My research explores new mathematics at the interface of applied and pure math, using differential geometry, biology, and biophysics to study single and collective cell migration in complex non-isotropic environments. Through a data-driven modelling approach, I formulate coupled systems of bulk-surface partial differential equations on domains and surfaces/manifolds that continuously evolve/deform in space and time. The goal is to develop in-silico computational cells that encode key biophysical and molecular properties of single cells, enabling rapid exploration of drug delivery and therapeutic drugs for disease modelling such as cancer.
Pattern formation on continuously deforming domains and evolving biological surfaces
Modelling, analysis and simulations of bulk and surface reaction-diffusion systems on convex and non-convex geometries
Mechanobiochemical modelling of 2- and 3-D cell deformation
Geometric bulk-surface PDEs for single and collective cell migration through confinement
Geometric surface PDEs for cell translocation through microchannels
Geometric bulk-surface PDEs: modelling of adhesion dynamics for cancer cell migration and invasion
Numerical analysis of bulk-surface finite element methods,
Numerical analysis of bulk-surface virtual elements
Adaptive multigrids for phase-field formulations of geometric surface evolution laws
Modelling COVID-19 modelling and analytics: A partnership with Brighton and Hove City Council, East Sussex County Council, West Sussex County Council, Sussex Commissioners (CCG), and East Sussex Brighton and Hove health Authority