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.

We consider the asymptotic theory for the dynamics of organizing filaments of three-dimensional scroll waves. For a generic autowave medium where two dimensional vortices do not meander, we show that some of the coefficients of the evolution equation are always zero. This simpler evolution equation predicts a monotonic change of the total filament length with time, independently of initial conditions. Whether the filament will shrink or expand is determined by a single coefficient, the filament tension, that depends on the medium parameters. We illustrate the behaviour of scroll wave filaments with positive and negative tension by numerical experiments. In particular, we show that in the case of negative filament tension, the straight filament is unstable, and its evolution may lead to a multiplication of vortices.

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The possible effects of intracellular Ca 2+ on the pacemaker of the heart, the sinoatrial node, are reviewed. In mammalian sinoatrial node, reduction or abolition of the intracellular Ca 2+ transient by ryanodine, sarcoplasmic reticulum Ca 2+ pump block or 1,2-bis(2-aminophenoxy)ethane-N,N,N ,N -tetraacetic acid (BAPTA) reduces the spontaneous rate by 21-32%, whereas in amphibian sinus venosus it abolishes spontaneous activity. In rabbit sinoatrial node, ryanodine/BAPTA reduces the T-type Ca 2+ current (i Ca,T ), perhaps slows inactivation of the L-type Ca 2+ current (i Ca,L ), reduces the inward Na + -Ca 2+ exchange current (i NaCa ), and reduces the rapid and slow delayed rectifier K + currents (i K,r and i K,s , respectively). Other evidence shows that a reduction of intracellular Ca 2+ inhibits the hyperpolarization-activated current (i f ). These putative intracellular Ca 2+ -dependent changes in ionic currents have been incorporated into different models of rabbit sinoatrial node action potentials. In the models, block of the Ca 2+ transient reduced the spontaneous rate by 24 and 26% in the central and peripheral models of Zhang and others, 13% in the Oxsoft model (Noble et al .), 9% in the model of Wilders and others, and 41% in the model of Demir and others. In all models, the reduction in rate was not primarily the result of the decrease in i NaCa , but instead the combination of all changes in ionic currents.

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