Inverse planning for radiotherapy using ridge functions

We apply ridge functions to the task of tomographic dose reconstruction for intensity modulated radiotherapy (IMRT). In recent years, new treatment machines have been developed in the field of IMRT in order to deliver the best plan for treating each patient. In this work we shall derive the basis for solving the inverse problem of determining the best beam orientations and modulation patterns from a dose prescription. Ridge functions are solutions of a system of integral equations and their sum results in the minimal norm solution of the reconstruction problem. Analytical inversion formulas based on ridge functions are derived. We show that the ridge functions comprise the first set of modulation patterns for a certain dose plan. The choice of optimum beam orientations that are clinically achievable is suggested. Results are illustrated by numerical experiments and comparison with existing techniques is presented.