Hysteresis phenomena in excitable cardiac tissues

Pulsed low-energy stimulation initiates electric turbulence in cardiac tissue

Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks. In particular, two very important questions are: 1) What determines the potential of a wave break to initiate re-entry? and 2) How do these breaks evolve such that the system is able to maintain spatiotemporally chaotic electrical activity? Here we approach these questions numerically using optogenetics in an in silico model of human atrial tissue that has undergone chronic atrial fibrillation (cAF) remodelling. In the lesser studied sub-threshold illumination régime, we discover a new mechanism of wave break initiation in cardiac tissue that occurs for gentle slopes of the restitution characteristics. This mechanism involves the creation of conduction blocks through a combination of wavefront-waveback interaction, reshaping of the wave profile and heterogeneous recovery from the excitation of the spatially extended medium, leading to the creation of re-excitable windows for sustained re-entry. This finding is an important contribution to cardiac arrhythmia research as it identifies scenarios in which low-energy perturbations to cardiac rhythm can be potentially life-threatening.

Identification of competing neural mechanisms underlying positive and negative perceptual hysteresis in the human visual system

Hysteresis is a well-known phenomenon in physics that relates changes in a system with its prior history. It is also part of human visual experience (perceptual hysteresis), and two different neural mechanisms might explain it: persistence (a cause of positive hysteresis), which forces to keep a current percept for longer, and adaptation (a cause of negative hysteresis), which in turn favors the switch to a competing percept early on. In this study, we explore the neural correlates underlying these mechanisms and the hypothesis of their competitive balance, by combining behavioral assessment with fMRI. We used machine learning on the behavioral data to distinguish between positive and negative hysteresis, and discovered a neural correlate of persistence at a core region of the ventral attention network, the anterior insula. Our results add to the understanding of perceptual multistability and reveal a possible mechanistic explanation for the regulation of different forms of perceptual hysteresis.

Functional distance in human gait transition

The emerging understanding of the behavioral transitions that accompany the ascending and descending method of limits is in terms of "functional distance" - the degree to which a perceiver is disengaged from ordinary exploratory activities. Increasing functional distance results in negative hysteresis in contrast to the classical positive hysteresis more typical of ongoing activity. In the present study of human gait transitions on a treadmill, the functional distance between a perceiver and ordinary exploratory activities was manipulated in two ways: (1) "Active" participants, walking or running on a treadmill, were asked to anticipate the gait that would be required if treadmill speed were increased or decreased; and (2) "passive" participants, standing off a moving treadmill, were asked to report the gait they would use if they were on the treadmill at its current speed. As expected, the increase of functional distance from (1) to (2) reduced the amount of classical hysteresis and promoted negative hysteresis, that is, a lower transition speed for walk-to-run transitions (ascending trials) than for run-to-walk transitions (descending trials). These results complement empirical findings in other behavioral transition experiments. More broadly, they signify the role of perception-action cycles for grounding natural on-going perception. In particular, they support the assertion that perception and action are intertwined and that lack of information about an impending action has consequences for perceptual judgments.

Negative hysteresis in the behavioral dynamics of the affordance "graspable"

One commonly perceives whether a visible object will afford grasping with one hand or with both hands. In experiments in which differently sized objects of a fixed type are presented, the transition from using one of these manual modes to the other depends on the ratio of object size to hand span and on the presentation sequence, with size increasing versus decreasing. Conventional positive hysteresis (i.e., a larger transition ratio for the increasing sequence) can be accommodated by the order parameter dynamics that typify self-organizing systems (Lopresti-Goodman, Turvey, and Frank, Attention, Perception, & Psychophysics 73:1948-1965, 2011). Here we identified and addressed conditions of unconventional negative hysteresis (i.e., a larger transition ratio for the decreasing sequence). They suggest a second control parameter in the self-organization of affordance perception, one that is seemingly regulated by inhibitory dynamics occurring in the agent-task-environment system. Our experimental results and modeling extend the investigation of affordance perception within dynamical systems theory.

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to reentrant waves, i.e., electrical wave(s) that recirculate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, have made it extremely difficult to pinpoint the detailed dynamics of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. Movies showing all the breakup mechanisms are available at http://arrhythmia.hofstra.edu/breakup and at ftp://ftp.aip.org/epaps/chaos/E-CHAOEH-12-039203/ INDEX.html. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols. (c) 2002 American Institute of Physics.

Existence of bistability and correlation with arrhythmogenesis in paced sheep atria

INTRODUCTION

Studies of the electrical dynamics of cardiac tissue are important for understanding the mechanisms of arrhythmias. This study uses high-frequency pacing to investigate the dynamics of sheep atria.

METHODS AND RESULTS

A 504-electrode mapping plaque was affixed to the right atrium in six sheep. Cathodal pacing stimuli were delivered to the center of the plaque. Pacing period (Tp) was decreased from 275 +/- 25 msec to 75 +/- 25 msec and then increased to 230 +/- 70 msec in steps of either 5 or 10 msec. In all 21 trials in six sheep, the atrium responded 1:1 at longer Tps and 2:1 at shorter Tps. As Tp was decreased, the response switched to 2:1 at a particular Tp. Conversely, as Tp was increased, the response switched back to 1:1 at a particular Tp. Over 21 trials, the 1:1-to-2:1 and 2:1-to-1:1 transitions occurred at 119.5 +/- 18.8 msec and 130.0 +/- 19.1 msec, respectively. This hysteretic behavior yielded bistability windows, 10.5 +/- 7.2 msec wide, wherein 1:1 and 2:1 responses existed at the same Tp. In 15 trials and in all animals, idiopathic wavefronts emanating from outside the mapped region passed through the mapped region. In 13 of those trials, the idiopathic wavefronts occurred at Tps within the bistability window or within 35 msec of its upper or lower limit.

CONCLUSION

Bistability windows and idiopathic wavefronts were observed and found to be correlated with each other, suggesting a connection between bistability and arrhythmogenesis.

Hysteresis and bistability in the direct transition from 1:1 to 2:1 rhythm in periodically driven single ventricular cells

The transmembrane potential of a single quiescent cell isolated from rabbit ventricular muscle was recorded using a suction electrode in whole-cell recording mode. The cell was then driven with a periodic train of current pulses injected into the cell through the same recording electrode. When the interpulse interval or basic cycle length (BCL) was sufficiently long, 1:1 rhythm resulted, with each stimulus pulse producing an action potential. Gradual decrease in BCL invariably resulted in loss of 1:1 synchronization at some point. When the pulse amplitude was set to a fixed low level and BCL gradually decreased, N+1:N rhythms (N>/=2) reminiscent of clinically observed Wenckebach rhythms were seen. Further decrease in BCL then yielded a 2:1 rhythm. In contrast, when the pulse amplitude was set to a fixed high level, a period-doubled 2:2 rhythm resembling alternans rhythm was seen before a 2:1 rhythm occurred. With the pulse amplitude set to an intermediate level (i.e., to a level between those at which Wenckebach and alternans rhythms were seen), there was a direct transition from 1:1 to 2:1 rhythm as the BCL was decreased: Wenckebach and alternans rhythms were not seen. When at that point the BCL was increased, the transition back to 1:1 rhythm occurred at a longer BCL than that at which the {1:1-->2:1} transition had initially occurred, demonstrating hysteresis. With the BCL set to a value within the hysteresis range, injection of a single well-timed extrastimulus converted 1:1 rhythm into 2:1 rhythm or vice versa, providing incontrovertible evidence of bistability (the coexistence of two different periodic rhythms at a fixed set of stimulation parameters). Hysteresis between 1:1 and 2:1 rhythms was also seen when the stimulus amplitude, rather than the BCL, was changed. Simulations using numerical integration of an ionic model of a single ventricular cell formulated as a nonlinear system of differential equations provided results that were very similar to those found in the experiments. The steady-state action potential duration restitution curve, which is a plot of the duration of the action potential during 1:1 rhythm as a function of the recovery time or diastolic interval immediately preceding that action potential, was determined. Iteration of a finite-difference equation derived using the restitution curve predicted the direct {1:1<-->2:1} transition, as well as bistability, in both the experimental and modeling work. However, prediction of the action potential duration during 2:1 rhythm was not as accurate in the experiments as in the model. Finally, we point out a few implications of our findings for cardiac arrhythmias (e.g., Mobitz type II block, ischemic alternans). (c) 1999 American Institute of Physics.

Wave-front curvature as a cause of slow conduction and block in isolated cardiac muscle

We have investigated the role of wave-front curvature on propagation by following the wave front that was diffracted through a narrow isthmus created in a two-dimensional ionic model (Luo-Rudy) of ventricular muscle and in a thin (0.5-mm) sheet of sheep ventricular epicardial muscle. The electrical activity in the experimental preparations was imaged by using a high-resolution video camera that monitored the changes in fluorescence of the potentiometric dye di-4-ANEPPS on the surface of the tissue. Isthmuses were created both parallel and perpendicular to the fiber orientation. In both numerical and biological experiments, when a planar wave front reached the isthmus, it was diffracted to an elliptical wave front whose pronounced curvature was very similar to that of a wave front initiated by point stimulation. In addition, the velocity of propagation was reduced in relation to that of the original planar wave. Furthermore, as shown by the numerical results, wave-front curvature changed as a function of the distance from the isthmus. Such changes in local curvature were accompanied by corresponding changes in velocity of propagation. In the model, the critical isthmus width was 200 microns for longitudinal propagation and 600 microns for transverse propagation of a single planar wave initiated proximal to the isthmus. In the experiments, propagation depended on the width of the isthmus for a fixed stimulation frequency. Propagation through an isthmus of fixed width was rate dependent both along and across fibers. Thus, the critical isthmus width for propagation was estimated in both directions for different frequencies of stimulation. In the longitudinal direction, for cycle lengths between 200 and 500 milliseconds, the critical width was < 1 mm; for 150 milliseconds, it was estimated to be between 1.3 and 2 mm; and for the maximum frequency of stimulation (117 +/- 15 milliseconds), it was > 2.5 mm. In the transverse direction, critical width was between 1.78 and 2.32 mm for a basic cycle length of 200 milliseconds. It increased to values between 2.46 and 3.53 mm for a basic cycle length of 150 milliseconds. The overall results demonstrate that the curvature of the wave front plays an important role in propagation in two-dimensional cardiac muscle and that changes in curvature may cause slow conduction or block.

Electrotonic inhibition and active facilitation of excitability in ventricular muscle

INTRODUCTION

The effects of subthreshold electrical pulses on the response to subsequent stimulation have been described previously in experimental animal studies as well as in the human heart. In addition, previous studies in cardiac Purkinje fibers have shown that diastolic excitability may decrease after activity (active inhibition) and, to a lesser extent, following subthreshold responses (electrotonic inhibition). However, such dynamic changes in excitability have not been explored in isolated ventricular muscle, and it is uncertain whether similar phenomena may play any role in the activation patterns associated with propagation abnormalities in the myocardium.

METHODS AND RESULTS

Experiments were performed in isolated sheep Purkinje fibers and papillary muscles, and in enzymatically dissociated guinea pig ventricular myocytes. In all types of preparations introduction of a conditioning subthreshold pulse between two suprathreshold pulses was followed by a transient decay in excitability (electrotonic inhibition). The degree of inhibition was directly related to the amplitude and duration of the conditioning pulse and inversely related to the postconditioning interval. Yet, inhibition could be demonstrated long after (> 1 sec) the end of the conditioning pulse. Electronic inhibition was found at all diastolic intervals and did not depend on the presence of a previous action potential. In Purkinje fibers, conditioning action potentials led to active inhibition of subsequent responses. In contrast, in muscle cells, such action potentials had a facilitating effect (active facilitation). Electrotonic inhibition and active facilitation were observed in both sheep ventricular muscle and guinea pig ventricular myocytes. Accordingly, during repetitive stimulation with pulses of barely threshold intensity, we observed: (1) bistability (i.e., with the same stimulating parameters, stimulus:response patterns were either 1:1 or 1:0, depending on previous history), and (2) abrupt transitions between 1:1 and 1:0 (absence of intermediate Wenckebach-like patterns). Simulations utilizing an ionic model of cardiac myocytes support the hypothesis that electrotonic inhibition in well-polarized ventricular muscle is the result of partial activation of IK following subthreshold pulses. On the other hand, active facilitation may be the result of an activity-induced decrease in the conductance of IK1.

CONCLUSION

Diastolic excitability of well-polarized ventricular myocardium may be transiently depressed following local responses and transiently enhanced following action potentials. On the other hand, diastolic excitability decreases during quiescence. Active facilitation and electrotonic inhibition may have an important role in determining the dynamics of excitation of the myocardium in the presence of propagation abnormalities.

Dynamics of the background outward current of single guinea pig ventricular myocytes. Ionic mechanisms of hysteresis in cardiac cells

Subthreshold potentials are thought to be mediated by time-independent, "passive" background currents. In this study, we show that the background current-voltage (I-V) relation of guinea pig ventricular myocytes is changed significantly by repetitive stimulation, in such a way that cell excitability becomes enhanced. Myocytes were used for whole-cell voltage-clamp experiments. A voltage-clamp ramp (100 mV/sec) to -50 mV was applied from a holding potential of -100 mV. Subsequently, a train of square voltage-clamp pulses to +10 mV (duration, 300 msec; interpulse interval, 300 msec) was delivered from a holding potential of -85 mV. A new ramp was applied again immediately after the train, and the resulting I-V curve was compared with that obtained before the train. Pulsing displaced the I-V relation to the right, the zero-current point becoming 1-2 mV less negative, and increased the degree of inward-going rectification. These changes were insensitive to tetrodotoxin (30 microM); disappeared during superfusion with cobalt (2 mM), verapamil (22 microM), or ryanodine (5 microM); and could not be mimicked by agonists of the protein kinase C system. In the presence of cesium (8 mM), pulsing still displaced the I-V curve to the right. However, the linear portion of the curve became steeper after the train. Subtraction of the cesium-sensitive current from control revealed that, although the zero-current point remained constant, the I-V relation showed a stronger inward-going rectification after pulsing. In accordance with these results, we have demonstrated hysteresis of excitability in ventricular myocytes. We conclude that the observed changes are mediated by an increase in intracellular calcium, which leads to an increase in rectification of IK1, as well as to activation of another membrane-conductance system, perhaps the Na-Ca exchange or the Ca(2+)-activated, nonselective current.

Hysteresis in the excitability of isolated guinea pig ventricular myocytes

Hysteresis phenomena were demonstrated in the excitability of single, enzymatically dissociated guinea pig ventricular myocytes. Membrane potentials were recorded with patch pipettes in the whole-cell current-clamp configuration. Repetitive stimulation with depolarizing current pulses of constant cycle length and duration but varying strength led to predictable excitation (1:1) and nonexcitation (1:0) patterns depending on current strength. However, transition between patterns depended on the direction of current strength change, and stable hysteresis loops were obtained in stimulus-response pattern versus current strength plots in 31 cells. Increase of pulse duration and decrease of stimulation rate contributed to a reduction in hysteresis loop areas. In addition, at the abrupt transitions from 1:0 to 1:1 patterns, a latency adaptation phenomenon was consistently observed. Bath application of tetrodotoxin (30 microM) produced no change of hysteresis, whereas hysteresis was substantially decreased in cobalt (2 mM) superfusion experiments. Analysis of the changes in amplitude and shape of the subthreshold responses during the transitions from one stable pattern to the other suggested that activity led to an increase in membrane resistance, particularly in the voltage domain between resting and threshold potentials. We therefore modeled the dynamic behavior of the single cells, using an analytical solution aimed at calculating the recovery of activation latency as a function of diastolic membrane resistance. Numerical iteration of the analytical model equations closely reproduced the experimental hysteresis loops in both qualitative and quantitative ways. The effect of stimulation frequency on the model was similar to the experimental findings. The overall study suggests that the excitability pattern of guinea pig ventricular myocytes is responsible for hysteresis and bistabilities when current intensity is allowed to fluctuate around threshold levels.