Inverse planning for x-ray rotation therapy: a general solution of the inverse problem

Rotation therapy with photons is currently under investigation for the deli very of intensity modulated radiotherapy (IMRT). An analytical approach for inverse treatment planning of this radiotherapy technique is described. Th e inverse problem for the delivery of arbitrary 2D dose profiles is first f ormulated and then solved analytically. In contrast to previously applied s trategies for solving the inverse problem, it is shown that the most genera l solution for the fluence profiles consists of two independent solutions o f different parity. A first analytical expression for both fluence profiles is derived. The mathematical derivation includes two different strategies, an elementary expansion of fluence and dose into polynomials and a more pr actical approach in terms of Fourier transforms. The obtained results are d iscussed in the context of previous work on this problem.