Combinatorial Benders cuts for decomposing IMRT fluence maps using rectangular apertures

Combinatorial Benders cuts for decomposing IMRT fluence maps using rectangular apertures

0.00 Avg rating0 Votes
Article ID: iaor20133032
Volume: 40
Issue: 9
Start Page Number: 2178
End Page Number: 2186
Publication Date: Sep 2013
Journal: Computers and Operations Research
Authors: ,
Keywords: programming: integer
Abstract:

We consider the problem of decomposing Intensity Modulated Radiation Therapy (IMRT) fluence maps using rectangular apertures. A fluence map can be represented as an integer matrix, which denotes the intensity profile to be delivered to a patient through a given beam angle. We consider IMRT treatment machinery that can form rectangular apertures using conventional jaws, and hence, do not need sophisticated multi‐leaf collimator (MLC) devices. The number of apertures used to deliver the fluence map needs to be minimized in order to treat the patient efficiently. From a mathematical point of view, the problem is equivalent to a minimum cardinality matrix decomposition problem. We propose a combinatorial Benders decomposition approach to solve this problem to optimality. We demonstrate the efficacy of our approach on a set of test instances derived from actual clinical data. We also compare our results with the literature and solutions obtained by solving a mixed‐integer programming formulation of the problem.

Reviews

Required fields are marked *. Your email address will not be published.