## Thursday, June 14, 2012

### Estimating the volume of intracranial hematoma on CT

The commonly used formula for estimating the volume of intracranial bleed on CT is

ABC/2
where

A is the maximal diameter of the hematoma by CT
B is the diameter 90° to A, and
C is the approximate number of CT slices with hemorrhage multiplied by the slice thickness

For a number of years, I could not really grasp why the formula is as such. I thought that the formula is derived from the formula of volume for a cylinder. The part of (C) in the formula I could understand as it involves the height of the cylinder. But what I could not grasp is that, if this formula is derived from the volume of a cylinder, the formula should entail the use of "pi" (π) which is taken to be 3.14 (up to 2 decimal points).  This is because the surface area of a circle is π * r *r; and therefore, the formula for volume of cylinder is π * r *r * h where h is the height of the cylinder.

This formula is actually derived from the volume of an ellipsoid object and NOT of cylinder.
Figure 1

The volume for an ellipsoid object is

4/3 * π * a *b * c (a, b, and c as of Figure 1 above)

Applying this formula to the hematoma object on CT,
a and b are actually half of the two diameters mentioned on 2 dimension plane; and c is half of the height of the hematoma.

Therefore, the volume of the hematoma is

4/3 * π * (A/2) * (B/2) * (C/2)

where
A is the maximal diameter of the hematoma by CT
B is the diameter 90° to A, and
C is the approximate number of CT slices with hemorrhage multiplied by the slice thickness

assuming π ~ 3, therefore,

the volume of the hematoma is therefore,
4/3 * 3 * (A/2) * (B/2) * (C/2) = ABC/2

In an article by Freeman et al (2008), it is found that the ABC/2 method accurately estimates smaller ellipsoid hematoma volumes but inaccurately measures larger, irregularly shaped hematoma, or multicompartment hemorrhage such as intraventricular hemotoma and subdural hematoma. This article by Freeman et al (2008) has great pictures showing the ellipsoid shape of intracranial hematoma.

The importance of estimating the volume is that if the volume is large (~20 - 30 cc), it may be one of the indications for neurosurgical intervention, depending on the local neurosurgical management protocol of the center.

References:
1. Kothari RU, Brott T, Broderick JP, Barsan WG, Sauerbeck LR, Zuccarello M, Khoury J. The ABCs of measuring intracerebral hemorrhage volumes. Stroke. 1996 Aug;27(8):1304-5. Click here.

2. Freeman WD, Barrett KM, Bestic JM, Meschia JF, Broderick DF, Brott TG. Computer-assisted volumetric analysis compared with ABC/2 method for assessing warfarin-related intracranial hemorrhage volumes. Neurocrit Care. 2008;9(3):307-12. Click here.