Richard Barnard

Oak Ridge National Laboratory
, BH 319

Abstract

Two optimal control problems inspired by radiotherapy treatment planning

Radiotherapy, one of the primary methods for treating cancer, involves depositing a targeted radiative dose to a tumor.  Recent advances in the numerical solution of Boltzmann-like transport equations suggest that using these equations’ more accurate dose calculation would provide better treatment planning tools by using a partial differential equation-constrained optimal control framework.  We will discuss a pair of optimal control problems motivated by challenges in radiotherapy.  First, we look at the problem of switching controls, where we have several independent control mechanisms (such as preselected beams of radiative particles) but only one may be active a given time due to physical or hardware limitations.  Second, we look at volumetric dose objectives, where our goal is to minimize the volume where a quantity (such as the dose on a tumor) violates a prescribed level (such as a level fatal to the cancerous tissue).  In each problem, tools from convex analysis in Hilbert spaces allows us to come up with efficient ways to solve these general problems that can be applied to the radiotherapy treatment planning problem.