The unique depth-dose characteristics of protons (Bragg curve) suggest their use in beam therapy can result in higher effectiveness and less side effects as compared to the use of X-rays. Clinical practice has not yet fully understood the level of medical precision that can accounted for with proton beam therapy due to vulnerabilities from various sources of uncertainty.
A first source of uncertainty is related to the patient’s anatomical changes (eg changes in the position of the target tissue between therapy sessions e.g. due to bowel contents, minor changes due to weight change associated with the treated illness or issues associated to breathing patterns): during each session, the direction of the proton beam is calibrated based on data – a scan of the patient – typically collected several days before, as well as being redone immediately before treatment to accommodate for any changes. The information that this data offers presents a degree of uncertainty in addition to the way in which it is used. Currently new technology is being developed to collect supplementary real-time data, specifically a so-called “Compton Camera”, detecting gamma rays emissioned by de-exitation of atoms in the tissue under a range of conditions. New uncertainty is then generated in the process of compounding the new image data with the old ones. There is also uncertainty coming from the fact that Gamma ray emission data reveal only imprecise information on the location in the patient body, and again uncertainty in the accuracy of the Compton Camera itself.
This project aims to detangle, quantify and harness all such layers of uncertainty by using principled, likelihood-based methods supported by state-of-the art probabilistic models of radiation transport.
Mathematical radiation transport modelling goes back about 80 years and is indeed gave birth to the very first Monte Carlo algorithms. Recently, much more advanced methodology in Monte Carlo simulation methods, particularly within the paradigm of Bayesian updating and Bayesian inverse models has picked up speed again. Mathematical advances match the prevelance of numerous important applications in engineering and medicine and to recent theoretical breakthroughs, which embed radiation trasport dynamics in the framework of e.g. randomised partial (integro-)differential equations (RPIDEs) in which coefficients present uncertainty, and links the particle behaviour in radiation with single particle trajectories given Feynman-Kac formulae. Building onto this theoretical foundation, we will seek effcient methods to solve a (Bayesian) inverse problem for radiation transport RPIDEs, interpreted as the source of clinical data (the likelihood function). RPIDE likelihoods are, in general, analytically intractable, thus part of the project will also entail deriving scalable computational methods to make such models amenable for inference, leveraging and linking with concurring existing projects on which MathRad network is actively engaged. Novel statistical machine-learning methods will also be sought, in combination with likelihood-based methods, to address issues of scalability and at the same time preserving the interpretability of the inferential results.
To assist in this endeavour we aim to build a theory-based computer model of the experiment, ideally with minimal epistemic uncertainty, in order to decompose of the aleatoric uncertainty using Bayesian approaches. Exploratory research with simpler photon (rather than proton) emission can be a promising first step to appraise the quality of the methodology with concrete data.
This project is being delivered via an PhD studentship supported by an EPSRC Industrial CASE award, and Jacobs Clean Energy. The project team are Dario Spano, Julia Brettschneider, Andreas Kyprianou, Paul Smith and Peter Matthews and will commence in October 2024.
