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).
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.
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).
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.
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).
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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Keywords:©2003The American College of Sports Medicine
KNEE EXTENSOR; AGING; MRI; CROSS-SECTIONAL AREA