Veronika holds a bachelor’s degree in Mathematical Physics from the University of Edinburgh, and a master’s degree in Applied Mathematics from the University of Gothenburg in Sweden. Her master’s thesis was on financial mathematics and focused on numerical simulation of two-factor interest rate models using Monte Carlo and multi-level Monte Carlo methods. Between graduating from the University of Gothenburg in 2020 and joining SAMBa, she spent a year working for Sociovestix Labs, a socially motivated enterprise in sustainable finance and financial data science. In her spare time, she enjoys knitting, craft beer, and outdoorsy adventures.

Project title:
Numerical methods for radiation transport and radiotherapy treatment planning

Supervisor(s):
Tristan Pryer

Project description:
Proton beam therapy is a type of radiotherapy treatment for cancer, which uses a ray of proton radiation to damage the tumour. The radiation deposits energy in the tissue, 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. Mathematically, the problem of formulating a suitable radiotherapy treatment plan can be formulated as an optimisation problem, subject to a constraint in the form of a PDE describing the physical behaviour of the radiation. The radiation dynamics can also be described in terms of a stochastic formulation, which details the behaviour of individual radiation particles. Connecting this formulation to the PDE formulation through Feynman-Kac formulae, it is possible to use Monte Carlo methods to obtain a numerical solution to the PDE. The main aims of Veronika’s research include developing new numerical methods for proton beam therapy treatment planning, improving accuracy, robustness, and computational efficiency.