Dynamics In Cardiac Tissue Research Articles

The Curie effect incorporation in the monodomain equation describing the action potential dynamics in cardiac tissue

In their in-depth study on cardiac tissue modeling, Clayton and Panfilov [1] present several monodomain or bidomain approaches for the mathematical description of the cardiac tissue action potential dynamics. For simulation of wave propagation in the cardiac tissue, the monodomain descriptions which use integer order derivatives reproduce many of the phenomena that are observed experimentally and are thus an appropriate analysis tool. The main objection concerning the monodomain approaches is that the electrical circuit capacitor, appearing in these descriptions, is considered ideal (the space between the capacitor plates is vacuum) and the Curie effect is ignored. The Curie effect consists of the fact that in case of a dielectric material, if at a moment of time a constant external voltage is applied, due to the capacitance of the capacitor and the properties of the dielectric, a supplementary electrical current is produced, besides the ohmic current. This supplementary contribution cannot be neglected in some cases. In this paper, the Curie effect, describing the action potential dynamics in cardiac tissue, assumed isotropic, is incorporated in the monodomain equation. The novelty is that this approach does not use fractional order derivatives and the obtained mathematical description with these equations is objective.

Dysfunctional Mitochondria in the Cardiac Fibers of a Williams-Beuren Syndrome Mouse Model.

Williams-Beuren syndrome (WBS) is a rare neurodevelopmental disorder that, together with a rather characteristic neurocognitive profile, presents a strong cardiovascular phenotype. The cardiovascular features of WBS are mainly related to a gene dosage effect due to hemizygosity of the elastin (ELN) gene; however, the phenotypic variability between WBS patients indicates the presence of important modulators of the clinical impact of elastin deficiency. Recently, two genes within the WBS region have been linked to mitochondrial dysfunction. Numerous cardiovascular diseases are related to mitochondrial dysfunction; therefore, it could be a modulator of the phenotype present in WBS. Here, we analyze mitochondrial function and dynamics in cardiac tissue from a WBS complete deletion (CD) model. Our research reveals that cardiac fiber mitochondria from CD animals have altered mitochondrial dynamics, accompanied by respiratory chain dysfunction with decreased ATP production, reproducing alterations observed in fibroblasts from WBS patients. Our results highlight two major factors: on the one hand, that mitochondrial dysfunction is probably a relevant mechanism underlying several risk factors associated with WBS disease; on the other, the CD murine model mimics the mitochondrial phenotype of WBS and could be a great model for carrying out preclinical tests on drugs targeting the mitochondria.

Initation of early afterdepolarizations by complex spatial dynamics in cardiac tissue.

Early afterdepolarizations (EADs) are thought to be complex depolarizing phenomena arising in the plateau phase of a cardiac action potential that can be lethal in certain conditions as they can cause arrhythmias. One possible mechanism of EADs is the reactivation of the L-type calcium channel (LTCC) in the repolarizing phase of the action potential. This reactivation of LTCC has been attributed to the cellular level properties such as increases of inward currents, decreases of outward currents, or uncharacteristically long pacing cycle lengths that promote longer action potential. In this study, we will show that geometry at the tissue level is also critical for the formation of EADs. We investigated how spatial action potential dynamics in tissue can give rise to EADs. We used a physiologically detailed model of a rabbit action potential to simulate a variety of different tissue geometries. We created 2-dimensional tissue (600×100 cells) featuring a horizontal channel of diffusive cells and a vertical source-sink gap of diffusive cells in the channel (both 2-20 cells wide). When an action potential was generated at one end of the channel, it propagates normally until colliding with the gap. At the source-sink gap, we found that the action potential exhibited three phenomena. When the size of the channel exceeded the size of the gap, the action potential continued to propagate normally. When the size of the channel was exceeded by the size of the gap, we observed conduction failure. When the size of the channel and the size of the gap were nearly the same, EADs formed in the cells right in front of the gap. Our findings underscore that tissue geometry is critical not only for the action potential wave propagation but also for the formation of EADs.

Bioinspired two-in-one nanotransistor sensor for the simultaneous measurements of electrical and mechanical cellular responses.

The excitation-contraction dynamics in cardiac tissue are the most important physiological parameters for assessing developmental state. We demonstrate integrated nanoelectronic sensors capable of simultaneously probing electrical and mechanical cellular responses. The sensor is configured from a three-dimensional nanotransistor with its conduction channel protruding out of the plane. The structure promotes not only a tight seal with the cell for detecting action potential via field effect but also a close mechanical coupling for detecting cellular force via piezoresistive effect. Arrays of nanotransistors are integrated to realize label-free, submillisecond, and scalable interrogation of correlated cell dynamics, showing advantages in tracking and differentiating cell states in drug studies. The sensor can further decode vector information in cellular motion beyond typical scalar information acquired at the tissue level, hence offering an improved tool for cell mechanics studies. The sensor enables not only improved bioelectronic detections but also reduced invasiveness through the two-in-one converging integration.

Stochastic termination of spiral wave dynamics in cardiac tissue.

Rotating spiral waves are self-organized features in spatially extended excitable media and may play an important role in cardiac arrhythmias including atrial fibrillation (AF). In homogeneous media, spiral wave dynamics are perpetuated through spiral wave breakup, leading to the continuous birth and death of spiral waves, but have a finite probability of termination. In non-homogeneous media, however, heterogeneities can act as anchoring sources that result in sustained spiral wave activity. It is thus unclear how and if AF may terminate following the removal of putative spiral wave sources in patients. Here, we address this question using computer simulations in which a stable spiral wave is trapped by an heterogeneity and is surrounded by spiral wave breakup. We show that, following ablation of spatial heterogeneity to render that region of the medium unexcitable, termination of spiral wave dynamics is stochastic and Poisson-distributed. Furthermore, we show that the dynamics can be accurately described by a master equation using birth and death rates. To validate these predictions in vivo, we mapped spiral wave activity in patients with AF and targeted the locations of spiral wave sources using radiofrequency ablation. Targeted ablation was indeed able to terminate AF, but only after a variable delay of up to several minutes. Furthermore, and consistent with numerical simulations, termination was not accompanied by gradual temporal or spatial organization. Our results suggest that spiral wave sources and tissue heterogeneities play a critical role in the maintenance of AF and that the removal of sources results in spiral wave dynamics with a finite termination time, which could have important clinical implications.

From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology.

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.

Complex restitution behavior and reentry in a cardiac tissue model for neonatal mice.

Spatiotemporal dynamics in cardiac tissue emerging from the coupling of individual cardiomyocytes underlie the heart's normal rhythm as well as undesired and possibly life‐threatening arrhythmias. While single cells and their transmembrane currents have been studied extensively, systematically investigating spatiotemporal dynamics is complicated by the nontrivial relationship between single‐cell and emergent tissue properties. Mathematical models have been employed to bridge this gap and contribute to a deepened understanding of the onset, development, and termination of arrhythmias. However, no such tissue‐level model currently exists for neonatal mice. Here, we build on a recent single‐cell model of neonatal mouse cardiomyocytes by Wang and Sobie (Am. J. Physiol. Heart Circ. Physiol. 294:H2565) to predict properties that are commonly used to gauge arrhythmogenicity of cardiac substrates. We modify the model to yield well‐defined behavior for common experimental protocols and construct a spatially extended version to study emergent tissue dynamics. We find a complex action potential duration (APD) restitution behavior characterized by a nonmonotonic dependence on pacing frequency. Electrotonic coupling in tissue leads not only to changes in action potential morphology but can also induce spatially concordant and discordant alternans not observed in the single‐cell model. In two‐dimensional tissue, our results show that the model supports stable functional reentry, whose frequency is in good agreement with that observed in adult mice. Our results can be used to further constrain and validate the mathematical model of neonatal mouse cardiomyocytes with future experiments.

Generation of fibrillatory dynamics in cardiac tissue: fractional diffusion as arrhythmogenic mechanism modelling tool

Generation of fibrillatory dynamics in cardiac tissue: fractional diffusion as arrhythmogenic mechanism modelling tool

Instability of spiral and scroll waves in the presence of a gradient in the fibroblast density: the effects of fibroblast–myocyte coupling

Fibroblast–myocyte coupling can modulate electrical-wave dynamics in cardiac tissue. In diseased hearts, the distribution of fibroblasts is heterogeneous, so there can be gradients in the fibroblast density (henceforth we call this GFD) especially from highly injured regions, like infarcted or ischemic zones, to less-wounded regions of the tissue. Fibrotic hearts are known to be prone to arrhythmias, so it is important to understand the effects of GFD in the formation and sustenance of arrhythmic re-entrant waves, like spiral or scroll waves. Therefore, we investigate the effects of GFD on the stability of spiral and scroll waves of electrical activation in a state-of-the-art mathematical model for cardiac tissue in which we also include fibroblasts. By introducing GFD in controlled ways, we show that spiral and scroll waves can be unstable in the presence of GFDs because of regions with varying spiral- or scroll-wave frequency ω, induced by the GFD. We examine the effects of the resting membrane potential of the fibroblast and the number of fibroblasts attached to the myocytes on the stability of these waves. Finally, we show that the presence of GFDs can lead to the formation of spiral waves at high-frequency pacing.

Nonequilibrium Arrhythmic States and Transitions in a Mathematical Model for Diffuse Fibrosis in Human Cardiac Tissue

We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to fibroblasts via a gap-junctional conductance , reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.

Erratum: Simulation of Reentrant Wave Dynamics in Cardiac Tissue According to the Severity of Fibrosis

This study investigated the spiral wave dynamics in cardiac tissue according to the severity of fibrosis in the hypertrophic human ventricle by simulating propagation of the electric wave. We used a model of the human ventricular cell to describe the cellular electrophysiology and a twodimensional monodomain method to compute the electric wave propagation in ventricular tissue using finite element approximation. To delineate the eect of fibrosis on the wave dynamics, a model of hypertrophic cardiac tissue with randomly distributed fibroblasts was simulated. The electrical conductivity of the fibroblasts was estimated from the experimental data. In the fibrotic cardiac tissue, we generated a reentrant wave and predicted its dynamic variation according to the severity of fibrosis. Compared to the reentrant wave in normal tissue, a conduction delay was observed in the fibrotic tissue. Furthermore, one spiral wave broke into several waves when fibroblasts constituted 40 % of the tissue, causing cardiac fibrillation.

Simulation of Reentrant Wave Dynamics in Cardiac Tissue According to the Severity of Fibrosis

Simulation of Reentrant Wave Dynamics in Cardiac Tissue According to the Severity of Fibrosis

Spiral-wave turbulence and its control in the presence of inhomogeneities in four mathematical models of cardiac tissue.

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Spiral Wave Attachment to Millimeter-Sized Obstacles

Functional reentry in the heart takes the form of spiral waves. Drifting spiral waves can become pinned to anatomic obstacles and thus attain stability and persistence. Lidocaine is an antiarrhythmic agent commonly used to treat ventricular tachycardia clinically. We examined the ability of small obstacles to anchor spiral waves and the effect of lidocaine on their attachment. Spiral waves were electrically induced in confluent monolayers of cultured, neonatal rat cardiomyocytes. Small, circular anatomic obstacles (0.6 to 2.6 mm in diameter) were situated in the center of the monolayers to provide an anchoring site. Eighty reentry episodes consisting of at least 4 revolutions were studied. In 36 episodes, the spiral wave attached to the obstacle and became stationary and sustained, with a shorter reentry cycle length and higher rate. Spiral waves could attach to obstacles as small as 0.6 mm, with a likelihood for attachment that increased with obstacle size. After attachment, both conduction velocity of the wave-front tip and wavelength near the obstacle adapted from their pre-reentry values and increased linearly with obstacle size. In contrast, reentry cycle length did not correlate significantly with obstacle size. Addition of lidocaine 90 mumol/L depressed conduction velocity, increased reentry cycle length, and caused attached spiral waves to become quasi- attached to the obstacle or terminate. Anchored spiral waves exhibit properties of both unattached spiral waves and anatomic reentry. Their behavior may be representative of functional reentry dynamics in cardiac tissue, particularly in the setting of monomorphic tachyarrhythmias.

COMPLICATED ELECTRICAL ACTIVITIES IN CARDIAC TISSUE

It has become widely accepted that ventricular fibrillation, the most dangerous cardiac arrhythmias, is a major cause of death in the industrialized world. Alternans and conduction block have recently been related to the progression from ventricular tachycardia to ventricular fibrillation. From the point of view in cellular electrophysiology, ventricular tachycardia is the formation of reentrant wave in cardiac tissue. And ventricular fibrillation arises from subsequent breakdown of reentrant wave into multiple drifting and meandering spiral waves. In this paper, we numerically study pulse and vortex dynamics in cardiac tissue. Our numerical results include 1:1 normal sinus rhythm, 2:1 conduction block, complete conduction block, spiral wave, and spiral breakup. All of our numerical findings can be corresponding to clinical measurements in electrocardiogram. Various electrical activities in cardiac tissue will be discussed in detail in the present manuscript.

Experimental and theoretical analysis of phase singularity dynamics in cardiac tissue.

Quantitative analysis of complex self-excitatory wave patterns, such as cardiac fibrillation and other high-order reentry, requires the development of new tools for identifying and tracking the most important features of the activation, such as phase singularities. Image processing operations can be used to detect the phase singularity at the tip of a spiral wave. The phase space behavior of a spatiotemporal sequence of data may be reconstructed using time-series analysis. The phase singularities then are localized efficiently by computing the topologic charge density as the curl of the spatial phase gradient. We analyzed the singularity interaction dynamics of both experimentally observed and numerically simulated instances of quatrefoil reentry and found that the singularity behavior in the experimental preparations can be classified into three categories on the basis of how their separation changes with time. Topologic charge densities can be calculated easily and efficiently to reveal phase singularity behavior. However, the differences between theoretical and experimental observations of singularity separation distances indicate the need for more sophisticated numerical models.

Strategy for control of complex low-dimensional dynamics in cardiac tissue.

Heart rate-dependent alterations in the duration of the electrically active state of cardiac cells, the action potential, are an important determinant of lethal heart rhythm disorders. The relationship between action potential duration and heart rate can be modelled as a nonlinear one-dimensional map. Iteration of the map over a range of physiologically relevant heart rates produces complex changes in action potential duration, including period doubling bifurcations, chaos and period doubling reversals. We present a computer algorithm that ensures, over the same range of heart rates, uniform state variable values (action potential durations) by application of small perturbing stimuli at appropriate intervals. The algorithm succeeds, even though the only parameter in the system (the heart rate) is immutable. Control of the dynamics is achieved by exploiting the inexcitability of the cardiac cells immediately after stimulation. This algorithm may have applications for the prevention of cardiac rhythm disturbances.

Modeling of Heart Excitation Patterns caused by a Local Inhomogeneity

We simulate wave propagation in the whole heart containing a local inhomogeneity whose properties mimic some properties of cardiac tissue during acute phase of infarction. The dynamics of cardiac tissue is described by a FitzHugh-Nagumo ( FHN) model. We show that two or several short-period stimulations of the heart lead to the development of a three-dimensional vortex ring, which is a temporal source of high frequency waves. The vortex ring is located near the boundary of the infarction and induces wave patterns which appear as several focal wave sources on the epicard and endocard. We have traced the filament of the vortex and show its dynamics. Continuous stimulation of the heart at high frequency resulted in the Wenckebach effect.

Evidence for chaotic behavior in driven ventricles

Toad ventricles were externally driven by periodic pulses while monophasic action potential (MAP) signals were recorded in seven excised and seven in situ ventricles. As the frequency was slowly increased in steps, the stimulated tissue displayed several dynamic characteristics. Hierarchies of periodic behavior, like phase-locking and period-doubling sequences leading to chaos, were observed. Results showed that subharmonic bifurcations (order one and two) and chaotic-like behavior may systematically occur in the MAP signal within a definite frequency interval in the 1:1 phase locking regime. The chaotic, or more cautiously expressed, chaotic-like behavior is characterized by the power spectrum, the autocorrelation function, the Poincaré map, and the reconstructed 2-D phase portrait. It is concluded that (a) bifurcations of order one and two and the characteristic irregular behavior are evidences of local universal chaotic dynamics in cardiac tissue; (b) there are no qualitative differences in the dynamics of the in situ and excised ventricles; and (c) fibrillation seems to be related to chaotic behavior, but whether they are similar or equivalent phenomena still remains to be seen.