Wave-train-induced termination of weakly anchored vortices in excitable media

Complete synchronization of two spirals by a messenger wave in a reaction diffusion system

Synchronization phenomena are ubiquitous in nature. They can be observed in physical, chemical, and biological systems. In the present study, we examine synchronization phenomena in chemical reaction-diffusion systems in the experimental Belousov-Zhabotinsky reaction. We study how two counter-rotating spirals pinned to unexcitable heterogeneities separated by a wall interact with a third free spiral of higher frequency. We found that the latter, which we call the messenger wave, synchronizes the two non-interacting pinned spirals. We also carried out numerical simulations of a model system with Barkley's reaction-diffusion equations and found corroborating results.

Dissolution of spiral wave's core using cardiac optogenetics

Rotating spiral waves in the heart are associated with life-threatening cardiac arrhythmias such as ventricular tachycardia and fibrillation. These arrhythmias are treated by a process called defibrillation, which forces electrical resynchronization of the heart tissue by delivering a single global high-voltage shock directly to the heart. This method leads to immediate termination of spiral waves. However, this may not be the only mechanism underlying successful defibrillation, as certain scenarios have also been reported, where the arrhythmia terminated slowly, over a finite period of time. Here, we investigate the slow termination dynamics of an arrhythmia in optogenetically modified murine cardiac tissue both in silico and ex vivo during global illumination at low light intensities. Optical imaging of an intact mouse heart during a ventricular arrhythmia shows slow termination of the arrhythmia, which is due to action potential prolongation observed during the last rotation of the wave. Our numerical studies show that when the core of a spiral is illuminated, it begins to expand, pushing the spiral arm towards the inexcitable boundary of the domain, leading to termination of the spiral wave. We believe that these fundamental findings lead to a better understanding of arrhythmia dynamics during slow termination, which in turn has implications for the improvement and development of new cardiac defibrillation techniques.

In silico optical modulation of spiral wave trajectories in cardiac tissue

Life-threatening cardiac arrhythmias such as ventricular tachycardia and fibrillation are common precursors to sudden cardiac death. They are associated with the occurrence of abnormal electrical spiral waves in the heart that rotate at a high frequency. In severe cases, arrhythmias are combated with a clinical method called defibrillation, which involves administering a single global high-voltage shock to the heart to reset all its activity and restore sinus rhythm. Despite its high efficiency in controlling arrhythmias, defibrillation is associated with several negative side effects that render the method suboptimal. The best approach to optimize this therapeutic technique is to deepen our understanding of the dynamics of spiral waves. Here, we use computational cardiac optogenetics to study and control the dynamics of a single spiral wave in a two-dimensional, electrophysiologically detailed, light-sensitive model of a mouse ventricle. First, we illuminate the domain globally by applying a sequence of periodic optical pulses with different frequencies in the sub-threshold regime where no excitation wave is induced. In doing so, we obtain epicycloidal, hypocycloidal, and resonant drift trajectories of the spiral wave core. Then, to effectively control the wave dynamics, we use a method called resonant feedback pacing. In this approach, each global optical pulse is applied when the measuring electrode positioned on the domain registers a predefined value of the membrane voltage. This enables us to steer the spiral wave in a desired direction determined by the position of the electrode. Our study thus provides valuable mechanistic insights into the success or failure of global optical stimulation in executing efficient arrhythmia control.

Terminating spiral waves with a single designed stimulus: Teleportation as the mechanism for defibrillation

We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.

Drift and termination of spiral waves in optogenetically modified cardiac tissue at sub-threshold illumination

The development of new approaches to control cardiac arrhythmias requires a deep understanding of spiral wave dynamics. Optogenetics offers new possibilities for this. Preliminary experiments show that sub-threshold illumination affects electrical wave propagation in the mouse heart. However, a systematic exploration of these effects is technically challenging. Here, we use state-of-the-art computer models to study the dynamic control of spiral waves in a two-dimensional model of the adult mouse ventricle, using stationary and non-stationary patterns of sub-threshold illumination. Our results indicate a light-intensity-dependent increase in cellular resting membrane potentials, which together with diffusive cell-cell coupling leads to the development of spatial voltage gradients over differently illuminated areas. A spiral wave drifts along the positive gradient. These gradients can be strategically applied to ensure drift-induced termination of a spiral wave, both in optogenetics and in conventional methods of electrical defibrillation.

Spiral wave unpinning facilitated by wave emitting sites in cardiac monolayers

Rotating spiral waves of electrical activity in the heart can anchor to unexcitable tissue (an obstacle) and become stable pinned waves. A pinned rotating wave can be unpinned either by a local electrical stimulus applied close to the spiral core, or by an electric field pulse that excites the core of a pinned wave independently of its localization. The wave will be unpinned only when the pulse is delivered inside a narrow time interval called the unpinning window (UW) of the spiral. In experiments with cardiac monolayers, we found that other obstacles situated near the pinning centre of the spiral can facilitate unpinning. In numerical simulations, we found increasing or decreasing of the UW depending on the location, orientation and distance between the pinning centre and an obstacle. Our study indicates that multiple obstacles could contribute to unpinning in experiments with intact hearts.

Simultaneous unpinning of multiple vortices in two-dimensional excitable media

There are many examples of excitable media, such as the heart, that can show complex dynamics and where control is a challenging task. Heavy means like a strong electric shock are nowadays still necessary to control and terminate ventricular fibrillation (VF). It is known that heterogeneities in an excitable medium can stabilize the activity, e.g., spiral waves can pin to such obstacles. This might also be a reason for the persistence of VF and the difficulty to control it. Previous studies investigated systems with a single pinned spiral wave and demonstrated how the spiral can be unpinned. In this article, we extend this case and investigate a generic excitable system with multiple pinned spiral waves. We describe a control technique that allows the simultaneous unpinning of pinned spiral waves. Apart from theoretical considerations, we provide numerical evidence that the proposed technique is superior to the underdrive pacing method that has reportedly high success rates when applied to a single pinned spiral.

Control of electrical turbulence by periodic excitation of cardiac tissue

Electrical turbulence in cardiac tissue is associated with arrhythmias such as life-threatening ventricular fibrillation. Recent experimental studies have shown that a sequence of low-energy electrical far-field pulses is able to terminate fibrillation more gently than a single high-energy pulse which causes severe side effects. During this low-energy antifibrillation pacing (LEAP), only tissue near sufficiently large conduction heterogeneities, such as large coronary arteries, is activated. In order to optimize LEAP, we performed extensive simulations of cardiac tissue perforated by blood vessels, employing two alternative cellular models that exhibit electrical turbulence at a similar length scale. Moreover, the scale of blood vessels in our two-dimensional simulations was chosen such that the threshold for single pulse defibrillation matches experimental values. For each of the 100 initial conditions, we tested different electrical field strengths, pulse shapes, numbers of pulses, and periods between the pulses. LEAP is successful for both models, albeit with substantial differences. One model exhibits a spectrum of chaotic activity featuring a narrow peak around a dominant frequency. In this case, the optimal period between low-energy pulses matches this frequency and LEAP greatly reduces the required energy for successful defibrillation. For pulses with larger energies, the system is perturbed such that underdrive pacing becomes advantageous. The spectrum of the second model features a broader peak, resulting in a less pronounced optimal pacing period and a decreased energy reduction. In both cases, pacing with five or six pulses which are separated by the dominant period maximizes the energy reduction.

Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential

This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q₁₀ and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

Dynamics of spiral waves rotating around an obstacle and the existence of a minimal obstacle

Pinning of vortices by obstacles plays an important role in various systems. In the heart, anatomical reentry is created when a vortex, also known as the spiral wave, is pinned to an anatomical obstacle, leading to a class of physiologically very important arrhythmias. Previous analyses of its dynamics and instability provide fine estimates in some special circumstances, such as large obstacles or weak excitabilities. Here, to expand theoretical analyses to all circumstances, we propose a general theory whose results quantitatively agree with direct numerical simulations. In particular, when obstacles are small and pinned spiral waves are destabilized, an accurate explanation of the instability in two-dimensional media is provided by the usage of a mapping rule and dimension reduction. The implications of our results are to better understand the mechanism of arrhythmia and thus improve its early prevention.

Mechanisms of vortices termination in the cardiac muscle

We propose a solution to a long-standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves.

Elimination of a spiral wave pinned at an obstacle by a train of plane waves: Effect of diffusion between obstacles and surrounding media

In excitable media such as cardiac tissue and Belousov-Zhabotinsky reaction medium, spiral waves tend to anchor (pin) to local heterogeneities. In general, such pinned waves are difficult to eliminate and may progress to spatio-temporal chaos. Heterogeneities can be classified as either the absence or presence of diffusive interaction with the surrounding medium. In this study, we investigated the difference in the unpinning of spiral waves from obstacles with and without diffusive interaction, and found a profound difference. The pacing period required for unpinning at fixed obstacle size is larger in case of diffusive obstacles. Further, we deduced a generic theoretical framework that can predict the minimal unpinning period. Our results explain the difference in pacing periods between for the obstacles with and without diffusive interaction, and the difference is interpreted in terms of the local decrease of spiral wave velocity close to the obstacle boundary caused in the case of diffusive interaction.

Propagation of spiral waves pinned to circular and rectangular obstacles

We present an investigation of spiral waves pinned to circular and rectangular obstacles with different circumferences in both thin layers of the Belousov-Zhabotinsky reaction and numerical simulations with the Oregonator model. For circular objects, the area always increases with the circumference. In contrast, we varied the circumference of rectangles with equal areas by adjusting their width w and height h. For both obstacle forms, the propagating parameters (i.e., wavelength, wave period, and velocity of pinned spiral waves) increase with the circumference, regardless of the obstacle area. Despite these common features of the parameters, the forms of pinned spiral waves depend on the obstacle shapes. The structures of spiral waves pinned to circles as well as rectangles with the ratio w/h∼1 are similar to Archimedean spirals. When w/h increases, deformations of the spiral shapes are observed. For extremely thin rectangles with w/h≫1, these shapes can be constructed by employing semicircles with different radii which relate to the obstacle width and the core diameter of free spirals.

Influence of excitability on unpinning and termination of spiral waves

Application of electrical forcing to release pinned spiral waves from unexcitable obstacles and to terminate the rotation of free spiral waves at the boundary of excitable media has been investigated in thin layers of the Belousov-Zhabotinsky (BZ) reaction, prepared with different initial concentrations of H_{2}SO_{4}. Increasing [H_{2}SO_{4}] raises the excitability of the reaction and reduces the core diameter of free spiral waves as well as the wave period. An electric current with density stronger than a critical value Junpin causes a pinned spiral wave to drift away from the obstacle. For a given obstacle size, Junpin increases with [H_{2}SO_{4}]. Under an applied electrical current, the rotation center of a free spiral wave drifts along a straight path to the boundary. When the current density is stronger than a critical value Jterm, the spiral tip is forced to hit the boundary, where the spiral wave is terminated. Similar to Junpin for releasing a pinned spiral wave, Jterm also increases with [H_{2}SO_{4}]. These experimental findings were confirmed by numerical simulations using the Oregonator model, in which the excitability was adjusted via the ratio of the excitation rate to the recovery rate of the BZ reaction. Therefore, our investigation shows that decreasing the excitability can facilitate elimination of spiral waves by electrical forcing, either in the presence of obstacles or not.

Influences of periodic mechanical deformation on pinned spiral waves

In a generic model of excitable media, we study the behavior of spiral waves interacting with obstacles and their dynamics under the influences of simple periodic mechanical deformation (PMD). Depending on the characteristics of the obstacles, i.e., size and excitability, the rotation of a pinned spiral wave shows different scenarios, e.g., embedding into or anchoring on an obstacle. Three different drift phenomena induced by PMD are observed: scattering on small partial-excitable obstacles, meander-induced unpinning on big partial-excitable obstacles, and drifting around small unexcitable obstacles. Their underlying mechanisms are discussed. The dependence of the threshold amplitude of PMD on the characteristics of the obstacles to successfully remove pinned spiral waves on big partial-excitable obstacles is studied.

Experimental evidence and mathematical modeling of thermal effects on human colonic smooth muscle contractility

It has been shown, in animal models, that gastrointestinal tract (GIT) motility is influenced by temperature; nevertheless, the basic mechanism governing thermal GIT smooth muscle responses has not been fully investigated. Studies based on physiologically tuned mathematical models have predicted that thermal inhomogeneity may induce an electrochemical destabilization of peristaltic activity. In the present study, the effect of thermal cooling on human colonic muscle strip (HCMS) contractility was studied. HCMSs were obtained from disease-free margins of resected segments for cancer. After removal of the mucosa and serosa layers, strips were mounted in separate chambers. After 30 min, spontaneous contractions developed, which were measured using force displacement transducers. Temperature was changed every hour (37, 34, and 31°C). The effect of cooling was analyzed on mean contractile activity, oscillation amplitude, frequency, and contraction to ACh (10(-5) M). At 37°C, HCMSs developed a stable phasic contraction (~0.02 Hz) with a significant ACh-elicited mean contractile response (31% and 22% compared with baseline in the circular and longitudinal axis, respectively). At a lower bath temperature, higher mean contractile amplitude was observed, and it increased in the presence of ACh (78% and 43% higher than the basal tone in the circular and longitudinal axis, respectively, at 31°C). A simplified thermochemomechanical model was tuned on experimental data characterizing the stress state coupling the intracellular Ca(2+) concentration to tissue temperature. In conclusion, acute thermal cooling affects colonic muscular function. Further studies are needed to establish the exact mechanisms involved to better understand clinical consequences of hypothermia on intestinal contractile activity.

Mechanism of unpinning spirals by a series of stimuli

Antitachycardia pacing (ATP) is widely used to terminate tachycardia before it proceeds to lethal fibrillation. The important prerequisite for successful ATP is unpinning of the spirals anchored to the obstacle by a series of stimuli. Here, to understand the mechanism of unpinning spirals by ATP, we propose a theoretical explanation based on a nonlinear eikonal relation and a kinematical model. The theoretical results are quantitatively consistent with the numerical simulations in both weak and high excitabilities.

Unpinning of spiral waves by electrical forcing in excitable chemical media

We present experimental observations on the electrically forced release of spiral waves pinned to unexcitable circular obstacles in the Belosov-Zhabotinsky reaction. When the applied electric current density reaches the necessary current density J(unpin), the spiral tip is detached and subsequently drifts away from the obstacle. J(unpin) is found to increase with the obstacle diameter d. The growth rate ΔJ(unpin)/Δd is much higher for obstacles larger than the free spiral core compared to that for smaller obstacles. The experimental findings are confirmed by numerical simulations using the Oregonator model. The results imply that it is more difficult to release spiral waves pinned to larger obstacles, especially when the obstacle size exceeds that of the free spiral core.

Emitting waves from heterogeneity by a rotating electric field

In a generic model of excitable media, we simulate wave emission from a heterogeneity (WEH) induced by an electric field. Based on the WEH effect, a rotating electric field is proposed to terminate existed spatiotemporal turbulence. Compared with the effects resulted by a periodic pulsed electric field, the rotating electric field displays several improvements, such as lower required intensity, emitting waves on smaller obstacles, and shorter suppression time. Furthermore, due to rotation of the electric field, it can automatically source waves from the boundary of an obstacle with small curvature.

Suppression of cardiac alternans by alternating-period-feedback stimulations

Alternans response, comprising a sequence of alternating long and short action potential durations in heart tissue, seen during rapid periodic pacing can lead to conduction block resulting in potentially fatal cardiac failure. A method of pacing with feedback control is proposed to reduce the alternans and therefore the probability of subsequent cardiac failure. The reduction is achieved by feedback control using small perturbations of constant magnitude to the original, alternans-generating pacing period T, viz., using sequences of two alternating periods of T+ΔT and T-ΔT, with ΔT<<T. Such a control scheme for alternans suppression is demonstrated experimentally in isolated whole heart experiments. This alternans suppression scheme is further confirmed and investigated in detail by simulations of ion-channel-based cardiac models both for a single cell and in one-dimensional spatially extended systems. The mechanism of the success of our method can be understood in terms of dynamics in phase space, viz., as the state of activity of the cell being confined within a narrow volume of phase space for the duration of control, resulting in extremely diminished variation in successive action potential durations. Our method is much more robust to noise than previous alternans reduction techniques based on fixed point stabilization and should thus be more efficient in terms of experimental implementation, which has implications for clinical treatment for arrhythmia.

Role of temperature on nonlinear cardiac dynamics

Thermal effects affecting spatiotemporal behavior of cardiac tissue are discussed by relating temperature variations to proarrhythmic dynamics in the heart. By introducing a thermoelectric coupling in a minimal model of cardiac tissue, we are able to reproduce experimentally measured dynamics obtained simultaneously from epicardial and endocardial canine right ventricles at different temperatures. A quantitative description of emergent proarrhythmic properties of restitution, conduction velocity, and alternans regimes as a function of temperature is presented. Complex discordant alternans patterns that enhance tissue dispersion consisting of one wave front and three wave backs are described in both simulations and experiments. Possible implications for model generalization are finally discussed.

A stochastic mathematical model to study the autoimmune progression towards type 1 diabetes

BACKGROUND

The integrity of the interactions and the 3D architecture among beta cell populations in pancreatic islets is critical for proper biosynthesis, storage and release of insulin. The aim of this study was to evaluate the effect on electrophysiological signalling of beta cells that is produced by progressive lymphocytic islet cell infiltration (insulitis), by modelling the disruption of pancreatic islet anatomy as a consequence of insulitis and altered glucose concentrations.

METHODS

On the basis of histopathological images of murine islets from non-obese diabetic mice, we simulated the electrophysiological dynamics of a 3D cluster of mouse beta cells via a stochastic model. Progressive damage was modelled at different glucose concentrations, representing the different glycaemic states in the autoimmune progression towards type 1 diabetes.

RESULTS

At 31% of dead beta cells (normoglycaemia) and 69% (hyperglycaemia), the system appeared to be biologically robust to maintain regular Ca(2+) ion oscillations guaranteeing an effective insulin release. Simulations at 84%, 94% and 98% grades (severe hyperglycemia) showed that intracellular calcium oscillations were absent. In such conditions, insulin pulsatility is not expected to occur.

CONCLUSIONS

Our results suggest that the islet tissue is biophysically robust enough to compensate for high rates of beta cell loss. These predictions can be experimentally tested in vitro by quantifying space and time electrophysiological dynamics of animal islets kept at different glucose gradients. The model indicates the necessity of maintaining glycaemia within the physiological range as soon as possible after diabetes onset to avoid a dramatic interruption of Ca(2+) pulsatility and the consequent drop of insulin release.

Termination of pinned vortices by high-frequency wave trains in heartlike excitable media with anisotropic fiber orientation

A variety of chemical and biological nonlinear excitable media, including heart tissue, exhibit vortices (spiral waves) that can anchor to nonexcitable obstacles. Such anchored vortices can be terminated by the application of high-frequency wave trains, as shown previously in isotropic excitable media. In this study, we examined the basic dependencies of the conduction velocities of planar waves and waves around curved obstacles as a function of anisotropy through numerical simulations of excitable media that mimic the fiber orientation in a real heart. We also investigated the unpinning of anchored spiral waves by high-frequency wave trains in an anisotropic excitable medium. Unlike the findings regarding the termination of spiral waves in isotropic excitable systems, we found a nonmonotonic relationship between the maximum unpinning period and the obstacle radius depending on the fiber orientation, where the formation of unwanted secondary pinned vortices or chaotic waves is seen over a wide range of parameters.

Anchoring of drifting spiral and scroll waves to impermeable inclusions in excitable media

Anchoring of spiral and scroll waves in excitable media has attracted considerable interest in the context of cardiac arrhythmias. Here, by bombarding inclusions with drifting spiral and scroll waves, we explore the forces exerted by inclusions onto an approaching spiral and derive the equations of motion governing spiral dynamics in the vicinity of inclusion. We demonstrate that these forces nonmonotonically depend on distance and can lead to complex behavior: (a) anchoring to small but circumnavigating larger inclusions; (b) chirality-dependent anchoring.

Electroelastic unpinning of rotating vortices in biological excitable media

Spiral waves in excitable biological media are associated with pathological situations. In the heart an action potential vortex pinned by an obstacle has to be removed through defibrillation protocols fine-tuned theoretically by using electrophysiological nonlinear mathematical models. Cardiac tissue, however, is an electroelastic medium whose electrical properties are strongly affected by large deformations. In this paper we specifically investigate the electroelastic pinning-unpinning mechanism in order to include cardiac contraction in the preexisting theoretically modeled defibrillation scenarios. Based on a two-dimensional minimal electromechanical model, we show numerically the existence of an unpinning band characterized by the size of the obstacle, the pacing site, and the frequency. Similar numerical simulations, performed in the absence of elastic coupling, show small differences in comparison with the electroelastic studies, suggesting for this specific scenario of pinning-unpinning dynamics a nonprominent role of elasticity.

Scroll-wave dynamics in human cardiac tissue: lessons from a mathematical model with inhomogeneities and fiber architecture

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study.

Anomalous drift of spiral waves in heterogeneous excitable media

We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in the distribution of ion-channel expression or cellular coupling. We report the anomalous drift of spiral waves toward regions having shorter period or stronger coupling, in reaction-diffusion models of excitable media. Such anomalous drift can promote the onset of complex spatiotemporal patterns, e.g., those responsible for life-threatening arrhythmias in the heart.

Phase-resolved analysis of the susceptibility of pinned spiral waves to far-field pacing in a two-dimensional model of excitable media

Life-threatening cardiac arrhythmias are associated with the existence of stable and unstable spiral waves. Termination of such complex spatio-temporal patterns by local control is substantially limited by anchoring of spiral waves at natural heterogeneities. Far-field pacing (FFP) is a new local control strategy that has been shown to be capable of unpinning waves from obstacles. In this article, we investigate in detail the FFP unpinning mechanism for a single rotating wave pinned to a heterogeneity. We identify qualitatively different phase regimes of the rotating wave showing that the concept of vulnerability is important but not sufficient to explain the failure of unpinning in all cases. Specifically, we find that a reduced excitation threshold can lead to the failure of unpinning, even inside the vulnerable window. The critical value of the excitation threshold (below which no unpinning is possible) decreases for higher electric field strengths and larger obstacles. In contrast, for a high excitation threshold, the success of unpinning is determined solely by vulnerability, allowing for a convenient estimation of the unpinning success rate. In some cases, we also observe phase resetting in discontinuous phase intervals of the spiral wave. This effect is important for the application of multiple stimuli in experiments.

Utilizing the eikonal relationship in strategies for reentrant wave termination in excitable media

Obstacle-anchored vortices can be terminated by the application of high-frequency wave trains in excitable media. We theoretically derived the dependency between the obstacle radius and the maximum unpinning period through reinterpretation of the well-known eikonal equation. Our theoretical result was confirmed by experiments with cardiomyocyte monolayers. This result may be useful for improving the stimulation protocol of implantable cardiac pacemakers.