Periodic Reporting for period 3 - iHEART (An Integrated Heart Model for the simulation of the cardiac function) Periodo di rendicontazione: 2020-12-01 al 2022-05-31 Sintesi del contesto e degli obiettivi generali del progetto The project aims at developing a fully integrated and rigorous mathematical model for the cardiac function. Mathematical and numerical modeling, as well as numerical simulations, represent the distinguishing features of the project, wherein several core components - electrophysiology, active and passive mechanics, fluid and valve dynamics, blood circulation - must be integrated in a unique coupled model. This is necessary to enhance the understanding of the human cardiac function, the main engine behind a healthy life of human beings. The integrated model so built represents the base for assisting and supporting clinicians in medical decisions and therapy planning in relation with the numerous pathologies that may affect the human heart. The latter have indeed a significant social and economic impact: it is estimated that around 45% of deaths in Europe are related to cardiac dysfunctions. For these reasons, the project also aims at exploiting mathematical modeling and numerical simulations for addressing a wide plethora of cardiac pathologies. Lavoro eseguito dall’inizio del progetto fino alla fine del periodo coperto dalla relazione e principali risultati finora ottenuti Core cardiac models and their integration have been extensively carried out in this part of the project. Electrophysiology models have been mostly developed in literature for the ventricles, while these are relatively less explored for the atria; in this respect, we studied and developed models for the electrophysiology of the atria modeled as surfaces (due to their thin structure), both in physiological and pathological conditions. Active and passive mechanics models for the contraction of the heart, mainly for the ventricles, have been significantly enhanced to better account for the orthotropic nature of the tissue, mainly due to collagen fibers; as the latter play a major role in the tissue, their characterization has been extensively studied. New active force generation models have been proposed to balance the extreme complexity of cellular models with the computational efficiency of phenomenological models; in this respect, our main contribution has been the definition of reduced active force models meant to be exploited in cardiac electromechanical simulations. Specifically considering the numerical coupling of the electrophysiology and mechanics models, we studied and proposed different monolithic and partitioned schemes for the cardiac integration. For the former, we developed ad hoc preconditioners for the solution of the algebraic problem obtained after full discretization; for partitioned schemes, we instead analyzed the efficiency of the procedure, other than comparing accuracy and computational efficiency of staggered schemes. Still for the numerical solution of the electromechanical model, we developed intergrid transfer operators for solving the electrophysiology and mechanics problems on different computational meshes for the Finite Element method to efficiently capture the multiscale nature of the problem. Poroelastic and perfusion models have been developed and numerically investigated to account for the supply of oxygen and nutrients to the tissue from the coronaries. In order to account for variability and uncertainty in electrophysiology and mechanics models, reduced order models and uncertainty quantification techniques have been exploited and developed; in particular, machine learning algorithms have been integrated in the framework of reduced order modeling to provide reliable and rapid evaluations of cardiac quantities of interest by changing physically meaningful parameters for cardiac electrophysiology. Aiming at personalized treatment, we dealt with patient-specific geometries provided by our clinical partners. With this aim, we established and developed (semi-automatic) computational pipelines for the numerical simulation starting from image acquisition, geometry segmentation, and meshing procedures of the computational domain. We started addressing a wide array of pathological conditions for the human heart in collaboration with several clinical partners. Among these, we tackled and numerically studied the most common and diffuse electric dysfunctions, like ischemia, ventricular tachycardia, and atrial fibrillation, other than highlighting their implications on the overall cardiac function in terms of mechanics and fluid dynamics behavior. Valve pathologies have been studied as well, mainly regarding the aortic and mitral valves. For the latter, our efforts were directed both on the understanding of the effects of the pathology, other than studying possible scenarios post-surgical intervention. Progressi oltre lo stato dell’arte e potenziale impatto previsto (incluso l’impatto socioeconomico e le implicazioni sociali più ampie del progetto fino ad ora) The research carried out within the project so far shows significant enhancements with respect to the state-of-the-art. The most remarkable one is the mathematical rigor that distinguishes all the advancements made in the development of core cardiac models, other than for their numerical integration. The work done in the first reporting period paves the way for a unique form of integration of core cardiac models towards the development of a fully coupled model for the whole cardiac function. Several outstanding clinical collaborations pushed mathematical modeling well towards clinical exploitation and the opportunity of effectively tackling cardiac pathological conditions with significant social and economic impacts. This is definitely beyond the state-of-the-art of current research in Mathematics. The major result expected by the end of the project will be the development of a mathematically rigorous and fully integrated model for the human heart function that is able to account for all the core cardiac components. Software libraries will be delivered to the general public for the accurate and efficient solution of such cardiac model. We also expect to deliver "game changer" computational pipelines for the systematic treatment of several cardiac diseases and establish their clinical exploitation.