A cooperative game solution approach for intensity modulated radiation therapy design: Nash Social Welfare optimization

Abstract

We study the fluency map optimization problem in Intensity Modulated Radiation Therapy from a cooperative game theory point of view. We consider the cancerous and healthy organs in a patient's body as players of a game, where cancerous organs seek to eliminate the cancerous cells and healthy organs seek to receive no harm. The goal is to balance the trade-offs between the utility of players by forming a grand coalition between them. We do so by proposing a methodology that solves a few convex optimization problems in order to transform the fluency map optimization problem into a bargaining game. To solve the bargaining game, we employ the concept of Nash Social Welfare (NSW) optimization due to the desirable efficiency and fairness properties of its outcomes. The proposed NSW optimization is convex and can be solved by powerful commercial solvers such as CPLEX. An additional advantage of the proposed approach is that it has a new control lever for the fluency map optimization, the so-called negotiation powers, which enables practitioners to put more emphasis on an organ by changing its negotiation power. To show the efficacy of our proposed methodology, we apply it to the TG-119 case and a liver case. We compare our proposed approach with a state-of-the-art approach through creating Dose Volume Histograms.

Keywords: IMRT; Nash Social Welfare optimization; fluency map optimization; game theory; radiotherapy.