A model of electrical conduction in cardiac tissue including fibroblasts

Atrial fibroblast-derived exosomal miR-21 upregulate myocardial KCa3.1 via the PI3K-Akt pathway during rapid pacing

Background

Fibroblast-derived exosomes can regulate the electrical remodeling of cardiomyocytes, and the intermediate-conductance calcium-activated potassium channel (KCa3.1) is important in atrial electrical remodeling. However, the underlying molecular mechanisms remain unclear. This study aimed to investigate the regulation of cardiac electrophysiology by exosomes linked to KCa3.1.

Methods

Atrial myocytes (AMs) and atrial fibroblasts were isolated from Sprague-Dawley suckling rats and cultured individually. The cellular atrial fibrillation (AF) model was established via electrical stimulation (1.0 v/cm, 10 Hz), and fibroblast-derived exosomes were isolated via ultracentrifugation. Exosomes were co-cultured with AMs to investigate their influences on KCa3.1 and the underlying mechanisms. Nanoparticle tracking analysis and transmission electron microscopy were used to measure exosome particle sizes and concentrations. Whole-cell patch clamp was applied to record the current density of KCa3.1 and action potential duration (APD). The expression of miR-21-5p was detected by reverse-transcription polymerase chain reaction (RT-PCR). Western blotting or immunofluorescence was used to measure the expression of exosomal markers, Akt phosphorylation, and KCa3.1.

Results

Rapid pacing promoted the secretion of exosomes from atrial fibroblasts and miR-21-5p expression in atrial fibroblasts and exosomes. KCa3.1 protein expression and current density significantly increased, and APD50 and APD90 were sharply shortened after rapid pacing in AMs. TRAM-34 (KCa3.1 blocker) extended APD and reduced susceptibility to AF. KCa3.1 and P-AKT expressions were amplified after co-culturing AMs with exosomes secreted by atrial fibroblasts. In contrast, the increase in KCa3.1 expression was reversed after the cells were co-cultured with exosomes secreted by atrial fibroblasts that were transfected with miR-21-5p inhibitors or after the use of LY294002, a PI3K/Akt pathway inhibitor.

Conclusions

Rapid pacing promoted the secretion of exosomes from fibroblasts, and miR-21-5p was upregulated in exosomes. Moreover, the miR-21-5p-enriched exosomes upregulated KCa3.1 expression in AMs via the PI3K/Akt pathway.

Re-entry in models of cardiac ventricular tissue with scar represented as a Gaussian random field

Introduction: Fibrotic scar in the heart is known to act as a substrate for arrhythmias. Regions of fibrotic scar are associated with slowed or blocked conduction of the action potential, but the detailed mechanisms of arrhythmia formation are not well characterised and this can limit the effective diagnosis and treatment of scar in patients. The aim of this computational study was to evaluate different representations of fibrotic scar in models of 2D 10 × 10 cm ventricular tissue, where the region of scar was defined by sampling a Gaussian random field with an adjustable length scale of between 1.25 and 10.0 mm. Methods: Cellular electrophysiology was represented by the Ten Tusscher 2006 model for human ventricular cells. Fibrotic scar was represented as a spatially varying diffusion, with different models of the boundary between normal and fibrotic tissue. Dispersion of activation time and action potential duration (APD) dispersion was assessed in each sample by pacing at an S1 cycle length of 400 ms followed by a premature S2 beat with a coupling interval of 323 ms. Vulnerability to reentry was assessed with an aggressive pacing protocol. In all models, simulated fibrosis acted to delay activation, to increase the dispersion of APD, and to generate re-entry. Results: A higher incidence of re-entry was observed in models with simulated fibrotic scar at shorter length scale, but the type of model used to represent fibrotic scar had a much bigger influence on the incidence of reentry. Discussion: This study shows that in computational models of fibrotic scar the effects that lead to either block or propagation of the action potential are strongly influenced by the way that fibrotic scar is represented in the model, and so the results of computational studies involving fibrotic scar should be interpreted carefully.

Myofibroblasts impair myocardial impulse propagation by heterocellular connexin43 gap-junctional coupling through micropores

Aim: Composite population of myofibroblasts (MFs) within myocardial tissue is known to alter impulse propagation, leading to arrhythmias. However, it remains unclear whether and how MFs alter their propagation patterns when contacting cardiomyocytes (CMs) without complex structural insertions in the myocardium. We attempted to unveil the effects of the one-sided, heterocellular CM-MF connection on the impulse propagation of CM monolayers without the spatial insertion of MFs as an electrical or mechanical obstacle. Methods and results: We evaluated fluo8-based spatiotemporal patterns in impulse propagation of neonatal rat CM monolayers cultured on the microporous membrane having 8-μm diameter pores with co-culture of MFs or CMs on the reverse membrane side (CM-MF model or CM-CM model, respectively). During consecutive pacing at 1 or 2 Hz, the CM monolayers exhibited forward impulse propagation from the pacing site with a slower conduction velocity (θ) and a larger coefficient of directional θ variation in the CM-MF model than that in the CM-CM model in a frequency-dependent manner (2 Hz >1 Hz). The localized placement of an MF cluster on the reverse side resulted in an abrupt segmental depression of the impulse propagation of the upper CM layer, causing a spatiotemporally non-uniform pattern. Dye transfer of the calcein loaded in the upper CM layer to the lower MF layer was attenuated by the gap-junction inhibitor heptanol. Immunocytochemistry identified definitive connexin 43 (Cx43) between the CMs and MFs in the membrane pores. MF-selective Cx43 knockdown in the MF layer improved both the velocity and uniformity of propagation in the CM monolayer. Conclusion: Heterocellular Cx43 gap junction coupling of CMs with MFs alters the spatiotemporal patterns of myocardial impulse propagation, even in the absence of spatially interjacent and mechanosensitive modulations by MFs. Moreover, MFs can promote pro-arrhythmogenic impulse propagation when in face-to-face contact with the myocardium that arises in the healing infarct border zone.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

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.

In silico Cell Therapy Model Restores Failing Human Myocyte Electrophysiology and Calcium Cycling in Fibrotic Myocardium

Myocardial delivery of human c-kit+ cardiac interstitial cells (hCICs) and human mesenchymal stem cells (hMSCs), an emerging approach for treating the failing heart, has been limited by an incomplete understanding of the effects on host myocardium. This computational study aims to model hCIC and hMSC effects on electrophysiology and calcium cycling of healthy and diseased human cardiomyocytes (hCM), and reveals a possible cardiotherapeutic benefit independent of putative regeneration processes. First, we developed an original hCIC mathematical model with an electrical profile comprised of distinct experimentally identified ion currents. Next, we verified the model by confirming it is representative of published experiments on hCIC whole-cell electrophysiology and on hCIC co-cultures with rodent cardiomyocytes. We then used our model to compare electrophysiological effects of hCICs to other non-excitable cells, as well as clinically relevant hCIC-hMSC combination therapies and fused hCIC-hMSC CardioChimeras. Simulation of direct coupling of hCICs to healthy or failing hCMs through gap junctions led to greater increases in calcium cycling with lesser reductions in action potential duration (APD) compared with hMSCs. Combined coupling of hCICs and hMSCs to healthy or diseased hCMs led to intermediate effects on electrophysiology and calcium cycling compared to individually coupled hCICs or hMSCs. Fused hCIC-hMSC CardioChimeras decreased healthy and diseased hCM APD and calcium transient amplitude compared to individual or combined cell treatments. Finally, to provide a theoretical basis for optimizing cell-based therapies, we randomized populations of 2,500 models incorporating variable hMSC and hCIC interventions and simulated their effects on restoring diseased cardiomyocyte electrophysiology and calcium handling. The permutation simulation predicted the ability to correct abnormal properties of heart failure hCMs in fibrotic, but not non-fibrotic, myocardium. This permutation experiment also predicted paracrine signaling to be a necessary and sufficient mechanism for this correction, counteracting the fibrotic effects while also restoring arrhythmia-related metrics such as upstroke velocity and resting membrane potential. Altogether, our in silico findings suggest anti-fibrotic effects of paracrine signaling are critical to abrogating pathological cardiomyocyte electrophysiology and calcium cycling in fibrotic heart failure, and support further investigation of delivering an optimized cellular secretome as a potential strategy for improving heart failure therapy.

Modelling the action potential propagation in a heart with structural heterogeneities: From high-resolution MRI to numerical simulations

Mathematical modelling and numerical simulation in cardiac electrophysiology have already been studied extensively. However, there is a clear lack of techniques and methodologies for studying the propagation of action potential in a heart with structural defects. In this article, we present a modified version of the bidomain model, derived using homogenisation techniques with the assumption of existence of diffusive inclusions in the cardiac tissue. The diffusive inclusions represent regions without electrically active myocytes, for example, fat, fibrosis, and so forth. We present an application of this model to a rat heart. Starting from high-resolution MRI, the geometry of the heart is built and meshed using image processing techniques. We perform a study of the effects of tissue heterogeneities induced by diffusive inclusions on the velocity and shape of the depolarisation wavefront. We present several test cases with different geometries of diffusive inclusions. We reach the conclusion that the conduction velocity is not affected in the best cases, while it is affected by up to 76% in the worst case scenario. Additionally, the shape of the wavefront was affected in some cases.

Multiparametric analysis of geometric features of fibrotic textures leading to cardiac arrhythmias

One of the important questions in cardiac electrophysiology is to characterise the arrhythmogenic substrate; for example, from the texture of the cardiac fibrosis, which is considered one of the major arrhythmogenic conditions. In this paper, we perform an extensive in silico study of the relationships between various local geometric characteristics of fibrosis on the onset of cardiac arrhythmias. In order to define which texture characteristics have better predictive value, we induce arrhythmias by external stimulation, selecting 4363 textures in which arrhythmia can be induced and also selecting 4363 non-arrhythmogenic textures. For each texture, we determine such characteristics as cluster area, solidity, mean distance, local density and zig-zag propagation path, and compare them in arrhythmogenic and non-arrhythmogenic cases. Our study shows that geometrical characteristics, such as cluster area or solidity, turn out to be the most important for prediction of the arrhythmogenic textures. Overall, we were able to achieve an accuracy of 67% for the arrhythmogenic texture-classification problem. However, the accuracy of predictions depends on the size of the region chosen for the analysis. The optimal size for the local areas of the tissue was of the order of 0.28 of the wavelength of the arrhythmia. We discuss further developments and possible applications of this method for characterising the substrate of arrhythmias in fibrotic textures.

Protein and Polysaccharide-Based Electroactive and Conductive Materials for Biomedical Applications

Electrically responsive biomaterials are an important and emerging technology in the fields of biomedical and material sciences. A great deal of research explores the integral role of electrical conduction in normal and diseased cell biology, and material scientists are focusing an even greater amount of attention on natural and hybrid materials as sources of biomaterials which can mimic the properties of cells. This review establishes a summary of those efforts for the latter group, detailing the current materials, theories, methods, and applications of electrically conductive biomaterials fabricated from protein polymers and polysaccharides. These materials can be used to improve human life through novel drug delivery, tissue regeneration, and biosensing technologies. The immediate goal of this review is to establish fabrication methods for protein and polysaccharide-based materials that are biocompatible and feature modular electrical properties. Ideally, these materials will be inexpensive to make with salable production strategies, in addition to being both renewable and biocompatible.

Novel mapping techniques for rotor core detection using simulated intracardiac electrograms

BACKGROUND

Catheter ablation is associated with limited success rates in patients with persistent atrial fibrillation (AF). Currently, existing mapping systems fail to identify critical target sites for ablation. Recently, we proposed and validated several techniques (multiscale frequency [MSF], Shannon entropy [SE], kurtosis [Kt], and multiscale entropy [MSE]) to identify pivot point of rotors using ex-vivo optical mapping animal experiments. However, the performance of these techniques is unclear for the clinically recorded intracardiac electrograms (EGMs), due to the different nature of the signals.

OBJECTIVE

This study aims to evaluate the performance of MSF, MSE, SE, and Kt techniques to identify the pivot point of the rotor using unipolar and bipolar EGMs obtained from numerical simulations.

METHODS

Stationary and meandering rotors were simulated in a 2D human atria. The performances of new approaches were quantified by comparing the "true" core of the rotor with the core identified by the techniques. Also, the performances of all techniques were evaluated in the presence of noise, scar, and for the case of the multielectrode multispline and grid catheters.

RESULTS

Our results demonstrate that all the approaches are able to accurately identify the pivot point of both stationary and meandering rotors from both unipolar and bipolar EGMs. The presence of noise and scar tissue did not significantly affect the performance of the techniques. Finally, the core of the rotors was correctly identified for the case of multielectrode multispline and grid catheter simulations.

CONCLUSION

The core of rotors can be successfully identified from EGMs using novel techniques; thus, providing motivation for future clinical implementations.

Approaches for determining cardiac bidomain conductivity values: progress and challenges

Modelling the electrical activity of the heart is an important tool for understanding electrical function in various diseases and conduction disorders. Clearly, for model results to be useful, it is necessary to have accurate inputs for the models, in particular the commonly used bidomain model. However, there are only three sets of four experimentally determined conductivity values for cardiac ventricular tissue and these are inconsistent, were measured around 40 years ago, often produce different results in simulations and do not fully represent the three-dimensional anisotropic nature of cardiac tissue. Despite efforts in the intervening years, difficulties associated with making the measurements and also determining the conductivities from the experimental data have not yet been overcome. In this review, we summarise what is known about the conductivity values, as well as progress to date in meeting the challenges associated with both the mathematical modelling and the experimental techniques. Graphical abstract Epicardial potential distributions, arising from a subendocardial ischaemic region, modelled using conductivity data from the indicated studies.

Human Induced Pluripotent Stem Cell-Derived Non-Cardiomyocytes Modulate Cardiac Electrophysiological Maturation Through Connexin 43-Mediated Cell-Cell Interactions

The functional maturation status of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) has a notable impact upon their use in pharmacological studies, disease modeling, and therapeutic applications. Non-cardiomyocytes (non-CMs) produced in the differentiation process have previously been identified as having an extrinsic influence upon hiPSC-CM development, yet the underlying mechanisms are not fully understood. Herein, we aimed to modulate electrophysiological properties of hiPSC-CMs within co-cultures containing varied proportions of non-CMs and investigate the nature of interactions between these different cell types. Therefore, we sorted cardiac differentiations on day 10 and subsequently replated the cells at ratios of 7:3, 1:1, 3:7, and 1:9 non-CMs to CMs. After a month of co-culture, we evaluated electrophysiological properties through the genetically encoded voltage indicator ArcLight. We ultimately identified that co-cultures with approximately 70%–90% CM purity demonstrated the highest action potential (AP) amplitude and maximum upstroke velocity by day 40 of differentiation, indicative of enhanced electrophysiological maturation, as well as more ventricular-like AP morphologies. Notably, these findings were distinct from those observed for co-cultures of hiPSC-CMs and dermal fibroblasts. We determined that the co-culture phenotypes could not be attributed to paracrine effects of non-CMs due to the inability of conditioned media to recapitulate the observed effects. This led to the further observation of a distinctive expression pattern of connexin 43 (Cx43) at cell-cell interfaces between both CMs and non-CMs. Depletion of Cx43 by short hairpin RNA (shRNA) specifically in the non-CM population within a co-culture environment was able to recapitulate electrophysiological phenotypes of a purer hiPSC-CM population. Collectively, our data demonstrate that abundant non-CM content exerts a significant negative influence upon the electrophysiological maturation of hiPSC-CMs through Cx43-mediated cell-cell-contacts, and thus should be considered regarding the future production of purpose-built hiPSC-CM systems.

Neurogenesis-on-Chip: Electric field modulated transdifferentiation of human mesenchymal stem cell and mouse muscle precursor cell coculture

A number of bioengineering strategies, using biophysical stimulation, are being explored to guide the human mesenchymal stem cells (hMScs) into different lineages. In this context, we have limited understanding on the transdifferentiation of matured cells to another functional-cell type, when grown with stem cells, in a constrained cellular microenvironment under biophysical stimulation. While addressing such aspects, the present work reports the influence of the electric field (EF) stimulation on the phenotypic and functionality modulation of the coculture of murine myoblasts (C2C12) with hMScs [hMSc:C2C12=1:10] in a custom designed polymethylmethacrylate (PMMA) based microfluidic device with in-built metal electrodes. The quantitative and qualitative analysis of the immunofluorescence study confirms that the cocultured cells in the conditioned medium with astrocytic feed, exhibit differentiation towards neural-committed cells under biophysical stimulation in the range of the endogenous physiological electric field strength (8 ± 0.06  mV/mm). The control experiments using similar culture protocols revealed that while C2C12 monoculture exhibited myotube-like fused structures, the hMScs exhibited the neurosphere-like clusters with SOX2, nestin, βIII-tubulin expression. The electrophysiological study indicates the significant role of intercellular calcium signalling among the differentiated cells towards transdifferentiation. Furthermore, the depolarization induced calcium influx strongly supports neural-like behaviour for the electric field stimulated cells in coculture. The intriguing results are explained in terms of the paracrine signalling among the transdifferentiated cells in the electric field stimulated cellular microenvironment. In summary, the present study establishes the potential for neurogenesis on-chip for the coculture of hMSc and C2C12 cells under tailored electric field stimulation, in vitro.

Influence of the distribution of fibrosis within an area of myocardial infarction on wave propagation in ventricular tissue

The presence of fibrosis in heart tissue is strongly correlated with an incidence of arrhythmia, which is a leading cause of sudden cardiac death (SCD). However, it remains incompletely understood how different distributions, sizes and positions of fibrotic tissues contribute to arrhythmogenesis. In this study, we designed 4 different ventricular models mimicking wave propagation in cardiac tissues under normal, myocardial infarction (MI), MI with random fibrosis and MI with gradient fibrosis conditions. Simulation results of ideal square tissues indicate that vulnerable windows (VWs) of random and gradient fibrosis distributions are similar with low levels of fibrosis. However, with a high level of fibrosis, the VWs significantly increase in random fibrosis tissue but not in gradient fibrosis tissue. In addition, we systematically analyzed the effects of the size and position of fibrosis tissues on VWs. Simulation results show that it is more likely for a reentry wave to appear when the length of the infarcted area is greater than 25% of the perimeter of the ventricle, when the width is approximately half that of the ventricular wall, or when the infarcted area is attached to the inside or outside of the ventricular wall.

Extended Bidomain Modeling of Defibrillation: Quantifying Virtual Electrode Strengths in Fibrotic Myocardium

Defibrillation is a well-established therapy for atrial and ventricular arrhythmia. Here, we shed light on defibrillation in the fibrotic heart. Using the extended bidomain model of electrical conduction in cardiac tissue, we assessed the influence of fibrosis on the strength of virtual electrodes caused by extracellular electrical current. We created one-dimensional models of rabbit ventricular tissue with a central patch of fibrosis. The fibrosis was incorporated by altering volume fractions for extracellular, myocyte and fibroblast domains. In our prior work, we calculated these volume fractions from microscopic images at the infarct border zone of rabbit hearts. An average and a large degree of fibrosis were modeled. We simulated defibrillation by application of an extracellular current for a short duration (5 ms). We explored the effects of myocyte-fibroblast coupling, intra-fibroblast conductivity and patch length on the strength of the virtual electrodes present at the borders of the normal and fibrotic tissue. We discriminated between effects on myocyte and fibroblast membranes at both borders of the patch. Similarly, we studied defibrillation in two-dimensional models of fibrotic tissue. Square and disk-like patches of fibrotic tissue were embedded in control tissue. We quantified the influence of the geometry and fibrosis composition on virtual electrode strength. We compared the results obtained with a square and disk shape of the fibrotic patch with results from the one-dimensional simulations. Both, one- and two-dimensional simulations indicate that extracellular current application causes virtual electrodes at boundaries of fibrotic patches. A higher degree of fibrosis and larger patch size were associated with an increased strength of the virtual electrodes. Also, patch geometry affected the strength of the virtual electrodes. Our simulations suggest that increased fibroblast-myocyte coupling and intra-fibroblast conductivity reduce virtual electrode strength. However, experimental data to constrain these modeling parameters are limited and thus pinpointing the magnitude of the reduction will require further understanding of electrical coupling of fibroblasts in native cardiac tissues. We propose that the findings from our computational studies are important for development of patient-specific protocols for internal defibrillators.

Modeling cardiac complexity: Advancements in myocardial models and analytical techniques for physiological investigation and therapeutic development in vitro

Cardiomyopathies, heart failure, and arrhythmias or conduction blockages impact millions of patients worldwide and are associated with marked increases in sudden cardiac death, decline in the quality of life, and the induction of secondary pathologies. These pathologies stem from dysfunction in the contractile or conductive properties of the cardiomyocyte, which as a result is a focus of fundamental investigation, drug discovery and therapeutic development, and tissue engineering. All of these foci require in vitro myocardial models and experimental techniques to probe the physiological functions of the cardiomyocyte. In this review, we provide a detailed exploration of different cell models, disease modeling strategies, and tissue constructs used from basic to translational research. Furthermore, we highlight recent advancements in imaging, electrophysiology, metabolic measurements, and mechanical and contractile characterization modalities that are advancing our understanding of cardiomyocyte physiology. With this review, we aim to both provide a biological framework for engineers contributing to the field and demonstrate the technical basis and limitations underlying physiological measurement modalities for biologists attempting to take advantage of these state-of-the-art techniques.

Representation of Multiple Cellular Phenotypes Within Tissue-Level Simulations of Cardiac Electrophysiology

Distinct electrophysiological phenotypes are exhibited by biological cells that have differentiated into particular cell types. The usual approach when simulating the cardiac electrophysiology of tissue that includes different cell types is to model the different cell types as occupying spatially distinct yet coupled regions. Instead, we model the electrophysiology of well-mixed cells by using homogenisation to derive an extension to the commonly used monodomain or bidomain equations. These new equations permit spatial variations in the distribution of the different subtypes of cells and will reduce the computational demands of solving the governing equations. We validate the homogenisation computationally, and then use the new model to explain some experimental observations from stem cell-derived cardiomyocyte monolayers.

Ca2+ Cycling Impairment in Heart Failure Is Exacerbated by Fibrosis: Insights Gained From Mechanistic Simulations

Heart failure (HF) is characterized by altered Ca²⁺ cycling, resulting in cardiac contractile dysfunction. Failing myocytes undergo electrophysiological remodeling, which is known to be the main cause of abnormal Ca²⁺ homeostasis. However, structural remodeling, specifically proliferating fibroblasts coupled to myocytes in the failing heart, could also contribute to Ca²⁺ cycling impairment. The goal of the present study was to systematically analyze the mechanisms by which myocyte–fibroblast coupling could affect Ca²⁺ dynamics in normal conditions and in HF. Simulations of healthy and failing human myocytes were performed using established mathematical models, and cells were either isolated or coupled to fibroblasts. Univariate and multivariate sensitivity analyses were performed to quantify effects of ion transport pathways on biomarkers computed from intracellular [Ca²⁺] waveforms. Variability in ion channels and pumps was imposed and populations of models were analyzed to determine effects on Ca²⁺ dynamics. Our results suggest that both univariate and multivariate sensitivity analyses are valuable methodologies to shed light into the ionic mechanisms underlying Ca²⁺ impairment in HF, although differences between the two methodologies are observed at high parameter variability. These can result from either the fact that multivariate analyses take into account ion channels or non-linear effects of ion transport pathways on Ca²⁺ dynamics. Coupling either healthy or failing myocytes to fibroblasts decreased Ca²⁺ transients due to an indirect sink effect on action potential (AP) and thus on Ca²⁺ related currents. Simulations that investigated restoration of normal physiology in failing myocytes showed that Ca²⁺ cycling can be normalized by increasing SERCA and L-type Ca²⁺ current activity while decreasing Na⁺–Ca²⁺ exchange and SR Ca²⁺ leak. Changes required to normalize APs in failing myocytes depended on whether myocytes were coupled to fibroblasts. In conclusion, univariate and multivariate sensitivity analyses are helpful tools to understand how Ca²⁺ cycling is impaired in HF and how this can be exacerbated by coupling of myocytes to fibroblasts. The design of pharmacological actions to restore normal activity should take into account the degree of fibrosis in the failing heart.

Dispersion of Recovery and Vulnerability to Re-entry in a Model of Human Atrial Tissue With Simulated Diffuse and Focal Patterns of Fibrosis

Fibrosis in atrial tissue can act as a substrate for persistent atrial fibrillation, and can be focal or diffuse. Regions of fibrosis are associated with slowed or blocked conduction, and several approaches have been used to model these effects. In this study a computational model of 2D atrial tissue was used to investigate how the spatial scale of regions of simulated fibrosis influenced the dispersion of action potential duration (APD) and vulnerability to re-entry in simulated normal human atrial tissue, and human tissue that has undergone remodeling as a result of persistent atrial fibrillation. Electrical activity was simulated in a 10 × 10 cm square 2D domain, with a spatially varying diffusion coefficient as described below. Cellular electrophysiology was represented by the Courtemanche model for human atrial cells, with the model parameters set for normal and remodeled cells. The effect of fibrosis was modeled with a smoothly varying diffusion coefficient, obtained from sampling a Gaussian random field (GRF) with length scales of between 1.25 and 10.0 mm. Twenty samples were drawn from each field, and used to allocate a value of diffusion coefficient between 0.05 and 0.2 mm²/ms. Dispersion of APD was assessed in each sample by pacing at a cycle length of 1,000 ms, followed by a premature beat with a coupling interval of 400 ms. Vulnerability to re-entry was assessed with an aggressive pacing protocol with pacing cycle lengths decreasing from 450 to 250 ms in 25 ms intervals for normal tissue and 300–150 ms for remodeled tissue. Simulated fibrosis at smaller spatial scales tended to lengthen APD, increase APD dispersion, and increase vulnerability to sustained re-entry relative to fibrosis at larger spatial scales. This study shows that when fibrosis is represented by smoothly varying tissue diffusion, the spatial scale of fibrosis has important effects on both dispersion of recovery and vulnerability to re-entry.

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.

Confocal Microscopy-Based Estimation of Parameters for Computational Modeling of Electrical Conduction in the Normal and Infarcted Heart

Computational modeling is an important tool to advance our knowledge on cardiac diseases and their underlying mechanisms. Computational models of conduction in cardiac tissues require identification of parameters. Our knowledge on these parameters is limited, especially for diseased tissues. Here, we assessed and quantified parameters for computational modeling of conduction in cardiac tissues. We used a rabbit model of myocardial infarction (MI) and an imaging-based approach to derive the parameters. Left ventricular tissue samples were obtained from fixed control hearts (animals: 5) and infarcted hearts (animals: 6) within 200 μm (region 1), 250-750 μm (region 2) and 1,000-1,250 μm (region 3) of the MI border. We assessed extracellular space, fibroblasts, smooth muscle cells, nuclei and gap junctions by a multi-label staining protocol. With confocal microscopy we acquired three-dimensional (3D) image stacks with a voxel size of 200 × 200 × 200 nm. Image segmentation yielded 3D reconstructions of tissue microstructure, which were used to numerically derive extracellular conductivity tensors. Volume fractions of myocyte, extracellular, interlaminar cleft, vessel and fibroblast domains in control were (in %) 65.03 ± 3.60, 24.68 ± 3.05, 3.95 ± 4.84, 7.71 ± 2.15, and 2.48 ± 1.11, respectively. Volume fractions in regions 1 and 2 were different for myocyte, myofibroblast, vessel, and extracellular domains. Fibrosis, defined as increase in fibrotic tissue constituents, was (in %) 21.21 ± 1.73, 16.90 ± 9.86, and 3.58 ± 8.64 in MI regions 1, 2, and 3, respectively. For control tissues, image-based computation of longitudinal, transverse and normal extracellular conductivity yielded (in S/m) 0.36 ± 0.11, 0.17 ± 0.07, and 0.1 ± 0.06, respectively. Conductivities were markedly increased in regions 1 (+75, +171, and +100%), 2 (+53, +165, and +80%), and 3 (+42, +141, and +60%). Volume fractions of the extracellular space including interlaminar clefts strongly correlated with conductivities in control and MI hearts. Our study provides novel quantitative data for computational modeling of conduction in normal and MI hearts. Notably, our study introduces comprehensive statistical information on tissue composition and extracellular conductivities on a microscopic scale in the MI border zone. We suggest that the presented data fill a significant gap in modeling parameters and extend our foundation for computational modeling of cardiac conduction.

Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

Gastrointestinal (GI) motility is regulated in part by electrophysiological events called slow waves, which are generated by the interstitial cells of Cajal (ICC). Slow waves propagate by a process of "entrainment," which occurs over a decreasing gradient of intrinsic frequencies in the antegrade direction across much of the GI tract. Abnormal initiation and conduction of slow waves have been demonstrated in, and linked to, a number of GI motility disorders. A range of mathematical models have been developed to study abnormal slow waves and applied to propose novel methods for non-invasive detection and therapy. This review provides a general outline of GI slow wave abnormalities and their recent classification using multi-electrode (high-resolution) mapping methods, with a particular emphasis on the spatial patterns of these abnormal activities. The recently-developed mathematical models are introduced in order of their biophysical scale from cellular to whole-organ levels. The modeling techniques, main findings from the simulations, and potential future directions arising from notable studies are discussed.

Unraveling the mechanistic effects of electric field stimulation towards directing stem cell fate and function: A tissue engineering perspective

Electric field (EF) stimulation can play a vital role in eliciting appropriate stem cell response. Such an approach is recently being established to guide stem cell differentiation through osteogenesis/neurogenesis/cardiomyogenesis. Despite significant recent efforts, the biophysical mechanisms by which stem cells sense, interpret and transform electrical cues into biochemical and biological signals still remain unclear. The present review critically analyses the variety of EF stimulation approaches that can be employed to evoke appropriate stem cell response and also makes an attempt to summarize the underlying concepts of this notion, placing special emphasis on stem cell based tissue engineering and regenerative medicine. This review also discusses the major signaling pathways and cellular responses that are elicited by electric stimulation, including the participation of reactive oxygen species and heat shock proteins, modulation of intracellular calcium ion concentration, ATP production and numerous other events involving the clustering or reassembling of cell surface receptors, cytoskeletal remodeling and so on. The specific advantages of using external electric stimulation in different modalities to regulate stem cell fate processes are highlighted with explicit examples, in vitro and in vivo.

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.

Cardiac Fibroblast Activation Post-Myocardial Infarction: Current Knowledge Gaps

In response to myocardial infarction (MI), the wound healing response of the left ventricle (LV) comprises overlapping inflammatory, proliferative, and maturation phases, and the cardiac fibroblast is a key cell type involved in each phase. It has recently been appreciated that, early post-MI, fibroblasts transform to a proinflammatory phenotype and secrete cytokines and chemokines as well as matrix metalloproteinases (MMPs). Later post-MI, fibroblasts are activated to anti-inflammatory and proreparative phenotypes and generate anti-inflammatory and proangiogenic factors and extracellular matrix (ECM) components that form the infarct scar. Additional studies are needed to systematically examine how fibroblast activation shifts over the timeframe of the MI response and how modulation at different activation stages could alter wound healing and LV remodeling in distinct ways. This review summarizes current fibroblast knowledge as the foundation for a discussion of existing knowledge gaps.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

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.

Computational modeling of cardiac fibroblasts and fibrosis

Altered fibroblast behavior can lead to pathologic changes in the heart such as arrhythmia, diastolic dysfunction, and systolic dysfunction. Computational models are increasingly used as a tool to identify potential mechanisms driving a phenotype or potential therapeutic targets against an unwanted phenotype. Here we review how computational models incorporating cardiac fibroblasts have clarified the role for these cells in electrical conduction and tissue remodeling in the heart. Models of fibroblast signaling networks have primarily focused on fibroblast cell lines or fibroblasts from other tissues rather than cardiac fibroblasts, specifically, but they are useful for understanding how fundamental signaling pathways control fibroblast phenotype. In the future, modeling cardiac fibroblast signaling, incorporating -omics and drug-interaction data into signaling network models, and utilizing multi-scale models will improve the ability of in silico studies to predict potential therapeutic targets against adverse cardiac fibroblast activity.

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.

Fibroblast electrical remodeling in heart failure and potential effects on atrial fibrillation

Fibroblasts are activated in heart failure (HF) and produce fibrosis, which plays a role in maintaining atrial fibrillation (AF). The effect of HF on fibroblast ion currents and its potential role in AF are unknown. Here, we used a patch-clamp technique to investigate the effects of HF on atrial fibroblast ion currents, and mathematical computation to assess the potential impact of this remodeling on atrial electrophysiology and arrhythmogenesis. Atrial fibroblasts were isolated from control and tachypacing-induced HF dogs. Tetraethylammonium-sensitive voltage-gated fibroblast current (IKv,fb) was significantly downregulated (by ?44%), whereas the Ba(2+)-sensitive inward rectifier current (IKir,fb) was upregulated by 79%, in HF animals versus controls. The fibroblast resting membrane potential was hyperpolarized (?53 ± 2 mV vs. ?42 ± 2 mV in controls) and the capacitance was increased (29.7 ± 2.2 pF vs. 17.8 ± 1.4 pF in controls) in HF. These experimental findings were implemented in a mathematical model that included cardiomyocyte-fibroblast electrical coupling. IKir,fb upregulation had a profibrillatory effect through shortening of the action potential duration and hyperpolarization of the cardiomyocyte resting membrane potential. IKv,fb downregulation had the opposite electrophysiological effects and was antifibrillatory. Simulated pharmacological blockade of IKv,fb successfully terminated reentry under otherwise profibrillatory conditions. We conclude that HF induces fibroblast ion-current remodeling with IKv,fb downregulation and IKir,fb upregulation, and that, assuming cardiomyocyte-fibroblast electrical coupling, this remodeling has a potentially important effect on atrial electrophysiology and arrhythmogenesis, with the overall response depending on the balance of pro- and antifibrillatory contributions. These findings suggest that fibroblast K(+)-current remodeling is a novel component of AF-related remodeling that might contribute to arrhythmia dynamics.

PerFlexMEA: a thin microporous microelectrode array for in vitro cardiac electrophysiological studies on hetero-cellular bilayers with controlled gap junction communication

The new microelectrode array device presented is called PerFlexMEA and it enables controlled coupling between myocytes and nonmyocytes used in cardiovascular conduction studies. The device consists of an 8 μm thin parylene microporous membrane with a 4 × 5 microelectrode array patterned on one side. Myocytes and nonmyocytes can be plated on either side of the parylene membrane to create a tissue bilayer. The 3-3.5 μm diameter pores allow inter-layer dye and electrical coupling without transmembrane cell migration. Cell migration was found to vary with cell-type and micropore diameter. Pore density can be varied based on desired coupling ratio. The flexible parylene membrane is packaged between two rigid thermoplastic layers, such that the microelectrode array region is exposed, while the rest of the device remains insulated. The packaged PerFlexMEA fits in a 60 mm culture dish. Recording experiments are performed by simply plugging it into a commercially available multielectrode amplifier system. Recorded signals were processed and analysed using scripts generated in MATLAB. Our experimental results provide evidence of the reliability of this device, as conduction velocity was observed to decrease after inducing lateral hetero-cellular controlled coupling between myocytes and HeLa cells expressing connexin 43.

Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study

In this study, the effects of cardiac fibroblast proliferation on cardiac electric excitation conduction and mechanical contraction were investigated using a proposed integrated myocardial-fibroblastic electromechanical model. At the cellular level, models of the human ventricular myocyte and fibroblast were modified to incorporate a model of cardiac mechanical contraction and cooperativity mechanisms. Cellular electromechanical coupling was realized with a calcium buffer. At the tissue level, electrical excitation conduction was coupled to an elastic mechanics model in which the finite difference method (FDM) was used to solve electrical excitation equations, and the finite element method (FEM) was used to solve mechanics equations. The electromechanical properties of the proposed integrated model were investigated in one or two dimensions under normal and ischemic pathological conditions. Fibroblast proliferation slowed wave propagation, induced a conduction block, decreased strains in the fibroblast proliferous tissue, and increased dispersions in depolarization, repolarization, and action potential duration (APD). It also distorted the wave-front, leading to the initiation and maintenance of re-entry, and resulted in a sustained contraction in the proliferous areas. This study demonstrated the important role that fibroblast proliferation plays in modulating cardiac electromechanical behaviour and which should be considered in planning future heart-modeling studies.

Remodeling of cardiac passive electrical properties and susceptibility to ventricular and atrial arrhythmias

Coordinated electrical activation of the heart is essential for the maintenance of a regular cardiac rhythm and effective contractions. Action potentials spread from one cell to the next via gap junction channels. Because of the elongated shape of cardiomyocytes, longitudinal resistivity is lower than transverse resistivity causing electrical anisotropy. Moreover, non-uniformity is created by clustering of gap junction channels at cell poles and by non-excitable structures such as collagenous strands, vessels or fibroblasts. Structural changes in cardiac disease often affect passive electrical properties by increasing non-uniformity and altering anisotropy. This disturbs normal electrical impulse propagation and is, consequently, a substrate for arrhythmia. However, to investigate how these structural changes lead to arrhythmias remains a challenge. One important mechanism, which may both cause and prevent arrhythmia, is the mismatch between current sources and sinks. Propagation of the electrical impulse requires a sufficient source of depolarizing current. In the case of a mismatch, the activated tissue (source) is not able to deliver enough depolarizing current to trigger an action potential in the non-activated tissue (sink). This eventually leads to conduction block. It has been suggested that in this situation a balanced geometrical distribution of gap junctions and reduced gap junction conductance may allow successful propagation. In contrast, source-sink mismatch can prevent spontaneous arrhythmogenic activity in a small number of cells from spreading over the ventricle, especially if gap junction conductance is enhanced. Beside gap junctions, cell geometry and non-cellular structures strongly modulate arrhythmogenic mechanisms. The present review elucidates these and other implications of passive electrical properties for cardiac rhythm and arrhythmogenesis.

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.

Interaction-based transition from passivity to excitability

In this paper we study the process of transition from passive to excitable behavior due to interaction between nonlinear dynamical systems. We show that under certain conditions a passive unit may demonstrate qualitatively new excitable dynamics. We study the properties of an excitable medium constructed on the basis of the proposed transition. The effects are demonstrated with the realistic Luo-Rudy model. Application to the cardiac dynamics and functioning is discussed. The qualitative analytic and numerical description is also given for the phenomenological FitzHugh-Nagumo system.

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.

Disease and region-related cardiac fibroblast potassium current variations and potential functional significance

AIMS

Fibroblasts, which play an important role in cardiac function/dysfunction, including arrhythmogenesis, have voltage-dependent (Kv) currents of unknown importance. Here, we assessed the differential expression of Kv currents between atrial and ventricular fibroblasts from control dogs and dogs with an atrial arrhythmogenic substrate caused by congestive heart failure (CHF).

METHODS AND RESULTS

Left atrial (LA) and ventricular (LV) fibroblasts were freshly isolated from control and CHF dogs (2-week ventricular tachypacing, 240 bpm). Kv currents were measured with whole-cell voltage-clamp, mRNA by quantitative polymerase chain reaction (qPCR) and fibroblast proliferation by (3)H-thymidine incorporation. Robust voltage-dependent tetraethylammonium (TEA)-sensitive K(+) currents (IC50 ∼1 mM) were recorded. The morphologies and TEA responses of LA and LV fibroblast Kv currents were similar. LV fibroblast Kv-current densities were significantly greater than LA, and Kv-current densities were significantly less in CHF than control. The mRNA expression of Kv-channel subunits Kv1.5 and Kv4.3 was less in LA vs. LV fibroblasts and was down-regulated in CHF, consistent with K(+)-current recordings. Ca(2+)-dependent K(+)-channel subunit (KCa1.1) mRNA and currents were less expressed in LV vs. LA fibroblasts. Inhibiting LA fibroblast K(+) current with 1 mmol/L of TEA or KCa1.1 current with paxilline increased proliferation.

CONCLUSIONS

Fibroblast Kv-current expression is smaller in CHF vs. control, as well as LA vs. LV. KCa1.1 current is greater in LA vs. LV. Suppressing Kv current with TEA enhances fibroblast proliferation, suggesting that Kv current might act to check fibroblast proliferation and that reduced Kv current in CHF may contribute to fibrosis. Fibroblast Kv-current remodelling may play a role in the atrial fibrillation (AF) substrate; modulating fibroblast K(+) channels may present a novel strategy to prevent fibrosis and AF.

Origin, development, and differentiation of cardiac fibroblasts

Cardiac fibroblasts are the most abundant cell in the mammalian heart. While they have been historically underappreciated in terms of their functional contributions to cardiac development and physiology, they and their activated form, myofibroblasts, are now known to play key roles in both development and disease through structural, paracrine, and electrical interactions with cardiomyocytes. The lack of specific markers for fibroblasts currently convolutes the study of this dynamic cell lineage, but advances in marker analysis and lineage mapping technologies are continuously being made. Understanding how to best utilize these tools, both individually and in combination, will help to elucidate the functional significance of fibroblast-cardiomyocyte interactions in vivo. Here we review what is currently known about the diverse roles played by cardiac fibroblasts and myofibroblasts throughout development and periods of injury with the intent of emphasizing the duality of their nature. This article is part of a Special Issue entitled "Myocyte-Fibroblast Signalling in Myocardium ".

Excitation-contraction coupling between human atrial myocytes with fibroblasts and stretch activated channel current: a simulation study

Myocytes have been regarded as the main objectives in most cardiac modeling studies and attracted a lot of attention. Connective tissue cells, such as fibroblasts (Fbs), also play crucial role in cardiac function. This study proposed an integrated myocyte-I_sac-Fb electromechanical model to investigate the effect of Fbs and stretch activated ion channel current (I_sac) on cardiac electrical excitation conduction and mechanical contraction. At the cellular level, an active Fb model was coupled with a human atrial myocyte electrophysiological model (including I_sac) and a mechanical model. At the tissue level, electrical excitation conduction was coupled with an elastic mechanical model, in which finite difference method (FDM) was used to solve the electrical excitation equations, while finite element method (FEM) was used for the mechanics equations. The simulation results showed that Fbs and I_sac coupling caused diverse effects on action potential morphology during repolarization, depolarized the resting membrane potential of the human atrial myocyte, slowed down wave propagation, and decreased strains in fibrotic tissue. This preliminary simulation study indicates that Fbs and I_sac have important implications for modulating cardiac electromechanical behavior and should be considered in future cardiac modeling studies.

Determinants of myocardial conduction velocity: implications for arrhythmogenesis

Slowed myocardial conduction velocity (θ) is associated with an increased risk of re-entrant excitation, predisposing to cardiac arrhythmia. θ is determined by the ion channel and physical properties of cardiac myocytes and by their interconnections. Thus, θ is closely related to the maximum rate of action potential (AP) depolarization [(dV/dt)_max], as determined by the fast Na⁺ current (I_Na); the axial resistance (r_a) to local circuit current flow between cells; their membrane capacitances (c_m); and to the geometrical relationship between successive myocytes within cardiac tissue. These determinants are altered by a wide range of pathophysiological conditions. Firstly, I_Na is reduced by the impaired Na⁺ channel function that arises clinically during heart failure, ischemia, tachycardia, and following treatment with class I antiarrhythmic drugs. Such reductions also arise as a consequence of mutations in SCN5A such as those occurring in Lenègre disease, Brugada syndrome (BrS), sick sinus syndrome, and atrial fibrillation (AF). Secondly, r_a, may be increased due to gap junction decoupling following ischemia, ventricular hypertrophy, and heart failure, or as a result of mutations in CJA5 found in idiopathic AF and atrial standstill. Finally, either r_a or c_m could potentially be altered by fibrotic change through the resultant decoupling of myocyte–myocyte connections and coupling of myocytes with fibroblasts. Such changes are observed in myocardial infarction and cardiomyopathy or following mutations in MHC403 and SCN5A resulting in hypertrophic cardiomyopathy (HCM) or Lenègre disease, respectively. This review defines and quantifies the determinants of θ and summarizes experimental evidence that links changes in these determinants with reduced myocardial θ and arrhythmogenesis. It thereby identifies the diverse pathophysiological conditions in which abnormal θ may contribute to arrhythmia.

Quantitative analysis of cardiac tissue including fibroblasts using three-dimensional confocal microscopy and image reconstruction: towards a basis for electrophysiological modeling

Electrophysiological modeling of cardiac tissue is commonly based on functional and structural properties measured in experiments. Our knowledge of these properties is incomplete, in particular their remodeling in disease. Here, we introduce a methodology for quantitative tissue characterization based on fluorescent labeling, 3-D scanning confocal microscopy, image processing and reconstruction of tissue micro-structure at sub-micrometer resolution. We applied this methodology to normal rabbit ventricular tissue and tissue from hearts with myocardial infarction. Our analysis revealed that the volume fraction of fibroblasts increased from 4.83±0.42% (mean ± standard deviation) in normal tissue up to 6.51±0.38% in myocardium from infarcted hearts. The myocyte volume fraction decreased from 76.20±9.89% in normal to 73.48±8.02% adjacent to the infarct. Numerical field calculations on 3-D reconstructions of the extracellular space yielded an extracellular longitudinal conductivity of 0.264±0.082 S/m with an anisotropy ratio of 2.095±1.11 in normal tissue. Adjacent to the infarct, the longitudinal conductivity increased up to 0.400±0.051 S/m, but the anisotropy ratio decreased to 1.295±0.09. Our study indicates an increased density of gap junctions proximal to both fibroblasts and myocytes in infarcted versus normal tissue, supporting previous hypotheses of electrical coupling of fibroblasts and myocytes in infarcted hearts. We suggest that the presented methodology provides an important contribution to modeling normal and diseased tissue. Applications of the methodology include the clinical characterization of disease-associated remodeling.

Cross talk between cardiac myocytes and fibroblasts: from multiscale investigative approaches to mechanisms and functional consequences

The heart is comprised of a syncytium of cardiac myocytes (CM) and surrounding nonmyocytes, the majority of which are cardiac fibroblasts (CF). CM and CF are highly interspersed in the myocardium with one CM being surrounded by one or more CF. Bidirectional cross talk between CM and CF plays important roles in determining cardiac mechanical and electrical function in both normal and diseased hearts. Genetically engineered animal models and in vitro studies have provided evidence that CM and CF can regulate each other's function. Their cross talk contributes to structural and electrical remodeling in both atria and ventricles and appears to be involved in the pathogenesis of various heart diseases that lead to heart failure and arrhythmia disorders. Mechanisms of CM-CF cross talk, which are not yet fully understood, include release of paracrine factors, direct cell-cell interactions via gap junctions and potentially adherens junctions and nanotubes, and cell interactions with the extracellular matrix. In this article, we provide an overview of the existing multiscale experimental and computational approaches for the investigation of cross talk between CM and CF and review recent progress in our understanding of the functional consequences and underlying mechanisms. Targeting cross talk between CM and CF could potentially be used therapeutically for the modulation of the cardiac remodeling response in the diseased heart and may lead to new strategies for the treatment of heart failure or rhythm disturbances.

A finite element approach for modeling micro-structural discontinuities in the heart

The presence of connective tissue as well as interstitial clefts forms a natural barrier to the electrical propagation in the heart. At a microscopic scale, such uncoupling structures change the pattern of the electrical conduction from uniform towards complex and may play a role in the genesis of cardiac arrhythmias. The anatomical diversity of conduction structures and their topology at a microscopic size scale is overwhelming for experimental techniques. Mathematical models have been often employed to study the behavior of the electrical propagation at a sub-cellular level. However, very fine and computationally expensive meshes are required to capture all microscopic details found in the cardiac tissue. In this work, we present a numerical technique based on the finite element method which allows to reproduce the effects of microscopic conduction barriers caused by the presence of uncoupling structures without actually resolving these structures in a high resolution mesh, thereby reducing the computational costs significantly.

Note on a possible proarrhythmic property of antiarrhythmic drugs aimed at improving gap-junction coupling

Reduced conduction velocity (CV) in the myocardium is well known to increase the probability of arrhythmia and can be caused by structural changes, reduced excitability of individual myocytes, or decreased electrical coupling in the tissue. Recently, investigators have developed antiarrhythmic drugs that target the connections between individual myocytes with the goal of restoring tissue CV, specifically through increasing gap-junction coupling. In a simple but qualitatively relevant mathematical model, we show here that the introduction of a drug that improves intercellular conductance will indeed increase the CV. However, conditions that would require such a drug, such as fibrotic remodeling, may also increase the load of fibroblasts. Fibroblasts may couple to myocytes in much the same way as myocytes couple to each other, and therefore the use of such an agent may also improve coupling between myocytes and fibroblasts. We present numerical examples illustrating that when the load of coupled fibroblasts on myocytes is low or nonexistent, the drug works as expected, i.e., the drug increases CV. On the other hand, when the fibroblast load is high, changes in CV are nonmonotonic, i.e., the CV first increases and then decreases with an increase in dosage. The existence of coupled fibroblasts may therefore impair the effect of the drug, and under unfortunate conditions may be proarrhythmic.

Modelling tissue electrophysiology with multiple cell types: applications of the extended bidomain framework

The bidomain framework has been extensively used to model tissue electrophysiology in a variety of applications. One limitation of the bidomain model is that it describes the activity of only one cell type interacting with the extracellular space. If more than one cell type contributes to the tissue electrophysiology, then the bidomain model is not sufficient. Recently, evidence has suggested that this is the case for at least two important applications: cardiac and gastrointestinal tissue electrophysiology. In the heart, fibroblasts ubiquitously interact with myocytes and are believed to play an important role in the organ electrophysiology. Along the GI tract, interstitial cells of Cajal (ICC) generate electrical waves that are passed on to surrounding smooth muscle cells (SMC), which are interconnected with the ICC and with each other. Because of the contribution of more than one cell type to the overall organ electrophysiology, investigators in different fields have independently proposed similar extensions of the bidomain model to incorporate multiple cell types and tested it on simplified geometries. In this paper, we provide a general derivation of such an extended bidomain framework applicable to any tissue and provide a generic and efficient implementation applicable to any geometry. Proof-of-concept results of tissue electrophysiology on realistic 3D organ geometries using the extended bidomain framework are presented for the heart and the stomach.

Clinical benefits of integrating cardiac and vascular models

INTRODUCTION

Recent advances in computational methods and medical imaging techniques have enabled non-invasive exploration of cardiovascular pathologies, from cardiac level to complex arterial networks. The potential of cardiac and vascular modeling in guiding and monitoring therapies could be further extended through the integration of the two systems.

AREAS COVERED

This review includes advances in methods for cardiac electromechanics and vascular flow simulations. The results of a literature search depicting the state of the art in cardiac and vascular modeling are reviewed. The paper goes on to address the benefits and challenges of combined cardiovascular modeling, highlighting the relevance of specific cardiovascular features and implementation. Various alternative approaches and insights on future directions are presented and analyzed with respect to their applicability to clinical practice.

EXPERT OPINION

The article has emerged from the exploration of currently available cardiac and vascular mathematical tools and their corresponding clinical application. The summarized analysis suggests that future efforts should be aimed at developing more accurate and patient-specific mathematical models integrating cardiac and vascular functions to enhance the knowledge of cardiovascular pathologies.

The maximal downstroke of epicardial potentials as an index of electrical activity in mouse hearts

The maximal upstroke of transmembrane voltage (dV(m)/dt(max)) has been used as an indirect measure of sodium current I(Na) upon activation in cardiac myocytes. However, sodium influx generates not only the upstroke of V(m), but also the downstroke of the extracellular potentials V(e) including epicardial surface potentials V(es). The purpose of this study was to evaluate the magnitude of the maximal downstroke of V(es) (|dV(es)/dt (min)|) as a global index of electrical activation, based on the relationship of dV(m)/dt(max) to I(Na). To fulfill this purpose, we examined |dV(es)/dt(min)| experimentally using isolated perfused mouse hearts and computationally using a 3-D cardiac tissue bidomain model. In experimental studies, a custom-made cylindrical "cage" array with 64 electrodes was slipped over mouse hearts to measure V(es) during hyperkalemia, ischemia, and hypoxia, which are conditions that decrease I(Na). Values of |dV(es)/dt(min)| from each electrode were normalized (|dV(es)/dt (min)|(n)) and averaged (|dV(es)/dt(min)|(na)). Results showed that |dV(es)/dt(min)|(na) decreased during hyperkalemia by 28, 59, and 79% at 8, 10, and 12 mM [K(+)](o), respectively. |dV(es)/dt(min)| also decreased by 54 and 84% 20 min after the onset of ischemia and hypoxia, respectively. In computational studies, |dV(es)/dt(min)| was compared to dV(m)/dt(max) at different levels of the maximum sodium conductance G(Na), extracellular potassium ion concentration [K(+)](o), and intracellular sodium ion concentration [Na(+)](i), which all influence levels of I(Na). Changes in |dV(es)/dt(min)|(n) were similar to dV(m)/dt (max) during alterations of G(Na), [K(+)](o), and [Na(+)](i). Our results demonstrate that |dV(es)/dt(min)|(na) is a robust global index of electrical activation for use in mouse hearts and, similar to dV(m)/dt(max), can be used to probe electrophysiological alterations reliably. The index can be readily measured and evaluated, which makes it attractive for characterization of, for instance, genetically modified mouse hearts and drug effects on cardiac tissue.

The cardiac fibroblast: functional and electrophysiological considerations in healthy and diseased hearts

Cardiac fibrosis occurs in a number of cardiovascular diseases associated with a high incidence of arrhythmias. A critical event in the development of fibrosis is the transformation of fibroblasts into an active phenotype or myofibroblast. This transformation results in functional changes including increased proliferation and changes in the release of signaling molecules and extracellular matrix deposition. Traditionally, fibroblasts have been considered to affect cardiac electrophysiology indirectly by physically isolating myocytes and creating conduction barriers. There is now increasing evidence that cardiac fibroblasts may play a direct role in modulating the electrophysiological substrate in diseased hearts. The purpose of this review is to summarize the functional changes associated with fibroblast activation, the membrane currents that have been identified in adult cardiac fibroblasts, and describe recent studies of fibroblast-myocyte electrical interactions with emphasis on the changes that occur with cardiac injury. Further analysis of fibroblast membrane electrophysiology and their interactions with myocytes will lead to a more complete understanding of the arrhythmic substrate. These studies have the potential to generate new therapeutic approaches for the prevention of arrhythmias associated with cardiac fibrosis.