Mathematical and numerical tumour development modelling for personalised treatment planning

This paper presents a mathematical and numerical framework for modelling and parametrising tumour evolution dynamics to enhance computer-aided diagnosis and personalised treatment. The model comprises six differential equations describing cancer cell and blood vessel concentrations, tissue stiffness, Ki- 67 marker distribution, and the apparent velocity of marker propagation. These equations are coupled through S-functions with adjustable coefficients. An inverse problem approach calibrates the model by fitting adjustable coefficients to patient-specific clinical data, thereby enabling disease progression and treatment response simulations. By integrating historical and prospective patient data supported by machine learning algorithms, this framework holds promise as a robust decision-support tool for optimising therapeutic strategies.