Supervisor: Prof Tristan Pryer
Partners: National Physical Laboratory
About the Project
This project is co-funded and co-supervised by the National Physical Laboratory (NPL), offering a unique opportunity to engage in applied mathematics research with direct clinical and industrial relevance.
Modern radiotherapy aims to deliver a precise dose of radiation to a tumour while minimising harm to surrounding healthy tissue. As delivery technologies become increasingly accurate, treatment success becomes more sensitive to uncertainty, both physical (e.g. anatomical variation, setup and delivery errors) and biological (e.g. individual differences in tissue response). These sources of uncertainty are typically treated independently or handled heuristically. There is currently no unified mathematical framework for quantifying and incorporating them into treatment planning.
This project addresses that gap. We aim to develop a rigorous, data-informed mathematical formalism to represent, propagate and mitigate uncertainty in radiotherapy. The focus is on building tractable models that support robust optimisation and personalised treatment decisions.
The project will draw on tools from probability, statistics, optimisation and PDE-constrained inverse problems. Candidates will investigate how to model uncertainties using stochastic processes and Bayesian approaches, how to propagate these uncertainties through transport or diffusion-based models of radiation dose and how to incorporate them into treatment plan optimisation via multi-objective or risk-aware formulations.
Project keywords: uncertainty quantification, robust optimisation, radiotherapy
Candidate Requirements
In addition to the SAMBa entrance requirements, the ideal candidate will have a good understanding of probability, statistics and differential equations, together with experience in numerical or computational modelling.
Contact the SAMBa team at samba@bath.ac.uk if you are unsure about your eligibility and would like to discuss your potential application.
Enquiries and Applications
Informal enquiries are encouraged and should be directed to supervisor Prof Tristan Pryer tmp38@bath.ac.uk.
Applications are open for entry in September 2026. Apply via the University of Bath’s online application form for an Integrated PhD in Statistical Applied Mathematics. Early applications are encouraged.
IMPORTANT:
When completing the application form:
Supervisor: Dr Matthias Ehrhardt
The medical imaging technique Positron Emission Tomography (PET) is an important cornerstone in modern medicine allowing non-invasive, sensitive, and specific detection of disease. For example, PET is routinely used in the diagnosis of various cancers. Small metastases at the edge of the PET resolution limit are difficult to be correctly diagnosed with the current technology, leaving clinicians in a very difficult situation.
In this PhD project, we are investigating Bayesian inference backed by sound mathematical and statistical theory to tackle this problem. In particular, we use approaches based on convex optimisation to make it computationally efficient and thus translatable to current clinical applications. The project is supported by a highly interdisciplinary team consisting of mathematicians (Bath, Heriot-Watt), engineers, physicists (National Physical Laboratory) and medical professionals.
Project keywords: Mathematics, inverse problems, uncertainty quantification, medical imaging, Positron Emission Tomography
In addition to the SAMBa entrance requirements, the ideal candidate would have undergraduate experience in one or more of the following areas: inverse problems, mathematical imaging, optimisation, or numerical methods, but training can be provided for a suitably motivated candidate. Experience in programming is desirable (e.g., MATLAB / Python).
Informal enquiries are encouraged and should be directed to supervisor Dr Matthias Ehrhardt m.ehrhardt@bath.ac.uk
1. In the Finance section, enter ‘SAMBa’ when asked to name the scholarship or PhD studentship you wish to be considered for.
2. In the Your research interests section, quote the project title of this project at the top of your statement and the name of the lead supervisor in the appropriate box.
