Mathematics of Cancer and Cardiovascular Dynamics: From High-Fidelity Simulation to Data-Driven Methods
 Organizer(s):
Name:
Affiliation:
Country:
Nikolaos Sfakianakis
University of St Andrews
Scotland
Zuzanna Szymańska
University of Warsaw
Poland
Niklas Kolbe
RWTH Aachen
Germany
 Introduction:  
  This Special Session will focus on advancing mathematical and computational approaches to complex biomedical phenomena, with particular emphasis on cancer growth, metastasis, and cardiovascular dynamics. These processes span across several scales and are governed by nonlinear PDEs over intricate, heterogeneous domains, including vascular networks and realistic organ geometries. Such challenges require the interplay of mathematical modelling, numerical analysis, and data-driven methods. We shall invite contributions from Applied Mathematics, Computational Sciences, and Biomedical Engineering to address: - Multiscale and Nonlinear phenomena, e.g. tumor invasion and multi-organ blood-flow, requiring high-order discretisation schemes, e.g. numerical solvers for interface-rich problems with strong coupling across scales and Discontinuous Galerkin (dG) methods. - Complex organ-level-geometries, derived from Medical Imaging, that require advanced remeshing and simulation strategies, including Adaptive Mesh Refinement (AMR). - Parameter uncertainty, arising from measurement and patient variability, motivating Machine Learning (ML)-based data assimilation, and Biology/Physics-Informed Neural Networks (B/PINNs) for model calibration, surrogate modelling, and uncertainty quantification. - Inter-organ dynamics, particularly in metastasis, where modelling of tumour-vascular interactions and organ-to-organ transport involves coupling macroscopic PDEs with experimental data and probabilistic transition models. - Error control and computational efficiency, through a-posteriori error-estimation and AMR, with analytical approaches and modern heuristics to guide computational effort.