Atrial and ventricular fibrillation: computational simulation of spiral waves in cardiac tissue

Abstract

This manuscript proposes a novel, efficient finite element solution technique for the computational simulation of cardiac electrophysiology. We apply a two-parameter model that is characterized through a fast action potential and a slow recovery variable. The former is introduced globally as a nodal degree of freedom, whereas the latter is treated locally as internal variable on the integration point level. This particular discretization is extremely efficient and highly modular since different cardiac cell models can be incorporated straightforwardly through only minor local modifications on the integration point level. In this manuscript, we illustrate the algorithm in terms of the Aliev-Panfilov model for cardiomyocytes. To ensure unconditional stability, a backward Euler scheme is applied to discretize the evolution equation for both the action potential and the recovery variable in time. To increase robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme and illustrate the consistent linearization of the weak form of the excitation problem. The proposed algorithm is illustrated by means of two-and three-dimensional examples of re-entrant spiral and scroll waves characteristic of cardiac arrhythmias in atrial and ventricular fibrillation.

A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis

“…Along the lines of a true multiscale approach, the response along the fiber direction can then be calibrated by means of experimentally measured length-tension relations. Moreover, we are in the process of including electrically activated contraction for the individual cardiomyocytes to explore the long-term impact of alterations in active and passive stress on cardiac growth Kuhl, 2009, 2010;Göktepe et al, 2010d;Kotikanyadanam et al). For more realistic simulations, it would also be essential to begin the simulation with a loaded state at growth equilibrium and include effects of residual stress (Omens et al, 1998;Rodriguez et al, 1994).…”

Electromechanics of the heart: a unified approach to the strongly coupled excitation–contraction problem

“…Note that apart from the primary field variables, as we briefly introduced in the preceding subsection, the recovery variable r appears among the arguments ofF φ e in (9). It describes the repolarization response of the action potential.…”

“…The values of the material parameters are selected to be the same as in Table 4 except that G s = 0 such that mechano-electric feedback effect is suppressed. To generate a scroll wave, we follow the conventional procedure suggested in [8,9]. To this end, we initiate a planar depolarization front in x-direction by assigning elevated initial values to the nodal action potentials Φ 0 = −40 mV on the plane located at x = 0 mm.…”

“…In our recent work on computational cardiac electrophysiology [8], we proposed a new, algorithmically efficient, fully implicit finite element approach based on the global-local split of the fast and slow variables. We have successfully applied this method to three-dimensional fibrillation simulations [9] and to patient-specific calculation of electrocardiograms [17]. The formulation proposed in this paper extends this approach to the fully coupled electromechanics of the heart where both the excitation-induced contraction of myocytes and the deformation-activated ion channels play an important role.…”

Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology

“…In the case where ionic variables are defined as internal variables, stored directly at the quadrature points, as in [6, 7, 20], then the evaluation of eqn. (15a) is unambiguous.…”