Variability in the voltage threshold of excitable tissue has been evaluated analytically and numerically in one-dimensional fibers as compared to membrane patches. A threshold increase is seen to occur in fibers as compared to membrane patches, i.e., a larger stimulus must be used to produce an action potential. The larger stimulus is needed to compensate for the fact that current flows away from the depolarized region following the stimulus. This paper extends the 1D analysis to provide a mathematical structure for evaluating stimulation of two-dimensional sheets of tissue. The 2D geometry is useful because it is much more similar to that of structures such as the cardiac atria. The analysis shows that an additional flow-away term is present, suggesting that even higher stimulus magnitudes will be needed in 2D as compared to 1D.
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