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A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems

Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida 32611-6595
Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida 32611-6595
Department of Radiation Oncology, College of Medicine, University of Florida, P.O. Box 100385, Gainesville, Florida 32610-0385
Innovative Scheduling, Inc., Gainesville Technology Enterprise Center (GTEC), 2153 SE Hawthorne Road, Suite 128, Gainesville, Florida 32641
romeijn{at}ise.ufl.edu
ahuja{at}ufl.edu
dempsey{at}ufl.edu
arvind{at}innovativescheduling.com

We consider the problem of radiation therapy treatment planning for cancer patients. During radiation therapy, beams of radiation pass through a patient, killing both cancerous and normal cells. Thus, the radiation therapy must be carefully planned so that a clinically prescribed dose is delivered to targets containing cancerous cells, while nearby organs and tissues are spared. Currently, a technique called intensity-modulated radiation therapy (IMRT) is considered to be the most effective radiation therapy for many forms of cancer. In IMRT, the patient is irradiated from several beams, each of which is decomposed into hundreds of small beamlets, the intensities of which can be controlled individually. In this paper, we consider the problem of designing a treatment plan for IMRT when the orientations of the beams are given. We propose a new model that has the potential to achieve most of the goals with respect to the quality of a treatment plan that have been considered to date. However, in contrast with established mixed-integer and nonlinear programming formulations, we do so while retaining linearity of the optimization problem, which substantially improves the tractability of the optimization problem. Furthermore, we discuss how several additional quality and practical aspects of the problem that have been ignored to date can be incorporated into our linear model. We demonstrate the effectiveness of our approach on clinical data.

Subject classifications: linear programming; applications; health care; treatment.
History: Received August 2003; revision received July 2004; accepted February 2005.

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