Calcium and Arrhythmogenesis

Triggered activity in cardiac muscle and intracellular Ca2+ have been linked in the past. However, today not only are there a number of cellular proteins that show clear Ca2+ dependence but also there are a number of arrhythmias whose mechanism appears to be linked to Ca2+-dependent processes. Thus we present a systematic review of the mechanisms of Ca2+ transport (forward excitation-contraction coupling) in the ventricular cell as well as what is known for other cardiac cell types. Second, we review the molecular nature of the proteins that are involved in this process as well as the functional consequences of both normal and abnormal Ca2+ cycling (e.g., Ca2+ waves). Finally, we review what we understand to be the role of Ca2+ cycling in various forms of arrhythmias, that is, those associated with inherited mutations and those that are acquired and resulting from reentrant excitation and/or abnormal impulse generation (e.g., triggered activity). Further solving the nature of these intricate and dynamic interactions promises to be an important area of research for a better recognition and understanding of the nature of Ca2+ and arrhythmias. Our solutions will provide a more complete understanding of the molecular basis for the targeted control of cellular calcium in the treatment and prevention of such.

ONSET AND TERMINATION OF REENTRANT EXCITATION IN HOMOGENEOUS HUMAN VIRTUAL ATRIAL TISSUE

Multicellular models of homogeneous and isotropic human atria have been developed by incorporating cellular models of membrane electrical activity of single human atrial myocyte into a parabolic partial differential equation. These models are used to study the rate dependent conduction velocity of excitation wave, vulnerability of tissue to reentry and dynamical behaviors of reentry. Bidomain models were also developed to study the actions of a large and brief external electrical stimulus on wave propagation in human atria. These studies provide basic insights to understand the onset and termination of atrial arrhythmias in the human heart.

Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model

Heterogeneity of cardiac tissue is an important factor determining the initiation and dynamics of cardiac arrhythmias. In this paper, we studied the effects of gradients of electrophysiological heterogeneity on reentrant excitation patterns using computer simulations. We investigated the dynamics of spiral waves in a two-dimensional sheet of cardiac tissue described by the Luo-Rudy phase 1 (LR1) ventricular action potential model. A gradient of action potential duration (APD) was imposed by gradually varying the local current density of K+ current or inward rectifying K+ current along one axis of the tissue sheet. We show that a gradient of APD resulted in spiral wave drift. This drift consisted of two components. The longitudinal (along the gradient) component was always directed toward regions of longer spiral wave period. The transverse (perpendicular to the gradient) component had a direction dependent on the direction of rotation of the spiral wave. We estimated the velocity of the drift as a function of the magnitude of the gradient and discuss its implications.

Entrainment and Annihilation of Reentrant Excitation in a Periodically Stimulated Ring of Excitable Media

Excitable media, such as nerve, heart and the Belousov-Zhabo- tinsky reaction, exhibit a large excursion from equilibrium in response to a small but finite perturbation. Assuming a one-dimensional ring geometry of sufficient length, excitable media support a periodic wave of circulation. As in the periodic stimulation of oscillations in ordinary differential equations, the effects of periodic stimuli of the periodically circulating wave can be described by a one-dimensional Poincaré map. Depending on the period and intensity of the stimulus as well as its initial phase, either entrainment or termination of the original circulating wave is observed. These phenomena are directly related to clinical observations concerning periodic stimulation of a class of cardiac arrhythmias caused by reentrant wave propagation in the human heart.