The generalized activating function

Abstract

Insight into the biophysical processes associated with electrical stimulation of the heart is important for the understanding of electrical pacing and defibrillation. When electrodes are physically placed on the myocardium, not only do they induce polarization changes in the cell membrane in regions in proximity to the electrodes, but they also induce polarization changes remote to the electrodes. How applied electrical currents are transduced into changes in cellular transmembrane potentials has been called the missing link,1 and many mechanisms have been proposed, including the so-called sawtooth pattern arising from discontinuities in fiber conductivity,2 dog-bone pattern arising from the anisotropic bido-main properties of cardiac tissue,3 surface polarization,4 fiber curvature, 4 fiber rotation,5 and heterogeneities in intracellular volume fraction6 (also see reviews7-9 that describe the similarities among nerve, brain, and cardiac stimulation). More recently, studies of cardiac cell cultures grown in user-designed patterns10 have permitted detailed investigations of electric field-induced responses of linear strands,11 intercellular cleft spaces,12 fiber branches, expansions and bends,.13 and curved fibers.14 The concept of the activating function was proposed by Rattay15 for electrical excitation of unmyelinated nerve axons (based on earlier ground-breaking work by McNeal16 on myeli-nated axons), where a nerve fiber is stimulated by an externally applied electric field. The electric field generates a gradient of electrical potential in space, which is impressed upon the outer surface of the axon. Depending on the distribution of potential, an electromotive force can arise across the surface membrane that causes the flow of membrane current, which in turn perturbs the transmembrane potential. The details of this process are most easily understood for the case of a one-dimensional fiber lying in a three-dimensional volume conductor, as described in the next section. The definition of the activating function will then be generalized for cardiac tissue, followed by examination of the generalized activating function for a number of examples. © 2009 Springer US.