Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node

Abstract

Mathematical models of the action potential in the periphery and center of the rabbit sinoatrial (SA) node have been developed on the basis of published experimental data. Simulated action potentials are consistent with those recorded experimentally: the model-generated peripheral action potential has a more negative takeoff potential, faster upstroke, more positive peak value, prominent phase 1 repolarization, greater amplitude, shorter duration, and more negative maximum diastolic potential than the model-generated central action potential. In addition, the model peripheral cell shows faster pacemaking. The models behave qualitatively the same as tissue from the periphery and center of the SA node in response to block of tetrodotoxin-sensitive Na(+) current, L- and T-type Ca(2+) currents, 4-aminopyridine-sensitive transient outward current, rapid and slow delayed rectifying K(+) currents, and hyperpolarization-activated current. A one-dimensional model of a string of SA node tissue, incorporating regional heterogeneity, coupled to a string of atrial tissue has been constructed to simulate the behavior of the intact SA node. In the one-dimensional model, the spontaneous action potential initiated in the center propagates to the periphery at approximately 0.06 m/s and then into the atrial muscle at 0.62 m/s.

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

“…Several mathematical models of the SAN action potential (AP) have been developed for mammalian species, including human (Chandler et al 2009), rabbit (Noble and Noble 1984, Demir et al 1994, Dokos et al 1996, Zhang et al 2000, Boyett et al 2001, Kurata et al 2002 and guinea pig . Comparing the dynamical behaviour of various SAN cell models, in particular the functional role of each individual ionic current in generating pacemaking APs, it can be seen that these models show consistency in some respects, but diversity in others.…”

“…As a consequence, the functional role of each individual current in these models may be different. Even in the most recently developed models-such as those by Zhang et al (2000) and Kurata et al (2002) discussed below-although the functional role of some major ionic currents is qualitatively similar, significant quantitative differences remain, as shown by differences in the sensitivities of the two models to model parameters (Kharche et al 2009). …”

“…Zhang et al (2000) developed a family of SAN cell models that successfully reproduce the differences in the electrical properties of 'central' and 'peripheral' SAN cells. Recent advances in experimental electrophysiology have determined the electrical heterogeneity across the SAN and the surrounding atrium-cells in the SAN present pronounced regional differences in their electrical APs and associated properties of ion channels .…”

“…1994, Dokos at al. 1996, Zhang et al 2000, Kurata et al (2002) developed an improved model for a primary SAN pacemaking cell. This model presented new formulations for the voltage-and calcium-dependent inactivation kinetics of I CaL and intracellular calcium regulation and buffering.…”

“…This model presented new formulations for the voltage-and calcium-dependent inactivation kinetics of I CaL and intracellular calcium regulation and buffering. Later on, this Kurata et al model was modified to account for the heterogeneous properties of the SAN (Kurata et al 2008), following the approach of the Zhang et al (2000) model. Obviously, model development for the electrical AP of SAN cells has been an evolutionary process, which, like the previously described development of ventricular cell models, closely follows experimental progress.…”