Sparse Solution for the Intensity-Modulated Radiotherapy Problem Using Conic Programming

We address the problem of planning an effective IMRT (Intensity Modulated Radiotherapy) treatment for cancer. IMRT is a modern method of radiotherapy. It irradiates cancerous tissues by administering lethal dose of radiation to those cells, while sparing the healthy tissues. This method’s greatest advantage is the large degree of freedom which it allows the treatment planning, but it is also its’ shortcoming. Achieving a good treatment plan is a long and sophisticated process which rarely results in the optimal solution. In this report we will demonstrate an approach for solving the inverse-IMRT problem automatically. We treat IMRT as a constrained convex optimization problem, where the physical limitations are defined by the constraints, so any solution must be feasible. We will show that minimizing an l norm based cost-function can produce a sparse solution. This solution usually produces radiation planning which utilizes small number of the radiation sources. This can give the radiotherapist a tool to treat the patient more quickly and efficiently. Using similar concept can also optimize the settings of the treatment machine, thus making the treatment safer and faster. keywords: Radiotherapy, IMRT, conic programming, l norm, sparse solution, inverse problem