Mixed-integer programming techniques for decomposing IMRT fluence maps using rectangular apertures

We consider a matrix decomposition problem arising in Intensity Modulated Radiation Therapy (IMRT). The problem input is a matrix of intensity values that are to be delivered to a patient via IMRT from some given angle, under the condition that the IMRT device can only deliver radiation in rectangular shapes. This paper studies the problem of minimizing the number of rectangles (and their associated intensities) necessary to decompose such a matrix. We propose an integer programming-based methodology for providing lower and upper bounds on the optimal solution, and demonstrate the efficacy of our approach on actual clinical data. ∗Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida 32611-6595; e-mail: [email protected]. †Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida 32611-6595; e-mail: [email protected]. ‡Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida 32611-6595; e-mail: [email protected]. The work of this author was supported by the National Science Foundation under grant no. DMI-0457394.