#### Equation Accuracy

Anthropometric measurement of leg volume using a geometric model, a truncated cone, was first reported by Jones et al. in 1969 (12). In the past 2 decades, CT and MRI have greatly improved the accuracy of measured component areas and, thus, total tissue volumes. Earlier investigators focused their analysis of volume reconstruction model accuracy solely on quantification of adipose tissue (7), and the model results were not compared with “actual” tissue volumes. This is because cadaver studies are difficult to perform, and it is hard to measure accurately the regional component's weight that corresponds exactly to the volume estimate provided by imaging methods.

Both Equations 4 (2, 4, 14, 15, 16, 17) and 5 (1, 6, 13, 18, 19, 20, 21, 22, 23, 24) were applied by earlier investigators to their CT and MRI volume calculations. Before the present investigation, the choice of reconstruction model was based largely on investigator preference rather than on experimental data. One goal of moving imaging methods toward reference method status is to establish the most accurate approach for deriving compartment volume from measured areas.

In the present study, we employed a novel approach by comparing model-derived volumes to a measure of “actual” tissue volume compiled from 1730 contiguous 1-mm-thick VW images. Unlike traditional cadaver dissection, volume and not mass of individual structures was evaluated. Thus, we were able to compare the reference volumes of the 12 compartments with the corresponding mean of volumes estimated by the two equations, and we also compared the CVs of data provided by the two equations to each other. Our main finding, based on slice intervals typically used by investigators, is that volume estimates derived using Equation 5 are consistently superior to those provided by Equation 4.

Our findings are based on only one cadaver, but the analyses included 4 regions and 12 compartments that varied greatly in their size and three-dimensional structure. Thus, we can conclude that Equation 5 is more accurate than Equation 4 in quantifying a wide range of human tissues, and Equation 5 should, accordingly, be adopted for imaging method tissue volume quantification. To our knowledge, this is the first study to evaluate volume models in several tissues distributed in different regions.

For a particular compartment, the means of Equation 4 were always smaller than the reference tissue volume, suggesting that most reference tissue volumes between adjacent slices are more convex than described by truncated cone or truncated pyramid models. This phenomenon was observed in all 4 regions and 12 compartments and with different slice intervals.

MRI is also used to quantify organ volumes. However, because organ volumes are usually derived from continuous scan protocols, the volume is actually calculated as:

Because there is no between-slice volume estimation in this calculation, the discussion of the accuracy of MRI for organ volume quantification is not relevant in the present study.

In addition to accuracy, Equation 5 also has advantages in quantifying the combined volumes of muscle, adipose tissue, and other tissues in a selected region. There are two methods available to calculate the combined volume. By using the first method, the volumes of muscle, adipose tissue, and other tissues are calculated separately by an equation and then summed to yield the combined volume “*V*_{1}”. With the second method, the areas of muscle, adipose tissue, and other tissues in each slice are summed to obtain the total area and the total volume (“*V*_{2}”) is then calculated using an equation. According to our calculation in Appendix 2, *V*_{1} is always equal to *V*_{2} for Equation 5, and *V*_{1} is always smaller than *V*_{2} for Equation 4. Because most reports do not state the detailed calculation steps, inconsistency may occur when different calculation methods are adopted. Although the percentage error might be small, investigators and readers might be confused if the sum of the region volume is not equal to the directly calculated volumes. For Equation 4, the more compartments in one region, the greater the difference between *V*_{1} and *V*_{2}. For Equation 5, no matter how many compartments are calculated, the total volume directly calculated from the areas will be equal to the sum of the volume of each compartment. A detailed derivation is provided in the Appendix 2.

The precision of the two equations is similar, and the difference in the accuracy between the two equations for major body components (i.e., SAT, visceral adipose, tissue and SM) is only ∼2–4% at the most commonly adopted 40-mm slice interval. Additionally, for a particular study, we cannot establish which equation yields an estimation closer to the true volume because the starting point is not controlled. Thus, there is no need to question the results of previous studies that may have used Equation 4. Nevertheless, the adoption of Equation 5 will improve both precision and accuracy at no additional cost; therefore, it is recommended for use in future studies.

#### Relationship of Accuracy to Interval

In the present study, we also examined the relationship between interval and accuracy. In general, as the between-slice interval increases, there is a trend toward an increasing CV of both equations as reported in a previous study (21). For example, at the between-slice intervals of 20 and 40 mm, the CVs of trunk adipose tissue for Equation 4 are 2.5% and 4.3%, respectively. The corresponding CVs for Equation 5 are 2.2% and 3.9%. Of these two between-slice intervals, the CVs of lower limb SM for Equation 4 are 2.1% and 5.1% and for Equation 5 are 1.8 and 4.4%, respectively. However, for a given compartment, the CV of a large interval might be less than that of a smaller interval. Although the actual shape of human tissues is complex, we provide a simple example to illustrate the above-mentioned situation. For the geometric shape in Figure 4, if we take the slices at a specific interval, the volume estimated by series one will be the smallest, whereas the volume estimated by series two will be the largest. The only difference between the two series is the starting point. Because both the smallest and the largest estimated volumes are within one group of the same interval but different starting points, it is possible for this group to have a higher CV. Were the intervals slightly larger, the estimated volumes would not include the smallest and the largest estimated volume. Thus, the CV of the group of a larger interval may be smaller than the CV of the group of this interval. This means that for some particular tissues at a specific starting point, there is a chance to have a less accurate estimation of the volume at a smaller interval. This phenomenon appears less in regularly shaped tissues such as SAT, whereas it more likely exists in comparatively irregularly shaped tissues such as VAT. Both the characteristic shape of VAT and the particular anatomy of the VW could account for the smaller CVs of larger intervals. However, based on the many whole-body MRI scans carried out in our laboratory and anatomical atlas knowledge, the VAT is always more irregularly shaped than other currently measured compartments. Thus, we believe that the inherent characteristic shape of VAT is the main cause of this phenomenon. In all compartments, the relationship of CV and interval is complicated; therefore, at present we cannot draw general conclusions.

When evaluating the reproducibility of segmentation of imaging methods, previous studies reported between-analyzer and intra-analyzer CVs in identifying the area of interest in each slice (25, 26, 27). The CVs in these studies are caused by individual analyzer variability and will vary among laboratories and analyzers. The CVs calculated and discussed in the present study are caused by design considerations and do not vary among laboratories or analyzers.

#### Conclusions

Equation 5 is more accurate for estimating the regional and whole-body tissue volume than Equation 4 in the VW when intervals are set at 10, 20, 30, 40, 50, 60, 70, or 80 mm and slice thickness is set at 10 mm. In other words, the parallel trapezium model and the two-column model are more accurate in estimating tissue volumes than the truncated pyramid model and the truncated cone model. Although there is no need to question the previous studies that adopted Equation 4, Equation 5 is recommended for future studies. The accuracy of Equation 5 should be further validated by continuous scans of human subjects differing in weight, height, sex, and age.