The heart undergoes some highly complex multi-scale multi-physics phenomena that must be accounted for in order to adequately model the biomechanical behavior of the complete organ. In this respect, a major focus of our work has been on formulating modeling ingredients that satisfy the most crucial thermomechanical requirements - in particular as regards energy balances - throughout the various forms of physical and scale-related couplings. This has led to a "beating heart" model for which some experimental and clinical validations have already been obtained. Concurrently, with the objective of building "patient-specific" heart models, we have investigated some original approaches inspired from data assimilation concepts to benefit from the available clinical data, with a particular concern for medical imaging. By combining the two fundamental sources of information represented by the model and the data, we are able to extract some most valuable quantitative knowledge on a given heart, e.g. as regards some uncertain constitutive parameter values characterizing a possible pathology, with important perspectives in diagnosis assistance. In addition, once the overall uncertainty has been adequately controlled via this adjustment process, the model can be expected to become "predictive", hence should provide clinically-relevant quantitative information, both in the current state of the patient and under various scenarii of future evolutions, such as for therapy planning.[-]

Emergence is a process by which coherent structures arise through interactions among elementary entities without being directly encoded in these interactions. In this course, we will address some of the key questions of emergence such as the deciphering of the hidden relation between individual behavior and emergent structures. We will start with presenting biologically relevant examples of microscopic individual-based models (IBM). Then, we will develop a systematic coarse-graining approach and derive corresponding coarse-grained models (CGM) using mathematical kinetic theory as the key methodology. We will highlight that novel kinetic theory concepts need to be developed as new mathematical problems arise with emergent systems such as the lack of conservations, the build-up of correlations, or the presence of phase transitions (or bifurcations). Our goal is to show how kinetic theory can be used to provide better understanding of emergence phenomena taking place in a wide variety of biological contexts.[-]