Composite Surface Integral Transforms in Neutron Therapy of Cancer

Abstract

Composite surface finite integral transforms are applied to formulate the optimal ballistic property for a temporally tuned multibeam neutron cancer 3D therapy as a single-valued dynamical system. By invoking Pontryagin's maximum principle, with the operation functions of the beams constituting the control vector, it is proved, in an inverse problem formulation, that for every spatial configuration of the neutron beams, there exists an optimal temporal control vector satisfying an a priori system of linear homogeneous Volterra integral equations of the first kind and convolution type. A version of this newly advanced, temporally optimalized, multibeam 3D irradiation therapy, with a linearized ballistic property, is shown to result from a shooting-type solution to a related, semihomogeneous dual system of linear integral equations of the first kind. A criterion for the controllability of this optimization problem has also been established.