Application of the scaling factor method to estimation of beta dose distributions for dissimilar media separated by a planar interface.

The most accurate method of calculating beta dose distribution currently relies on the Monte Carlo technique. The major drawback of the method is the long computing time required to follow a large number of "electron histories" in order to achieve good statistics, which makes the method unattractive for practical radiation therapy. A way to avoid the Monte Carlo calculations for homogeneous media was suggested by Cross and co-workers (AECL Report Nos. 7617, 1982; 10521, 1992), and is known as the "scaling factor" method. It consists of the determination of the depth dose distribution in a medium based on known data about the dose distribution in an arbitrary reference medium (e.g., air, water) by the use of a scaling factor on distance and a closely related renormalization factor imposed by energy conservation. This work is an attempt to extend the applicability of the scaling factor method to dissimilar media to a planar interface. The investigation was done for an isotropic source of the radioisotope 32P and an interface between water and medium "i," where medium "i" could be any medium with atomic number in the range 8 < Z < 50. The method was checked using three randomly chosen elements 40Zr, 32Ge, and 26Fe, each forming planar interfaces with water at either 100 or 350 mg/cm2. Discrepancies of less than 5% were detected (acceptable for practical radiotherapy) for the depth within which at least 95% of the initial energy is deposited.