Geometry and Subdural Hematoma Volume
To the Editor:
Gebel and colleagues1 reported a seemingly simple and accurate method for estimating the volume of a subdural hematoma. However, as 17th century philosopher and mathematician Thomas Hobbes wrote about a similarly bewildering calculation, “To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad.”2
The ABC/2 method for an intraparenchymal hematoma is based on the formula for the volume of a ellipsoid which is given by 4/3 π r1r2r3 (where the r represents each radius). With an approximation of 3 for π, and substitution of each of the radii with each diameter (d) divided by 2, the formula becomes d1d2d3/2, or ABC/2.
At first, it seems quite unlikely that this formula should be useful in the estimation of the volume of a crescent-shaped subdural hematoma. Nevertheless, the method has proven accuracy, and its derivation must be explained. Consider the 3-dimensional crescent as the difference between 1 large outer ellipsoid and 1 small inner ellipsoid, which is then cut in half (ie, the crescent is akin to a solid semicircle). The volume of the crescent is then given by (4/3 π r1r2r3 −4/3 π r4r5r6)/2. Using the measurements as defined by Gebel et al1 (Figure⇓ ), the length (L) represents 1 diameter, the thickness (T) represents another, and these are the same for both the inner and outer ellipsoids. The width (w) of the 2 ellipsoids differs, so the formula can then be approximated as (LTw2−LTw1)/2. Since the difference between the widths is represented by W, the entire formula simplifies to LTW/2, or ABC/2.
Thus, “Though this be madness, yet there is method in ’t.”3 Was this the method of Gebel et al?
- Copyright © 1999 by American Heart Association
Gebel JM, Sila CA, Sloan MA, Granger CB, Weisenberger JP, Green CL, Topol EJ, Mahaffey KW. Comparison of the ABC/2 estimation technique to computer-assisted volumetric analysis of intraparenchymal and subdural hematomas complicating the GUSTO-1 trial. Stroke. 1998;29:1799–1801.
Hobbes T. In: Rose N, ed. Mathematical Maxims and Minims. Raleigh, NC: Rome Press Inc; 1988.
Shakespeare W. Hamlet. New York, NY: Bantam Books; 1988.
We wish to thank Dr Kasner for his most eloquent and convincing mathematical explanation of our serendipitous madness.