A shortest path-based approach to the multileaf collimator sequencing problem

AbstractThe multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms

Operations Research Methods for Optimization in Radiation Oncology

Operations Research has a successful tradition of applying mathematical analysis to a wide range of applications, and problems in Medical Physics have been popular over the last couple of decades. The original application was in the optimal design of the uence map for a radiotherapy treatment, a problem that has continued to receive attention. However, Operations Research has been applied to other clinical problems like patient scheduling, vault design, and image alignment. The overriding theme of this article is to present how techniques in Operations Research apply to clinical problems, which we accomplish in three parts. First, we present the perspective from which an operations researcher addresses a clinical problem. Second, we succinctly introduce the underlying methods that are used to optimize a system, and third, we demonstrate how modern software facilitates problem design. Our discussion is supported by several publications to foster continued study. With numerous clinical, medical, and managerial decisions associated with a clinic, operations research has a promising future at improving how radiotherapy treatments are designed and delivered

Sensitivity analysis for lexicographic ordering in radiation therapy treatment planning

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134937/1/mp0218.pd

Dose-volume-based IMRT fluence optimization: A fast least-squares approach with differentiability

AbstractIn intensity-modulated radiation therapy (IMRT) for cancer treatment, the most commonly used metric for treatment prescriptions and evaluations is the so-called dose-volume constraint (DVC). These DVCs induce much needed flexibility but also non-convexity into the fluence optimization problem, which is an important step in the IMRT treatment planning. Currently, the models of choice for fluence optimization in clinical practice are weighted least-squares models. When DVCs are directly incorporated into the objective functions of least-squares models, these objective functions become not only non-convex but also non-differentiable. This non-differentiability is a problem when software packages designed for minimizing smooth functions are routinely applied to these non-smooth models in commercial IMRT planning systems. In this paper, we formulate and study a new least-squares model that allows a monotone and differentiable objective function. We devise a greedy approach for approximately solving the resulting optimization problem. We report numerical results on several clinical cases showing that, compared to a widely used existing model, the new approach is capable of generating clinically relevant plans at a much faster speed. This improvement can be more than one-order of magnitude for some large-scale problems