Intensity modulated radiation therapy with field rotation—a time-varying fractionation study Delal Dink & Mark P. Langer & Ronald L. Rardin & Joseph F. Pekny & Gintaras V. Reklaitis & Behlul Saka Received: 11 April 2011 / Accepted: 2 January 2012 / Published online: 10 January 2012 # Springer Science+Business Media, LLC 2012 Abstract This paper proposes a novel mathematical ap- proach to the beam selection problem in intensity modulated radiation therapy (IMRT) planning. The approach allows more beams to be used over the course of therapy while limiting the number of beams required in any one session. In the proposed field rotation method, several sets of beams are interchanged throughout the treatment to allow a wider selection of beam angles than would be possible with fixed beam orientations. The choice of beamlet intensities and the number of identical fractions for each set are determined by a mixed integer linear program that controls jointly for the distribution per fraction and the cumulative dose distribution delivered to targets and critical structures. Trials showed the method allowed substantial increases in the dose objective and/or sparing of normal tissues while maintaining cumula- tive and fraction size limits. Trials for a head and neck site showed gains of 25%–35% in the objective (average tumor dose) and for a thoracic site gains were 7%–13%, depending on how strict the fraction size limits were set. The objective did not rise for a prostate site significantly, but the tolerance limits on normal tissues could be strengthened with the use of multiple beam sets. Keywords IMRT . Optimization . Fractionation . Field rotation . Time-varying 1 Introduction Choosing treatment beam orientations is an important and difficult step in radiation therapy planning. The complexity of using automated methods to produce a preferred set of beam angles in IMRT is well recognized, and angle selec- tion remains a problem to be addressed in the general frame- works for optimization. While algorithms to guide the choice of beam angle have been proposed and studied, they are not typically trusted within available IMRT optimization systems. The lack of a trusted method to establish a pre- ferred set of beam angles confounds interpretation of studies evaluating the importance for improving IMRT plans of optimizing beam angles. In general there is a tradeoff between dose distribution gains and the employment of more beam angles. Using more beam angles lengthens the treatment session, slows machine throughput, risks the stability of patient position- ing, and taxes available mechanisms for quality assurance. In investigations of beam angle selection, a goal has been to reduce the number of beams needed in treatment without compromising a dose objective [1–3]. Some studies indicate that expanding the set of examined beam angles is not fruitful in improving the dose distribution [4–9], as others indicate that the mean dose sparing is improved [10]. Some approaches have applied evolutionary or genetic algorithms [11–14], simulated annealing [1, 15–17], particle swarm algorithms [18] and integer programming [19–22] to the problem of choosing beam angles if the total number is limited. Recent beam angle optimization approaches are proposed based on nested partitions framework [ 23], D. Dink : J. F. Pekny : G. V. Reklaitis School of Chemical Engineering, Purdue University, W. Lafayette, IN 47907, USA M. P. Langer Department of Radiation Oncology, Indiana University, Indianapolis, IN 46202, USA R. L. Rardin : B. Saka (*) Department of Industrial Engineering, 4207 Bell Engineering Center, University of Arkansas, Fayetteville, AR 72701, USA e-mail: bsaka@uark.edu Health Care Manag Sci (2012) 15:138–154 DOI 10.1007/s10729-012-9190-2