The transient far-field response of a discontinuous one-dimensional cardiac fiber to subthreshold stimuli

It is hypothesized that the discontinuous structure of cardiac tissue is at least partly responsible for the ability of extracellular field stimuli to affect those regions of cardiac tissue very far from the stimulating electrodes. Yet, the details of this "far-field" interaction are still poorly understood. This paper derives analytical closed-form equations that describe the far-field spatial and temporal behaviors of the axial currents and transmembrane voltages along a discontinuous cardiac fiber in response to any applied subthreshold stimulus. Moreover, these derivations incorporate the influences of both junctional resistance and postulated junctional capacitance on such responses. Thus, as compared with previously-derived techniques, these equations extend and simplify the generation and analysis of such far-field responses. Frequency analysis of this system demonstrates that the fiber generally behaves as a low-pass filter, with the location of its corner frequency highly dependent on the magnitudes of both junctional resistance and especially junctional capacitance. Increasing either junctional resistance or capacitance significantly and monotonically decreases the value of the corner frequency--equivalently manifest as a large increase in the duration of the transient response to a step input stimulus. Such changes to these initial excitation dynamics might prove relevant during the far-field stimulation of cardiac tissue, such as during defibrillation-type shocks.