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.
Voronoi partitioning, Optimization, Particle therapy, Dose optimization, LET optimization
Level of Degree
Department of Computer Science
First Committee Member (Chair)
Second Committee Member
National Science Foundation, Fulbright & Senescyt scholarship, Office of Graduate Studies Research Project Travel Grant, Graduate and Professional Student Association Student Research and Allocations Committee Grant.
Riofrio, Daniel. "Applications of Voronoi partitions in particle therapy." (2012). https://digitalrepository.unm.edu/cs_etds/60