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While it is widely believed that conduction in cardiac tissue is regulated by gap junctions, recent experimental evidence suggests that the extracellular space may play a significant role in action potential propagation. Cardiac tissue with low gap junctional coupling still exhibits conduction, with conflicting degrees of slowing that may be due to variations in the extracellular space. Inhomogeneities in the extracellular space caused by the complex cellular structure in cardiac tissue can lead to ephaptic, or field effect, coupling. Here, we present data from simulations of a cylindrical strand of cells in which we see the dramatic effect highly resistant extracellular spaces have on propagation velocity. We find that ephaptic effects occur in all areas of small extracellular spaces and are not restricted to the junctional cleft between cells. This previously unrecognized type of field coupling, which we call lateral coupling, can allow conduction in the absence of gap junctions. We compare our results with the classically used cable theory, demonstrating the quantitative difference in propagation velocity arising from the cellular geometry. Ephaptic effects are shown to be highly dependent upon parameter values, frequently enhancing, but sometimes decreasing propagation speed. Our mathematical analysis incorporates the inhomogeneities in the extracellular microdomains that cannot be directly measured by experimental techniques and will aid in optimizing cardiac treatments that require manipulation of the cellular geometry and understanding heart functionality.