Adaptive treatment-length optimization in spatiobiologically integrated radiotherapy

Recent theoretical research on spatiobiologically integrated radiotherapy has focused on optimization models that adapt fluence-maps to the evolution of tumor state, for example, cell densities, as observed in quantitative functional images acquired over the treatment course. We propose an optimization model that adapts the length of the treatment course as well as the fluence-maps to such imaged tumor state. Specifically, after observing the tumor cell densities at the beginning of a session, the treatment planner solves a group of convex optimization problems to determine an optimal number of remaining treatment sessions, and a corresponding optimal fluence-map for each of these sessions. The objective is to minimize the total number of tumor cells remaining (TNTCR) at the end of this proposed treatment course, subject to upper limits on the biologically effective dose delivered to the organs-at-risk. This fluence-map is administered in future sessions until the next image is available, and then the number of sessions and the fluence-map are re-optimized based on the latest cell density information. We demonstrate via computer simulations on five head-and-neck test cases that such adaptive treatment-length and fluence-map planning reduces the TNTCR and increases the biological effect on the tumor while employing shorter treatment courses, as compared to only adapting fluence-maps and using a pre-determined treatment course length based on one-size-fits-all guidelines.