Numerical methods for radiation transport and radiotherapy treatment planning

点击翻译按钮获取中文摘要

The motivation for this project comes from clinical challenges in the context of radiotherapy for cancer treatment. When radiation moves through living tissue it deposits energy, which causes DNA damage, stopping the tumour cells from replicating. Since radiation will also damage the DNA in non-tumour cells, it is important to as far as possible spare the healthy tissue surrounding the tumour. This becomes even more important if the tumour is located near a vital organ. To ensure that a planned course of radiotherapy treatment delivers a high enough radiation dose to the tumour, whilst sparing important surrounding organs, an optimisation procedure is carried out over possible treatment configurations. The main aims of this project include investigating the physical assumptions behind models for radiation transport that are currently used in a clinical setting, and developing improved numerical methods for radiotherapy treatment planning in terms of accuracy, robustness, and computational efficiency. The starting point will be a simplified one-dimensional model for radiation transport, which can be equivalently formulated either as a stochastic model on the individual particle level, or as a partial differential equation (PDE) model, which describes the average macroscopic behaviour of many particles. We aim to extend this model to three spatial dimensions, and to include further physical behaviour where relevant. By leveraging the range of different numerical methods which can be applied to either the stochastic or PDE model, we aim to develop new more efficient numerical approaches to the optimisation problem of radiotherapy treatment planning. This may include using serialisation or parallelisation to accelerate our numerical simulations on specific computer architechtures, such as on a GPU (graphics processing unit). We also aim to investigate the use of strong stability preserving (SSP) numerical methods, which preserve the monotonicity of a solution in space between timesteps. These methods are useful when simulating conservation laws or physical systems in general, as they yield numerical solutions that still obey the laws of physics.As the focus of this project is on investigating numerical and mathematical methods for radiotherapy treatment planning, no data collection will be necessary. The methodology includes writing code and conducting numerical simulations in the programming language Python, and theoretical mathematical analysis of convergence results related to the numerical simulations. Improving the speed and accuracy of the numerical methods used for treatment planning will have a positive impact on how cancer treatment is carried out, with a more accurately planned treatment helping to guarantee a minimised radiation exposure of healthy tissue surrounding the tumour. Faster treatment planning software would enable clinicians to recalibrate the treatment plan to changes in patient physiology more often than what is currenlty done in practice, helping to minimise uncertainties in the delivered treatment.