The increased availability of experimental data on the mechanics of cells and tissues has stimulated the emergence of the field of mechanobiology, in which mathematics and mechanics are combined to enhance our understanding of biological materials and of the processes involved in physiological activities. The development of mathematical models for such complex systems is challenging, but the possible outcomes in terms of our capability to diagnose and treat pathological conditions provide a strong motivation for pursuing this research direction.
The present project focuses on continuum mechanical models and on a careful analysis of their mathematical properties, with particular emphasis on the description of activation processes. These are important for the control of any physiological activity, as they bring to life what would otherwise be a passive aggregate of heterogeneous substances. Among the many active elements of the human body, we restrict attention to skeletal muscles and neuronal cells, as they feature a rich phenomenology.
The planned research includes both applied and theoretical aspects. On the practical side, its outcomes can open new possibilities in the context of digital twins for personalized medicine. On the mathematical side, a new class of models can stimulate studies of broad interest in continuum mechanics and analysis.