THE DERIVATION OF TISSUE-MAXIMUM RATIO FROM PERCENTAGE DEPTH-DOSE REQUIRES PEAK SCATTER FACTOR TO BE CONSIDERED A FUNCTION OF SOURCE-TO-SURFACE DISTANCE

A formula for the calculation of tissue-maximum ratio (TMR) from perce ntage depth dose (PDD) and peak scatter factor (PSF) is derived from f irst principles using a simple geometric model for the case when the h eld size for PDD and PSF is defined at the surface. The derivation is carried out in two ways: (a) taking field size for PDD and PSF as defi ned at the depth of maximum dose and then applying a conversion factor , and (b) by a direct derivation. The first of these methods yields a formula which agrees with BJR Supplement 25, but the latter yields a r esult which differs from it. Numerically, this difference is insignifi cant, but it has implications for the theoretical basis of the convers ion formulae. The difference arises due to the translation of field si ze from one depth to another when calculating PSF: two different value s of source-to-surface distance (SSD) yield two apparently different P SFs for the same size of field at the depth of maximum dose. Disagreem ents of this type are prevalent throughout the standard conversion for mulae given in BJR Supplement 25 when field size for PDD and PSF is de fined at the surface rather than at the depth of dose maximum. These d isagreements are illustrated here using the conversion of PDD from one SSD to another as an example. The difficulty is overcome by consideri ng PSF to be a function of SSD as well as field size.