Applications of mathematical network theory

This thesis is a collection of papers on a variety of optimization problems where network structure can be used to obtain efficient algorithms. The considered applications range from the optimization of radiation treatment plkans in cancer therapy to maintenance planning for maximizing the throughput in bulk good supply chains

Approximated multileaf collimator field segmentation

In intensity-modulated radiation therapy the aim is to realize given intensity distributions as a superposition of differently shaped fields. Multileaf collimators are used for field shaping. This segmentation task leads to discrete optimization problems, that are considered in this dissertation. A variety of algorithms for exact and approximated segmentation, for different objective functions and various technical as well as dosimetric constraints are developed

On the minimum cardinality problem in intensity modulated radiotherapy

The thesis examines an optimisation problem that appears in the treatment planning of intensity modulated radiotherapy. An approach is presented which solved the optimisation problem in question while also extending the approach to execute in a massively parallel environment. The performance of the approach presented is among the fastest available

The accuracy of a varian 600CD LINAC and the Pinnacle³ (v6.2b) treatment planning system with regard to IMRT implementation.

With IMRT now the future for the accurate delivery of radiation therapy, an investigation into the beam delivery system and the radiotherapy planning system has been undertaken to determine the accuracy and limitations of both systems. Results outlined in the following investigation have shown limitations in the beam delivery system as a result of the individual leaf construction and the Linac mechanics. Results from this investigation have shown limitations applied to IMRT fluence conversion and machine delivery process must include a minimum 2cm equivalent segment size with the smallest possible secondary collimator setting encompassing all segments, 400 MU/min dose rate and 4MU/segment to provide optimum IMRT delivery employing the Pinnacle³ planning system and the varian 600CD LINAC. Appying these limitations was also shown to minimize the effects due to the leaf construction.Thesis (M.Sc.(Med.Physics)) -- University of Adelaide, School of Chemistry and Physics, 200

Approximated MLC shape matrix decomposition with interleaf collision constraint

Shape matrix decomposition is a subproblem in radiation therapy planning. A given fluence matrix A has to be decomposed into a sum of shape matrices corresponding to homogeneous fields that can be shaped by a multileaf collimator (MLC). We solve the problem of minimizing the delivery time for an approximation of A satisfying certain prescribed bounds, under the additional condition that the used MLC requires the interleaf collision constraint

Approximated MLC shape matrix decomposition with interleaf collision constraint

Shape matrix decomposition is a subproblem in radiation therapy planning. A given fluence matrix A has to be decomposed into a sum of shape matrices corresponding to homogeneous fields that can be shaped by a multileaf collimator (MLC). We solve the problem of minimizing the delivery time for an approximation of A satisfying certain prescribed bounds, under the additional condition that the used MLC requires the interleaf collision constraint