Using the widespread method of conformal radiotherapy, beams are positioned at multiple angles, each shaped to match the projection of the tumor. Both absolute dose limits and dose volume demands that a required fraction of organ volume receive a dose below its threshold for damage must be observed for all healthy tissues. However, problem sizes found in practice exceed the limits of available general purpose solvers. This research, which is being conducted jointly by Purdue University and the Indiana University School of Medicine, seeks to develop specialized branch and bound algorithms that can compute implementable plans within a specified percent of optimum in the 24-48 hours available for treatment planning. One line of investigation strengthens LP relaxations of MIP formulations for the dose-volume constraints by constructing and adding new valid inequalities.
Preliminary results show considerable promise.
A second body research adapts the well known column-generation approach to dealing with the massive IMRT formulations. Instead of modeling the intensity of each beamlet within an IMRT beam, whole patterns of beamlet intensities will be represented as single columns and added as required. This requires a coupling of image processing methods with MIP to select columns worthy of entering the solution. In addition to presenting this research in progress, Dr. Rardin will make some brief remarks about programs and opportunities in operations research at the National Science Foundation. Click here to return to the Seminars Page.