The derivation of tissue-maximum ratio from percentage depth dose requires peak scatter factor to be considered a...

A formula for the calculation of tissue-maximum ratio (TMR) from percentage depth dose (PDD) and peak scatter factor (PSF) is derived from first principles using a simple geometric model for the case when the field 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 defined 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 result which differs from it. Numerically, this difference is insignificant, but it has implications for the theoretical basis of the conversion formulae. The difference arises due to the translation of field size from one depth to another when calculating PSF: two different values of source-to-surface distance (SSD) yield two apparently different PSFs for the same size of field at the depth of maximum dose. Disagreements of this type are prevalent throughout the standard conversion formulae given in BJR Supplement 25 when field size for PDD and PSF is defined at the surface rather than at the depth of dose maximum. These disagreements are illustrated here using the conversion of PDD from one SSD to another as an example. The difficulty is overcome by considering PSF to be a function of SSD as well as field size.