Tissue Electrical Response

The global electrical analysis assumes a monodomain response:

where the flux term, $q$, characterizes the propagating nature of the electrical waves:

The term, $D$, is a second-order diffusion tensor, which can account for anisotropic diffusion.

The source term, $f^{\varphi }$, characterizes the local action potential profile:

The local biochemical portion of the analysis is modeled through a temporal evolution of the recovery variable, $r$:

The source term, $f^r$, characterizes the slow features of the action potential:

where with parameters as defined in the table below.

Table 1. Constitutive Parameters for the Electrical Response

Parameters	Description
$c$	Scaling parameter for the source term, $f^{\varphi }$
$\alpha$	Oscillation threshold (positive values characterize stable nonpacemaker cells, negative values characterize oscillatory pacemaker cells)
$\gamma$	Refractoriness that governs the time it takes the tissue to repolarize (that is, the time to get back to the resting potential)
$b$	A phenomenological scaling parameter
${\mu }_1,{\mu }_2$	Scaling factors that control the shape of the restitution curve

The electrical properties are calibrated to provide physiologically observed activation times; see Conduction System Tutorial. The bundle of His and Purkinje fibers are assigned conduction parameters that generate the physically observed wave propagation pattern within the heart in which the electrical signal first travels down the ventricular septum to the apex and then up the ventricular side walls.