The colour and the shape Numerical modelling of energy transport for forensic and biomedical applications

The modelling of energy transport is crucial for many scientific applications, e.g., to measure time, non-invasively classify material compositions, and estimate the local effects of energy deposition. In this thesis, we developed, implemented, and validated powerful numerical approaches to model and utilize energy transport in the form of heat and light to address urgent needs in three distinct application domains: (i) forensic time of death estimation, (ii) early detection of tissue pathologies, and (iii) photothermal treatment of tissue pathologies. To this end, we derived mathematical frameworks describing the transport processes and implemented them within numerical solution schemes to yield predictions of the spatio-temporal distributions of the transported quantities. By combining these with imaged-derived model geometries (specifying the sample-specific structure, shape, and composition) and advanced parameter optimization schemes, we were able to ensure the versatility, and hence wide applicability and utility, of our approaches.