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Evaluation of the strength-size relationship in vivo using various muscle size indices


Medicine & Science in Sports & Exercise: July 2000 - Volume 32 - Issue 7 - p 1307-1313
Applied Sciences: Physical Fitness And Performance

BAMMAN, M. M., B. R. NEWCOMER, D. E. LARSON-MEYER, R. L. WEINSIER, and G. R. HUNTER. Evaluation of the strength-size relationship in vivo using various muscle size indices. Med. Sci. Sports Exerc., Vol. 32, No. 7, pp. 1307–1313, 2000.

Purpose It is well accepted that maximum strength is related to muscle size. The primary purpose of this study was to determine whether anthropometric or dual-energy x-ray absorptiometry (DEXA) estimates of muscle size were valid predictors of plantar flexor maximum voluntary contraction (MVC) strength and could be used in lieu of more sophisticated techniques (e.g., magnetic resonance imaging (MRI)). Additionally, we compared the relationship among MVC and three MRI-determined muscle size measures; anatomical (ACSA) and physiological (PCSA) cross-sectional areas; and muscle volume (VOLm).

Methods We measured plantar flexor MVC at 1.83 rad and various indices of muscle size: 1) body weight, 2) total body lean mass (LM) (DEXA), 3) lower leg LM (DEXA), 4) lower leg circumference, 5) estimated muscle+bone cross-sectional area (CSA) from circumference and calf skin-fold, 6) triceps surae ACSA, 7) triceps surae PCSA, and (8) triceps surae volume (VOLm), in 39 premenopausal women (mean ± SD: 36 ± 8 yr, 165 ± 6 cm, and 65 ± 9 kg).

Results Zero-order correlations showed significant (P < 0.05) associations between MVC and total body LM (r = 0.365), lower leg LM (r = 0.381), circumference (r = 0.584), estimated muscle+bone CSA (r = 0.447), ACSA (r = 0.733), PCSA (r = 0.715), and VOLm (r = 0.649). By using the Fisher Z-transformation, ACSA and PCSA correlated significantly higher with MVC (P < 0.05) than anthropometric and DEXA indices. Further, only ACSA and PCSA regressed to the origin, indicating the ability to predict MVC was greatest with these two measures.

Conclusions The MRI-determined muscle size indices, which were specific to the triceps surae, correlated with strength better than whole limb anthropometric and DEXA indices. In this group of women, both ACSA and PCSA appeared superior to VOLm for predicting strength. PCSA was not found to be more precise than ACSA. ACSA appears to provide adequate precision for estimating plantar flexor specific tension in vivo.

Exercise Physiology Laboratory, Department of Human Studies, Center for Nuclear Imaging Research, and Division of Physiology and Metabolism, Department of Nutrition Sciences, The University of Alabama at Birmingham, Birmingham, AL 35294

Submitted for publication March 1999.

Accepted for publication October 1999.

Address for correspondence: Marcas M. Bamman, Ph.D., Exercise Physiology, Department of Human Studies, EB207, 901 13th Street South, The University of Alabama at Birmingham, Birmingham, AL 35294-1250; E-mail:

It is well accepted that maximum strength is related to muscle size. Cross-sectional differences in strength between groups varying in age (1), development (13), or gender (10) are typically attributed to group differences in muscle size. Longitudinally, we and several others have shown that increased strength consequent to resistance training is associated with muscle hypertrophy (17) and, conversely, decreased strength consequent to unloading is associated with muscle atrophy (2). Although neural conditioning or deconditioning has also been shown to play a role in short-term strength changes after resistance training (20) or unloading (6), respectively, strength differences between or within groups often disappear after adjusting maximum strength for some measure of muscle size.

Isometric maximum voluntary contraction (MVC) is a valid and highly reliable measure of in vivo force production (test-retest reliability > 0.94) (3,4,18). The measure of muscle size in vivo that best relates to MVC, however, is less clear. Current technology offers several muscle size assessment methods: 1) muscle volume (VOLm) by magnetic resonance imaging (MRI) (1,17), 2) muscle anatomical cross-sectional area (ACSA) by MRI or computed tomography (1,14), 3) muscle physiological cross-sectional area (PCSA) by MRI (11), 4) limb segment lean mass (LM) by dual energy x-ray absorptiometry (DEXA) (17), or 5) muscle layer thickness by B-mode ultrasound (4,14). Less sophisticated alternatives such as limb circumference and estimated muscle+bone CSA from limb circumference and skin-folds have also been employed (10). Muscle size estimates from DEXA and anthropometric measures include lean mass of an entire limb segment. By including antagonist muscles and/or nonmuscle tissues, these estimates would be less likely to predict muscle strength than more specific measures of muscle size such as MRI-determined ACSA, PCSA, or VOLm.

The maximum amount of force a whole muscle or agonist muscle group can produce is a function of the tension generated by each individual fiber in the direction of the muscle’s line of pull. In humans, the limb muscle groups typically tested for strength are composed largely of pennate muscles. By design, the total capacity for tension development is enhanced in pennate muscle by having more sarcomeres arranged in parallel and less in series within a given volume of muscle (19). This architecture, however, imposes two major limitations when attempting to relate muscle force production to measurements of muscle ACSA in vivo. First, for pennate muscle, and even for parallel muscle, individual fibers are not oriented in true parallel to the long axis of the muscle. If the angle (θ) of fiber pennation (from the long axis) is substantial, the shortening force transferred to the tendon at the muscle’s insertion is less than the total force generated by [(cosine θ)(total force)]. Second, individual fibers do not span the entire length of the muscle. Consequently, a CSA “snap-shot” of the muscle will not include all fibers contributing to the force. Because it corrects for fiber pennation, PCSA is thought to be a better predictor of force capacity than ACSA (19). In human subjects, however, true PCSA in vivo cannot be determined and must be estimated using cadaver data (19,22) for fiber length/muscle length ratios and angles of pennation.

The primary purpose of this study was to determine whether anthropometric or DEXA estimates of muscle size were valid predictors of maximum voluntary strength and could be used in lieu of more sophisticated techniques (e.g., MRI). Additionally, we compared the relationship among MVC and three MRI-determined muscle size measures (ACSA, PCSA, VOLm). We focused our investigation on the antigravity plantar flexor muscle group which is often studied in loading and unloading models. Muscle size was estimated/measured by: 1) body weight, 2) DEXA-determined total body LM, 3) DEXA-determined lower leg LM, 4) maximum lower leg circumference, 5) lower leg muscle+bone CSA estimated from circumference and skin-fold, 6) MRI-determined ACSA of triceps surae, 7) triceps surae VOLm, and (8) triceps surae PCSA.

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Healthy, premenopausal women were recruited as either endurance-trained or untrained for a larger study (16). As a result, our subset of 39 women represented a broad range of training levels and consisted of 7 trained and 32 untrained participants. Untrained subjects were considered sedentary and performed no formal exercise training for at least 1 yr before the study. Trained subjects exercised regularly (at least 5 d·wk1) in aerobic sports including distance running, cycling, triathlons, and aerobic dance. Many placed regularly at local competitions but none were national caliber athletes. All subjects were screened for any musculoskeletal disorder that could interfere with testing procedures and gave written informed consent before participation. All procedures were approved by the Institutional Review Board of The University of Alabama at Birmingham.

For descriptive purposes, percentage body fat was determined by hydrodensitometry and maximum oxygen uptake (O2max) was assessed using a modified Bruce graded treadmill test. We have detailed the methods for both procedures elsewhere (16).

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Magnetic resonance imaging.

1H Magnetic resonance images (MRIs) were collected on a 4.1 T whole-body imaging and spectroscopy system. Subjects were requested to fast and abstain from caffeinated beverages for at least 6 h and from exercise for at least 24 h before testing. A series of resting calf muscle MRIs were collected to measure CSA of the triceps surae muscle group in the right leg. The images were collected using a toroid coil with a protocol of: TR = 1000 ms, TE = 14.5 ms, 256 mm field of view (FOV), 5-mm slice thickness with a slice separation of 10 mm. The total set of images covered a distance between the most proximal and most distal images in which muscle was visible. CSA was determined by manually tracing the area around the muscles on a computer-generated image of each slice in the set (PvWave, Precision Visuals, Inc., Boulder, CO). The image yielding the largest CSA was used as ACSA. To determine triceps surae muscle volume (VOLm), each CSA slice was extrapolated to 1 cm thickness (based on 1-cm slice separation), yielding a slice volume in cm3. The slice volumes were then summed along the length of the muscle group.

The PCSA of triceps surae was estimated from VOLm, angle of pennation, and fiber length for each individual muscle in triceps surae (soleus, SOL; medial gastrocnemius, MG; lateral gastrocnemius, LG) as described previously (11,19) and shown in the following equation:MATH

By using data from cadaveric studies, fiber length for each muscle was estimated from muscle length using fiber length/muscle length ratios reported previously for SOL (0.06), MG (0.14), and LG (0.23) (22). Angles of pennation used for SOL, MG, and LG were, respectively, 25°, 17°, and 8° (22). PCSA was computed as the sum of the individual PCSAs for SOL, MG, and LG.

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Plantar flexor maximum voluntary strength.

Subjects were placed in an exercise bench that was lab-constructed (see Fig. 1) and designed to be mounted onto the patient table of the magnet system. The bench is made of nonmetallic materials and is routinely used in spectroscopy studies inside the magnet. The subject’s right foot was restrained at the ankle using three 4.5-cm straps which held the foot against a 10.6-cm foot pedal mounted at 1.83 rad (105° or 15° plantar flexion). Force was measured 10.6 cm above the bottom of the heel. This distance was selected to allow the pedal mounted to the force transducer to be approximately half the length of an average foot (7). This design minimized contributions from the foot muscles when measuring force output during plantar flexor MVC. A 2-cm wide strap was placed above the knee to keep the leg straight and minimize contributions to the force from the quadriceps muscles. Force output was measured using a calibrated force transducer (Tedea no. 1250, 300 kg) that was radio-frequency filtered using a seven-pole Butterworth filter and interfaced to a 386 PC clone. The transducer was calibrated with loads ranging from 200.2 to 1201.2 N yielding R2 = 0.999.

Figure 1

Figure 1

MVC strength was determined during 3-s contractions separated by 10-s rest. Subjects were verbally encouraged to press as hard as possible against the foot plate during each effort. Each subject completed 5–6 repetitions and the single peak force attained was accepted as the MVC. One day before MVC testing, subjects were familiarized with the testing protocol. The familiarization session followed MRI imaging and consisted of the same contraction paradigm used during the actual MVC test.

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Dual energy x-ray absorptiometry.

Total body LM and right lower leg LM were determined from a whole-body DEXA scan (Lunar DPX-L, Madison, WI) using the manufacturer’s software (version 1.3z). DEXA uses a constant x-ray source and a k-edge filter with energy levels of 38 and 70 keV. The differential attenuation of soft tissue and bone mineral at the two energy levels is detected by the scanner; the measurement of fat is derived from the ratio of these measures (Rst) (21). The R-value is determined for all pixels that contain soft tissue but no significant bone. After a series of iterations, DEXA provides the in vivo fat mass, LM, and bone mineral content for the total body and specific regions of interest. From the total body scan, the right lower leg was isolated according to manufacturer’s instructions.

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Anthropometric measurements.

Right calf skin-fold thickness and maximum circumference were measured in the standing position using a calibrated Harpenden skin-fold caliper and a standard measuring tape, respectively. Measurements were repeated twice and the computed means were used in data analysis. Anthropometric measurements were conducted by two investigators with common training in the procedures. Muscle+bone CSA was estimated from calf skin-fold and circumference using methods developed previously (12).

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Statistical analysis.

Zero-order correlations were tested between plantar flexor MVC and 1) body weight, 2) total body LM, 3) lower leg LM, 4) circumference, 5) estimated muscle+bone CSA, 6) ACSA, 7) VOLm, and 8) PCSA. To determine whether correlations were significantly different, the 95% confidence interval was established for each correlation using Fisher’s Z-transformation. Specific tension was calculated as MVC/CSA using both ACSA and PCSA. Linear regression was used to further study the relationship between MVC (dependent variable) and six assessments of lower leg muscle size (independent variable) (lower leg LM, circumference, estimated muscle+bone CSA, ACSA, VOLm, and PCSA). For regression analysis, the Y-intercept was considered different from zero if the 95% confidence limits did not contain zero. Group differences between endurance-trained (N = 7) and untrained (N = 32) subjects were tested by one-tailed independent t-test with the a priori assumption that the trained group would have more LM in the lower leg than the untrained group. Significance for all tests was accepted at a P < 0.05 level of confidence.

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O2max and percent body fat were assessed to better describe the trained and untrained subjects. O2max differed between trained (52.3 ± 4.2 mL O2·kg1·min1) and untrained (31.6 ± 5.4 mL O2·kg1·min1) groups (P < 0.001). Percent body fat also differed between trained (14 ± 4%) and untrained (32 ± 7%) groups (P < 0.001). Descriptive characteristics are shown in Table 1. In this sample population of trained and untrained women, the range for each dependent variable was rather large. For measures of lower leg LM or triceps surae muscle mass, much of the variance can be attributed to differences between the untrained and trained groups. Groups differed (P < 0.05) in body weight, total body LM, lower leg LM, estimated muscle+bone CSA, ACSA, VOLm, and PCSA. The trained group exhibited significantly greater values for all of these variables with the exception of body weight. Specific tension (N·cm2) using ACSA or PCSA was not different (P > 0.05) between groups.

Table 1

Table 1

Zero-order correlations are shown in Table 2. All indices of muscle size other than body weight were significantly related to MVC (P < 0.05). ACSA was most strongly related to MVC followed by PCSA and VOLm. These three MRI-derived variables shared 42.2–53.7% of the variance in MVC. DEXA-determined total body LM and lower leg LM were significantly correlated with MVC but shared only 13.3% and 14.6%, respectively, of the variance in MVC. Both anthropometric measures, circumference and estimated muscle+bone CSA, shared more of the variance in MVC (34.1% and 19.9%, respectively) than either DEXA assessment. Based on the 95% confidence intervals for each correlation with MVC in Table 2, ACSA and PCSA correlations were both significantly higher than correlations for estimated muscle+bone CSA and the DEXA measures (total body LM and lower leg LM). The VOLm correlation was also significantly greater than the DEXA measures.

Table 2

Table 2

Linear regression results for muscle size indices localized to the lower leg are shown in Table 3. Regression scatter plots with 95% confidence intervals for the muscle size indices specific to triceps surae are presented in Figure 2. With ACSA or PCSA as the independent variable (Fig. 2, A and B), the Y-intercept was not different from zero. However, VOLm (Fig. 2C) and all other estimates of lower limb muscle size that were not specific to the triceps surae muscle group yielded intercepts different from zero. Intercepts are shown in Table 3.

Table 3

Table 3

Figure 2

Figure 2

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As might be expected, the plantar flexor strength-size relationship in this group of women was strongest when the measurement of muscle size was specific to the active musculature. Measurements of the lower leg other than ACSA, PCSA, and VOLm included inactive musculature in the anterior compartment. This reduced the specificity of these three other measures (lower leg LM, circumference, estimated muscle+bone CSA). For DEXA-determined lower leg LM, bone mass was subtracted from the LM compartment, which might be expected to improve specificity. However, the simple and less expensive circumference and estimated muscle+bone CSA values, which included the bone compartment, appeared more strongly related to MVC than DEXA-determined lower leg LM (although within 95% confidence limits, see Table 2).

As Bruce et al. (9) point out, with linear regression analysis there cannot be a true intercept when comparing force with muscle size because if there is no muscle (i.e., independent variable equals zero), there must be no force (i.e., dependent variable must equal zero). A positive intercept would exist, though, if the agonist muscle group was not maximally activated during MVC, which has been suggested (9). In support, it has previously been shown with twitch interpolation that 50% of subjects tested for voluntary plantar flexor strength did not fully activate the muscle group (5). With neural activation less than 100% and varying between subjects, differences in muscle size alone would not account entirely for differences in strength.

In this study, intercepts were significantly different from zero for four estimates of muscle size (i.e., circumference, estimated muscle+bone CSA, lower leg LM, VOLm) and were positive for all but circumference. However, the intercept was not different from zero for ACSA or PCSA. Lack of a positive intercept for ACSA or PCSA indicates most subjects achieved maximal activation during MVC. In light of this, positive intercepts for the alternate measures of muscle size suggest some form of error in the measurement(s). Specific tension is typically expressed as strength per unit muscle area but occasionally is also expressed as strength per unit muscle volume (1). Because ACSA and PCSA were most strongly correlated with MVC and they both regressed to the origin, ACSA or PCSA appears to be the most appropriate muscle size index to use when computing specific tension or when relating MVC to muscle size. Computed PCSA in vivo requires that VOLm of each muscle first be measured as it is the numerator in the PCSA derivation. Because PCSA did not predict MVC with any more precision than ACSA, the single-slice ACSA appears more practical and has been adopted in our laboratory.

The utility of ACSA is obviously limited by availability of a MRI laboratory. An alternate, less expensive, and more convenient technique would certainly benefit the masses. However, we compared the anthropometric and DEXA muscle size estimates with ACSA and found significant (P < 0.001) but only modest correlations with circumference (r = 0.690), estimated muscle+bone CSA (r = 0.668), and lower leg LM (r = 0.721). These estimates apparently introduce error into the assessment of triceps surae muscle size as they account for only 45–52% of the variance in ACSA (Table 4). All three estimates include muscle in the anterior compartment, which could be a source of error. However, none of our subjects had trained specifically for hypertrophy in only the anterior or only the posterior compartment. It therefore seems logical to assume that individuals with more muscle mass in the posterior compartment (i.e., ACSA) would also have more anterior muscle, negating any potential impact on the correlation. However, Knapik et al. (15) report a correlation between MRI-determined total thigh CSA and an anthropometric estimate of thigh CSA substantially higher (r = 0.96) than ours, suggesting our assumption requires further investigation.

Table 4

Table 4

Linear regression results for estimating ACSA from circumference, estimated muscle+bone CSA, or lower leg LM are shown in Table 4. Although the correlations are moderate, these equations may prove useful to some researchers who wish to estimate maximum triceps surae ACSA from anthropometric or DEXA measurements of the lower leg.

Although our findings support the use of ACSA in determining plantar flexor specific tension, it is noteworthy that ACSA explained only 54% of the variance in MVC. We suggest several possible explanations for this lack of precision. First, as reported by Roy and Edgerton (19), the MRI slice in which total plantar flexor area is maximum (i.e. ACSA) does not represent the maximum area for each individual muscle in triceps surae. The slice in which soleus area is maximum, which is typically ACSA for the group, is several cm distal to the maximum areas of medial and lateral gastrocnemius (19). In an isolated muscle such as adductor pollicis, maximum force is highly related (r = 0.88) to the muscle’s maximum ACSA (8). Fukunaga et al. (11) previously found in men that plantar flexor MVC is more strongly related to a sum of the maximum areas of individual triceps surae muscles (r = 0.75) than to the single slice yielding the largest area for the muscle group as a whole (r = 0.61). To accomplish this, however, requires multiple serial slices. Whether determined by a single slice or by maximum areas of each triceps surae muscle, including the medial and lateral gastrocnemius areas, does not appear to improve the correlation found with soleus area alone (11).

Second, for the pennate muscles of triceps surae, not all of the fibers contributing to force production are included in ACSA (or any other single slice for that matter). For this to be a major source of imprecision, though, VOLm or PCSA should have improved the correlation with MVC because both of these measures include the entire triceps surae volume. This was not the case in our sample.

Third, we isolated the triceps surae in the MR images since these are the prime movers in plantar flexion. By doing so the contributions to force of smaller synergistic muscles such as flexor digitorum longus, flexor hallucis longus, peroneus longus, peroneus brevis, plantaris, and tibialis posterior were not accounted for in ACSA (or in VOLm or PCSA). Although their collective contribution to force can be considered minor, it cannot be overlooked as a source of imprecision in the strength-size relationship (i.e., using only triceps surae size to predict collective force production of all plantar flexors). However, Fukunaga et al. (11) compared the plantar flexor strength-size relationship with and without these small synergistic muscles included in ACSA and PCSA and found similar correlations.

Fourth, the important role of neural activation in testing MVC cannot be ignored. If neural activation was less than 100% for some subjects, differences in muscle size alone would not account entirely for differences in strength. Based on data from Belanger et al. (5), less than maximal activation by some subjects is a distinct possibility. Because the MVC-ACSA relationship regressed to the origin, though, the implication is that our group of subjects as a whole performed at or near maximum effort during MVC. We administered several familiarization/practice trials before MVC trials in an effort to minimize this limitation.

Lastly, force as measured by our force transducer 10.6 cm above the bottom of the heel was not a direct measure of tension at the Achilles tendon. The distance of 10.6 cm was selected to allow the pedal mounted to the force transducer to be approximately half the length of an average foot (7) in order to minimize contributions from intrinsic foot muscles. The correlation between single-slice ACSA and force (r = 0.73) using our methods appeared higher than the same correlation using tendon tension reported by Fukunaga et al. (11) (r = 0.61). However, PCSA and tendon tension yielded a much higher correlation (r = 0.93) (11) than PCSA and pedal force in our study (r = 0.72). Specific tension calculated using ACSA is similar in this study as in others (11,23) but when using PCSA, specific tension in the current study is grossly underestimated. An accurate determination of tendon tension appears necessary to yield a true specific tension using PCSA (11). In this context, we acknowledge the term specific tension is loosely applied to our data based on pedal force.

In summary, we recognize none of the muscle size measures are without error and this error cannot be ignored when interpreting the muscle strength-size relationship (see ref. 9 for details). Of the size measurements tested in this study, ACSA and PCSA were most strongly related to MVC strength with the highest correlations and zero intercept. For our purposes, ACSA is preferred over PCSA because of its practicality; 1) less magnet time and 2) much reduced image analysis time (1–3 slices to find ACSA vs 25–40 for PCSA). If true specific tension in vivo is a measurement of interest, however, PCSA and tendon tension should probably be determined.

We thank the participants for their effort and patience during data collection. For those subjects enrolled in a diet intervention study, Stouffer’s Lean Cuisine Entrees were kindly provided, free of charge, by the Nestle Food Co., Solon, OH.

This work was supported by NIH RO1 DK 49779–03, RO1 DK 51684–01, and GCRC MO1 RR00032.

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