A modified power-law formula for inhomogeneity corrections in beams of high-energy x rays

The Batho power-law formula is in common use in many treatment planning systems to correct for the presence of lungs and other inhomogeneities. While giving excellent agreement with measurement for Cobalt-60 radiation, it tends to underestimate the lung correction required for higher energy x rays and is undefined for distances beyond an interface less than the buildup distance. This paper suggests a simple modification that greatly improves the agreement with measured data and gives a continuously defined function at all depths. Measurements have been made in a polystyrene and cork phantom to simulate the effects of lung; data are presented for beams of 8-MV x rays, 16-MV x rays, and Cobalt-60 gamma rays.