Reflection after delayed excitation in a computer model of a single fiber

Specific decreasing of Na+ channel expression on the lateral membrane of cardiomyocytes causes fatal arrhythmias in Brugada syndrome

Reduced cardiac sodium (Na+) channel current (INa) resulting from the loss-of-function of Na+ channel is a major cause of lethal arrhythmias in Brugada syndrome (BrS). Inspired by previous experimental studies which showed that in heart diseases INa was reduced along with expression changes in Na+ channel within myocytes, we hypothesized that the local decrease in INa caused by the alteration in Na+ channel expression in myocytes leads to the occurrence of phase-2 reentry, the major triggering mechanism of lethal arrhythmias in BrS. We constructed in silico human ventricular myocardial strand and ring models, and examined whether the Na+ channel expression changes in each myocyte cause the phase-2 reentry in BrS. Reducing Na+ channel expression in the lateral membrane of each myocyte caused not only the notch-and-dome but also loss-of-dome type action potentials and slowed conduction, both of which are typically observed in BrS patients. Furthermore, the selective reduction in Na+ channels on the lateral membrane of each myocyte together with spatial tissue heterogeneity of Na+ channel expression caused the phase-2 reentry and phase-2 reentry-mediated reentrant arrhythmias. Our data suggest that the BrS phenotype is strongly influenced by expression abnormalities as well as genetic abnormalities of Na+ channels.

Directed fusion of cardiac spheroids into larger heterocellular microtissues enables investigation of cardiac action potential propagation via cardiac fibroblasts

Multicellular spheroids generated through cellular self-assembly provide cytoarchitectural complexities of native tissue including three-dimensionality, extensive cell-cell contacts, and appropriate cell-extracellular matrix interactions. They are increasingly suggested as building blocks for larger engineered tissues to achieve shapes, organization, heterogeneity, and other biomimetic complexities. Application of these tissue culture platforms is of particular importance in cardiac research as the myocardium is comprised of distinct but intermingled cell types. Here, we generated scaffold-free 3D cardiac microtissue spheroids comprised of cardiac myocytes (CMs) and/or cardiac fibroblasts (CFs) and used them as building blocks to form larger microtissues with different spatial distributions of CMs and CFs. Characterization of fusing homotypic and heterotypic spheroid pairs revealed an important influence of CFs on fusion kinetics, but most strikingly showed rapid fusion kinetics between heterotypic pairs consisting of one CF and one CM spheroid, indicating that CMs and CFs self-sort in vitro into the intermixed morphology found in the healthy myocardium. We then examined electrophysiological integration of fused homotypic and heterotypic microtissues by mapping action potential propagation. Heterocellular elongated microtissues which recapitulate the disproportionate CF spatial distribution seen in the infarcted myocardium showed that action potentials propagate through CF volumes albeit with significant delay. Complementary computational modeling revealed an important role of CF sodium currents and the spatial distribution of the CM-CF boundary in action potential conduction through CF volumes. Taken together, this study provides useful insights for the development of complex, heterocellular engineered 3D tissue constructs and their engraftment via tissue fusion and has implications for arrhythmogenesis in cardiac disease and repair.

Spatial Patterns of Excitation at Tissue and Whole Organ Level Due to Early Afterdepolarizations

Early after depolarizations (EAD) occur in many pathological conditions, such as congenital or acquired channelopathies, drug induced arrhythmias, and several other situations that are associated with increased arrhythmogenicity. In this paper we present an overview of the relevant computational studies on spatial EAD dynamics in 1D, 2D, and in 3D anatomical models and discuss the relation of EADs to cardiac arrhythmias. We also discuss unsolved problems and highlight new lines of research in this area.

Myofibroblasts Electrotonically Coupled to Cardiomyocytes Alter Conduction: Insights at the Cellular Level from a Detailed In silico Tissue Structure Model

Fibrotic myocardial remodeling is typically accompanied by the appearance of myofibroblasts (MFBs). In vitro, MFBs were shown to slow conduction and precipitate ectopic activity following gap junctional coupling to cardiomyocytes (CMCs). To gain further mechanistic insights into this arrhythmogenic MFB-CMC crosstalk, we performed numerical simulations in cell-based high-resolution two-dimensional tissue models that replicated experimental conditions. Cell dimensions were determined using confocal microscopy of single and co-cultured neonatal rat ventricular CMCs and MFBs. Conduction was investigated as a function of MFB density in three distinct cellular tissue architectures: CMC strands with endogenous MFBs, CMC strands with coating MFBs of two different sizes, and CMC strands with MFB inserts. Simulations were performed to identify individual contributions of heterocellular gap junctional coupling and of the specific electrical phenotype of MFBs. With increasing MFB density, both endogenous and coating MFBs slowed conduction. At MFB densities of 5-30%, conduction slowing was most pronounced in strands with endogenous MFBs due to the MFB-dependent increase in axial resistance. At MFB densities >40%, very slow conduction and spontaneous activity was primarily due to MFB-induced CMC depolarization. Coating MFBs caused non-uniformities of resting membrane potential, which were more prominent with large than with small MFBs. In simulations of MFB inserts connecting two CMC strands, conduction delays increased with increasing insert lengths and block appeared for inserts >1.2 mm. Thus, electrophysiological properties of engineered CMC-MFB co-cultures depend on MFB density, MFB size and their specific positioning in respect to CMCs. These factors may influence conduction characteristics in the heterocellular myocardium.

Persistent reflection underlies ectopic activity in multiple sclerosis: a numerical study

Ectopic activity in multiple sclerosis (MS) patients has been traditionally attributed to hyperexcitability of the demyelinated axon segments. Here, we propose that the same outcome may be the result of persistent reflection--the continuous reactivation of the axonal nodes that limit a demyelinated internodal segment. Using computer simulations, we studied the patterns of impulse propagation for a wide range of electrophysiological conditions. In uniformly myelinated fibers, increasing the temperature enabled successful propagation with no blocks in more severe conditions of demyelination. Secondary activations that were originated at the paranodes were formed for temperatures lower than T = 305 K, and at the condition of high sodium channel excitability. Non-sustained and persistent reflections appeared in the case of focally demyelinated fibers, and only within a narrow range of parameters of high temperature and membrane excitability. Persistent reflection reached steady state in ionic currents within 4 ms, and was characterized with a very high activation frequency of 1.504 (+/- 0.039 kHz. We conclude that persistent reflection is a possible mechanism for ectopic activity in MS patients, being more prominent in higher temperatures and severe axonal demyelination. Eliminating these symptoms may be addressed by cooling the body or by applying pharmacological agents to alter excitability properties.

A model of electrical conduction in cardiac tissue including fibroblasts

Fibroblasts are abundant in cardiac tissue. Experimental studies suggested that fibroblasts are electrically coupled to myocytes and this coupling can impact cardiac electrophysiology. In this work, we present a novel approach for mathematical modeling of electrical conduction in cardiac tissue composed of myocytes, fibroblasts, and the extracellular space. The model is an extension of established cardiac bidomain models, which include a description of intra-myocyte and extracellular conductivities, currents and potentials in addition to transmembrane voltages of myocytes. Our extension added a description of fibroblasts, which are electrically coupled with each other and with myocytes. We applied the extended model in exemplary computational simulations of plane waves and conduction in a thin tissue slice assuming an isotropic conductivity of the intra-fibroblast domain. In simulations of plane waves, increased myocyte-fibroblast coupling and fibroblast-myocyte ratio reduced peak voltage and maximal upstroke velocity of myocytes as well as amplitudes and maximal downstroke velocity of extracellular potentials. Simulations with the thin tissue slice showed that inter-fibroblast coupling affected rather transversal than longitudinal conduction velocity. Our results suggest that fibroblast coupling becomes relevant for small intra-myocyte and/or large intra-fibroblast conductivity. In summary, the study demonstrated the feasibility of the extended bidomain model and supports the hypothesis that fibroblasts contribute to cardiac electrophysiology in various manners.

Reentry in an accessory atrioventricular pathway as a trigger for atrial fibrillation initiation in manifest Wolff-Parkinson-White syndrome: a matter of reflection?

BACKGROUND

Patients with an accessory pathway (AP) have an increased propensity to develop atrial fibrillation (AF), but the mechanism is unknown.

OBJECTIVE

The purpose of this study was to identify crucial risk factors and to test the hypothesis that reflection and/or microreentry of atrial impulses propagating into the AP triggers AF.

METHODS

Five hundred thirty-four patients successfully treated with radiofrequency ablation of AP at two university hospitals were evaluated. Patients were separated into those with concealed vs those with manifest AP in terms of their propensity to develop AF. To investigate AF triggering mechanisms, linear and branched two-dimensional models of atrium-to-ventricle propagation across a heterogeneous 1 x 6 AP using human ionic kinetics were simulated.

RESULTS

A history of AF was twice as common in patients with manifest AP vs concealed AP irrespective of AP location. AF was more likely to occur in older males and in patients with larger atria. There was no correlation between AF history and AP refractory measures. However, the electrophysiologic properties of APs seemed to fulfill the prerequisites for reflection and/or microreentry of atrially initiated impulses. In the linear AP model, repetitive atrial stimulation resulted in progressively larger delay of atrium-to-ventricle propagation across the passive segment. Eventually, sufficient time for repolarization of the atrial segment allowed for reflection of an impulse that activated the entire atrium and by wavefront-wavetail interaction with a new atrial stimulus AF reentry was initiated. Simulations using the branched model showed that microreentry at the ventricular insertion of the AP could also initiate AF via retrograde atrial activation as a result of unidirectional block at the AP-ventricle junction.

CONCLUSION

Propensity for AF in patients with an AP is strongly related to preexcitation, larger atria, male gender, and older age. Reflection and microreentry at the AP may be important for AF initiation in patients with manifest (preexcited) Wolff-Parkinson-White syndrome. Similar mechanisms also may trigger AF in patients without an AP.

Electrophysiological modeling of fibroblasts and their interaction with myocytes

Experimental studies have shown that cardiac fibroblasts are electrically inexcitable, but can contribute to electrophysiology of myocardium in various manners. The aim of this computational study was to give insights in the electrophysiological role of fibroblasts and their interaction with myocytes. We developed a mathematical model of fibroblasts based on data from whole-cell patch clamp and polymerase chain reaction (PCR) studies. The fibroblast model was applied together with models of ventricular myocytes to assess effects of heterogeneous intercellular electrical coupling. We investigated the modulation of action potentials of a single myocyte varying the number of coupled fibroblasts and intercellular resistance. Coupling to fibroblasts had only a minor impact on the myocyte's resting and peak transmembrane voltage, but led to significant changes of action potential duration and upstroke velocity. We examined the impact of fibroblasts on conduction in one-dimensional strands of myocytes. Coupled fibroblasts reduced conduction and upstroke velocity. We studied electrical bridging between ventricular myocytes via fibroblast insets for various coupling resistors. The simulations showed significant conduction delays up to 20.3 ms. In summary, the simulations support strongly the hypothesis that coupling of fibroblasts to myocytes modulates electrophysiology of cardiac cells and tissues.

Soliton-like regimes and excitation pulse reflection (echo) in homogeneous cardiac purkinje fibers: results of numerical simulations

On the basis of numerical simulations of the partial McAllister-Noble-Tsien equations quantitatively describing the dynamics of electrical processes in conductive cardiac Purkinje fibers we reveal unusual - soliton-like - regimes of interaction of nonlinear excitation pulses governing the heart contraction rhythm: reflection of colliding pulses instead of their annihilation. The phenomenological mechanism of the reflection effects is that in a narrow (but finite) range of the system parameters the traveling pulse presents a doublet consisting of a high-amplitude leader followed by a low-amplitude subthreshold wave. Upon collisions of pulses the leaders are annihilated, but subthreshold waves summarize becoming superthreshold and initiating two novel echo-pulses traveling in opposite directions. The phenomenon revealed presents an analogy to the effect of reflection of colliding nerve pulses, predicted recently, and can be of use in getting insight into the mechanisms of heart rhythm disturbances.

Modeling triggered cardiac activity: an analysis of the interactions between potassium blockade, rhythm pauses, and cellular coupling

It is known that under certain conditions, a combination of potassium channel blockade, sympathetic nervous activity, and pauses in sinus rhythm can increase the occurrence of cardiac arrhythmias. Although the arrhythmogenic interactions of these three factors are not completely understood, it is believed that the associated arrhythmias may be initiated by afterpotentials via a process that we refer to as propagated triggered activity. Using a two-cell computational model of ventricular action potential kinetics, we simulate nonuniform potassium blockade, sympathetic nervous activity, and pauses in sinus rhythm under conditions of hypokalemia. Under these conditions, the two-cell model suggests that (1) the arrhythmogenic interactions of potassium blockade and sympathetic nervous activity are highly dependent on heart rate; (2) triggered activity induced by potassium blockade would most likely occur during a pause in sinus rhythm; (3) during a sufficiently large pause in sinus rhythm, potassium blockade can induce triggered activity at normal levels of sympathetic activity; and (4) potassium blockade can increase the probability of triggered activity only if heart rate falls within a critical range. We also show that during pauses in sinus rhythm, two-cell triggering interactions between potassium blockade and sympathetic activity closely parallel the parametric displacement of the dynamic instability underlying the afterpotentials. Our results indicate that the behavior of the triggering mechanism studied here is consistent with that of pause-induced arrhythmias.

Failure of impulse propagation in a mathematically simulated ischemic border zone: influence of direction of propagation and cell-to-cell electrical coupling

INTRODUCTION

It is suggested that heterogeneous extracellular potassium concentration, cell-to-cell coupling, and geometric nonuniformities of the ischemic border zone contribute to the incidence of unidirectional block and subsequent development of lethal ventricular arrhythmias.

METHOD AND RESULTS

A discrete electrical network was used to model a single cardiac fiber with a [K+]e gradient characteristic of an ischemic border zone. Directional differences in propagation were evaluated by creating discrete regions with increased gap junctional resistance within the [K+]e gradient. Furthermore, the effect of homogeneity/heterogeneity of call length on impulse propagation through the [K+]e gradient in the presence of increased gap junctional resistance was evaluated. The results indicate that failure of impulse propagation occurs at the junction between partially uncoupled and normally coupled cells. Furthermore, propagation failure was more likely to occur as the impulse propagated from a region of high [K+]e to low [K+]e. Heterogeneity in cell length contributes to the variability in the occurrence of unidirectional and bidirectional block.

CONCLUSIONS

The onset of cellular uncoupling in an ischemic border zone may interact with the inherent [K+]e gradient leading to unidirectional conduction block. This mechanism may be important for the generation of reentrant arrhythmias at the ischemic border zone.

Unidirectional block in a computer model of partially coupled segments of cardiac Purkinje tissue

The initiation of a reentrant circuit requires a zone of slow conduction and a zone of unidirectional block. This study used computer model conditions under which partial coupling between segments of cardiac Purkinje tissue resulted in unidirectional block. The structure used was one-dimensional and divided into three segments: a middle segment of variable length coupled to two long (semi-infinite in concept) segments. The DiFrancesco-Noble equations represented the ionic currents of the membrane. The results show that the possibility of unidirectional block depends on the size of the middle segment and the coupling resistances between the segments. No combination of coupling resistances allowed unidirectional block for middle segments with a length of two space constants (4 mm) or longer. Unidirectional block occurred for many combinations of coupling resistances as the length of the middle segment decreased to around half a space constant (1 mm). The number of length combinations that caused unidirectional block decreased again as segment length further decreased. These results provide a possible mechanism of unidirectional block for situations where islands of viable tissue are connected through nonviable tissue, such as in a healed myocardial infarction.