Reduced Order Modeling for Cardiac Electrophysiology and Mechanics: New Methodologies, Challenges and Perspectives

Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning

“…Despite several works have exploited POD‐Galerkin ROMs for the simulation of the cardiac function, 50‐54 for the sake of computational efficiency here we consider a generalization of the usual POD approach, requiring the construction of local RB spaces , as proposed in Reference 47. In this respect, clustering algorithms, such as the k‐means algorithm, are employed, prior to performing POD, to partition snapshots (of both the solution to the parametrized coupled monodomain‐ionic model (1), and the nonlinear terms) into N c clusters, for a chosen number N c ≥ 1; then, a local reduced basis is built for each cluster through POD 55 …”

Coupling reduced-order blood flow and cardiac models through energy-consistent strategies: modeling and discretization

“…The energy balance (5) shows that the energy defined in (3) is a decreasing function of time if there is no blood flow imposed at the inlet and the outlet. But of course, System (1) should be completed with more realistic boundary conditions, typically relating the input flux (output flux, respectively) or the pressure described in (6) at the inlet (outlet, respectively) with the flux or pressure in other systems.…”

“…The importance of reduced-order (RO) models in clinical applications has been extensively assessed in the last years. In particular, RO models are nowadays very widespread in the scientific literature [1][2][3][4][5] concerning cardiovascular applications for patient-specific model predictions. Lumped-parameter zero-dimensional (0D) models-typically Windkessel models [6][7][8]-can provide a general view on the global response, e.g.…”

8 Reduced-order modeling for applications to the cardiovascular system

“…To reduce the computational complexity of the FOM in all these contexts, reducedorder models (ROMs) such as the reduced basis (RB) method for parameterized PDEs represent efficient techniques for the approximation of the parameterized PDE solution. Although several works have focused on problems related to both hemodynamics [5,6,43] and the simulation of cardiac function [12,11,21,27,41,47], applying stateof-the-art ROMs is not straightforward for cardiac problems because of (i) nonlinear behavior (like sharp moving fronts in the case of cardiac electrophysiology) and (ii) parameterization of complex geometries. For these reasons, suitable strategies must be devised to build low-dimensional RB spaces able to capture the manifold of the problem solutions when varying the parameters, by keeping the cost of the ROM construction sufficiently low.…”