Intensity modulated radiation therapy (IMRT) is a relatively new treatment techniqueused to treat different kinds of cancer. Each beam delivering radiation to the patientis split into smaller beamlets whose intensities can be set individually. This increasedresolution makes it possible to achieve better conformance with the target structure (tumour)while sparing critical structures.The inverse problem of IMRT concerns to how to assign intensities to the beamlets in orderto achieve a satisfactory dose distribution in the patient. Based on an establishedmodel of IMRT and authentic patient data provided by Oslo University Hospital arealistic scenario for benchmarking algorithms is created.
The main goal of this thesis is to extend and modify the relaxation methodfor linear inequalities in order to obtain a method with better performancewhen applied to inverse problems resulting from a linear model of IMRT.A preprocessing technique exploiting dose influence data is presented, and the performance of the relaxationmethod in combination with the preprocessing technique is compared to that of theoriginal relaxation method and the algorithms provided by CPLEX.
In addition a simplified version of the inverse problem resultingfrom a simplified model of radiation treatment is studied, anda graph bashed algorithm for solving such problems is presented.
Finally, preliminary numerical results regarding the capabilitiesof CPLEX to take advantage of a solution to the inverse problemobtained using the relaxation method combined with the preprocessingtechnique when solving a more sophisticated linear programming approachto the inverse problem are presented.