This is a project in collaboration with colleagues in the NHS and the University of Reading with funding for a studentship kindly provided by Proton Partners Ltd with further support through an IMI fellowship at Bath.
Approximately 360,000 patients are diagnosed with cancer each year in the UK (CRUK, 2013-14 data). 27% of these patients currently receive radiotherapy as part of their treatment, a figure which is predicted to rise. Radiotherapy with high energy protons has been the subject of significant investment world-wide for many years. In the UK, NHS England has recently invested ~£250M for the provision of high energy proton centres in Manchester and London. In the private healthcare sector, Proton Partners International are similarly investing in proton treatment facilities in several UK locations.
Mathematically this is an extremely challenging problem. Proton transport can be described deterministically through the Boltzmann-Fokker-Planck equation, a high-dimensional transport-type partial differential equation. It’s numerical treatment is delicate to say the least.
Making use of discontinuous Galerkin finite element methods for the spatial variable, spherical harmonics for the angular variable and a multigroup approach for the energy variable we can discretise the problem. This results in a huge linear system to be solved which we precondition with an algebraic multigrid method.
Tristan Pryer 