Propagation Versus Delayed Activation During Field Stimulation of Cardiac Muscle

Optimizing defibrillation waveforms for ICDs

While no simple electrical descriptor provides a good measure of defibrillation efficacy, the waveform parameters that most directly influence defibrillation are voltage and duration. Voltage is a critical parameter for defibrillation because its spatial derivative defines the electrical field that interacts with the heart. Similarly, waveform duration is a critical parameter because the shock interacts with the heart for the duration of the waveform. Shock energy is the most often cited metric of shock strength and an ICD's capacity to defibrillate, but it is not a direct measure of shock effectiveness. Despite the physiological complexities of defibrillation, a simple approach in which the heart is modeled as passive resistor-capacitor (RC) network has proved useful for predicting efficient defibrillation waveforms. The model makes two assumptions: (1) The goal of both a monophasic shock and the first phase of a biphasic shock is to maximize the voltage change in the membrane at the end of the shock for a given stored energy. (2) The goal of the second phase of a biphasic shock is to discharge the membrane back to the zero potential, removing the charge deposited by the first phase. This model predicts that the optimal waveform rises in an exponential upward curve, but such an ascending waveform is difficult to generate efficiently. ICDs use electronically efficient capacitive-discharge waveforms, which require truncation for effective defibrillation. Even with optimal truncation, capacitive-discharge waveforms require more voltage and energy to achieve the same membrane voltage than do square waves and ascending waveforms. In ICDs, the value of the shock output capacitance is a key intermediary in establishing the relationship between stored energy-the key determinant of ICD size-and waveform voltage as a function of time, the key determinant of defibrillation efficacy. The RC model predicts that, for capacitive-discharge waveforms, stored energy is minimized when the ICD's system time constant taus equals the cell membrane time constant taum, where taus is the product of the output capacitance and the resistance of the defibrillation pathway. Since the goal of phase two is to reverse the membrane charging effect of phase one, there is no advantage to additional waveform phases. The voltages and capacitances used in commercial ICDs vary widely, resulting in substantial disparities in waveform parameters. The development of present biphasic waveforms in the 1990s resulted in marked improvements in defibrillation efficacy. It is unlikely that substantial improvement in defibrillation efficacy will be achieved without radical changes in waveform design.

Spatiotemporal effects of syncytial heterogeneities on cardiac far-field excitations during monophasic and biphasic shocks

INTRODUCTION

It has recently been postulated that syncytial (anatomic) heterogeneities inherent within cardiac tissue might represent a significant mechanism underlying field-induced polarization of the bulk myocardium. This simulation study examines and characterizes the spatiotemporal excitatory dynamics associated with this newly hypothesized mechanism.

METHODS AND RESULTS

Two-dimensional regions of syncytially heterogeneous cardiac tissue were simulated with active membrane kinetics. Heterogeneities were manifested via random spatial variations of intracellular volume fractions over multiple length scales. Excitation thresholds were determined for uniform rectangular monophasic (M) and symmetric biphasic (B) far-field stimuli, from which strength-duration and strength-interval relationships were constructed. For regions measuring 5.4 x 5.4 mm, baseline diastolic thresholds for longitudinal (L) and transverse (T) shocks of 5-msec total duration averaged (in V/cm, n = 10) M-L = 2.87+/-0.26, M-T = 6.71+/-0.83, B-L = 3.22+/-0.25, and B-T = 7.93+/-0.51. These thresholds decreased by 15% to 25% when the region sizes were increased to 10.8 x 10.8 mm. Strength-duration relationships correlated strongly with the Weiss-Lapicque hyperbolic relationship, with rheobases and chronaxies of 2.33 V/cm and 1.15 msec for M-L stimuli, and 2.28 V/cm and 2.04 msec for B-L stimuli. Strength-interval relationships for M-L and B-L stimuli decreased monotonically with increasing coupling intervals, with similar minimum coupling intervals at absolute refractoriness. However, the B-L thresholds were substantially less sensitive to changes in coupling intervals than their M-L counterparts.

CONCLUSION

This study provides strong additional support for and understanding of the syncytial heterogeneity hypothesis and its manifested properties. Furthermore, these results predict that syncytial heterogeneities of even modest proportions could represent a significant mechanism contributing to the far-field excitation process.

Progressive depolarization: a unified hypothesis for defibrillation and fibrillation induction by shocks

Experimental studies of defibrillation have burgeoned since the introduction of the upper limit of vulnerability (ULV) hypothesis for defibrillation. Much of this progress is due to the valuable work carried out in pursuit of this hypothesis. The ULV hypothesis presented a unified electrophysiologic scheme for linking the processes of defibrillation and shock-induced fibrillation. In addition to its scientific ramifications, this work also raised the possibility of simpler and safer means for clinical defibrillation threshold testing. Recent results from an optical mapping study of defibrillation suggest, however, that the experimental data supporting the ULV hypothesis could instead be interpreted in a manner consistent with traditional views of defibrillation such as the critical mass hypothesis. This review will describe the evidence calling for such a reinterpretation. In one regard the ULV hypothesis superseded the critical mass hypothesis by linking the defibrillation and shock-induced fibrillation processes. Therefore, this review also will discuss the rationale for developing a new defibrillation hypothesis. This new hypothesis, progressive depolarization, uses traditional defibrillation concepts to cover the same ground as the ULV hypothesis in mechanistically unifying defibrillation and shock-induced fibrillation. It does so in a manner consistent with experimental data supporting the ULV hypothesis but which also takes advantage of what has been learned from optical studies of defibrillation. This review will briefly describe how this new hypothesis relates to other contemporary viewpoints and related experimental results.

Mechanisms of cardiac cell excitation with premature monophasic and biphasic field stimuli: a model study

The mechanisms by which extracellular electric field stimuli induce the (re)excitation of cardiac cells in various stages of refractoriness are still not well understood. We modeled the interactions between an isolated cardiac cell and imposed extracellular electric fields to determine the mechanisms by which relatively low-strength uniform monophasic and biphasic field stimuli induce premature reexcitations. An idealized ventricular cell was simulated with 11 subcellular membrane patches, each of which obeyed Luo-Rudy (phase 1) kinetics. Implementing a standard S1-S2 pulse protocol, strength-interval maps of the cellular excitatory responses were generated for rectangular monophasic and symmetric biphasic field stimuli of 2, 5, 10, and 20 ms total duration. In contrast to previously documented current injection studies, our results demonstrate that a cardiac cell exhibits a significantly nonmonotonic excitatory response to premature monophasic and, to a much lesser degree, biphasic field stimuli. Furthermore, for monophasic stimuli at low field strengths, the cell is exquisitely sensitive to the timing of the shock, demonstrating a classic all-or-none depolarizing response. However, at higher field strengths this all-or-none sensitivity reverts to a more gradual transition of excitatory responses with respect to stimulus prematurity. In contrast, biphasic stimuli produce such graded responses at all suprathreshold stimulus strengths. Similar behaviors are demonstrated at all S2 stimulus durations tested. The generation of depolarizing (sodium) currents is triggered by one or more of the sharp field gradient changes produced at the stimulus edges-i.e., make, break, and transphasic (for biphasic stimuli)-with the magnitude of these edge-induced current contributions dependent on both the prematurity and the strength of the applied field. In all cases, however, depolarizing current arises from the partial removal of sodium inactivation from at least part of the cell, because of either the natural process of repolarization or a localized acceleration of this process by the impressed field.

Spatial distribution of cardiac transmembrane potentials around an extracellular electrode: dependence on fiber orientation

Recent theoretical models of cardiac electrical stimulation or defibrillation predict a complex spatial pattern of transmembrane potential (Vm) around a stimulating electrode, resulting from the formation of virtual electrodes of reversed polarity. The pattern of membrane polarization has been attributed to the anisotropic structure of the tissue. To verify such model predictions experimentally, an optical technique using a fluorescent voltage-sensitive dye was used to map the spatial distribution of Vm around a 150-microns-radius extracellular unipolar electrode. An S1-S2 stimulation protocol was used, and vm was measured during an S2 pulse having an intensity equal to 10x the cathodal diastolic threshold of excitation. The recordings were obtained on the endocardial surface of bullfrog atrium in directions parallel and perpendicular to the cardiac fibers. In the longitudinal fiber direction, the membrane depolarized for cathodal pulses (and hyperpolarized for anodal pulses) but only in a region within 445 +/- 112 microns (and 616 +/- 78 microns for anodal pulses) from the center of the electrode (n = 9). Outside this region, vm reversed polarity and reached a local maximum at 922 +/- 136 microns (and 988 +/- 117 microns for anodal pulses) (n = 9). Beyond this point vm decayed to zero over a distance of 1.5-2 mm. In the transverse fiber direction, the membrane depolarized for cathodal pulses (and hyperpolarized for anodal pulses) at all distances from the electrode. The amplitude of the response decreased with distance from the electrode with an exponential decay constant of 343 +/- 110 microns for cathodal pulses and 253 +/- 91 microns for anodal pulses (n = 7). The results were qualitatively similar in both fiber directions when the atrium was bathed in a solution containing ionic channel blockers. A two-dimensional computer model was formulated for the case of highly anisotropic cardiac tissue and qualitatively accounts for nearly all the observed spatial and temporal behavior of vm in the two fiber directions. The relationships between vm and both the "activating function" and extracellular potential gradient are discussed.

A minimal model of the single capacitor biphasic defibrillation waveform

A quantitative model of the single capacitor biphasic defibrillation waveform is proposed. The primary hypothesis of this model is that the first phase leaves a residual charge on the membranes of the unsynchronized cells, which can then reinitiate fibrillation. The second phase diminishes this charge, reducing the potential for refibrillation. To suppress this potential refibrillation, a monophasic shock must be strong enough to synchronize a critical mass of nearly 100% of the myocytes. Since the biphasic waveform performs this protection function by removing the residual charge (with its second phase), its first phase may be of a lower strength than a monophasic shock of equivalent performance. A quantitative model was developed to calculate the residual membrane voltage, Vm, assuming a capacitive membrane being alternately charged and discharged by the first and second phases, respectively. It was further assumed that the amplitude of the first phase would be predicted by a minimum value plus a term proportional to Vm2. The model was evaluated on the pooled data of three relevant published studies comparing biphasic waveforms. The model explained 79% of the variance in the first phase amplitude and predicted optimal durations for various defibrillator capacitances and electrode resistances. Assuming a first phase of optimal duration, the optimal second phase duration appears to be about 2.5 msec for all capacitances and resistances now seen clinically.

CONCLUSION

The effectiveness of the single capacitor biphasic waveform may be explained by the second phase "burping" of the deleterious residual charge of the first phase that, in turn, reduces the synchronization requirement and the amplitude requirements of the first phase.

Virtual electrode effects in myocardial fibers

The changes in transmembrane potential during a stimulation pulse in the heart are not known. We have used transmembrane potential sensitive dye fluorescence to measure changes in transmembrane potential along fibers in an anisotropic arterially perfused rabbit epicardial layer. Cathodal or anodal extracellular point stimulation produced changes in transmembrane potential within 60 microns of the electrode that were positive or negative, respectively. The changes in transmembrane potential did not simply decrease to zero with increasing distance, as would occur with a theoretical fiber space constant, but instead became reversed beyond approximately 1 mm from the electrode consistent with a virtual electrode effect. Even stimulation from a line of terminals perpendicular to the fibers produced negative changes in transmembrane potential for cathodal stimulation with the largest negative changes during a 50-ms pulse at 3-4 mm from the electrode terminals. Negative changes as large as the amplitude of the action potential rising phase occurred during a 50-ms pulse for 20-volt cathodal stimulation. Switching to anodal stimulation reversed the directions of changes in transmembrane potential at most recording spots, however for stimulation during the refractory period negative changes in transmembrane potential were significantly larger than positive changes in transmembrane potential. Anodal stimulation during diastole with 3-ms pulses produced excitation in the region of depolarization that accelerated when the stimulation strength was increased to > 3 times the anodal threshold strength. Thus, virtual electrode effects of unipolar stimulation occur in myocardial fibers, and for sufficiently strong stimuli the virtual electrode effects may influence electrical behavior of the myocardium.