A nondimensional formulation of the passive bidomain equation

Simulation studies of ST depression arising from subendocardial ischemia show a marked difference in the resulting epicardial potential distributions depending on which of the 3 common experimentally determined bidomain conductivity data sets is chosen. Here, the governing equation is rendered nondimensional by dividing by the difference in normal and ischemic transmembrane potentials during the ST segment and by the sum of the intracellular and extracellular conductivities in the transverse direction, yielding the ratio of the sum of the intracellular and extracellular longitudinal conductivities divided by the sum of the intracellular and extracellular transverse conductivities as a dimensionless group. Averaging this ratio over the 3 sets of experimentally determined data gives the value of 3.21 ± 0.08. The effect of this narrow range means that the left-hand side of the governing equation can be considered, as a good approximation, to be the same for all these sets of conductivity data. Hence, the right hand of the nondimensional differential equation contains all the necessary information to compare the effect different conductivity data sets have on the epicardial potential distribution. As an example, an explanation is given as to why values from one data set give rise to epicardial distributions that are markedly different from those obtained from the other 2 data sets.