| The characteristics of the cardiac propagating action potential (PAP) in one and two-dimensional tissue and the effects of spatial gradients in the coupling cellular resistance and cellular resting potential on propagation characteristics are studied.;Dynamic boundary conditions are developed for the one-dimensional case, that terminate the cable of cells without reflection, helping avoid possibly misleading propagation characteristics near the boundaries.;The propagation of the cardiac PAP is discontinuous due to lumping of the cell-to-cell resistance at the cell-to-cell junctions and the tortuosity of the pathway due to distribution of connective tissue between cells.;The impulse is more likely to be blocked when abrupt step-downs are encountered in resistance spatial gradient, due to impedance mismatch in both one and two-dimensional cases. Fractionated waveforms have isochrones with small radius of curvature in the longitudinal direction compared with the transverse direction. It is shown that in this case, propagation will fail first in the longitudinal direction. Thin walls of elevated resistance located in the border zone between ischemic and normal tissue, increase the likelihood for conduction and unidirectional block, due to the introduced asymmetries in the spatial distribution of resistance. Spatial gradients of cellular coupling resistance, was found to be more important in causing conduction block than the elevated resting potential.;The effects of barriers in plane wave propagation in two-dimensional sheet of tissue are studied. It was found that it is very difficult to produce conduction block in a two-dimensional medium, and that the plane wave recovers very fast after encountering a barrier, indicating that cardiac tissue is a very robust system. An example of unidirectional block in a two-dimensional structure is demonstrated. |
