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The I-V curve for repolarization, (fr) with only two parameters, is similar to the time-independent potassium current (IK1), which dominates during rapid repolarization (phase 3) that contains 10 or more parameters in traditional [http://www.selleckchem.com/products/byl719.html Alpelisib mw] ionic models. Theoretical analysis of the cable equation over the past 50 years has improved our understanding of wave propagation. This work provides significant insight into the relationship of the nonlinear I-V curve and propagation characteristics such as CV and the wavefront shape. CV and the exact shape of the propagating upstroke are interrelated and depend on the complex interdependence of axial and transmembrane current pathways as shown in Fig.?S1. One advantage of theoretical studies is that analytical descriptions relating CV and wavefront shape to I-V can be formulated in certain situations. One of the restrictions for analytical predictions is that the shape of the wavefront (hence Im) is symmetric ( 29?and?30). Our results suggest that theoretical work on how wavefront asymmetry affects wave propagation is of paramount importance in cardiac electrophysiology. Although cubic and quintic functions for fd can be used to determine CV analytically ( 29), we found that these functions did not represent the data as well as our empirically derived Eq. 6. Although, to our knowledge, our novel model represents the complete action potential [http://en.wikipedia.org/wiki/Mannose-binding_protein-associated_serine_protease Mannose-binding protein-associated serine protease] shape during propagation, threshold, the membrane resistance at rest, and during the plateau, it does not contain any gating variables and thus will not exhibit action potential duration or CV restitution. Adding one or more gating variables could rectify this limitation and still maintain analytical tractability similar to the Fitzhugh [http://www.selleckchem.com/products/MG132.html MG-132 research buy] approach ( 31). Consistent with similar previous studies (5, 8, 9, 11?and?32), all the results in this study are based on the assumption of stable propagation in which the spread of electrical activity through the three-dimensional heart is effectively reduced to a 1-D problem by assuming no dependencies in the directions perpendicular to the direction of propagation. This assumption is accurate (and bidomain is equivalent to the monodomain) as long as propagation is planar and either parallel or perpendicular to the fiber direction (33). Our data in Fig.?S7 show that both Im and Ic are the same whether they are computed from Vi or Vm, supporting our assumption of planar propagation. We neglected transmural effects, but we estimated this contribution to be