A three-dimensional adaptive strategy for the finite element simulation of phase change problems is presented, discussed and validated. A semi-phase-field formulation is used for the solution of the Stefan problem. The adaptive method is based on the definition of edge length using a solution dependent metric and produces strongly anisotropic meshes. Numerical results illustrating the performance and accuracy of the proposed method are presented.
In this work, a time-dependent remeshing strategy and a numerical method are presented for the simulation of the action potential propagation of the human heart. The main purpose of these simulations is to accurately predict the depolarization-repolarization front position, which is essential to the understanding of the electrical activity in the myocardium. A bidomain model, which is commonly used for studying electrophysiological waves in the cardiac tissue, will be employed for the numerical simulations. Numerical results are enhanced by the introduction of an anisotropic remeshing strategy. The illustration of the performance and the accuracy of the proposed method are presented using a 2-D analytical solution and a test case with re-entrant waves.
Cardiac alternans is a heart rhythm instability that is associated with cardiac arrhythmias and may lead to sudden cardiac death. The onset of this instability, which is linked to period-doubling bifurcation and may be a route to chaos, is of particular interest. Mechano-electric feedback depicts the effects of tissue deformation on cardiac excitation. The main effect of mechano-electric feedback is delivered via the so-called stretch-activated ion channels and is caused by stretch-activated currents. Mechano-electric feedback, which is believed to have proarrhythmic and antiarrhythmic effects on cardiac electrophysiology, affects the action potential duration in a manner dependent on cycle length, but the mechanisms by which this occurs remain to be elucidated. In this study, a biophysically detailed electromechanical model of cardiac tissue is employed to show how a stretch-activated current can affect the action potential duration at cellular and tissue levels, illustrating its effects on the onset of alternans. Also, using a two-dimensional iterated map that incorporates stretch-activated current effects, we apply linear stability analysis to study the stability of the bifurcation. We show that alternans bifurcation can be prevented depending on the strength of the stretch-activated current.
A persistent alternation in the cardiac action potential duration has been linked to the onset of ventricular arrhythmia, which may lead to sudden cardiac death. A coupling between these cardiac alternans and the intracellular calcium dynamics has also been identified in previous studies. In this paper, the system of PDEs describing the small amplitude of alternans and the alternation of peak intracellular Ca(2+) are stabilized by optimal boundary and spatially distributed actuation. A simulation study demonstrating the successful annihilation of both alternans on a one-dimensional cable of cardiac cells by utilizing the full-state feedback controller is presented. Complimentary to these studies, a three variable Nash-Panfilov model is used to investigate alternans annihilation via mechanical (or stretch) perturbations. The coupled model includes the active stress which defines the mechanical properties of the tissue and is utilized in the feedback algorithm as an independent input from the pacing based controller realization in alternans annihilation. Simulation studies of both control methods demonstrate that the proposed methods can successfully annihilate alternans in cables that are significantly longer than 1 cm, thus overcoming the limitations of earlier control efforts.
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