Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and fibroblasts

Effects of fibroblast on electromechanical dynamics of human atrial tissue—insights from a 2D discrete element model

Roughly 75% of normal myocardial tissue volume is comprised of myocytes, however, fibroblasts by number are the most predominant cells in cardiac tissue. Previous studies have shown distinctive differences in cellular electrophysiology and excitability between myocytes and fibroblasts. However, it is still unclear how the electrical coupling between the two and the increased population of fibroblasts affects the electromechanical dynamics of cardiac tissue. This paper focuses on investigating effects of fibroblast-myocyte electrical coupling (FMEC) and fibroblast population on atrial electrical conduction and mechanical contractility by using a two-dimensional Discrete Element Method (DEM) model of cardiac tissue that is different to finite element method (FEM). In the model, the electro-mechanics of atrial cells are modelled by a biophysically detailed model for atrial electrical action potentials and myofilament kinetics, and the atrial fibroblasts are modelled by an active model that considers four active membrane ionic channel currents. Our simulation results show that the FMEC impairs myocytes’ electrical action potential and mechanical contractibility, manifested by reduced upstroke velocity, amplitude and duration of action potentials, as well as cell length shortening. At the tissue level, the FMEC slows down the conduction of excitation waves, and reduces strain of the tissue produced during a contraction course. These findings provide new insights into understandings of how FMEC impairs cardiac electrical and mechanical dynamics of the heart.

Action potential propagation and block in a model of atrial tissue with myocyte-fibroblast coupling

The electrical coupling between myocytes and fibroblasts and the spacial distribution of fibroblasts within myocardial tissues are significant factors in triggering and sustaining cardiac arrhythmias, but their roles are poorly understood. This article describes both direct numerical simulations and an asymptotic theory of propagation and block of electrical excitation in a model of atrial tissue with myocyte-fibroblast coupling. In particular, three idealized fibroblast distributions are introduced: uniform distribution, fibroblast barrier and myocyte strait-all believed to be constituent blocks of realistic fibroblast distributions. Primary action potential biomarkers including conduction velocity, peak potential and triangulation index are estimated from direct simulations in all cases. Propagation block is found to occur at certain critical values of the parameters defining each idealized fibroblast distribution, and these critical values are accurately determined. An asymptotic theory proposed earlier is extended and applied to the case of a uniform fibroblast distribution. Biomarker values are obtained from hybrid analytical-numerical solutions of coupled fast-time and slow-time periodic boundary value problems and compare well to direct numerical simulations. The boundary of absolute refractoriness is determined solely by the fast-time problem and is found to depend on the values of the myocyte potential and on the slow inactivation variable of the sodium current ahead of the propagating pulse. In turn, these quantities are estimated from the slow-time problem using a regular perturbation expansion to find the steady state of the coupled myocyte-fibroblast kinetics. The asymptotic theory gives a simple analytical expression that captures with remarkable accuracy the block of propagation in the presence of fibroblasts.

Myocardial Fibrosis in a 3D Model: Effect of Texture on Wave Propagation

Non-linear electrical waves propagate through the heart and control cardiac contraction. Abnormal wave propagation causes various forms of the heart disease and can be lethal. One of the main causes of abnormality is a condition of cardiac fibrosis, which, from mathematical point of view, is the presence of multiple non-conducting obstacles for wave propagation. The fibrosis can have different texture which varies from diffuse (e.g., small randomly distributed obstacles), patchy (e.g., elongated interstitional stria), and focal (e.g., post-infarct scars) forms. Recently, Nezlobinsky et al. (2020) used 2D biophysical models to quantify the effects of elongation of obstacles (fibrosis texture) and showed that longitudinal and transversal propagation differently depends on the obstacle length resulting in anisotropy for wave propagation. In this paper, we extend these studies to 3D tissue models. We show that 3D consideration brings essential new effects; for the same obstacle length in 3D systems, anisotropy is about two times smaller compared to 2D, however, wave propagation is more stable with percolation threshold of about 60% (compared to 35% in 2D). The percolation threshold increases with the obstacle length for the longitudinal propagation, while it decreases for the transversal propagation. Further, in 3D, the dependency of velocity on the obstacle length for the transversal propagation disappears.

Development of endomyocardial fibrosis model using a cell patterning technique: In vitro interaction of cell coculture of 3T3 fibroblasts and RL-14 cardiomyocytes

Cardiac functions can be altered by changes in the microstructure of the heart, i.e., remodeling of the cardiac tissue, which may activate pathologies such as hypertrophy, dilation, or cardiac fibrosis. Cardiac fibrosis can develop due to an excessive deposition of extracellular matrix proteins, which are products of the activation of fibroblasts. In this context, the anatomical-histological change may interfere with the functioning of the cardiac tissue, which requires specialized cells for its operation. The purpose of the present study was to determine the cellular interactions and morphological changes in cocultures of 3T3 fibroblasts and RL-14 cardiomyocytes via the generation of a platform an in vitro model. For this purpose, a platform emulating the biological characteristics of endomyocardial fibrosis was generated using a cell patterning technique to study morphological cellular changes in compact and irregular patterns of fibrosis. It was found that cellular patterns emulating the geometrical distributions of endomyocardial fibrosis generated morphological changes after interaction of the RL-14 cardiomyocytes with the 3T3 fibroblasts. Through this study, it was possible to evaluate biological characteristics such as cell proliferation, adhesion, and spatial distribution, which are directly related to the type of emulated endomyocardial fibrosis. This research concluded that fibroblasts inhibited the proliferation of cardiomyocytes via their interaction with specific microarchitectures. This behavior is consistent with the histopathological distribution of cardiac fibrosis; therefore, the platform developed in this research could be useful for the in vitro assessment of cellular microdomains. This would allow for the experimental determination of interactions with drugs, substrates, or biomaterials within the engineering of cardiac tissues.

Self-organization of conducting pathways explains electrical wave propagation in cardiac tissues with high fraction of non-conducting cells

Cardiac fibrosis occurs in many forms of heart disease and is considered to be one of the main arrhythmogenic factors. Regions with a high density of fibroblasts are likely to cause blocks of wave propagation that give rise to dangerous cardiac arrhythmias. Therefore, studies of the wave propagation through these regions are very important, yet the precise mechanisms leading to arrhythmia formation in fibrotic cardiac tissue remain poorly understood. Particularly, it is not clear how wave propagation is organized at the cellular level, as experiments show that the regions with a high percentage of fibroblasts (65-75%) are still conducting electrical signals, whereas geometric analysis of randomly distributed conducting and non-conducting cells predicts connectivity loss at 40% at the most (percolation threshold). To address this question, we used a joint in vitro-in silico approach, which combined experiments in neonatal rat cardiac monolayers with morphological and electrophysiological computer simulations. We have shown that the main reason for sustainable wave propagation in highly fibrotic samples is the formation of a branching network of cardiomyocytes. We have successfully reproduced the morphology of conductive pathways in computer modelling, assuming that cardiomyocytes align their cytoskeletons to fuse into cardiac syncytium. The electrophysiological properties of the monolayers, such as conduction velocity, conduction blocks and wave fractionation, were reproduced as well. In a virtual cardiac tissue, we have also examined the wave propagation at the subcellular level, detected wavebreaks formation and its relation to the structure of fibrosis and, thus, analysed the processes leading to the onset of arrhythmias.

Cardiac arrhythmias are one of the major causes of death in the industrialized world. The most dangerous ones are often caused by the blocks of propagation of electrical signals. One of the common factors that contribute to the likelihood of these blocks, is a condition called cardiac fibrosis. In fibrosis, excitable cardiac tissue is partially replaced with the inexcitable and non-conducting connective tissue. The precise mechanisms leading to arrhythmia formation in fibrotic cardiac tissue remain poorly understood. Therefore, it is important to study wave propagation in fibrosis from cellular to tissue level. In this paper, we study tissues with high densities of non-conducting cells in experiments and computer simulations. We have observed a paradoxical ability of the tissue with extremely high portion of non-conducting cells (up to 75%) to conduct electrical signals and contract synchronously, whereas geometric analysis of randomly distributed cells predicted connectivity loss at 40% at the most. To explain this phenomenon, we have studied the patterns that cardiac cells form in the tissue and reproduced their self-organisation in a computer model. Our virtual model also took into account the polygonal shapes of the spreading cells and explained high arrhythmogenicity of fibrotic tissue.

Intraluminal three-dimensional optical coherence tomography - a tool for imaging of the Eustachian tube?

OBJECTIVES

The cause of Eustachian tube dysfunction often remains unclear. Therefore, this study aimed to examine the feasibility and possible diagnostic use of optical coherence tomography in the Eustachian tube ex vivo.

METHODS

Two female blackface sheep cadaver heads were examined bilaterally. Three conditions of the Eustachian tube were investigated: closed (resting position), actively opened and stented. The findings were compared (and correlated) with segmented histological cross-sections.

RESULTS

Intraluminal placement of the Eustachian tube with the optical coherence tomography catheter was performed without difficulty. Regarding the limited infiltration depth of optical coherence tomography, tissues can be differentiated. The localisation of the stent was accurate as was the lumen.

CONCLUSION

The application of optical coherence tomography in the Eustachian tube under these experimental conditions is considered to be a feasible, rapid and non-invasive diagnostic method, with possible diagnostic value for determining the luminal shape and superficial lining tissue of the Eustachian tube.

Cardiac spiral wave drifting due to spatial temperature gradients - A numerical study

Cardiac rotors are believed to be a major driver source of persistent atrial fibrillation (AF), and their spatiotemporal characterization is essential for successful ablation procedures. However, electrograms guided ablation have not been proven to have benefit over empirical ablation thus far, and there is a strong need of improving the localization of cardiac arrhythmogenic targets for ablation. A new approach for characterize rotors is proposed that is based on induced spatial temperature gradients (STGs), and investigated by theoretical study using numerical simulations. We hypothesize that such gradients will cause rotor drifting due to induced spatial heterogeneity in excitability, so that rotors could be driven towards the ablating probe. Numerical simulations were conducted in single cell and 2D atrial models using AF remodeled kinetics. STGs were applied either linearly on the entire tissue or as a small local perturbation, and the major ion channel rate constants were adjusted following Arrhenius equation. In the AF-remodeled single cell, recovery time increased exponentially with decreasing temperatures, despite the marginal effect of temperature on the action potential duration. In 2D models, spiral waves drifted with drifting velocity components affected by both temperature gradient direction and the spiral wave rotation direction. Overall, spiral waves drifted towards the colder tissue region associated with global minimum of excitability. A local perturbation with a temperature of T = 28 °C was found optimal for spiral wave attraction for the studied conditions. This work provides a preliminary proof-of-concept for a potential prospective technique for rotor attraction. We envision that the insights from this study will be utilize in the future in the design of a new methodology for AF characterization and termination during ablation procedures.

Quantitative systems models illuminate arrhythmia mechanisms in heart failure: Role of the Na+ -Ca2+ -Ca2+ /calmodulin-dependent protein kinase II-reactive oxygen species feedback

Quantitative systems modeling aims to integrate knowledge in different research areas with models describing biological mechanisms and dynamics to gain a better understanding of complex clinical syndromes. Heart failure (HF) is a chronic complex cardiac disease that results from structural or functional disorders impairing the ability of the ventricle to fill with or eject blood. Highly interactive and dynamic changes in mechanical, structural, neurohumoral, metabolic, and electrophysiological properties collectively predispose the failing heart to cardiac arrhythmias, which are responsible for about a half of HF deaths. Multiscale cardiac modeling and simulation integrate structural and functional data from HF experimental models and patients to improve our mechanistic understanding of this complex arrhythmia syndrome. In particular, they allow investigating how disease-induced remodeling alters the coupling of electrophysiology, Ca²⁺ and Na⁺ handling, contraction, and energetics that lead to rhythm derangements. The Ca²⁺ /calmodulin-dependent protein kinase II, which expression and activity are enhanced in HF, emerges as a critical hub that modulates the feedbacks between these various subsystems and promotes arrhythmogenesis. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

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.

Reentry via high-frequency pacing in a mathematical model for human-ventricular cardiac tissue with a localized fibrotic region

Localized heterogeneities, caused by the regional proliferation of fibroblasts, occur in mammalian hearts because of diseases like myocardial infarction. Such fibroblast clumps can become sources of pathological reentrant activities, e.g., spiral or scroll waves of electrical activation in cardiac tissue. The occurrence of reentry in cardiac tissue with heterogeneities, such as fibroblast clumps, can depend on the frequency at which the medium is paced. Therefore, it is important to study the reentry-initiating potential of such fibroblast clumps at different frequencies of pacing. We investigate the arrhythmogenic effects of fibroblast clumps at high- and low-frequency pacing. We find that reentrant waves are induced in the medium more prominently at high-frequency pacing than with low-frequency pacing. We also study the other factors that affect the potential of fibroblast clumps to induce reentry in cardiac tissue. In particular, we show that the ability of a fibroblast clump to induce reentry depends on the size of the clump, the distribution and percentage of fibroblasts in the clump, and the excitability of the medium. We study the process of reentry in two-dimensional and a three-dimensional mathematical models for cardiac tissue.

Gq-activated fibroblasts induce cardiomyocyte action potential prolongation and automaticity in a three-dimensional microtissue environment

Cardiac fibroblasts (CFs) are known to regulate cardiomyocyte (CM) function in vivo and in two-dimensional in vitro cultures. This study examined the effect of CF activation on the regulation of CM electrical activity in a three-dimensional (3-D) microtissue environment. Using a scaffold-free 3-D platform with interspersed neonatal rat ventricular CMs and CFs, G_q-mediated signaling was selectively enhanced in CFs by Gα_q adenoviral infection before coseeding with CMs in nonadhesive hydrogels. After 3 days, the microtissues were analyzed by signaling assay, histological staining, quantitative PCR, Western blots, optical mapping with voltage- or Ca²⁺-sensitive dyes, and microelectrode recordings of CF resting membrane potential (RMP_CF). Enhanced G_q signaling in CFs increased microtissue size and profibrotic and prohypertrophic markers. Expression of constitutively active Gα_q in CFs prolonged CM action potential duration (by 33%) and rise time (by 31%), prolonged Ca²⁺ transient duration (by 98%) and rise time (by 65%), and caused abnormal electrical activity based on depolarization-induced automaticity. Constitutive G_q activation in CFs also depolarized RMP_CF from -33 to -20 mV and increased connexin 43 and connexin 45 expression. Computational modeling confers that elevated RMP_CF and increased cell-cell coupling between CMs and CFs in a 3-D environment could lead to automaticity. In conclusion, our data demonstrate that CF activation alone is capable of altering action potential and Ca²⁺ transient characteristics of CMs, leading to proarrhythmic electrical activity. Our results also emphasize the importance of a 3-D environment where cell-cell interactions are prevalent, underscoring that CF activation in 3-D tissue plays a significant role in modulating CM electrophysiology and arrhythmias.NEW & NOTEWORTHY In a three-dimensional microtissue model, which lowers baseline activation of cardiac fibroblasts but enables cell-cell, paracrine, and cell-extracellular matrix interactions, we demonstrate that selective cardiac fibroblast activation by enhanced G_q signaling, a pathophysiological trigger in the diseased heart, modulates cardiomyocyte electrical activity, leading to proarrhythmogenic automaticity.

Illuminating Myocyte-Fibroblast Homotypic and Heterotypic Gap Junction Dynamics Using Dynamic Clamp

Fibroblasts play a significant role in the development of electrical and mechanical dysfunction of the heart; however, the underlying mechanisms are only partially understood. One widely studied mechanism suggests that fibroblasts produce excess extracellular matrix, resulting in collagenous septa that slow propagation, cause zig-zag conduction paths, and decouple cardiomyocytes, resulting in a substrate for cardiac arrhythmia. An emerging mechanism suggests that fibroblasts promote arrhythmogenesis through direct electrical interactions with cardiomyocytes via gap junction (GJ) channels. In the heart, three major connexin (Cx) isoforms, Cx40, Cx43, and Cx45, form GJ channels in cell-type-specific combinations. Because each Cx is characterized by a unique time- and transjunctional voltage-dependent profile, we investigated whether the electrophysiological contributions of fibroblasts would vary with the specific composition of the myocyte-fibroblast (M-F) GJ channel. Due to the challenges of systematically modifying Cxs in vitro, we coupled native cardiomyocytes with in silico fibroblast and GJ channel electrophysiology models using the dynamic-clamp technique. We found that there is a reduction in the early peak of the junctional current during the upstroke of the action potential (AP) due to GJ channel gating. However, effects on the cardiomyocyte AP morphology were similar regardless of the specific type of GJ channel (homotypic Cx43 and Cx45, and heterotypic Cx43/Cx45 and Cx45/Cx43). To illuminate effects at the tissue level, we performed multiscale simulations of M-F coupling. First, we developed a cell-specific model of our dynamic-clamp experiments and investigated changes in the underlying membrane currents during M-F coupling. Second, we performed two-dimensional tissue sheet simulations of cardiac fibrosis and incorporated GJ channels in a cell type-specific manner. We determined that although GJ channel gating reduces junctional current, it does not significantly alter conduction velocity during cardiac fibrosis relative to static GJ coupling. These findings shed more light on the complex electrophysiological interplay between cardiac fibroblasts and myocytes.

Computational modeling for cardiac safety pharmacology analysis: Contribution of fibroblasts

INTRODUCTION

Drug-induced proarrhythmic potential is an important regulatory criterion in safety pharmacology. The application of in silico approaches to predict proarrhythmic potential of new compounds is under consideration as part of future guidelines. Current approaches simulate the electrophysiology of a single human adult ventricular cardiomyocyte. However, drug-induced proarrhythmic potential can be different when cardiomyocytes are surrounded by non-muscle cells. Incorporating fibroblasts in models of myocardium is important particularly for predicting a drugs cardiac liability in the aging population - a growing population who take more medications and exhibit increased cardiac fibrosis. In this study, we used computational models to investigate the effects of fibroblast coupling on the electrophysiology and response to drugs of cardiomyocytes.

METHODS

A computational model of cardiomyocyte electrophysiology and ion handling (O'Hara, Virag, Varro, & Rudy, 2011) is coupled to a passive model of fibroblast electrophysiology to test the effects of three compounds that block cardiomyocyte ion channels. Results are compared to model results without fibroblast coupling to see how fibroblasts affect cardiomyocyte action potential duration at 90% repolarization (APD₉₀) and propensity for early after depolarization (EAD).

RESULTS

Simulation results show changes in cardiomyocyte APD₉₀ with increasing concentration of three drugs that affect cardiac function (dofetilide, vardenafil and nebivolol) when no fibroblasts are coupled to the cardiomyocyte. Coupling fibroblasts to cardiomyocytes markedly shortens APD₉₀. Moreover, increasing the number of fibroblasts can augment the shortening effect.

DISCUSSION

Coupling cardiomyocytes and fibroblasts are predicted to decrease proarrhythmic susceptibility under dofetilide, vardenafil and nebivolol block. However, this result is sensitive to parameters which define the electrophysiological function of the fibroblast. Fibroblast membrane capacitance and conductance (C_FB and G_FB) have less of an effect on APD₉₀ than the fibroblast resting membrane potential (E_FB). This study suggests that in both theoretical models and experimental tissue constructs that represent cardiac tissue, both cardiomyocytes and non-muscle cells should be considered when testing cardiac pharmacological agents.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.

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.

Termination of atrial spiral waves by traction into peripheral non 1:1 conducting regions - A numerical study

Atrial ablation has been recently utilized to treat atrial fibrillation (AF) by isolation or destruction of arrhythmia drivers. In chronic or persistent AF patients these drivers often consist of one or few rotors at unknown locations, and several ablations are commonly conducted before arrhythmia is terminated. However, the irreversible damage done to the tissue may lead to AF recurrence. We propose an alternative strategy to terminate rotor activity by its attraction into a non 1:1 conducting region. The feasibility of the method was numerically tested in 2D models of chronic AF human atrial tissue. Left-to-right gradients of either acetylcholine (ACh) or potassium conductance were employed to generate regions of 1:1 and non 1:1 conduction, characterized by their dominant frequency (DF) ratios. Spiral waves were established in the 1:1 conducting region and raster scanning was employed using a stimulating probe to attract the spiral wave tip. The probe was then linearly moved towards the boundary between the two regions. Successful attraction of spiral waves to the probe was demonstrated when the probe was <8mm from the spiral wave tip. Maximal traction velocity without loss of anchoring increased in a non-linear way with increasing values of ACh. Success rate of spiral wave termination was over 90% for regional DF ratios of as low as 1:1.2. Given that normally much higher ratios are measured in physiological atrial tissues, we envision this technique to provide a feasible, safer alternative to ablation procedures performed in persistent AF patients.

Effect of the electrograms density in detecting and ablating the tip of the rotor during chronic atrial fibrillation: an in silico study

AIMS

Identification in situ of arrhythmogenic mechanisms could improve the rate of ablation success in atrial fibrillation (AF). Our research group reported that rotors could be located through dynamic approximate entropy (DApEn) maps. However, it is unknown how much the spatial resolution of catheter electrodes could affect substrates localization. The present work looked for assessing the electrograms (EGMs) spatial resolution needed to locate the rotor tip using DApEn maps.

METHODS AND RESULTS

A stable rotor in a two-dimensional computational model of human atrial tissue was simulated using the Courtemanche electrophysiological model and implementing chronic AF features. The spatial resolution is 0.4 mm (150 × 150 EGM). Six different lower resolution arrays were obtained from the initial mesh. For each array, DApEn maps were constructed using the inverse distance weighting (IDW) algorithm. Three simple ablation patterns were applied. The full DApEn map detected the rotor tip and was able to follow the small meander of the tip through the shape of the area containing the tip. Inverse distance weighting was able to reconstruct DApEn maps after applying different spatial resolutions. These results show that spatial resolutions from 0.4 to 4 mm accurately detect the rotor tip position. An ablation line terminates the rotor only if it crosses the tip and ends at a tissue boundary.

CONCLUSION

A previous work has shown that DApEn maps successfully detected simulated rotor tips using a high spatial resolution. In this work, it was evinced that DApEn maps could be applied using a spatial resolution similar to that available in commercial catheters, by adding an interpolation stage. This is the first step to translate this tool into medical practice with a view to the detection of ablation targets.

The Multi-Domain Fibroblast/Myocyte Coupling in the Cardiac Tissue: A Theoretical Study

Cardiac fibroblast proliferation and concomitant collagenous matrix accumulation (fibrosis) develop during multiple cardiac pathologies. Recent studies have demonstrated direct electrical coupling between myocytes and fibroblasts in vitro, and assessed the electrophysiological implications of such coupling. However, in the living tissues, such coupling has not been demonstrated, and only indirect coupling via the extracellular space is likely to exist. In this study we employed a multi-domain model to assess the modulation of the cardiac electrophysiological properties by neighboring fibroblasts assuming only indirect coupling. Numerical simulations in 1D and 2D human atrial models showed that extracellular coupling sustains a significant impact on conduction velocity (CV) and a less significant effect on the action potential duration. Both CV and the slope of the CV restitution increased with increasing fibroblast density. This effect was more substantial for lower extracellular conductance. In 2D, spiral waves exhibited reduced frequency with increasing fibroblast density, and the propensity of wavebreaks and complex dynamics at high pacing rates significantly increased.

A Computational Study of the Factors Influencing the PVC-Triggering Ability of a Cluster of Early Afterdepolarization-Capable Myocytes

Premature ventricular complexes (PVCs), which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.

Lessons learned from multi-scale modeling of the failing heart

Heart failure constitutes a major public health problem worldwide. Affected patients experience a number of changes in the electrical function of the heart that predispose to potentially lethal cardiac arrhythmias. Due to the multitude of electrophysiological changes that may occur during heart failure, the scientific literature is complex and sometimes ambiguous, perhaps because these findings are highly dependent on the etiology, the stage of heart failure, and the experimental model used to study these changes. Nevertheless, a number of common features of failing hearts have been documented. Prolongation of the action potential (AP) involving ion channel remodeling and alterations in calcium handling have been established as the hallmark characteristics of myocytes isolated from failing hearts. Intercellular uncoupling and fibrosis are identified as major arrhythmogenic factors. Multi-scale computational simulations are a powerful tool that complements experimental and clinical research. The development of biophysically detailed computer models of single myocytes and cardiac tissues has contributed greatly to our understanding of processes underlying excitation and repolarization in the heart. The electrical, structural, and metabolic remodeling that arises in cardiac tissues during heart failure has been addressed from different computational perspectives to further understand the arrhythmogenic substrate. This review summarizes the contributions from computational modeling and simulation to predict the underlying mechanisms of heart failure phenotypes and their implications for arrhythmogenesis, ranging from the cellular level to whole-heart simulations. The main aspects of heart failure are presented in several related sections. An overview of the main electrophysiological and structural changes that have been observed experimentally in failing hearts is followed by the description and discussion of the simulation work in this field at the cellular level, and then in 2D and 3D cardiac structures. The implications for arrhythmogenesis in heart failure are also discussed including therapeutic measures, such as drug effects and cardiac resynchronization therapy. Finally, the future challenges in heart failure modeling and simulation will be discussed.

Computational Approaches to Understanding the Role of Fibroblast-Myocyte Interactions in Cardiac Arrhythmogenesis

The adult heart is composed of a dense network of cardiomyocytes surrounded by nonmyocytes, the most abundant of which are cardiac fibroblasts. Several cardiac diseases, such as myocardial infarction or dilated cardiomyopathy, are associated with an increased density of fibroblasts, that is, fibrosis. Fibroblasts play a significant role in the development of electrical and mechanical dysfunction of the heart; however the underlying mechanisms are only partially understood. One widely studied mechanism suggests that fibroblasts produce excess extracellular matrix, resulting in collagenous septa. These collagenous septa slow propagation, cause zig-zag conduction paths, and decouple cardiomyocytes resulting in a substrate for arrhythmia. Another emerging mechanism suggests that fibroblasts promote arrhythmogenesis through direct electrical interactions with cardiomyocytes via gap junctions. Due to the challenges of investigating fibroblast-myocyte coupling in native cardiac tissue, computational modeling and in vitro experiments have facilitated the investigation into the mechanisms underlying fibroblast-mediated changes in cardiomyocyte action potential morphology, conduction velocity, spontaneous excitability, and vulnerability to reentry. In this paper, we summarize the major findings of the existing computational studies investigating the implications of fibroblast-myocyte interactions in the normal and diseased heart. We then present investigations from our group into the potential role of voltage-dependent gap junctions in fibroblast-myocyte interactions.

Turbulent states and their transitions in mathematical models for ventricular tissue: the effects of random interstitial fibroblasts

We study the dynamical behaviors of two types of spiral- and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling G_{j} and (2) the number N_{f} of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) G_{j} is large or (b) the maximum possible number of fibroblasts per myocyte N_{f}^{max} is large. We also observe that the minimum value of G_{j}, for the transition from the ST to the RS state, decreases as N_{f}^{max} increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) G_{j} increases, with fixed N_{f}^{max}, and (2) N_{f}^{max} increases, with fixed G_{j}. We obtain the boundary between ST and RS stability regions in the N_{f}^{max}-G_{j} plane. In particular, for low values of N_{f}^{max}, the value of G_{j}, at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as N_{f}^{max} increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral- and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.

Human cardiac systems electrophysiology and arrhythmogenesis: iteration of experiment and computation

Human cardiac electrophysiology (EP) is a unique system for computational modelling at multiple scales. Due to the complexity of the cardiac excitation sequence, coordinated activity must occur from the single channel to the entire myocardial syncytium. Thus, sophisticated computational algorithms have been developed to investigate cardiac EP at the level of ion channels, cardiomyocytes, multicellular tissues, and the whole heart. Although understanding of each functional level will ultimately be important to thoroughly understand mechanisms of physiology and disease, cardiac arrhythmias are expressly the product of cardiac tissue-containing enough cardiomyocytes to sustain a reentrant loop of activation. In addition, several properties of cardiac cellular EP, that are critical for arrhythmogenesis, are significantly altered by cell-to-cell coupling. However, relevant human cardiac EP data, upon which to develop or validate models at all scales, has been lacking. Thus, over several years, we have developed a paradigm for multiscale human heart physiology investigation and have recovered and studied over 300 human hearts. We have generated a rich experimental dataset, from which we better understand mechanisms of arrhythmia in human and can improve models of human cardiac EP. In addition, in collaboration with computational physiologists, we are developing a database for the deposition of human heart experimental data, including thorough experimental documentation. We anticipate that accessibility to this human heart dataset will further human EP computational investigations, as well as encourage greater data transparency within the field of cardiac EP.

A Comparative Study of Early Afterdepolarization-Mediated Fibrillation in Two Mathematical Models for Human Ventricular Cells

Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.

Electrophysiological and structural remodeling in heart failure modulate arrhythmogenesis. 1D simulation study

Background

Heart failure is a final common pathway or descriptor for various cardiac pathologies. It is associated with sudden cardiac death, which is frequently caused by ventricular arrhythmias. Electrophysiological remodeling, intercellular uncoupling, fibrosis and autonomic imbalance have been identified as major arrhythmogenic factors in heart failure etiology and progression.

Objective

In this study we investigate in silico the role of electrophysiological and structural heart failure remodeling on the modulation of key elements of the arrhythmogenic substrate, i.e., electrophysiological gradients and abnormal impulse propagation.

Methods

Two different mathematical models of the human ventricular action potential were used to formulate models of the failing ventricular myocyte. This provided the basis for simulations of the electrical activity within a transmural ventricular strand. Our main goal was to elucidate the roles of electrophysiological and structural remodeling in setting the stage for malignant life-threatening arrhythmias.

Results

Simulation results illustrate how the presence of M cells and heterogeneous electrophysiological remodeling in the human failing ventricle modulate the dispersion of action potential duration and repolarization time. Specifically, selective heterogeneous remodeling of expression levels for the Na⁺/Ca²⁺ exchanger and SERCA pump decrease these heterogeneities. In contrast, fibroblast proliferation and cellular uncoupling both strongly increase repolarization heterogeneities. Conduction velocity and the safety factor for conduction are also reduced by the progressive structural remodeling during heart failure.

Conclusion

An extensive literature now establishes that in human ventricle, as heart failure progresses, gradients for repolarization are changed significantly by protein specific electrophysiological remodeling (either homogeneous or heterogeneous). Our simulations illustrate and provide new insights into this. Furthermore, enhanced fibrosis in failing hearts, as well as reduced intercellular coupling, combine to increase electrophysiological gradients and reduce electrical propagation. In combination these changes set the stage for arrhythmias.

Detection of abnormal cardiac activity using principal component analysis--a theoretical study

Electrogram-guided ablation has been recently developed for allowing better detection and localization of abnormal atrial activity that may be the source of arrhythmogeneity. Nevertheless, no clear indication for the benefit of using electrograms guided ablation over empirical ablation was established thus far, and there is a clear need of improving the localization of cardiac arrhythmogenic targets for ablation. In this paper, we propose a new approach for detection and localization of irregular cardiac activity during ablation procedures that is based on dimension reduction algorithms and principal component analysis (PCA). Using an 8×8 electrode array, our method produces manifolds that allow easy visualization and detection of possible arrhythmogenic ablation targets characterized by irregular conduction. We employ mathematical modeling and computer simulations to demonstrate the feasibility of the new approach for two well established arrhythmogenic sources for irregular conduction--spiral waves and patchy fibrosis. Our results show that the PCA method can differentiate between focal ectopic activity and spiral wave activity, as these two types of activity produce substantially different manifold shapes. Moreover, the technique allows the detection of spiral wave cores and their general meandering and drifting pattern. Fibrotic patches larger than 2 mm(2) could also be visualized using the PCA method, both for quiescent atrial tissue and for tissue exhibiting spiral wave activity. We envision that this method, contingent to further numerical and experimental validation studies in more complex, realistic geometrical configurations and with clinical data, can improve existing atrial ablation mapping capabilities, thus increasing success rates and optimizing arrhythmia management.

Electrophysiological and structural remodeling in heart failure modulate arrhythmogenesis. 2D simulation study

BACKGROUND

Heart failure is operationally defined as the inability of the heart to maintain blood flow to meet the needs of the body and it is the final common pathway of various cardiac pathologies. Electrophysiological remodeling, intercellular uncoupling and a pro-fibrotic response have been identified as major arrhythmogenic factors in heart failure.

OBJECTIVE

In this study we investigate vulnerability to reentry under heart failure conditions by incorporating established electrophysiological and anatomical remodeling using computer simulations.

METHODS

The electrical activity of human transmural ventricular tissue (5 cm × 5 cm) was simulated using the human ventricular action potential model Grandi et al. under control and heart failure conditions. The MacCannell et al. model was used to model fibroblast electrical activity, and their electrotonic interactions with myocytes. Selected degrees of diffuse fibrosis and variations in intercellular coupling were considered and the vulnerable window (VW) for reentry was evaluated following cross-field stimulation.

RESULTS

No reentry was observed in normal conditions or in the presence of HF ionic remodeling. However, defined amount of fibrosis and/or cellular uncoupling were sufficient to elicit reentrant activity. Under conditions where reentry was generated, HF electrophysiological remodeling did not alter the width of the VW. However, intermediate fibrosis and cellular uncoupling significantly widened the VW. In addition, biphasic behavior was observed, as very high fibrotic content or very low tissue conductivity hampered the development of reentry. Detailed phase analysis of reentry dynamics revealed an increase of phase singularities with progressive fibrotic components.

CONCLUSION

Structural remodeling is a key factor in the genesis of vulnerability to reentry. A range of intermediate levels of fibrosis and intercellular uncoupling can combine to favor reentrant activity.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity θ and the wavelength λ of a plane wave; we show that PD leads to a periodic, spatial modulation of θ and a temporally periodic modulation of λ; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNP04 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNP04 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Modelling the transition from simple to complex Ca²⁺ oscillations in pancreatic acinar cells

A mathematical model is proposed which systematically investigates complex calcium oscillations in pancreatic acinar cells. This model is based on calcium-induced calcium release via inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR) and includes calcium modulation of inositol (1,4,5) trisphosphate (IP3) levels through feedback regulation of degradation and production. In our model, the apical and the basal regions are separated by a region containing mitochondria, which is capable of restricting Ca2+ responses to the apical region. We were able to reproduce the observed oscillatory patterns, from baseline spikes to sinusoidal oscillations. The model predicts that calcium-dependent production and degradation of IP3 is a key mechanism for complex calcium oscillations in pancreatic acinar cells. A partial bifurcation analysis is performed which explores the dynamic behaviour of the model in both apical and basal regions.

Electrical wave propagation in an anisotropic model of the left ventricle based on analytical description of cardiac architecture

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher–Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation.

Fibroblast-myocyte electrotonic coupling: does it occur in native cardiac tissue?

Heterocellular electrotonic coupling between cardiac myocytes and non-excitable connective tissue cells has been a long-established and well-researched fact in vitro. Whether or not such coupling exists in vivo has been a matter of considerable debate. This paper reviews the development of experimental insight and conceptual views on this topic, describes evidence in favour of and against the presence of such coupling in native myocardium, and identifies directions for further study needed to resolve the riddle, perhaps less so in terms of principal presence which has been demonstrated, but undoubtedly in terms of extent, regulation, patho-physiological context, and actual relevance of cardiac myocyte–non-myocyte coupling in vivo. This article is part of a Special Issue entitled "Myocyte-Fibroblast Signalling in Myocardium."

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Electrical coupling of cardiomyocytes and fibroblasts is well-established in vitro

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Whether such hetero-cellular coupling exists in vivo has been a matter of debate

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We review the development of experimental and conceptual insight into the topic

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Conclusion 1: hetero-cellular coupling in heart tissue has been shown in principle

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Conclusion 2: extent, regulation, context, and relevance remain to be established

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.