A maximum-entropy method for the planning of conformal radiotherapy

The maximum entropy method (MEM) is a powerful inverse analysis technique that is used in many fields of science and engineering to perform tasks such as image reconstruction and processing of nuclear magnetic resonance signals. Unlike other methods, MEM naturally incorporates a priori knowledge of the problem into the optimized cost function. This feature is especially important in radiotherapy planning, because some knowledge is usually available about the stage of tumor development and about the prescription doses, including some dose constraints to the surrounding normal organs. Inverse planning is inherently consistent with the ability of MEM to estimate parameters inversely. In this investigation, an entropy function determines the homogeneity of dose distribution in the planning target volume; a least-squares function is added to the maximum entropy function as a constraint to measure the quality of reconstructed doses in organs at risk; and an iterative Newton-Ralphson algorithm searches for the optimization solution. Here we provide two examples that validate this application of MEM and the results were compared with manual plans. Although the examples involve conformal radiotherapy, we think MEM can be adopted to optimize intensity-modulated radiation therapy.