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

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.     

The Gurvich waveform has lower defibrillation threshold than the rectilinear waveform and the truncated exponential waveform in the rabbit heart

Implantable cardioverter defibrillator studies have established the superiority of biphasic waveforms over monophasic waveforms. However, external defibrillator studies of biphasic waveforms are not as widespread. Our objective was to compare the defibrillation efficacy of clinically used biphasic waveforms, i.e., truncated exponential, rectilinear, and quasi-sinusoidal (Gurvich) waveforms in a fibrillating heart model. Langendorff-perfused rabbit hearts (n = 10) were stained with a voltage-sensitive fluorescent dye, Di-4-ANEPPS. Transmembrane action potentials were optically mapped from the anterior epicardium. We found that the Gurvich waveform was significantly superior (p < 0.05) to the rectilinear and truncated exponential waveforms. The defibrillation thresholds (mean +/- SE) were as follows: Gurvich, 0.25 +/- 0.01 J; rectilinear-1, 0.34 +/- 0.01 J; rectilinear-2, 0.33 +/- 0.01 J; and truncated exponential, 0.32 +/- 0.02 J. Using optically recorded transmembrane responses, we determined the shock-response transfer function, which allowed us to predict the cellular response to waveforms at high accuracy. The passive parallel resistor-capacitor model (RC-model) predicted polarization superiority of the Gurvich waveform in the myocardium with a membrane time constant (taum) of less than 2 ms. The finding of a lower defibrillation threshold with the Gurvich waveform in an in vitro model of external defibrillation suggests that the Gurvich waveform may be important for future external defibrillator designs.     

The Role of Pulse Shape in Motor Cortex Transcranial Magnetic Stimulation Using Full-Sine Stimuli

A full-sine (biphasic) pulse waveform is most commonly used for repetitive transcranial magnetic stimulation (TMS), but little is known about how variations in duration or amplitude of distinct pulse segments influence the effectiveness of a single TMS pulse to elicit a corticomotor response. Using a novel TMS device, we systematically varied the configuration of full-sine pulses to assess the impact of configuration changes on resting motor threshold (RMT) as measure of stimulation effectiveness with single-pulse TMS of the non-dominant motor hand area (M1). In young healthy volunteers, we (i) compared monophasic, half-sine, and full-sine pulses, (ii) applied two-segment pulses consisting of two identical half-sines, and (iii) manipulated amplitude, duration, and current direction of the first or second full-sine pulse half-segments. RMT was significantly higher using half-sine or monophasic pulses compared with full-sine. Pulses combining two half-sines of identical polarity and duration were also characterized by higher RMT than full-sine stimuli resulting. For full-sine stimuli, decreasing the amplitude of the half-segment inducing posterior-anterior oriented current in M1 resulted in considerably higher RMT, whereas varying the amplitude of the half-segment inducing anterior-posterior current had a smaller effect. These findings provide direct experimental evidence that the pulse segment inducing a posterior-anterior directed current in M1 contributes most to corticospinal pathway excitation. Preferential excitation of neuronal target cells in the posterior-anterior segment or targeting of different neuronal structures by the two half-segments can explain this result. Thus, our findings help understanding the mechanisms of neural stimulation by full-sine TMS.     

Mechanisms of superiority of ascending ramp waveforms: new insights into mechanisms of shock-induced vulnerability and defibrillation

Monophasic ascending ramp (AR) and descending ramp (DR) waveforms are known to have significantly different defibrillation thresholds. We hypothesized that this difference arises due to differences in mechanisms of arrhythmia induction for the two waveforms. Rabbit hearts (n = 10) were Langendorff perfused, and AR and DR waveforms (7, 20, and 40 ms) were randomly delivered from two line electrodes placed 10 mm apart on the anterior ventricular epicardium. We optically mapped cellular responses to shocks of various strengths (5, 10, and 20 V/cm) and coupling intervals (CIs; 120, 180, and 300 ms). Optical mapping revealed that maximum virtual electrode polarization (VEP) was reached at significantly different times for AR and DR of the same duration (P < 0.05) for all tested CIs. As a result, VEP for AR were stronger than for DR at the end of the shock. Postshock break excitation resulting from AR generated faster propagation and typically could not form reentry. In contrast, partially dissipated VEP resulting from DR generated slower propagation; the wavefront was able to propagate into deexcited tissue and thus formed a shock-induced reentry circuit. Therefore, for the same delivered energy, AR was less proarrhythmic compared with DR. An active bidomain model was used to confirm the electrophysiological results. The VEP hypothesis explains differences in vulnerability associated with monophasic AR and DR waveforms and, by extension, the superior defibrillation efficacy of the AR waveform compared with the DR waveform.     

The effect of lidocaine and bretylium on the defibrillation threshold during cardiac arrest and cardiopulmonary resuscitation

The effect of intravenous lidocaine, 2 mg/kg, and bretylium, 5 mg/kg, on defibrillation threshold (DFT) was investigated in alpha-chloralose anesthetized dogs undergoing conventional closed chest cardiopulmonary resuscitation (CPR) following induced ventricular fibrillation. Ventricular fibrillation was induced electrically and CPR was performed by a pneumatic device set to compress the chest 60 times and inflate the lung 12 times a minute. Defibrillation was achieved using underdamped sinusoidal current shocks from a special defibrillator which allowed determination of delivered energy. The DFT was defined as the peak current which defibrillated, but no more than 20% higher than a current which did not defibrillate. All DFTs were obtained within 5 min of CPR. The mean +/- SD current and energy thresholds required for defibrillation during lidocaine-CPR (seven dogs) were 17.0 +/- 8.9 A and 53.0 +/- 40.7 J as compared to 12.5 +/- 6.2 A and 34.3 +/- 30.7 J, respectively during control-CPR (P less than 0.05). The mean +/- SD current and energy thresholds during bretylium-CPR were 11.0 +/- 3.4 A and 24.1 +/- 1.3 J as compared to 11.8 +/- 1.7 A and 29.4 +/- 9.6 J, respectively, during control-CPR (NS). These results show that lidocaine acutely elevated defibrillation threshold whereas bretylium did not produce such an effect. The effect on DFT along with other pharmacologic properties should be considered when lidocaine or bretylium is used in the setting of cardiac arrest and CPR.     

Calcium channels and excitation-contraction coupling in cardiac cells. I. Two components of contraction in guinea-pig papillary muscle

Biphasic contractions have been obtained in guinea-pig papillary muscle by inducing partial depolarization in K+-rich solution (17 mM) containing 0.3 microM isoproterenol; whereas in guinea-pig atria, the same conditions led to monophasic contractions corresponding to the first component of contraction in papillary muscle. The relationships between the amplitude of the two components of the biphasic contraction and the resting membrane potential were sigmoidal curves. The first component of contraction was inactivated for membrane potentials less positive than those for the second component. In Na+-low solution (25 mM), biphasic contraction became monophasic subsequent to the loss of the second component, but tetraethylammonium unmasked the second component of contraction. The relationship between the amplitude of the first component of contraction and the logarithm of extracellular Ca2+ concentration was complex, whereas for the second component it was linear. When Ca2+ ions were replaced by Sr2+ ions, only the second component of contraction was observed. It is suggested that the first component of contraction may be triggered by a Ca2+ release from sarcoplasmic reticulum, induced by the fast inward Ca2+ current and (or) by the depolarization. The second component of contraction may be due to a direct activation of contractile proteins by Ca2+ entering the cell along with the slow inward Ca2+ current and diffusing through the sarcoplasm. These results do not exclude the existence of a third "tonic" component, which could possibly be mixed with the second component of contraction.     

A Novel Solution for the High Defibrillation Threshold in Patients with a DF-4 Lead: Adding a High Voltage Adaptor/Splitter

A high defibrillation threshold occurs in approximately 6% of implants. The defibrillation threshold can be improved by addition of a defibrillation lead. However, the DF-4 high energy ICD header precludes the addition of a defibrillation lead. Here we report on use of a new high voltage adaptor/splitter that enables the addition of an extra defibrillation lead.     

Success and failure of biphasic shocks: results of bidomain simulations.

The mechanisms behind the superiority of optimal biphasic defibrillation shocks over monophasic are not fully understood. This simulation study examines how the shock polarity and second-phase magnitude of biphasic shocks influence the virtual electrode polarization (VEP) pattern, and thus the outcome of the shock in a bidomain model representation of ventricular myocardium. A single spiral wave is initiated in a two-dimensional sheet of myocardium that measures 2 x 2 cm(2). The model incorporates non-uniform fiber curvature, membrane kinetics suitable for high strength shocks, and electroporation. Line electrodes deliver a spatially uniform extracellular field. The shocks are biphasic, each phase lasting 10 ms. Two different polarities of biphasic shocks are examined as the first-phase configuration is held constant and the second-phase magnitude is varied between 1 and 10 V/cm. The results show that for each polarity, varying the second-phase magnitude reverses the VEP induced by the first phase in an asymmetric fashion. Further, the size of the post-shock excitable gap is dependent upon the second-phase magnitude and is a factor in determining the success or failure of the shock. The maximum size of a post-shock excitable gap that results in defibrillation success depends on the polarity of the shock, indicating that the refractoriness of the tissue surrounding the gap also contributes to the outcome of the shock.     

Theory of the acoustic instability and behavior of the phase velocity of acoustic waves in a weakly ionized plasma

The amplification of acoustic waves due to the transfer of thermal energy from electrons to the neutral component of a glow discharge plasma is studied theoretically. It is shown that, in order for acoustic instability (sound amplification) to occur, the amount of energy transferred should exceed the threshold energy, which depends on the plasma parameters and the acoustic wave frequency. The energy balance equation for an electron gas in the positive column of a glow discharge is analyzed for conditions typical of experiments in which acoustic wave amplification has been observed. Based on this analysis, one can affirm that, first, the energy transferred to neutral gas in elastic electron-atom collisions is substantially lower than the threshold energy for acoustic wave amplification and, second, that the energy transferred from electrons to neutral gas in inelastic collisions is much higher than that transferred in elastic collisions and thus may exceed the threshold energy. It is also shown that, for amplification to occur, there should exist some heat dissipation mechanism more efficient than gas heat conduction. It is suggested that this may be convective radial mixing within a positive column due to acoustic streaming in the field of an acoustic wave. The features of the phase velocity of sound waves in the presence of acoustic instability are investigated.     

Resonance interaction of electrons with a slow transverse wave in a weakly inhomogeneous plasma

Excitation of a circularly polarized slow wave by external sources and its subsequent propagation in a weakly inhomogeneous plasma with a positive density gradient are described in terms of the adiabatic approach. It is shown that the wave dispersion is mainly determined by the ratio between the contributions of trapped and nonresonant untrapped electrons to the total wave current. The relationship between the wave amplitude and its phase velocity and the limiting phase velocity above which the wave is strongly damped are found using the energy balance equation and the dispersion relation.     

Electroreceptor model of weakly electric fish Gnathonemus petersii: II. Cellular origin of inverse waveform tuning.

In part I (. Biophys. J. 75:1712-1726), we presented a cellular model of the A- and B-electroreceptors of the weakly electric fish Gnathonemus petersii. The model made clear the cellular origin of the differences in the response functions of A- and B-receptors, which sensitively code the intensity of the fish's own electric organ discharge (EOD) and the variations in the EOD waveform, respectively. The main purpose of the present paper is to clarify the cellular origin of the inverse waveform tuning of the B-receptors by using the receptor model. Inverse waveform tuning means that B-receptors respond more sensitively to the 180 degrees inverted EOD than to undistorted or less distorted EODs. We investigated how the A- and B-receptor models respond to EODs with various waveforms, which are the phase-shifted EODs, whose shift angle is varied from -1 degrees to -180 degrees, and single-period sine wave stimuli of various frequencies. We show that the tuning properties of the B-receptors arise mainly from the combination of two attributes: 1) The waveform of the stimuli (Bstim) effectively sensed by the B-receptor cells. This consists of a first smaller and a second larger positive peak, even though in the original phase-shifted EOD stimuli, the amplitudes of the two positive peaks are reversed. 2) The effective time constant of dynamical response of the receptor cells. It is on the order of the duration of a single EOD pulse. We also calculated the response properties of the A- and B-receptor models when stimulated with natural EODs distorted by various capacitive and resistive objects. Furthermore, we investigated the effect of EOD amplitude on the receptor responses to capacitive and resistive objects. The models presented can systematically reproduce the experimentally observed response properties of natural A- and B-receptor cells. The mechanism producing these properties can be reasonably explained by the variation in the stimulus waveforms effectively sensed by the A- and B-receptor cells and by time constants.     

Phase resetting curves and oscillatory stability in interneurons of rat somatosensory cortex

Synchronous oscillations in neural activity are found over wide areas of the cortex. Specific populations of interneurons are believed to play a significant role in generating these synchronized oscillations through mutual synaptic and gap-junctional interactions. Little is known, though, about the mechanism of how oscillations are maintained stably by particular types of interneurons and by their local networks. To obtain more insight into this, we measured membrane-potential responses to small current-pulse perturbations during regular firing, to construct phase resetting curves (PRCs) for three types of interneurons: nonpyramidal regular-spiking (NPRS), low-threshold spiking (LTS), and fast-spiking (FS) cells. Within each cell type, both monophasic and biphasic PRCs were observed, but the proportions and sensitivities to perturbation amplitude were clearly correlated to cell type. We then analyzed the experimentally measured PRCs to predict oscillation stability, or firing reliability, of cells for a complex stochastic input, as occurs in vivo. To do this, we used a method from random dynamical system theory to estimate Lyapunov exponents of the simplified phase model on the circle. The results indicated that LTS and NPRS cells have greater oscillatory stability (are more reliably entrained) in small noisy inputs than FS cells, which is consistent with their distinct types of threshold dynamics.     

Dynamics of turtle horizontal cell response

The small- and large-field (cone) horizontal cells produce similar dynamic responses to a stimulus whose mean luminance is modulated by a white-noise signal. Nonlinear components increase with an increase in the mean luminance and may produce a mean square error (MSE) of up to 15%. Increases in the mean luminance of the field stimulus bring about three major changes: the incremental sensitivity defined by the amplitude of the kernels decreases in a Weber-Fechner fashion; the waveforms of the kernels are transformed from monophasic (integrating) to biphasic (differentiating); the peak response time of the kernels becomes shorter and the cells respond to much higher-frequency inputs. The dynamics of the horizontal cell response also depend on the area of the retina stimulated. Smaller spots of light produce monophasic kernels of a longer peak response time. The presence of a steady background produces three major changes in the spot kernels: the kernel's amplitude becomes larger (incremental sensitivity increases); the peak response times become shorter; the waveform of the kernels changes in a fashion similar to that observed with an increase in the mean luminance of the field stimulus. A similar enhancement in the incremental sensitivity by a steady background has also been observed in catfish, which shows that this phenomenon is a common feature of the horizontal cells in the lower vertebrate retina.     

Opposing actions of 5HT1A and 5HT2-like serotonin receptors on modulations of the electric signal waveform in the electric fish Brachyhypopomus pinnicaudatus

Serotonin (5-HT) is an indirect modulator of the electric organ discharge (EOD) in the weakly electric gymnotiform fish, Brachyhypopomus pinnicaudatus. Injections of 5-HT enhance EOD waveform "masculinity", increasing both waveform amplitude and the duration of the second phase. This study investigated the pharmacological identity of 5-HT receptors that regulate the electric waveform and their effects on EOD amplitude and duration. We present evidence that two sets of serotonin receptors modulate the EOD in opposite directions. We found that the 5HT1AR agonist 8-OH-DPAT diminishes EOD duration and amplitude while the 5HT1AR antagonist WAY100635 increases these parameters. In contrast, the 5HT2R agonist alpha-Me-5-HT increases EOD amplitude but not duration, yet 5-HT-induced increases in EOD duration can be inhibited by blocking 5HT2A/2C-like receptors with ketanserin. These results show that 5-HT exerts bi-directional control of EOD modulations in B. pinnicaudatus via action at receptors similar to mammalian 5HT1A and 5HT2 receptors. The discordant amplitude and duration response suggests separate mechanisms for modulating these waveform parameters.     

Optimal parameters for electrical auricular defibrillation

In acute experiments on dogs the chest was opened and auricular flutter and fibrillation were induced. Current, energy and charge thresholds which eliminated this arrhythmia by the monopolar direct impulse of 1--15 ms duration were determined. The current and energy values that evoked the auricular defibrillation during direct application of the electrodes to them were minimal when the impulses of 8 ms were used: 113 +/- 13.7 mA and 10.4 +/- 2.6 mWs in elimination of the flutter, and 275 +/- 18.2 mA and 62.3 +/- +/- 9.0 mWsec in elimination of the fibrillation. The current that restored the nomotopic rhythm during direct auricular defibrillation was 50 times less than that determined during the transthoracic auricular defibrillation in dogs. The efficacy of direct auricular defibrillation indicated the necessity of the elaboration of an adequate method for its application in clinical practice.     

Paradoxical loss of excitation with high intensity pulses during electric field stimulation of single cardiac cells

Transmembrane potential responses of single cardiac cells stimulated at rest were studied with uniform rectangular field pulses having durations of 0.5-10 ms. Cells were enzymatically isolated from guinea pig ventricles, stained with voltage sensitive dye di-8-ANEPPS, and stimulated along their long axes. Fluorescence signals were recorded with spatial resolution of 17 microm for up to 11 sites along the cell. With 5 and 10 ms pulses, all cells (n = 10) fired an action potential over a broad range of field amplitudes (approximately 3-65 V/cm). With 0.5 and 1 ms pulses, all cells (n = 7) fired an action potential for field amplitudes ranging from the threshold value (approximately 4-8 V/cm) to 50-60 V/cm. However, when the field amplitude was further increased, five of seven cells failed to fire an action potential. We postulated that this paradoxical loss of excitation for higher amplitude field pulses is the result of nonuniform polarization of the cell membrane under conditions of electric field stimulation, and a counterbalancing interplay between sodium current and inwardly rectifying potassium current with increasing field strength. This hypothesis was verified using computer simulations of a field-stimulated guinea pig ventricular cell. In conclusion, we show that for stimulation with short-duration pulses, cells can be excited for fields ranging between a low amplitude excitation threshold and a high amplitude threshold above which the excitation is suppressed. These results can have implications for the mechanistic understanding of defibrillation outcome, especially in the setting of diseased myocardium.     

Effect of a strong monochromatic electromagnetic wave with circular polarization on one-dimensional wake waves in plasma

A study is made of the excitation of wake waves by a one-dimensional bunch of charged particles in an electron plasma in the presence of an intense monochromatic pump wave with circular polarization. In the main state (in the absence of a bunch), the interaction between a pump wave and a plasma is described by the Maxwell equations and the nonlinear relativistic hydrodynamic equations for a cold plasma. The excitation of linear waves by a one-dimensional bunch is investigated against a cold plasma background. It is shown that, in a certain range of the parameter values of the bunch, pump wave, and plasma, the amplitude of the excited transverse waves grows as the energy of the bunch particles increases until the relativistic factor of the bunch reaches a certain threshold value above which the transverse wave amplitude becomes essentially independent of the bunch particle energy and grows as the intensity and frequency of the pump wave increase. The amplitude and wavelength of the longitudinal field, which is shown to depend weakly on the energy of the bunch particles, grows with increasing the pump wave intensity.     

Anodal excitation in the Hodgkin-Huxley nerve model.

Computations show that cathodal rheobase increases with temperature from 0 degrees C to 30 degrees C. Anodal rheobase (stimulation at the end of an indefinitely long anodal pulse) also increases with temperature, but goes to infinity at a critical temperature 17.13 degrees C, above which such excitation is impossible. For a stimulus consisting of any step change of current from I0 to I1, a threshold curve of I1 is plotted against I0. As the temperature increases, this curve rises. Its intersection with the horizontal axis, which determines the anodal rheobase, goes to infinity at the critical temperature. This phenomenon is caused by the saturation of the variables m, h, n for strongly hyperpolarized potentials, combined with the relative speeding up of the inhibitory process with increasing temperature. The threshold charge Q in an instantaneous anodal current pulse (of zero duration) goes to infinity at the same temperature, with a similar explanation in terms of threshold curves in the I1 vs. Q plane. The fact that the critical temperature for both cases is the same is generalized by the conjecture that for any anodal current waveform whatever, as its amplitude approaches infinity, the trajectory in the phase space following its cessation approaches the same limiting trajectory. This limiting trajectory changes from suprathreshold to subthreshold at the critical temperature.     

The role of biphasic shocks for transthoracic cardioversion of atrial fibrillation

The modern generation of transthoracic defibrillators now employ impedance compensated biphasic waveforms. These new devices are superior to those with monophasic waveforms and practice is currently switching to biphasic defibrillators for the treatment of both ventricular and atrial fibrillation. However, there is no universal guideline for the use of biphasic defibrillators in direct current cardioversion of atrial fibrillation. This article reviews the use of biphasic defibrillation waveforms for transthoracic cardioversion of atrial fibrillation.