Column generation for IMRT cancer therapy optimization with implementable segments

A radiation beam passes through normal tissue to reach tumor. The latest devices for the radiotherapy of cancer provide intensity modulated radiation treatment, or IMRT. This method refines cancer treatment by varying the intensity profile across the face of a radiation beam. Intensity modulation is usually accomplished by partitioning each beam, distinguished by its angle of entry, into an array of smaller sized units, called beamlets, assigned different intensities. Planning treatment calls for an optimization over beamlet intensities to maximize the dose delivered to the targeted tumor while keeping the distribution of dose throughout the various organs within physician prescribed bounds. The choice of beam angles can be entered into the optimization as well. A common method to produce an intensity pattern is to block out different parts of the beam for different amounts of time. This can be done sliding narrow blocks (leafs) of unit width into the beam from either of two opposing sides to create different beam shapes called segments. A sequence of segments with their exposure times is superimposed to yield the dose distribution actually received in the patient. Current two stage treatment is derived in separate steps: optimization over independently considered beamlet intensities, and generation of a sequence of segments to approximate the planned intensity map. The approximation degrades the solution, and the separate search for segments adds to planning time. We present a mixed integer programming alternative employing column generation to optimize dose over segments themselves. Only segments that can be realized with delivery devices are generated, and adjustments made for the effects of block edges, so that the optimized plans are directly implementable. Preliminary testing demonstrates gains in both planning efficiency and quality of the plans produced. A portion of the work of Dr. Langer, Mr. Thai and Dr. Preciado-Walters was supported by National Science Foundation grant ECS-0120145 and National Cancer Institute 1R41CA91688-01.