A gradient model of cardiac pacemaker myocytes.

We have formulated a spatial-gradient model of action potential heterogeneity within the rabbit sinoatrial node (SAN), based on cell-specific ionic models of electrical activity from its central and peripheral regions. The ionic models are derived from a generic cell model, incorporating five background and exchange currents, and seven time-dependent currents based on three- or four-state Markov schemes. State transition rates are given by non-linear sigmoid functions of membrane potential. By appropriate selection of parameters, the generic model is able to accurately reproduce a wide range of action potential waveforms observed experimentally. Specifically, the model can fit recordings from central and peripheral regions of the SAN with RMS errors of 0.3987 and 0.7628 m V, respectively. Using a custom least squares parameter optimisation routine, we have constructed a spatially-varying gradient model that exhibits a smooth transition in action potential characteristics from the central to the peripheral region, whilst ensuring individual membrane currents remain physiologically accurate. Smooth transition action potential characteristics include maximum diastolic potential, overshoot potential, upstroke velocity, action potential duration and cycle length. The gradient model is suitable for developing higher dimensional models of the right atrium, in which action potential heterogeneity within nodal tissue may be readily incorporated.