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:
"We found participating in the ITT to be an unique and engaging environment for exchanging ideas and it was also good fun. Above all it produced some truly innovative thinking."
"The collaboration between SAMBa, UNAM and CIMAT has strengthened us in tools and techniques to visualize new perspectives of development and collaboration with a focus on generating value for other institutions."
There were a couple of ongoing personal research collaborations with Novartis in the Department of Mathematical Sciences that were brought together to develop a set of challenges for Novartis’s participation in ITT12. These consisted of questions exploring modelling and data integration in pharmacokinetics models, and finding effective routes to drug development for liver disease.
“We have a great track record of successful collaboration with SAMBa, as we share a common aim – applying the latest thinking in mathematics and statistics to solve real-world problems."
“Alongside the specific potential benefits to applied flood and coastal risk management, I have seen first-hand that the SAMBa CDT produces high calibre doctoral graduates with excellent skills in problem formulation and collaborative problem solving...”
"We are working with SAMBa to develop new tools for managing risk by combining deterministic and probabilistic methods."
"The students at SAMBa were engaging and motivated, above all interested in solving real world problems with their skills. As a result of SAMBa we have taken huge strides forward in a new technique in the assessment of arthritis related to psoriasis and the effect of treatment.
"For a small company like ours, this research is vital in delivering our vision to create digital technologies that change what’s possible for clinicians and patients."
"Working with SAMBa students to relay how our industry understands the daily challenges in aerospace design and manufacture and for them to translate them into statistical/mathematical models and methods was a refreshing and rewarding concept."
