, but also for examination on the relationship between muscle dimensions and force under a contracted condition. However, little attention has been paid to contraction-induced changes in muscle dimensions and their relations to the force exerted.

Muscle thickness (MT) measured by ultrasonography correlates closely with muscle CSA (1,25) and its squared value has been used as an index of muscle CSA (8,19,20). This index was derived from the idea that the cross-section of the whole skeletal muscle can be approximated by a circle and its diameter is equal to MT. But in reality, it is not the case, and muscle thickness is not always equal to width (the length of the distance between peripheries of the muscle perpendicular to MT). This has not been taken into consideration. On the other hand, the squared value of circumference (C) of a limb has been used to estimate muscle and bone CSA (5,7,11,23). Although C involves other tissues besides the muscle, it should reflect muscle dimensions including both muscle thickness and width. Because the muscle CSA is a function of length to the second power, we hypothesized that the product of MT and C (MT × C) can be an index for estimating muscle dimensions both at rest and in a contracted condition. We tested this hypothesis in the case of the elbow flexors in young adults. The main purposes of the present study were to investigate i) validity of MT × C through a comparison with muscle CSA determined by MRI and ii) the relationships between muscle strength and MT × C determined at rest and during the maximal isometric contraction.


Experimental Approach to the Problem

The present study involved two experiments in relation to its purposes. To develop the index of muscle CSA, the MT of elbow flexors (biceps brachii and brachialis) and the C of upper arm were determined at the level of 60% of the upper arm length (the distance from the acromial process of the scapula to the lateral epicondyle of the humerus) as described in a prior study (2). This measurement site was almost the maximal CSA in the upper arm (14). MT × C was calculated and defined as an index of muscle CSA. In the first experiment, the relationship between MT × C and muscle CSA measured by MRI at rest condition was tested to examine the validity of the index. In the second experiment, the relationships between muscle strength and MT × C not only at rest but also during maximal voluntary contraction (MVC) were examined. Some prior studies (13,18,24) found no significant difference in the force-area relationship between men and women. Hence, its relationship was examined with no distinction between men and women in the present study.


A total of 38 healthy men (n = 29) and women (n = 9) volunteered as subjects. Their means (±standard deviations, SDs) in age, body height, and mass were 24.8 (±3.1) yr, 170.1 (±6.6) cm and 64.0 (±9.0) kg, respectively. Two of the subjects were university officials, 8 of them were university students and the remainders were graduate students. This study was approved by the ethical committee of the Faculty of Sport Sciences at Waseda University, and was consistent with their requirement for human experimentation. Each subject was informed of the purpose and procedures of this study and possible risks of the measurements beforehand. Written informed consent was obtained from each subject.


Examination for the Validity of MT × C as Muscle CSA Index

Of the subjects, 26 men and 8 women participated in the experiment for examining the validity of MT × C. All measurements were performed for the subjects' right arms. They had no orthopedic abnormality in their right arms. In the measurements of the upper arm length and the forearm length (the distance from the head of radius to the processus styloideus), the elbow joint was kept in an extended position. After these measurements were made using a steel measure, the measurement site was marked with a pen. A B-mode ultrasonic apparatus (SSD-900, Aloka, Tokyo, Japan) was used for the MT measurements. An electronic linear array probe (UST-579T, 7.5 MHz wave frequency, Aloka, Tokyo, Japan) was prepared with water-soluble transmission gel and applied on the anterior skin surface. The obtained ultrasonographic images were printed out by echo copier (SSZ-309, Aloka, Tokyo, Japan). The MT was determined as the distance from the adipose tissue-muscle interface to the muscle-bone interface in 0.5 mm (Figure 1). The C was measured in 0.1 cm by a cloth measure.

Figure 1:
Ultrasonographic images of elbow flexors (a) at rest and (b) during maximal voluntary contraction (MVC).

The measurements of MT and C at rest condition (MTr and Cr) were performed while the subjects seated on a test chair and their right arms were secured to a torque meter (VTE-002R, VINE, Tokyo, Japan) by using an unelastic belt (Figure 2). The subjects kept 90° of shoulder joint flexion angle and elbow joint angle, and their wrists were fixed in a position halfway between supination and pronation.

Figure 2:
Schematic presentation on the experimental setup.

The measurement CSA of elbow flexors was performed as stated below. A series of cross-sectional images of the right arm were obtained using MRI (Signa 1.5T, GE, Milwaukee, Wisc.) with a 3 inch and a 5 inch round GP coils. Transverse scans were performed with a conventional T1-weighted Spin-echo technique (a repetition time: 950 ms, an echo time: 9 ms, a slice thickness: 5 mm, an interspaced distance: 0 mm). Imaging was carried out on a field view of 16 × 16 cm with a 256 × 192 matrix. A marker was applied on the subjects' skin surface at the level of 60% of the upper arm length. Within the device, the subjects lay in the supine position and their right arms were relaxed on a handmade wooden armrest. Their wrists were fixed in a position halfway between supination and pronation by using an unelastic belt. Since the armrest had slight list, their elbows were slight bent (10° of elbow joint angle). From scanned images, outlines of elbow flexors were digitized and each cross-sectional image was measured using a personal computer (LaVie LL350/8, NEC, Tokyo, Japan). The measurement was carried out 2 times and the averaged values at the level of 60% of the upper arm length and the maximal averaged values were adopted as CSA60 and CSAmax, respectively. The CVs of the two measured values were less than 2% and the intraclass correlation coefficients for them in CSA60 and CSAmax were more than 0.999.

Examination for the Relationship Between Muscle Strength and MT × C

All of the subjects participated in the examination for the relationships between muscle strength and MT × C. First, the measurements of MTr and Cr were performed as stated above. Second, MT and C were determined in the contracted condition, in which the subjects performed MVC of isometric elbow joint flexion for 3 seconds at 90° of elbow joint angle, and referred to as MTm and Cm, respectively. The torque (TQ) data during the elbow joint flexion was recorded through an A/D converter (PowerLab/16SP, ADinstruments, Bella Vista, Australia) into the aforementioned personal computer (LaVie LL350/8, NEC, Tokyo, Japan) at 100 Hz sampling frequency and processed with a low-pass filter (cutoff frequency: 20 Hz). The TQ measurements were performed two times with at least a 5 minute interval. If the difference between two values of TQ was more than 5% of the higher one, the TQ was measured 1 more time. In 2 or 3 TQ measurements, the highest value was adopted. The MT was measured on the first trial and the C was measured on the second one. In the case of performing the third trial, the MT or C was measured once again according to the following conditions. If the first measured TQ was lower, the MT was measured on the third trial. If not so, the C was measured on the third trial. The MT and C were measured while TQ output peaked and was stable. According to a prior study (14), TQ was converted to muscle strength (F) by dividing by the forearm length of each subject.

Reproducibility of Measurement Variables

The measurements of MT, C and TQ were repeated on another day to ensure the reproducibility of them. Of the subjects, 14 men and 2 women participated in these measurements.

Statistical Analyses

Descriptive data were presented as means ± SDs. The reproducibility of MT, C and TQ was assessed by using a coefficient of variance (CV) and an intraclass correlation coefficient. To assess the validity of MT × C, a simple regression analysis was performed to calculate Pearson's product-moment correlation coefficients between MTr × Cr and CSA measured by MRI (CSA60 and CSAmax) and to confirm whether each regression intercept for each regression line differs from zero. A Student's paired t-test was used to test the differences in MT, C and MT × C between at rest and during MVC. According to prior studies (3,6,10), the following statistical processing was performed to test which MT × C was more closely related to F, that at rest or during MVC. First, Pearson's product-moment correlation coefficients were calculated between F and MT × C both at rest and during MVC. Second, a stepwise multiple regression analysis was performed, including MTr × Cr and MTm × Cm as the independent variables and F as the dependent variable. Third, a simple regression analysis was performed to confirm whether the regression intercepts for the relationships between either MTr × Cr or MTm × Cm and F differ from zero. Lastly, the CVs of F per MT × C at rest and during MVC were calculated to compare between the interindividual variations of the two variables. Statistical significance was set at P ≤ 0.05.


Reproducibility of Measurement Variables

Table 1 summarizes the CVs and intraclass correlation coefficients of MT, C and TQ. The CVs of the two measured values were less than 2.6% and the intraclass correlation coefficient in each of them was more than 0.985.

Reproducibility of MT, C and TQ (n=16).

Validity of MT × C for Estimating Muscle CSA

Figure 3 shows the relationship between MTr × Cr and CSA measured by MRI. MTr × Cr was significantly correlated to both CSA60 and CSAmax (P < 0.001) and both intercepts of their regression lines were not significantly different from zero.

Figure 3:
Relationship between MTr × Cr and CSA measured by MRI (n = 34). MTr = muscle thickness at rest; Cr = circumference at rest; CSA60 = cross-sectional area of elbow flexors at the level of 60% of the upper arm length measured by MRI; CSAmax = the maximal cross-sectional area of elbow flexors measured by MRI.

Relationship Between MT × C and F

Descriptive data on MT, C and MT × C at rest and during MVC are shown in Table 2. Each of the variables during MVC was significantly (P < 0.001) higher than that at rest. The CV of MTm × Cm (23.6%) was lower than that of MTr × Cr (26.2%).

Descriptive data on MT, C, MT × C and F per MT × C at rest and during MVC (n=38).

Figure 4 shows the relationships between MT × C and F. Both MTm × Cm and MTr × Cr were significantly correlated to F (P < 0.001), with similar correlation coefficients in them. As a result of the stepwise multiple regression analysis, however, only MTm × Cm was selected as a significant contributor for estimating F. The intercept of the regression line for the relationship between MTr × Cr and F was significantly different from zero (P < 0.05). In addition, the CV of F per MT × C during MVC (12.8%) was lower than that at rest (14.5%) (Table 2).

Figure 4:
Relationship between F and MT × C at rest and during MVC (n = 38). MT = muscle thickness; C = circumference; F = muscle strength; MVC = maximal voluntary contraction. *Significant difference from zero, P < 0.05.


The main findings of this study were that i) MTr × Cr was significantly correlated with both CSA60 and CSAmax, ii) the MT, C and MT × C during MVC were significantly higher than those at rest, and iii) although both MTm × Cm and MTr × Cr were significantly correlated with F, the stepwise multiple regression analysis selected only MTm × Cm as a significant contributor for estimating F.

Some researchers pointed out that anthropometry overestimates muscle and bone CSA due to an underestimation of skin and subcutaneous tissue (5,7,11,23). To take the arm muscle area as an example, this has been attributed to the assumption that the shape of the arm is circular (11). To resolve this problem, the MT and C were adopted as the variables in the present study. On the other hand, the C includes not only elbow flexors but also elbow extensors. Hence, MT × C may include the error in evaluating muscle CSA attributed to it. However, MTr × Cr was highly correlated with both CSA60 and CSAmax and each intercept of each regression line was not significantly different from zero (Figure 3). This result indicates that MT × C can be the index of the muscle CSA.

The MTm and Cm were significantly higher than MTr and Cr. Consequently, the MTm × Cm was significantly higher than MTr × Cr (Table 1). When a joint is fixed at a given joint angle, a muscle-tendon complex is constant in length. However, a tendon is stretched during isometric contraction (16) and consequently muscle length is shortened. Since muscle volume hardly changes by contraction (4), the shortening of muscle length results in an increase of muscle thickness and CSA. Thus, it is reasonable to assume that the greater MT × C during MVC as compared to that at rest is attributed to the elongation of a tendon during contraction. Another possibility is the effect of gravity on muscle geometry. A relaxed muscle is deformed by gravity due to its slackness. During contraction, stiffened muscle might resist gravity by maintaining its shape, which could also influence different MT, C and MT × C at rest and during MVC.

Bruce et al. (6) have reported that the regression line for the relationship between muscle CSA and force cannot have a true intercept because if there is no muscle (i.e., independent variable equals zero), there must be no force (i.e., dependent variable must equal zero). Moreover, when each data is plotted closer to this regression line, the CV of force per CSA (i.e., dependent variable per independent variable) will probably come close to zero. In the present result, the regression intercept for the relationship between MTr × Cr and F was significantly different from zero unlike that during MVC (Figure 4), and the CV of F per MTm × Cm (12.8%) was lower than that of F per MTr × Cr (14.5%) (Table 2). Considering the results of the Pearson's product-moment correlation coefficients and the stepwise multiple regression analysis, these results suggest that MT × C during MVC is similarly or more closely related to F than that at rest. In the relationship between muscle strength and MT × C, the observed difference between at rest and during MVC is probably attributed to the difference of the interindividual variation in muscle CSA. In the present study, the CV of MTm × Cm (23.6%) was lower than that of MTr × Cr (26.2%) (Table 2). As mentioned above, a relaxed muscle is deformed by gravity that could lead to greater interindividual variation in the muscle CSA in the relaxed condition. Further investigation is needed to clear the difference between the relationship of MT × C and F at rest and that during MVC by examining other populations such as strength trained athletes and elderly individuals.

Practical Applications

The present study indicates that MT × C is highly correlated with muscle CSA determined by MRI and it can be an index for assessing muscle CSA not only at rest but also during contracted conditions. In addition, the findings obtained here showed a possibility that MT × C during MVC is more closely related to F than that at rest. This suggests the importance of determining muscle dimensions during contracted conditions to examine the relationship between muscle CSA and strength. As described in the earlier part, ultrasonography and anthropometry make it possible to determine muscle dimensional changes during contraction. The MT × C developed using ultrasonography and anthropometry may be useful for evaluating the relationship between muscle CSA and strength in individuals whose muscle dimensions during contracted conditions largely differ from those at rest.


1. Abe, T, Kawakami, Y, Suzuki, Y, Gunji, A, and Fukunaga, T. Effects of 20 days bed rest on muscle morphology. J Gravit Physiol 4: S10-S14, 1997.
2. Abe, T, Kondo, M, Kawakami, Y, and Fukunaga, T. Prediction equations for body composition of Japanese adults by B-mode ultrasound. Am J Hum Biol 6: 161-170, 1994.
3. Bamman, MM, Newcomer, BR, Larson-Meyer, DE, Weinsier, RL, and Hunter, GR. Evaluation of the strength-size relationship in vivo using various muscle size indices. Med Sci Sports Exerc 32: 1307-1313, 2000.
4. Baskin, RJ and Paolini, PJ. Volume change and pressure development in muscle during contraction. Am J Physiol 213: 1025-1030, 1967.
5. Baumgartner, RN, Rhyne, RL, Troup, C, Wayne, S, and Garry, PJ. Appendicular skeletal muscle areas assessed by magnetic resonance imaging in older persons. J Gerontol 47: M67-M72, 1992.
6. Bruce, SA, Phillips, SK, and Woledge, RC. Interpreting the relation between force and cross-sectional area in human muscle. Med Sci Sports Exerc 29: 677-683, 1997.
7. De Koning, FL, Binkhorst, RA, Kauer, JM, and Thijissen, HO. 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.
8. Fukunaga, T, Miyatani, M, Tachi, M, Kouzaki, M, Kawakami, Y, and Kanehisa, H. Muscle volume is a major determinant of joint torque in humans. Acta Physiol Scand 172: 249-255, 2001.
9. Fukunaga, T, Roy, RR, Shellock, FG, Hodgson, JA, and Edgerton, VR. Specific tension of human plantar flexors and dorsiflexors. J Appl Physiol 80: 158-165. 1996.
    10. Gadeberg, P, Andersen, H, and Jakobsen, J. Volume of ankle dorsiflexors and plantar flexors determined with stereological techniques. J Appl Physiol 86: 1670-1675, 1999.
    11. Heymsfield, SB, McManus, C, Smith, J, Stevens, V, and Nixon, DW. Anthropometric measurement of muscle mass: revised equations for calculating bone-free arm muscle area. Am J Clin Nutr 36: 680-690, 1982.
    12. Hodges, PW, Pengel, LH, Herbert, RD, and Gandevia, SC. Measurement of muscle contraction with ultrasound imaging. Muscle Nerve 27: 682-692, 2003.
    13. Ikai, M, and Fukunaga, T. Calculation of muscle strength per unit cross-sectional area of human muscle by means of ultrasonic measurement. Int Z Angew Physiol 26: 26-32, 1968.
    14. Kanehisa, H, and Fukunaga, T. Velocity associated characteristics of force production in college weight lifters. Br J Sports Med 33: 113-116, 1999.
    15. Kanehisa, H, Ikegawa, S, Tsunoda, N, and Fukunaga, T. Cross-sectional areas of fat and muscle in limbs during growth and middle age. Int J Sports Med 15: 420-425, 1994.
      16. Kubo, K, Kawakami, Y, and Fukunaga, T. Influence of elastic properties of tendon structures on jump performance in humans. J Appl Physiol 87: 2090-2096, 1999.
      17. Maughan, RJ and Nimmo, MA. The influence of variations in muscle fibre composition on muscle strength and cross-sectional area in untrained males. J Physiol 351: 299-311, 1984.
      18. Maughan, RJ, Watson, JS, and Weir, J. Strength and cross-sectional area of human skeletal muscle. J Physiol 338: 37-49, 1983.
      19. Miyatani, M, Kanehisa, H, and Fukunaga, T. Validity of bioelectrical impedance and ultrasonographic methods for estimating the muscle volume of the upper arm. Eur J Appl Physiol 82: 391-396, 2000.
      20. Miyatani, M, Kanehisa, H, Kuno, S, Nishijima, T, and Fukunaga, T. Validity of ultrasonograph muscle thickness measurements for estimating muscle volume of knee extensors in humans. Eur J Appl Physiol 86: 203-208, 2002.
      21. Narici, MV, Landoni, L, and Minetti, AE. Assessment of human knee extensor muscles stress from in vivo physiological cross-sectional area and strength measurements. Eur J Appl Physiol Occup Physiol 65: 438-444, 1992.
      22. Nygaard, E, Houston, M, Suzuki, Y, Jorgensen, K, and Saltin, B. Morphology of the brachial biceps muscle and elbow flexion in man. Acta Physiol Scand 117: 287-292, 1983.
      23. Rice, CL, Cunningham, DA, Paterson, DH, and Lefcoe, MS. A comparison of anthropometry with computed tomography in limbs of young and aged men. J Gerontol 45: M175-M179, 1990.
      24. Schantz, P, Randall-Fox, E, Hutchison, W, Tyden, A, and Astrand, PO, Muscle fibre type distribution, muscle cross-sectional area and maximal voluntary strength in humans. Acta Physiol Scand 117: 219-226, 1983.
      25. Sipila, S and Suominen, H. Ultrasound imaging of the quadriceps muscle in elderly athletes and untrained men. Muscle Nerve 14: 527-533, 1991.

      elbow flexors; muscle thickness; circumference; maximal isometric contraction; ultrasonography

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