This thesis investigates the exact minimisation of treatment delivery time for Intensity Modulated Radiation Therapy (IMRT) for the treatment of cancer using Multileaf Collimators (MLC). Although patients are required to remain stationary during the delivery of IMRT, inevitably some patient movement will occur, particularly if treatment times are longer than necessary. Therefore minimising the treatment delivery time of IMRT may result in less patient movement, less inaccuracy in the dosage received and a potentially improved outcome for the patient. When IMRT is delivered using multileaf collimators in 'step and shoot' mode, it consists of a sequence of multileaf collimator configurations, or shape matrices; for each, time is needed to set up the configuration, and in addition the patient is exposed to radiation for a specified time, or beam-on time. The 'step and shoot leaf sequencing' problems for minimising treatment time considered in this thesis are the constant set-up time Total Treatment Time (TTT) problem and the Beam-on Time Constrained Minimum Cardinality (BTCMC) problem. The TTT problem minimises a weighted sum of total beam-on time and total number of shape matrices used, whereas the BTCMC problem lexicographically minimises the total beam-on time then the number of shape matrices used in a solution. The vast majority of approaches to these strongly NP-hard problems are heuristics; of the few exact approaches, the formulations either have excessive computation times or their solution methods do not easily incorporate multileaf collimator mechanical constraints (which are present in most currently used MLC systems). In this thesis, new exact mixed integer and integer programming formulations for solving the TTT and BTCMC problems are developed. The models and solution methods considered can be applied to the unconstrained and constrained versions of the problems, where 'constrained' refers to the modelling of additional MLC mechanical constraints. Within the context of integer programming formulations, new and existing methods for improving the computational efficiency of the models presented are investigated. Numerical results for all variations considered are provided. This thesis demonstrates that significant computational improvement can be achieved for the exact mixed integer and integer programming models investigated, via solution approaches based on an idea of systematically 'stepping-up' through the number of shape matrices used in a formulation, via additional constraints (particularly symmetry breaking constraints) and via the application of improved bounds on variables. This thesis also makes a contribution to the wider field of integer programming through the examination of an interesting substructure of an exact integer programming model. In summary, this thesis presents a thorough analysis of possible integer programming models for the strongly NP-hard 'step and shoot' leaf sequencing problems and investigates and applies methods for improving the computational efficiency of such formulations. In this way, this thesis contributes to the field of leaf sequencing for the application of Intensity Modulated Radiation Therapy using Multileaf Collimators.
|Qualification||Doctor of Philosophy|
|Publication status||Unpublished - 2009|