The multi-scale approach to partial differential equations and novel asymptotic analysis open new pathways to solving fundamental problems in healthcare. This includes:
- Novel modelling and forecast of fatigue damage for stents in blood vessels.
- Multiscale mathematical models for extrapolation of in-vitro experiments to predictions of drug toxicity in humans.
- Multi-scale modelling of a human eye.
Advanced models for registration / segmentation offer unparalleled reliability and accuracy, capable for integrating longitudinal data in multi-modalities for direct clinical and biomedical use, to assist other image related themes, and to optimise the use of multiple biomarkers for personalised medicine. These include:
- Novel 3D variational segmentation models for medical imaging incorporating incomplete and partially segmented information.
- Development of clinical imaging models to predict tumour growth and metastasis.
- Multiple biomarker selection for personalised medicine.
Better understanding of strain competition dynamics in heterogeneous networks is fundamental to understanding and controlling influenza and anti-microbial resistance (AMR). With scaling up methods, we will address:
- AMR dynamics and the mathematics of strain competition on networks.
- Influenza dynamics and generating networks from ego-centric data.
- AMR dynamics within host -impact of spatial aspects on AMR evolution.