Neoadjuvant chemotherapy (NACT) is a widely used treatment for patients with locally advanced breast cancer. However, some breast cancer subtypes exhibit pathological complete response rates as low as 10%. Non-responsive patients endure NACT side-effects without therapeutic benefit. It is essential to identify non-responsive tumours as early as possible, to enable clinicians to discontinue the unsuccessful NACT and proceed with alternative treatments. Furthermore, recognising exceptional responders could allow clinicians to minimise their unnecessary exposure to NACT.
A promising new approach, gaining traction in breast tumour modelling over the past decade, is the integration of patient-specific imaging data into mathematical models of tumour physiology and treatment response. Among these, predictive models based on reaction-diffusion (RD) equations have been widely explored. This thesis presents a family of four mathematical models based on these and tailored to each individual patient using magnetic resonance imaging (MRI) data. These models are designed to predict tumour progression throughout the course of NACT.
Models were implemented in FEniCSx and personalised using diffusion-weighted (DW) and dynamic contrast-enhanced (DCE) MRI from 34 patients, acquired before and after one NACT cycle, to predict response after three cycles. After the first cycle, up to three model parameters are calibrated to each patient: tumour cell proliferation, diffusion and drug efficacy.
The best-performing model was the simplest, one that accounts solely for the effects of chemotherapy without incorporating tumour growth. This model distinguished responders from non-responders after just one cycle of NACT, achieving 82% sensitivity, 75% specificity and an 86% negative predictive value. These findings suggest that tumour cell diffusion is not a critical factor in predicting response to NACT, which aligns with the observation that breast tumours do not exhibit significant growth over NACT timescales.
