Application of a least-squares parameter estimation approach for 2-D spatial modelling of compensators for intensity-modulated radiotherapy

A spatial modelling technique is presented to model inversely the attenuation behaviour of poly-energetic high-energy photon beams within a metal compensator for intensity-modulated radiotherapy. The algorithm aims to predict modulators (compensators), which produce an intended intensity-modulated beam after the beam has passed through the metal. The proposed method considers two spatial dimensions and is based on a least-squares approach. The nonlinear system is modelled by means of an initial 2-D spatial model, which is linear in the parameters, and which takes into account primary and scattered radiation. This model is then refined and simplified resulting in a rotational-symmetrical 2-D spatial representation, which reduces the calculation time and makes the model more generally applicable. Compared with other techniques, it is not necessary to know the linear absorption coefficient of the compensator material.