Transmural differences in action potential shape and duration (APD) have been identified in ventricular muscle (Antzelevitch et al. 2001), and these differences may be important in both the initiation and the evolution of re-entrant arrhythmias. The aim of this study was to use a simplified computational model of electrical activity in the ventricular wall to investigate the relative effects of electrotonic current flow and differences in cellular properties on transmural APD differences during the propagation of a normal beat.

Our simulated ventricular wall had cellular electrophysiology described by the Luo-Rudy phase 1 equations, with parameters modified as in Qu et al. (2000). The dimensions approximated a wedge from the canine LV free wall with dimensions of 4 X 4 X 10 mm, and fibre rotation of 120 deg between endocardial and epicardial surfaces. Anisotropic conduction was produced by a diffusion tensor with components of 0.002 cm² ms^-1 parallel to fibres and 0.0005 cm² ms^-1 perpendicular to fibres, and these values gave plane wave conduction velocities of 0.81 ms^-1 and 0.36 ms^-1 respectively. Numerical solutions used an adaptive time step of between 10 and 100 µs, and a space step of 200 µm, with no-flux boundary conditions at each surface.

We simulated propagation of four normal beats by endocardial activation with a cycle length of 500 ms in each of two models. In the first model, the maximal K⁺ conductance was set to 0.3 mS cm^-2 throughout. In single cells paced at a cycle length of 500 ms this value gives an APD of 163 ms. In the second model we imposed a linear change in maximal K⁺ conductance from 0.2 mS cm^-2 at the endocardium (single cell APD of 189 ms), to 0.4 mS cm^-2 at the epicardium (single cell APD of 144 ms).

For the first model with uniform maximal K⁺ conductance, APD varied with transmural distance from 168 ms on the endocardial surface to 150 ms on the epicardial surface. The ratio (epi/endo) of these values is 0.89, which compares with a value of 0.83 reported from experimental studies (Antzelevitch, et al. 2001). For the second model with non-uniform maximal K⁺ conductance slab, APD varied from 175 ms on the endocardial surface to 143 ms on the epicardial surface, giving the ratio 0.81. We suggest that during normal transmural propagation of the action potential, electrotonic current flow prolongs repolarisation of endocardial layers and shortens repolarisation of epicardial layers. Transmural differences in APD can potentially arise from electrotonic effects as well as differences in the expression of ion channels.

This work has been funded by British Heart Foundation Basic Science Lectureship BS 98001 awarded to R.C.