Characterising uncertainty in radiotherapy towards treatment optimisation (University of Warwick & industrial partner Jacobs & NHS-UCLH)

Contact: Andreas Kyprianou

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 [1]. 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 [4]. 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 [3], which embed radiation trasport dynamics in the framework of e.g. randomised partial (integro-)differential equations (RPIDEs) in which coefficients present uncertainty [2], 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 [5]. 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.

More information about applying for a PhD at Warwick may be found here

[1] Mohan, R. and Grosshans, D., 2017. Proton therapy–present and future. Advanced drug delivery reviews, 109, pp.26-44. https://www.sciencedirect.com/science/article/abs/pii/S0169409X16303192

[2] Graham, I., Parkinson, M. and Scheichl, R. 2021. Error analysis and uncertainty quantification for the heterogeneous transport equation in slab geometry. IMA Journal of Numerical Analysis, 41 (4), 2331–2361.

[3] E. Horton, A. E. Kyprianou and D. Villemonais. Stochastic methods for the neutron transport equation I: linear semigroup asymptotics. Ann. Appl. Probab. 30(6):2573–2612, 2020.

[4] Parajuli, R.K., Sakai, M., Parajuli, R. and Tashiro, M., 2022. Development and applications of Compton Camera—a review. Sensors, 22(19), p.7374.

[5] Volodina, V. and Challenor, P., 2021. The importance of uncertainty quantification in model reproducibility. Philosophical Transactions of the Royal Society A, 379(2197), p.20200071.

Innovation Internship with Aurora Health Physics

We are pleased to announce an exciting opportunity for a UK-based PhD student to undertake an Innovation Internship with MaThRad partner Aurora Health Physics Services (Aurora), one of the UK’s leading Radiation Protection Advisers.

About Aurora Health Physics Services
Aurora provides a range of radiological protection services including radiation monitoring of soil, aiding land cleanup from previous radioactive contamination. Their work ensures safe handling and disposal of radioactive materials.

Job Description
Aurora and MaThRad are seeking a researcher to study how ground properties influence monitoring results using their AuroraRadMap (ARM) and Gamma Eye systems. This project involves analysing existing data and creating experiments to reveal key factors affecting the systems’ outcomes.

Your Role
You’ll analyse data and conduct experiments to understand the impact of ground conditions and radioactive material distribution on monitoring outcomes. This could involve practical tests with soil samples or theoretical simulations using MCNP software. Your findings will help create an algorithm to tailor detection limits for various sites, enhancing accuracy.

Why It Matters
Your work will lead to:

• Improved reporting of ARM survey results, considering diverse ground conditions and radioactive distribution. This ensures better safety measures during excavations.
• Enhanced reporting of Gamma Eye monitoring outcomes, factoring in ground variations and radioactive distribution, for precise material disposal decisions.
• More accurate reporting of errors in ARM and Gamma Eye results, leading to better-informed decisions.

This is a great opportunity to make meaningful impact on radiation monitoring and land remediation, as well as a chance to put your technical and research skills to work within a commercially focused environment.

Further details and how to apply

This is a paid opportunity, for a period of 3 months for a UK-based PhD student. The start date is flexible and will be agreed once a candidate has been successfully appointed.

To apply please send a copy of you CV and a covering letter to info@mathrad.ac.uk.

Shortlisted candidates will be invited to attend an interview.

For further details on the project, or if you have any further questions please email info@mathrad.ac.uk