A commonly used approach for measuring volume doubling times of lung tumors relies on the “Modified Schwartz Equation.” This approach was first introduced in 1994 by Usada and allows for tumor volumes and growth rates to be calculated based on measurements obtained on a two-dimensional (2D) image such as a chest radiograph and subsequently this approach has been used for volume estimates on axial computed tomography images in widely cited articles where only two measurements were obtained . The “Modified” approach used in these articles assumes that the unmeasured third dimension is equal to the shorter of the two measured dimensions, thus making the shape of the tumor an ellipsoid with a long axis and two identical short axes. Usada cited the original article by Schwartz as a reference for this approach; however, in reviewing the original Schwartz article, this assumption was not made. Instead, Schwartz put forth an approach for calculating the volume doubling time on 2D images where he measured the length and width of a lesion and for the third dimension, he used the geometric mean of the length and width rather than assuming that it was equal to the measured width. Calculating the volume, assuming that the third dimension is equal to the width (ie, a prolate ellipsoid), is useful for assessing the left ventricular volume . However, for lung nodules, this is not a good assumption. Definitional to a nodule is the assumption that it is basically round (in 3D, a sphere not a prolate ellipsoid) and therefore using the geometric mean of the length and width for the unmeasured third dimension is more appropriate as it optimizes the assumption of sphericity. Although the choice of using the “Modified Schwartz Equation” in this form appears to be an inaccurate characterization of the method described by Schwartz for measuring volume, it likely had little effect on doubling time measurements in those articles . Its use results in a downward bias of the volume estimate as using the geometric mean for the third dimension would be larger than the short axis; however, this bias would be in the same direction for both time points and its effect would therefore be minimized as volume doubling times are based on the ratio of the two volumes.
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