Numerical methods for radiation transport and radiotherapy treatment planning

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.

Combining specialised modelling techniques with complex data analysis in order to deliver prediction with quantified uncertainties lies at the heart of many of the major challenges facing UK industry and society over the next decades. Indeed, the recent Government Office for Science report "Computational Modelling, Technological Futures, 2018" specifies putting the UK at the forefront of the data revolution as one of their Grand Challenges.

The beneficiaries of our research portfolio will include a wide range of UK industrial sectors such as the pharmaceutical industry, risk consultancy, telecommunications and advanced materials, as well as government bodies, including the NHS, the Met Office and the Environment Agency.

Examples of current impactful projects pursued by students and in collaboration with stake-holders include:

- Using machine learning techniques to develop automated assessment of psoriatic arthritis from hand X-Rays, freeing up consultants' time (with the NHS).

- Uncertainty quantification for the Neutron Transport Equation improving nuclear reactor safety (co-funded by Wood).

- Optimising the resilience and self-configuration of communication networks with the help of random graph colouring problems (co-funded by BT).

- Risk quantification of failure cascades on oil platforms by using Bayesian networks to improve safety assessment for certification (co-funded by DNV-GL).

- Krylov regularisation in a Bayesian framework for low-resolution Nuclear Magnetic Resonance to assess properties of porous media for real-time exploration (co-funded by Schlumberger).

- Machine learning methods to untangle oceanographic sound data for a variety of goals in including the protection of wildlife in shipping lanes (with the Department of Physics).

Future committed partners for SAMBa 2.0 are: BT, Syngenta, Schlumberger, DNV GL, Wood, ONS, AstraZeneca, Roche, Diamond Light Source, GKN, NHS, NPL, Environment Agency, Novartis, Cytel, Mango, Moogsoft, Willis Towers Watson.

SAMBa's core mission is to train the next generation of academic and industrial researchers with the breadth and depth of skills necessary to address these challenges. SAMBa's most sustained impact will be through the contributions these researchers make over the longer term of their careers. To set the students up with the skills needed to maximise this impact, SAMBa has developed a bespoke training experience in collaboration with industry, at the heart of its activities. Integrative Think Tanks (ITTs) are week-long workshops in which industrial partners present high-level research challenges to students and academics. All participants work collaboratively to formulate mathematical
models and questions that address the challenges. These outputs are meaningful both to the non-academic partner, and as a mechanism for identifying mathematical topics which are suitable for PhD research. Through the co-ownership of collaboratively developed projects, SAMBa has the capacity to lead industry in capitalising on recent advances in mathematics. ITTs occur twice a year and excel in the process of problem distillation and formulation, resulting in an exemplary environment for developing impactful projects.

SAMBa's impact on the student experience will be profound, with training in a broad range of mathematical areas, in team working, in academic-industrial collaborations, and in developing skills in communicating with specialist and generalist audiences about their research. Experience with current SAMBa students has proven that these skills are highly prized: "The SAMBa approach was a great template for setting up a productive, creative and collaborative atmosphere. The commitment of the students in getting involved with unfamiliar areas of research and applying their experience towards producing solutions was very impressive." - Dr Mike Marsh, Space weather researcher, Met Office.