A Graph-Based Approach to Bioheat Modelling: a Case Study on Tissue Heat under Electrical Stimulation

The work presented in this thesis develops a graph-based computational framework for modelling and simulating coupled thermal–electrical dynamics in biological tissues subjected to electrical stimulation. The study aims to provide a physically consistent yet computationally efficient approach for predicting heat propagation and electrical behaviour during electrosurgical procedures. Starting from an existing lumped-parameter bioheat model, the tissue domain is reformulated as a three-dimensional network of interconnected nodes governed by energy conservation laws. The model incorporates conduction, convection, and Joule heating, with the electrical and thermal subsystems. Calibration of the model parameters against experimental data is performed through constrained optimisation in MATLAB, ensuring agreement between simulated and measured temperature profiles. A global sensitivity analysis using the SAFE toolbox identifies the parameters that most influence temperature evolution, revealing the dominant role of geometric and boundary conditions. The proposed framework demonstrates the feasibility of using graph-based methods as an intermediate approach between analytical and distributed parameter models, combining physical interpretability with numerical flexibility. The results contribute to the broader effort of developing predictive and controllable heat treatments.