Modelling polychromatic high energy photon beams by superposition

A unified three dimensional superposition approach to dose calculations used in treatment planning of polychromatic high energy photon beams in radiotherapy is developed. The approach we have used involves computing the dose at all points in a medium by superposing the dose spread array (DSA) from the interaction of a photon at a point in the medium with an array of data representing the TERMA (photon fluence times the photon energy) at points in the beam. The polychromatic nature of the beam is accounted for by modelling the beam as having ten spectral components. A "polychromatic dose spread array" (PDSA) for an interaction from a beam with this spectrum was derived. The TERMA array is calculated from a weighted average of the TERMA arrays for the ten photon energies to give a "polychromatic TERMA array". Thus the method accounts for the effect of beam hardening of the TERMA. But it does not account for the effect of beam hardening on the PDSA since a single PDSA (usually for the spectrum at the surface of the medium) is used at all depths. However, by considering measured and calculated beam central axis data, this model is shown to be adequate for computing depth doses for beams in a homogeneous medium penetrating to extreme radiological depths. A computation time advantage is gained because only one superposition per beam is required.