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Applications of Voronoi partitions in particle therapy

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/20783

Applications of Voronoi partitions in particle therapy

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Title: Applications of Voronoi partitions in particle therapy
Author: Riofrio, Daniel
Advisor(s): Luan, Shuang
Committee Member(s): Holzscheiter, Michael
Heintz, Philip
Department: University of New Mexico. Dept. of Computer Science
Subject(s): Voronoi partitioning
Optimization
Particle therapy
Dose optimization
LET optimization
LC Subject(s): Cancer--Radiotherapy--Mathematical models.
Radiotherapy, High energy--Mathematical models.
Particle beams--Therapeutic use--Mathematical models.
Voronoi polygons.
Mathematical optimization.
Degree Level: Masters
Abstract: Treating cancer using charged particles heavier than electrons is becoming more and more popular in modern cancer management due to its increased dose to the targeted tumors and improved sparing of surrounding normal tissues and critical structures. Many challenging and interesting mathematical optimization problems arise in the planning of charged particle radiation therapy. In this thesis, we study three important optimization problems in particle therapy, which includes dose optimization, energy modulation change reduction, and LET (linear energy transfer) painting. Generally speaking the goal of treatment planning is to use computer based algorithms and software to find a therapeutic plan that maximizes the “dose” delivered to the target tumor while at the meantime minimizing that to the surrounding normal tissues and critical structures. The word “dose” here can refer to physical dose, i.e., energy imparted by the incoming ionizing radiation to the patient, radiobiological dose such as percentage of cells killed, or a combination of both. As an example, the LET painting problem that we studied can be viewed as a combination of physical dose and radiobiological dose, because the LET distribution of a treatment plan can be viewed as a “surrogate” for beam quality and increasing the LET can lead to increased cell killing efficiency under certain circumstances. Various machine properties are also considered in these optimizations. In most particle facilities, changing the beam energies requires an undesirable delay; therefore, in the energy modulation change reduction we aim to reduce the number of energy changes without compromising the final physical dose distribution. The contributions of this thesis include the following. (1) We have developed a parameterizable prototype treatment planning system for physical dose optimizations which implements kernel based dose calculations for non-uniform mediums, and dose optimization using non-negative least squares. (2) We found that Voronoi partitions can provide effective heuristic solutions to the energy modulation change reduction and LET painting problems. In addition, this thesis also identified an array of important and challenging computational problems that are not only of importance to the clinicians but also of considerable interests to computer scientists.
Graduation Date: May 2012
URI: http://hdl.handle.net/1928/20783

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