No abstract

We compare and contrast the excitation properties of cardiac myocytes and cardiac tissue modeled by (a) a Hodgkin-Huxley-model (HHM) and (b) Markov-chain-model (MM) formalisms for the sodium (Na) ion channel. Specifically, we bring out the differences between HHM and MM formalisms, for both wild-type (WT) and mutant (MUT) models, for ion-channel kinetics, single-myocyte action potentials, and the spatiotemporal evolutions of spiral and scroll waves in different mathematical models of cardiac tissue. We show that the kinetic properties of Na ion channels are not the same for HHM and MM models; in particular, the range of values of the trans-membrane potential V m , in which there is a significant window current, depends significantly on these models, so there are marked differences in the opening times of the Na ion channels, the maximal amplitude of the Na current, and the presence or absence of a late Na current. Furthermore, these changes lead to different excitation behaviors in cardiac tissue; specifically, two of the WT models show stable spiral waves, but the other one shows meandering and transiently breaking spiral waves. Our results are based on extensive direct numerical simulations of waves of electrical activation in these models, in two-and three-dimensional (2D and 3D) homogeneous simulation domains and also in domains with localized heterogeneities, either obstacles with randomly distributed inexcitable regions or mutant cells in a wild-type background. Our study brings out the sensitive dependence of spiral-and scroll-wave dynamics on these five models and the parameters that define them. We list desiderata for a good model for the Na wild-type ion channel; we use these desired properties to select one of the MM models that we study.

Spiral waves are ubiquitous spatiotemporal patterns that occur in various excitable systems. In cardiac tissue, the formation of these spiral waves is associated with life-threatening arrhythmias, and, therefore, it is important to study the dynamics of these waves. Tracking the trajectory of a spiral-wave tip can reveal important dynamical features of a spiral wave, such as its periodicity, and its vulnerability to instabilities. We show how to employ the data-driven spectral-decomposition method, called dynamic mode decomposition (DMD), to detect a spiral tip trajectory (TT) in three settings: (1) a homogeneous medium; (2) a heterogeneous medium; and (3) with external noise. We demonstrate that the performance of DMD-based TT (DMDTT) is either comparable to or better than the conventional tip-tracking method, called the isopotential-intersection method (IIM), in the cases ( 1)-( 3): (1) Both IIM and DMDTT capture TT patterns at small values of the imagesampling interval τ ; however, IIM is more sensitive than DMDTT to the changes in τ . (2) In a heterogeneous medium, IIM yields TT patterns, but with a background of scattered noisy points, which are suppressed in DMDTT. (3) DMDTT is more robust to external noise than IIM. We show, finally, that DMD can be used to reconstruct, and hence predict, the spatiotemporal evolution of spiral waves in the models we study.

Spiral waves of excitation in cardiac tissue are associated with life-threatening cardiac arrhythmias. It is, therefore, important to study the electrophysiological factors that affect the dynamics of these spiral waves. By using an electrophysiologically detailed mathematical model of a myocyte (cardiac cell), we study the effects of cellular parameters, such as membrane-ion-channel conductances, on the properties of the action-potential (AP) of a myocyte. We then investigate how changes in these properties, specifically the upstroke velocity and the AP duration (APD), affect the frequency ω of a spiral wave in the mathematical model that we use for human-ventricular tissue. We find that an increase (decrease) in this upstroke-velocity or a decrease (increase) in the AP duration increases (decreases) ω. We also study how other intercellular factors, such as the fibroblast-myocyte coupling, diffusive coupling strength, and the effective number of neighboring myocytes, modulate ω. Finally, we demonstrate how a spiral wave can drift to a region with a high density of fibroblasts. Our results provide a natural explanation for the anchoring of spiral waves in highly fibrotic regions in fibrotic hearts.

Spiral waves of excitation in cardiac tissue are associated with life-threatening cardiac arrhythmias. It is, therefore, important to study the electrophysiological factors that affect the dynamics of these spiral waves. By using an electrophysiologically detailed mathematical model of a myocyte (cardiac cell), we study the effects of cellular parameters, such as membrane-ion-channel conductances, on the properties of the action-potential (AP) of a myocyte. We then investigate how changes in these properties, specifically the upstroke velocity and the AP duration (APD), affect the frequency ω of a spiral wave in the mathematical model that we use for human-ventricular tissue. We find that an increase (decrease) in this upstroke-velocity or a decrease (increase) in the AP duration increases (decreases) ω. We also study how other intercellular factors, such as the fibroblast-myocyte coupling, diffusive coupling strength, and the effective number of neighboring myocytes and fibroblasts, modulate ω. Finally, we demonstrate how a spiral wave can drift to a region with a high density of fibroblasts. Our results provide a natural explanation for the anchoring of spiral waves in highly fibrotic regions in fibrotic hearts.