This project has the ambition to set up a mathematical research platform for the simulation of the heart function. The aim is to deliver a variety of mathematical tools that can successfully fulfill the requests made by clinical specialists on classes of pathological cardiac dysfunctions. For that we will develop physics-based numerical models that are accurate, computationally efficient, and suitable to treat the intra-patients variability.
From a mathematical perspective, this project addresses new and tremendously challenging problems that are concerned with physical models involving interactions of multiple scales in space and time, as well as the corresponding numerical treatment of coupled systems of nonlinear time-dependent partial differential equations (PDEs). We are committed to use mathematical models that are appropriate to describe the heart function, by coupling electro-mechanics and fluid dynamics processes, especially in those pathological situations that provide a continuous inspiration for our research. A central endeavor will consist in the realization of high-order numerical methods that make the approximate solution of the afore-mentioned mathematical models computationally feasible, efficient, numerically accurate, and scalable on parallel HPC architectures.
Although this mathematical platform can be potentially exploited in a broad variety of situations and applications in science and industry, we will nonetheless stay focused on the cardiac context. The aim is to provide our clinical partners with reliable results to enhance physiological understanding of heart function, support medical decisions, and improve therapeutic treatments. In particular, we will address two pathological scenarios, with high morbidity in the population, which are related to the processes of electric wave propagation and cardiac perfusion: a) the dysfunctional wave propagation originated by electrical anomalies in the atrial and ventricular conduction systems, i.e cardiac arrhythmias such as tachycardia and fibrillation; b) the effect of ischemia, a reduction of blood supply to the myocardial tissues, in terms of blood perfusion downstream the coronaries and cardiac output such as the ejection fraction (the quantity of blood ejected from the left ventricle).
These pathologies are still relatively little understood because of their intrinsic complexity. It is our belief that a sound mathematical investigation, supported by extensive information supplied by the computational results, may unveil emergent patterns and unexpected correlations that are key for the cardiac patho-physiology. In particular our landmark contributions will be:
1) The development of biophysically detailed membrane and excitation-contraction models for the electro-mechanical activity of cardiac myocytes and their integration in macroscopic 3D models for healthy and pathological cardiac tissue;
2) The construction of models that are suitable to simulate the heart perfusion based on the geometric multiscale description of the vascular tree;
3) The development of high-order numerical methods in space (spectral elements, isogeometric analysis, hp-fem) and time (splitting techniques and implicit-explicit schemes) for cardiac PDE models;
4) The development of scalable domain decomposition preconditioners (like BDDC and Parareal), which will enable the efficient solution of cardiac PDE models defined in complex subject-specific geometries;
5) The quantification of uncertainty (UQ) for the solution of forward and inverse problems due to uncertain coefficients and data. Forward UQ problems aim at exploring the impact of intra-patients variability on outcomes of clinical interest; inverse UQ problems are instead related with parameters estimation and model calibration based on patients;
6) The set-up of statistical learning inspired algorithms that allow the exploration of large databases related to geometrical, biological and functional data characterizing e