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A More Efficient Magnetic Resonance Imaging–Based Strategy for Measuring Quadriceps Muscle Volume


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Medicine & Science in Sports & Exercise: March 2003 - Volume 35 - Issue 3 - p 425-433
doi: 10.1249/01.MSS.0000053722.53302.D6
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Accurate measurement of muscle size, atrophy, and hypertrophy is an important concern in strength training (27,32), aging (2,21), metabolic (24), immobilization (29), simulated microgravity (7), and space flight (1,15) research. Although various anthropometric measures have been employed previously to estimate muscle size (4,25,33), magnetic resonance images (MRI) and computed tomography (CT) images offer the obvious advantage of direct tissue visualization (6,26). Many strength-training (ST) studies that used MRI or CT employed a single axial anatomical cross-sectional area (ACSA) measurement as the measure of muscle size (11,20,22). Fewer reports, however, describe the measurement of multiple axial sections along the whole muscle length (19,32). This is likely due to the investigator time required to manually digitize many muscle cross-sections on large numbers of subjects, radiation exposure during CT, and the expense of longer MRI scan times.

Muscle volume (MV) can be determined by measuring muscle ACSA in multiple axial sections along the entire length of the muscle (8,27,32). As a measure of muscle size, MV is preferable to ACSA because it is a closer approximation of a physiological cross-sectional area (PCSA). PCSA is the cross-sectional area of all muscle fibers oriented perpendicular to the longitudinal axis of the muscle and thus is more closely associated with maximal muscle force (8,16,23).

Recently, we determined quadriceps MV in a longitudinal training study by measuring ACSA in images acquired at a very close interval (9-mm sections, 1-mm gap) along the entire thigh (32). Although this method captures the muscle contour precisely, it is laborious and time consuming. From the standpoint of efficiency, it would be advantageous to know the amount of error associated with increasing intervals between axial sections. Investigators who desire a measure of muscle size at either one time point or in a longitudinal study may then choose a suitable interval. To our knowledge, there are no reports in the literature that have addressed this issue. Therefore, the purpose of this study was to describe the error associated with different intervals between sections for measurements of MV at one time point and for changes in MV during a ST program.



Forty-seven sedentary volunteers (13 young men (25 ± 3 yr), 10 young women (26 ± 2 yr), 13 older men (69 ± 3 yr), and 11 older women (68 ± 3 yr)) were studied before and after a ST program (Table 1). The posttraining MRI data were missing for three young men, thus the hypertrophy results were presented for 10 subjects from that group. Only healthy subjects were used, as determined by a physician who performed a medical history, physical examination, and maximal graded exercise test. They reported no regular exercise for at least 6 months before the study. All subjects provided written informed consent before participation. All procedures were approved by the Human Subjects Institutional Review Boards of the University of Maryland College Park, the Baltimore Veterans Affairs Medical Center, and the Johns Hopkins Bayview Medical Center (Baltimore, MD).

Subject characteristics.

Strength testing.

After three familiarization sessions using low to moderate resistance, measurement of one-repetition maximum (1-RM) was performed before and after training. Subjects lifted a submaximal load one time through a standard range of motion, with rest between attempts. The resistance was increased incrementally until the range of motion could not be successfully performed. The maximal load that could be lifted only once was recorded as the 1-RM. Approximately the same number of trials (5–7) and similar vocal encouragement was used before and after training. Seat adjustments and strap stabilization were also standardized for each testing condition. To determine the initial resistance for the first regular training session, the heaviest resistance that could be performed exactly five times (5-RM) was also measured. The procedures for testing were the same as for the 1-RM test.

Strength training.

All of the subjects participated in 9 wk of heavy resistance unilateral (one-legged) ST of the dominant knee extensor muscles. The contralateral limb performed no training over the 9-wk period. The training program was designed to provide heavy resistance and high-volume training through near maximal effort on each of 50 repetitions divided into four training sets and one warm-up set. Training consisted of five sets of exercises performed 3 d·wk−1 on a Keiser K-300 knee extension machine. The sets were performed in the following manner: first set, five repetitions at 50% of the 1-RM; second set, five repetitions at 100% of 5-RM; third set, 10 repetitions starting at or near 5-RM; fourth set, 15 repetitions starting at or near 5-RM; and fifth set, 20 repetitions starting at or near 5-RM. During the third, fourth, and fifth sets, resistance was adjusted downward in small increments so that the subject could complete only one to two more repetitions after each increment, such that each repetition in the set was performed at or near maximal effort.


A Picker Edge 1.5-T MRI scanner was used to obtain serial axial images that encompassed the entire quadriceps femoris muscle group. The T1-weighted images were acquired from the proximal border of the patella to the anterior superior iliac spine using 9-mm-thick sections with a 1-mm gap, an echo time of 14 ms, and a relaxation time of 700 ms. The images consisted of a 50-cm field of view and a 256 × 256 pixel matrix. Subjects were supine for approximately 10 min before the 9-min T1 scan. The number of sections acquired ranged from 38 to 45, depending on thigh length. Subjects did not eat or drink for 8 h before their morning scans.

Image analysis.

NIH Image version 1.61 (National Institutes of Health, was used to manually outline the entire quadriceps femoris ACSA as a region of interest (ROI) in each axial section from the knee to the hip. Muscle ACSA was not corrected for intramuscular adipose tissue. The same number of sections proximal from the patella were measured before and after training for a particular subject. Great care was taken to ensure agreement on measurement strategies between the two investigators who performed the measurements. The same investigator, blinded to subject identification and time point, performed measurements in a particular subject before and after training. To establish intra-investigator reliability of cross-sectional area (CSA) measurement, the same investigator performed three separate measurements of quadriceps CSA in 300 different images. The repeat measurements were separated by measurement of other images or rest periods. The average coefficient of variation (CV), across the 300 images, was 0.78%. The measurements presented here are from the trained leg, before and after training, totaling approximately 2000 individual ROIs. Validity of volume measurement was determined by analysis of images obtained from a beef phantom that approximated the size of the quadriceps femoris muscle group. The volume of the phantom, measured by water displacement 5 h after MRI scanning, was 94% of the MRI-determined value. A portion of the difference may have been due to dehydration of the specimen between measurements. There was a 0.12% difference between repeat volume measurements of the phantom by the same investigator.

Data analysis.

The volume of each axial section (cm3) was calculated by multiplying the ACSA of the section by the section thickness (0.9 cm). The volume of the gaps between slices was calculated using the truncated cone formula (28). The volumes of the sections and gaps were summed to arrive at MV. For the purpose of the present investigation, the value of MV (9-mm section, 1-mm gap) is the criterion measure. Subsequently, several other estimates of MV were calculated from the preexisting CSA measurements, using increasingly larger intervals between sections. These alternative measures ranged from the most time consuming to least time consuming. They included every 2nd section (1.1-cm gap, MV2), every 4th section (3.1-cm gap, MV4), every 6th section (5.1-cm gap, MV6), every 8th section (7.1-cm gap, MV8), and every 10th section (9.1-cm gap, MV10) along the thigh, starting from the patella. The same number of sections and gaps were included for each measure before and after training. For each alternative measure, the section and gap volumes were summed to arrive at an estimate of MV. The aim of the study was to compare these alternative measures with a criterion measure of MV. However, in many instances the length of thigh covered proximal from the patella was slightly different for the criterion and alternative measures. Therefore, a companion criterion measure was calculated for each alternative measure that encompassed the same distance from the patella. Importantly, this meant that differences in longitudinal coverage did not contribute to the error observed between the criterion and alternative measures.

The largest single quadriceps femoris ACSA value (L1) was determined from the preexisting measurements before training. The posttraining L1 was chosen at the same distance from the patella. The alternative measures MV2, MV4, MV6, MV8, and MV10 were expressed in cubic centimeters and L1 in square centimeters. Absolute change with training was calculated for the criterion and alternative measures (ΔMV, ΔMV2, ΔMV4, ΔMV6, ΔMV8, ΔMV10, ΔL1).

Statistical analysis.

Agreement of each of the alternative measures with the criterion measure was assessed using Bland and Altman plots (5). These plots display, for individual subjects, the differences between an alternative and the criterion method on the ordinate, against average values of the measure on the abscissa (5,31). Along the ordinate, a 95% (± 2 SD) confidence interval, or limit of agreement, is constructed around the mean difference between the methods (Figs. 1 and 3). The mean difference between methods, if significantly different from zero, represents either underestimation or overestimation of the criterion measure. Using the Bland and Altman strategy, an investigator may identify the alternative method that, depending on the experimental goals, results in appropriately narrow limits of agreement compared with the criterion measure (5).

Bland and Altman plots demonstrating the limits of agreement (± 2 SD) and the underestimation bias (mean of the ordinate value) for each of the alternative measures: MV10 (A), MV8 (B), MV6 (C), MV4 (D), MV2 (E), compared with the criterion measure MV. The limits of agreement narrow as the interval between sections is reduced. The bias was significantly different from zero for all alternative measures.
Bland and Altman plots demonstrating the limits of agreement (± 2 SD) and the bias or difference from zero (mean of the ordinate value) for change in each of the alternative measures: ΔMV10 (A), ΔMV8 (B), ΔMV6 (C), ΔMV4 (D), ΔMV2 (E), compared with change in the criterion measure (ΔMV). The limits of agreement narrow as the interval between sections is reduced. For the pooled group of subjects, the bias was significantly different from zero only for ΔMV8 and ΔMV10.

Because L1 and ΔL1 were measured in different units (cm2) than the criterion measure (cm3), the Bland and Altman approach (5) was not appropriate for these comparisons. Therefore, univariate regression was used to predict MV from L1 and ΔMV from ΔL1. The standard error of the estimate (SEE) was obtained from these regressions. The SEE provides the SD of the prediction errors, which is a measure of the error of prediction (9,10). For any given value of the independent (predictor) variable, the predicted value will fall within ± 1 SEE of the actual value of the dependent (predicted) variable approximately 68% of the time, whereas 95% of the time the predicted value will fall within ± 2 SEE (9,10). To provide for a large (conservative) confidence interval of prediction, ± 2 SEE was used.

Repeated measures analysis of variance was used to determine differences across time for strength and MV variables.


Strength and hypertrophy.

Across groups, there was an average 29% increase in 1-RM strength after the 9-wk ST program. In addition, all groups displayed significant increases in quadriceps femoris MV in response to ST, as previously reported (12,32). Young men, young women, older men, and older women exhibited MV increases of 280 ± 123 cm3 (12.5 ± 6.5%), 108 ± 57.7 cm3 (7.8 ± 4.5%), 208 ± 80.6 cm3 (12.1 ± 4.9%), and 136 ± 74.2 cm3 (12.6 ± 6.5%), respectively. The increase in MV for the combined groups was 184 ± 106 cm3 (11.3 ± 5.8%). MV in the untrained contralateral leg did not change significantly in young and old women. The untrained leg of young and old men exhibited an increase in MV of 1.6% and 1.9%, respectively. The untrained leg exhibited an increase in 1-RM strength ranging from 10% to 14% across groups (P < 0.05).

Baseline MV.

The limits of agreement (± 2 SD) with the criterion measure for all subjects combined are displayed in a separate Bland and Altman plot (5) for each of the alternative measures (Fig. 1). The 95% limits of agreement for the combined subject group amounted to 0.7%, 1.7%, 2.8%, 3.5%, and 6.4% of total MV for MV2, MV4, MV6, MV8, and MV10, respectively (Fig. 1, Table 2). The limits of agreement for each sex/age group are presented in Table 2.

Limits of agreement with the criterion measure at baseline.

Each of the alternative measures also resulted in a significant (P < 0.001) underestimation of MV, which was least for MV2 (4.4 cm3, or 0.26% of MV) and greatest for MV10 (140.4 cm3, or 8.4% of MV) (Table 2, Fig. 1).

At baseline, L1 was correlated (P < 0.001) with MV in each of the age/sex groups (young men r2 = 0.89, SEE × 2 = 372 cm3; young women r2 = 0.96, SEE × 2 = 119 cm3; old men r2 = 0.64, SEE × 2 = 188 cm3; old women r2 = 0.87, SEE × 2 = 137 cm3) (Fig. 2, Table 2). For the combined subject group, the r2 value was 0.96, and the 95% confidence interval (± 2 SEE) amounted to 14.1% of total MV (236 cm3) (Table 2).

The relation between L1 and MV in young men (A), young women (B), old men (C), and old women (D) at baseline. All correlations were significantly different from zero.

Change in MV.

The limits of agreement (± 2 SD) with change in the criterion measure for all subjects combined are displayed in separate plots for each of the alternative measures (Fig. 3). The 95% limits of agreement for the combined subject group amounted to 10.3%, 16.4%, 19.2%, 25.4%, and 26.3% of the change in total MV for ΔMV2, ΔMV4, ΔMV6, ΔMV8, and ΔMV10, respectively (Fig. 3, Table 3). The limits of agreement for each sex/age group are presented in Table 3.

Limits of agreement with the criterion measure for hypertrophy with training.

For the pooled group of subjects, change in MV was significantly underestimated (P < 0.01) by both ΔMV8 (9.1 cm3, or 5.0% of ΔMV) and ΔMV10 (16.1 cm3, or 8.8% of ΔMV). However, ΔMV2, ΔMV4, and ΔMV6 did not result in statistically significant underestimation of change in the criterion measure (Fig. 3, Table 3).

For all subjects combined, when ΔL1 was used to predict ΔMV the SEE × 2 (110 cm3) amounted to 60% of the total change in MV (r2 = 0.74, SEE = 55 cm3, P < 0.0001). The correlation of ΔL1 with ΔMV was significantly different from zero (P < 0.01) in all age/sex groups except young women (P = 0.065) (Table 3, Fig. 4).

The relation between ΔL1 and ΔMV in young men (A), young women (B), old men (C), and old women (D) at baseline. All correlations were significantly different from zero (P < 0.05) except for young women (P = 0.065).

When regression was used to predict MV from L1 or ΔMV from ΔL1, the amount of error (SEE × 2), expressed as a percent of MV or ΔMV was always substantially larger than the limits of agreement provided by the alternative measures (MV10, MV8, MV6, MV4, MV2) that comprised multiple sections (Tables 2 and 3).


The principal outcomes of this study were: 1) a quantification of the increasing error associated with using increasingly larger intervals between axial MRI sections when measuring MV at one time point or changes in MV longitudinally; 2) demonstration that the use of a single mid-thigh section to predict MV or changes in MV resulted in substantial error of prediction; and 3) observation of no consistent age- or sex-based differences in the amount of error associated with different intervals between MRI sections.

Accurate determination of MV in the least time-consuming and most economical fashion is important to investigators who use MRI technology. Although other studies have employed multiple cross-sections to measure MV at one point in time (3,14,24) or in response to an intervention (1,27,32), to our knowledge none have compared different intervals between sections both at baseline and after an intervention that results in muscle hypertrophy. Our existing database was unique in that serial ACSA measurements were taken: 1) at a close interval (9-mm sections, 1-mm gap); 2) before and after a longitudinal ST study; and 3) in young and older men and women. This allowed for the designation of a criterion measure, MV, and provided the ability to assess the effectiveness of several different section intervals to estimate MV at baseline and the change in MV resulting from the ST program.

Because the correlation coefficients between the criterion measure (MV) and the alternative measures (L1, MV10, MV8, MV6, MV4, MV2) were very high before training (0.978, 0.998, 0.999, 0.999, 1.0, and 1.0, respectively), it is tempting to conclude that all of the alternative measures would provide similar accuracy. However, the correlation coefficient does not quantify the agreement between a criterion measure and a proposed alternative measure. In simple regression, the SEE quantifies the spread of data points around a line of best fit and thus represents the amount of prediction error around the actual value of the dependent variable (9,10). This allowed us to determine the error associated with prediction of MV by L1 or ΔMV by ΔL1. However, criterion and alternative measures are more commonly expressed using the same units, therefore the Bland and Altman approach was used to assess agreement between the criterion measure and the alternative measures (5).

Prediction of MV at one time point.

To accurately measure MV with MRI, it is important to choose an interval between sections that accurately reflects the longitudinal contour of a muscle, while consuming the least image acquisition and analysis time. Previous reports that have used 1-cm intervals have presumably obtained accurate measures of MV similar to our criterion measure (1,3,12,32). However, the present results suggest that adequate accuracy can be attained by much less frequent sampling of images along the thigh. Indeed, the present data indicate that use of MV4 (3.1-cm interval between sections), for example, can provide a measure of MV accurate to ± 1.7% of total MV 95% of the time in a large, mixed group of subjects (Table 2). Examined within each age/sex group, MV4 provides an excellent estimate of MV accurate to within ± 1.0%, 1.6%, 1.4%, and 0.7% of the criterion measure for older men, older women, young men, and young women, respectively. The amount of bias, or underestimation of the criterion measure, is also minimal with MV2 (0.3% of MV), whereas it becomes larger for MV6 (3.3% of MV), MV8 (5.3% of MV), and MV10 (8.4% of MV). In Figure 1 it is apparent that for MV10, MV8, and MV6 the underestimation bias is greater for subjects with larger MV. Indeed, the correlations in these plots are significant (MV10 R2 = 0.55, MV8 R2 = 0.35, MV6 R2 = 0.35, all P < 0.0001). This indicates that the error away from the true value of MV is larger for subjects with larger muscles. Thus, for measurement of MV at one time point, an interval between sections that is close to 3.1 cm (i.e., MV4) appears to be a prudent and less time-consuming strategy. Nonetheless, other investigators must choose a strategy that is suitable for their research context.

Measurement of changes in MV with ST.

Anthropometry, dual energy x-ray absorptiometry, ultrasound, CT, and MRI have all been employed to measure changes in the quantity of muscle in response to various interventions (2,17,18,30,32). Investigators who use CT or MRI are able to directly visualize a muscle or muscle group of interest and perform computer-based manual measurements on regions of interest. The manual analysis of many images, however, consumes a large amount of investigator time, especially when the analysis is performed before and after an intervention. Our results indicate that increasing intervals between sections substantially increases the error of prediction of the change in MV. For example, using intervals of 1.1 cm (MV2) predicts change in MV within ± 10.3% of the change in the criterion measure in 95% of cases, whereas the error increases substantially for 9.1-cm intervals (MV10) to ± 26.3%. We are not aware of previous reports that have quantified the ability of more time efficient MRI-based methods to detect a small amount of muscle hypertrophy.

As with the underestimation of MV observed at one time point, greater intervals also resulted in significant underestimation of change in MV. For example, while change in MV2 or MV4 does not significantly overestimate change in MV (P > 0.05), MV6 tends to (1.9%, P = 0.19), and MV8 (5.0%, P = 0.01) and MV10 (8.8%, P < 0.0001) do result in increasingly larger underestimation of change in the criterion value. Furthermore, it is apparent in Figure 3 that for MV10 the amount of underestimation is slightly larger in subjects whose MV changed more (R2 = 0.21, P < 0.01). This indicates that the error away from the true change in MV is larger for subjects with a greater training response and provides further evidence against the use of such a wide interval between sections.

The utility of the present results can be illustrated using a previous study from our group (13), in which quadriceps MV in both legs of 42 subjects at three different time points was measured using 9-mm sections with a 1-mm gap between sections. This data set required the measurement of approximately 11,000 muscle cross-sections, which consumed an estimated 370 h of analysis time. The present data suggest that those measurements could have been accomplished with adequate accuracy in one fourth the analysis time, for a total savings of approximately 280 h. The practical application of these results can be implemented by other investigators as they decide the interval between sections, and thus the amount of error that is acceptable in their research context.

It is intuitive that more frequent sampling along the thigh would reduce measurement error and conversely that less frequent sampling would increase measurement error. However, the maximal interval that still provides minimal error was not previously known. The finding that a 3.1-cm interval (MV4) provides an adequately low error may be related to the longitudinal contour of the quadriceps femoris muscle group. Our observations indicate that in the mid-thigh area, there is a 6–8 cm region where the CSA of the quadriceps muscle is maximal and the CSA values of the adjoining images do not greatly differ from each other (32). This is the area where the greatest absolute amount of hypertrophy is observed compared with proximal and distal regions (32). Any measurement strategy designed to accurately capture absolute change in MV certainly must include sections in this important region. In the context of the present analysis, use of a 3.1-cm interval (MV4) between sections would allow for the inclusion of at least two images from this area in most cases, whereas a 5.1-cm interval (MV6) might only include one image from this region, and a 7.1 cm or 9.1 cm interval (MV8, MV10) might miss this region altogether. Thus, an interval of approximately 3.1 cm presumably captures the muscle contour such that the error from the true contour is not likely to be high for a particular subject. There is no data to suggest that the longitudinal contour of the quadriceps femoris muscle is substantially different between sexes or with age, therefore these results are universally applicable.

Use of one muscle cross-section.

Although the correlation coefficient between L1 and MV was very high, there was considerable variability between subjects as observed in the spread of data points around the line of best fit (Fig. 2). For the relation between change in L1 and change in MV, the correlation was much lower and the spread in the data was much greater (Fig. 4). These findings clearly suggest that a single mid-thigh section should only be used if the experimental effect is expected to be relatively large.

We have no explanation for the isolated finding of a correlation of borderline significance between change in the largest CSA (ΔL1) and change in MV (ΔMV) in our sample of young women (Fig. 4). We are not aware of any age or sex differences in the gross morphology of the quadriceps femoris muscle group that would lead to an expectation of different results for young women. However, we have reported a significantly greater increase in muscle quality (1-RM/MV) in these young women compared with the other three groups (13). Whether this could affect the relation between training-induced increases in the largest CSA and MV in young women is unknown. The small sample size and low statistical power in this group may underlie this finding.

In summary, these results provide a quantitative basis for selection of a larger and more efficient interval of 3.1 cm between axial MRI sections in the measurement of quadriceps MV. This strategy provides adequate precision, allows for the detection of relatively small changes in MV, and results in substantial savings in image acquisition and analysis time compared with our criterion measure. Such a strategy appears appropriate for use in young and older men and women. These results could be applied in other muscles or anatomical structures that have a longitudinal profile similar to that of the quadriceps femoris. Furthermore, use of the single largest anatomical cross-sectional area results in substantial error when predicting MV at one time point or changes in MV over time and therefore is recommended only when the difference between groups or after an intervention is expected to be large.

This study was supported by National Institute on Aging grants 1-AG-4–2148 and T32 AG00219. The authors thank Dan Barlow for data analysis, Dr. Moriel NessAiver for technical assistance, and the research subjects for their time and effort in this study.


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