The activity of the "Mathematical Methods in Medicine and Life Sciences Group" (M3LS) lies at the intersection between Mathematical Modelling and Numerical Simulation, seeking quantitative answers to practical problems arising in medicine, biology and physiology. The group aims at building bridges between Mathematics and other Life Science disciplines, providing medical doctors with innovative simulation tools to be efficiently used for in silico pathology assessment and in support of clinical decision making.
In silico models are today a regular support for the investigative activity of medical doctors and life scientists, alongside the in vivo and in vitro experiments. Medical doctors can benefit from effective and reliable non-invasive, patient-specific, instruments to improve diagnosis and prognosis. In return, mathematical and numerical models can provide rigorous tools for quantitative analyses with a diagnostic and prognostic content, and patient specific simulations are made possible by integrating such models with data and medical images. Still, problems from biomedical research are extremely complex and challenging from the modeling viewpoint. On the one hand, they are typically characterised by remarkable heterogeneities and multi-scale dynamics, both in space and time. On the other hand, they are imbued with uncertainty, whose primary sources may result from input variability (aleatory/irreducible uncertainty), such as the anatomical definition, the tissue characteristics and unknown boundary conditions, or from a lack of knowledge (epistemic/reducible uncertainty), such as the modeling assumption, or the influence of yet unknown physical phenomena. A reliable predictive mathematical model should be able to soundly cope with all these aspects. In this perspective, the main activities of the group encompass the following topics:
- Numerical approximation of PDE
- Uncertainty quantification
- Multiscale modeling
- Fractional diffusion
- Endocardiac radiofrequency ablation
- Infectious diseases and ecology