A dynamic programming approach to adaptive fractionation

Abstract

Abstract. We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive fractionation, because it allows us to assess how close to optimal different methods are, and (ii) heuristic methods proposed in this paper are near-optimal, and therefore, can be used to evaluate the best possible benefit of using an adaptive fraction size.The essence of adaptive fractionation is to increase the fraction size when the tumor and organ-at-risk (OAR) are far apart (a "favorable" anatomy) and to decrease the fraction size when they are close together. Given that a fixed prescribed dose must be delivered to the tumor over the course of the treatment, such an approach results in a lower cumulative dose to the OAR when compared to that resulting from standard fractionation. We first establish a benchmark by using the DP algorithm to solve the problem exactly. In this case, we characterize the structure of an optimal policy, which provides guidance for our choice of heuristics. We develop two intuitive, numerically near-optimal heuristic policies, which could be used for more complex, high-dimensional problems. Furthermore, one of the heuristics requires only a statistic of the motion probability distribution, making it a reasonable method for use in a realistic setting. Numerically, we find that the amount of decrease in dose to the OAR can vary significantly (5 -85%) depending on the amount of motion in the anatomy, the number of fractions, and the range of fraction sizes allowed. In general, the decrease in dose to the OAR is more pronounced when: (i) we have a high probability of large tumor-OAR distances, (ii) we use many fractions (as in a hyper-fractionated setting), and (iii) we allow large daily fraction size deviations.arXiv:1109.4524v3 [physics.med-ph]

Optimization of Radiation Therapy Fractionation Schedules in the Presence of Tumor Repopulation

“…Using imaging information obtained between treatment days, dynamic optimization models have been developed to adaptively compensate for past accumulated errors in dose to the tumor ( [12,10,11,49]). There also has been work on online approaches which adapt the dose and treatment plan based on images obtained immediately prior to treatment ( [30,9,24,23,14,25,45]).…”

“…The opportunity to then adapt the treatment to the observed data, rather relying on a model, becomes a possibility. While previous works have investigated using imaging technology to select dose fractions ( [30,9,24,23,14,45]), they have not done so to counter accelerated repopulation. While the problem in this paper can be seen as a special case of the general one presented in [25], the effect of tumor proliferation, which is our main focus, was not analyzed therein.…”

A feasibility study of dynamic adaptive radiotherapy for nonsmall cell lung cancer

“…They concluded that the larger fractional (prescription) dose is optimal when there is a larger distance between the tumor and OAR. 48 They showed that there is potential to decrease the dose to the OAR using ART if there is a large variation in the distance between the tumor and OAR during a treatment course. In this case, the state of the system is the distance between the tumor and OAR subject to uncertainty, thereby requiring a motion probability distribution.…”

Adaptive fractionation at the MR-linac

“…However, in principle inter-fraction tumor motion can even be exploited, that is, a better treatment quality may be achieved in the presence of motion compared to a static patient geometry. Adaptive fractionation (AF) (Chen et al 2008, Ramakrishnan et al 2012 is one approach to exploit inter-fraction motion. In this approach, a treatment plan is not only adapted to the daily patient geometry, but also the dose delivered to the tumor in each fraction is modified: the dose is increased on favorable treatment days, i.e.…”