Six Conductivity Values to Use in the Bidomain Model of Cardiac Tissue

Goal: The aim of this work is to produce a consistent set of six conductivity values for use in the bidomain model of cardiac tissue. Methods: Studies in 2007 by Hooks et al. and in 2009 by Caldwell et al. have found that, in the directions longitudinal:transverse:normal (l:t:n) to the cardiac fibers, ratios of bulk conductivities and conduction velocities are each approximately in the ratio 4:2:1. These results are used here as the basis for a method that can find sets of six normalized bidomain conductivity values. Results: It is found that the ratios involving transverse and normal conductivities are quite consistent, allowing new light to be shed on conductivity in the normal direction. For example, it is found that the ratio of transverse to normal conductivity is much greater in the intracellular (i) than the extracellular (e) domain. Using parameter values from experimental studies leads to the proposal of a new nominal six conductivity dataset: $g_{il}=2.4, g_{el}=2.4, g_{it}=0.35, g_{et}=2.0, g_{{in}}=0.08$, and $g_{en}=1.1$ (all in mS/cm). Conclusion: When it is used to model partial thickness ischaemia, this dataset produces epicardial potential distributions in accord with experimental studies in an animal model. It is, therefore, suggested that the dataset is suitable for use in numerical simulations. Significance: Since the bidomain approach is the most commonly used method for modeling cardiac electrophysiological phenomena, new information about conductivity in the normal direction, as well as a consistent set of six conductivity values, is valuable for researchers who perform simulation studies.