Clarification of abc/2 Rule for ICH Volume
To the Editor:
There appears to be a common misperception that the denominator of 2 in the ICH calculation for Volume=abc/2 is attributable to use of 5-mm slices in CT. This is not the case.
Calculating Volume=abc/2 is based on the assumption that the ICH volume can be approximated by an ellipsoid. This is a good assumption as long as the hemorrhage is not multilobulated or otherwise very irregular in shape.
An ellipsoid can be described in Cartesian coordinates using its 3 perpendicular axes, commonly identified on CT or MRI as the largest cross-sectional diameter (a), a second diameter drawn at right angles to the first (b) and the height of the ellipsoid (c), estimated from the number and thickness of slices in which the hemorrhage is visible. This last element has the potential to introduce confusion, however.
Note that in this general expression, c is expressed in the same units as the other axes. The number or thickness of slices on CT has not yet been considered. Using the approximation that π≈3, the equation simplifies to:
Thus, the factor of 2 is necessary to calculate the volume of an ICH ellipsoid using Cartesian coordinates. The length of c should be calculated in centimeters, using the number of slices and slice thickness, before entering the value of c into the equation. (That is, even if the CT slices were 1 cm thick, division by 2 would still be necessary for calculating volume.) In retrospect, this division by 2 is intuitively logical because otherwise application of the rule would be tantamount to calculating height×width×length, which is the volume of a rectangular cube, and would clearly overestimate the volume of an ellipsoid which fits within that cube.
ICH volume is an essential factor for offering prognosis and planning management. Therefore, it is important that the basis of this factor of 2 be clearly recognized to avoid incorrectly doubling estimates of lesion volume.