Inverse thermal-wave modelling of heat transfer in biological tissues

ongoing

Many practical applications related to biomedical, wind, seismic or noise excitations require reconstructing structural properties from the knowledge of some appropriate output responses. In the field of biomedical engineering, the importance of the topic can easily be demonstrated by the significant impact on organs malfunctioning caused by abnormalities within biological tissues, such as tumour formation and growth. These disorders must be detected and treated early in order to save lives and improve the general health. Understanding the heat transfer in biological tissues and, in particular, the determination of tissue’s properties and the blood perfusion rate are important yet difficult tasks, and, in such sense, this project will seek to maximise the efficiency in providing rapid, intelligent and cost-effective solutions to unexplored impactful challenges. To contribute to achieving such an admirable goal, this proposal aims to accomplish, for the first time, the nonlinear identification of biological properties in thermal-wave heat transfer using inverse methods that are non-invasive and non-destructive. More concretely, reconstructions of the time- or space-dependent blood perfusion coefficient in the hyperbolic thermal-wave equation from transient measurements of the temperature at tissue’s boundary will be investigated. This analysis requires understanding the ill-posedness of the new inverse nonlinear problems for hyperbolic partial differential equations that are formulated to govern the heat propagation in biological tissues. Proving the uniqueness and stability of solution using the technique of Carleman estimates will be challenged, and developing globally convergent and stable methods of reconstruction will be attempted. Moreover, to add practical significance to the research in a way that may ultimately help to monitor and control the integrity of biological tissues, noisy numerically simulated and experimentally measured data will be inverted.