Finite element and finite volume-element simulation of pseudo-ECGs and cardiac alternans

Abstract

In this paper, we are interested in the spatio-temporal dynamics of the transmembrane potential in paced isotropic and anisotropic cardiac tissues. In particular, we observe a specific precursor of cardiac arrhythmias that is the presence of alternans in the action potential duration. The underlying mathematical model consists of a reaction-diffusion system describing the propagation of the electric potential and the nonlinear interaction with ionic gating variables. Either conforming piecewise continuous finite elements or a finite volume-element scheme are employed for the spatial discretization of all fields, whereas operator splitting strategies of first and second order are used for the time integration. We also describe an efficient mechanism to compute pseudo-ECG signals, and we analyze restitution curves and alternans patterns for physiological and pathological cardiac rhythms.

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

“…In this regard we first list some of the straightforward extensions to the model compartments we have been already studied in previous contributions [185,216,219]. Some specific aspects of modelling cardiac function that have not been covered include the fast conduction system (Purkinje network [264] and Purkinje-muscle junctions), cardiac perfusion [46] and its coupling with coronary flow [66,169], autoregulation aspects of heart rate [139], myocardial tissue damage and remodelling [101], the modelling of the atria [47,64,252], the heart-torso coupling that is needed for the simulation of an ECG [33,55,75], fluid dynamics in idealized ventricles [194,248,249], and many others. As discussed in Sect.…”

“…[82,83]). Again, note that the benchmark test does not considers rotational anisotropy, which according to [85], is key in obtaining reasonable accuracy in all directions of propagation (see also [75]). …”

Simulating the effect of sodium channel blockage on cardiac electromechanics

“…the QT interval), to assess ventricular activation and repolarization over the cardiac cycle. 51 Figure 3 superimposes the corresponding pseudo-ECGs predicted for a Na + channel blocker which exhibits clear prolongation to its QRS complex, explained by a decreased rate of depolarization. Even though such blockage does not affect repolarization, the T-wave experiences a shift forward as a result of delayed activation.…”

Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator–prey model

“…This method is a hybrid concept between finite elements and finite volume discretizations that features some desirable properties including the ability to deal with unstructured meshes on arbitrarily shaped domains, the conservativity of inter-element fluxes, and the feasibility of error estimates in L 2 and H 1 norms. FVE methods have historically been applied for flow equations [11,12,34,46] and recently also for several applicative time-dependent convection-diffusion problems [8,9,17,18,35,45]. Other numerical methods for similar problems include finite differences [20,53,59], finite volume methods [1,5,51], and finite elements [4,21,60].…”