Optimal Control of Dose Delivery in Brachytherapy

Abstract

Brachytherapy is a well-established form of internal radiotherapy, widely used in the treatment of localised cancers, such as prostate and cervical cancer. The treatment consists of placing sealed radioactive sources directly onto the tumour, or in its vicinity. The success of this treatment is dependent on delivering a critical radiation dose to the tumour while minimising exposure to surrounding healthy tissue and organs at risk.

Current clinical dose calculation methods, such as the TG-43 formalism, rely on simplified assumptions that limit accuracy, particularly in heterogeneous domains and for complex seed configurations. This thesis develops a mathematically rigorous and physics informed framework for personalised brachytherapy treatment planning. We model the transport of radiation in the body from a brachytherapy source using a diffusion approximation of the linear Boltzmann transport equation. This model reduction reduces the computational complexity of the full seven-dimensional Boltzmann equation while still capturing the essential physics of radiation transport. The treatment planning problem is posed as an inverse problem and formulated as a PDE-constrained optimal control problem. Our approach incorporates advanced finite element methods and regularisation strategies which improve solution accuracy while reducing computational cost.

This thesis contributes novel ideas to the field of brachytherapy treatment planning and PDE-constrained optimal control. Our methodology allows for the incorporation of patient-specific anatomical data which supports the generation of personalised optimised treatment plans. Additionally, this work contributes novel adaptive regularisation techniques for PDE-constrained optimisation, enabling the dynamic adjustment of regularisation parameters based on rigorous a posteriori finite element error analysis. The results demonstrate the potential of this methodology to enhance clinical brachytherapy planning.

Date of Award	24 Jun 2026
Original language	English
Awarding Institution	University of Bath
Supervisor	Tristan Pryer (Supervisor) & Silvia Gazzola (Supervisor)