The effect of spatial scale of resistive inhomogeneity on defibrillation of cardiac tissue

Abstract

Defibrillation of cardiac tissue can be viewed in the context of dynamical systems theory as the attempt to move a dynamical system from the basin of attraction of one attractor (fibrillation) to another (the uniform rest state) by applying a stimulus whose form is physically constrained. Here we give an introduction to the physical mechanism of cardiac defibrillation from this dynamical perspective and examine the role of resistive inhomogeneity on defibrillation efficacy. Using numerical simulations with rotating waves on a one-dimensional periodic ring, we study the role of the spatial scale of resistive inhomogeneity on defibrillation.For a rotating wave on a periodic ring there are three stable attractors, namely the uniform rest state, a wave traveling clockwise and a wave traveling counterclockwise. As a result, the application of a stimulus has the potential for three different outcomes, namely elimination of the wave, phase resetting of the wave, and reversal of the wave.The results presented here show that with resistive inhomogeneities of large spatial scale, all three of these transitions are possible with large amplitude shocks, so that the probability of defibrillation is bounded well below one, independent of stimulus amplitude. On the other hand, resistive inhomogeneities of small spatial scale produce a defibrillation threshold that is qualitatively consistent with that found experimentally, namely the probability of defibrillation success is an increasing function that approaches one for large enough stimulus amplitude.Extending these results to higher dimensions, we describe conditions for successful defibrillation of functional reentry with large scale spatial inhomogeneity, but find that elimination of anatomical reentry is quite difficult. With small spatial scale inhomogeneity, there are no similar restrictions. Acknowledgment: This research was supported in part by NSF Grant DMS-99700876 and DMS-0211366. We acknowledge N. Trayanova for clarifying several misconceptions we had concerning her work, and S. Folias for valuable discussions and numerical simulations.

The topology of defibrillation

“…We conclude from this that large scale virtual electrodes do not adequately explain the mechanism of defibrillation, but that some other mechanism must account for the success. The mechanism we favor remains the small scale hypothesis, however, further discussion of this hypothesis must be relegated to other publications (for example, (Keener and Cytrynbaum 2003)). …”

“…The answer that we have favored is small scale spatial inhomogeneities, and this hypothesis has been explored in several previous papers (Fishler 1998;Fishler and Vepa 1998;Keener 1996;Keener 1998;Keener and Cytrynbaum 2003;Keener and Lewis 1999;Keener and Panfilov 1996;Krinsky and Pumir 1998). Because the largest contribution to small scale inhomogeneities was thought to be gap junctional resistance, and because gap junctional resistance should lead to "sawtooth" profiles of transmembrane potential, this hypothesis is sometimes referred to as the sawtooth hypothesis (Krassowska et al 1987;Krassowska et al 1990).…”

Alternans amplification following a two-stimulus protocol in a one-dimensional cardiac ionic model of reentry: From annihilation to double-wave quasiperiodic reentry

“…The simplified representation used herein can be an acceptable approximation for low amplitude stimuli or to mimic the effect spontaneous firing of a group of cells. However it is known that current spread of the stimulus depend on the properties of the external and internal medium [40,41]. The MBR representation of the ionic properties is also oversimplified.…”

How the Spatial Frequency of Polarization Influences the Induction of Reentry in Cardiac Tissue

“…4). At short intervals (30–60 msec), hyperpolarization deexcites a region of the S1 wave front, rather than the wave back, which the wave front then reinvades, resulting in reentry (not shown) 17 …”