Optimal adaptive control of treatment planning in radiation therapy

Radiation treatment plans, such as in oncological therapy, require the determination of a nonlinear optimal control policy, which should be adapted to the given individual and to the stage of the treatment. All too often, the treatment plans formulated assume a simplified representation. The aim of this paper is to show that the full complex representation can be adopted, if suitable routines are defined to solve the nonlinear stochastic problem which arises and if sufficiently powerful simultaneous identification and optimization algorithms are used. Thus to determine the optimal treatment plan it is required to solve an optimization problem both in the space of the control variables and in the space of the parameters to be estimated. The outline of the paper is the following. After the introduction in Section 2, radiotherapy treatments are discussed. In Section 3 the simultaneous identification and optimization algorithm is described and the appropriate convergence results are stated. In Section 4 some preliminary experimental results are presented. Finally in Section 5 conclusions are drawn.