Empirical equations for the representation of depth dose data for computerized treatment planning

Equations of the form (see article) have been used to represent the variation of central axis percentage depth dose P or tissue-air ratio (TAR) with depth d below the dose maximum. The equations were originally developed for the representation of cobalt 60 depth dose data but have also been fitted to the central axis depth dose data published in the British Journal of Radiology Supplement 11, for radiations ranging in energy from 1-5 mm Cu HVT to 8 MV. Values of the constants Q and M for standard field sizes are presented together with an estimate of the goodness of fit in each case. Two different approaches have been used in determining the dose at points other than those on the central axis. In the simpler method, used for rotation techniques, the off-axis ratio (OAR) is calculated from the equation. (see article) where x is the off-axis distance, w the field width at the depth and k1 and k2 are constants. In the more accurate method, used for fixed field techniques, different equations are used within the main beam, within the geometrical penumbra and outside the beam.