Dissertation Abstract

Novel methods for intensity modulated radiation therapy treatment planning

We have considered the problem of radiation therapy treatment planning for cancer patients. Recent technological advancements have led to rapid development and widespread clinical implementation of an external-beam radiation delivery technique known as intensity modulated radiation therapy (IMRT). IMRT allows for the creation of very complex non-uniform dose distributions that allow the delivery of sufficiently high radiation doses to targets while limiting the radiation dose delivered to healthy tissues. In IMRT, the patient is irradiated from several beams, each of which is decomposed into hundreds of small beamlets, the intensities of which can be controlled individually. We consider the problem of designing a treatment plan (determining intensity of each beamlet, also referred as intensity modulation) for IMRT when the beam orientations are given. We have proposed a new formulation that incorporates all aspects which control the quality of a treatment plan that have been considered to date. However, in contrast with established mixed-integer and global optimization formulations, we do so while retaining linearity of the optimization problem, and thereby ensuring that the problem can be solved efficiently. We also developed a linear programming based algorithm to integrate beam orientation optimization with intensity modulation. We have developed neighborhood search methods based on fast sensitivity analysis and greedy search based heuristics for solving this integrated problem.

Delivering complex dose distributions sometimes requires a set of very complex beam cross sections (fluence profiles). The most widespread hardware to achieve this is the multileaf collimator (MLC), and the most common mode of operation for the MLC, called step-and-shoot delivery, is based on a decomposition of the fluence profile into apertures with associated intensities. We develop network flow based algorithms for solving this decomposition problem. Polynomial-time algorithms are developed to solve the decomposition problem while accounting for the constraints that the apertures must satisfy in one or more of the currently available commercial IMRT equipment. We also consider the problem of integrating the problem of intensity modulation with the final decomposition step. The problem is formulated as a large-scale convex programming problem, and solved via a column generation approach.

[Dr. Kumar is an ARRT registrant.]

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