From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales

Measurement bias in activation-recovery intervals from unipolar electrograms

The activation-recovery interval (ARI) calculated from unipolar electrograms is regularly used as a convenient surrogate measure of local cardiac action potential durations (APD). This method enables important research bridging between computational studies and in vitro and in vivo human studies. The Wyatt method is well established as a theoretically sound method for calculating ARIs; however, some studies have observed that it is prone to a bias error in measurement when applied to positive T waves. This article demonstrates that recent theoretical and computational studies supporting the use of the Wyatt method are likely to have underestimated the extent of this bias in many practical experimental recording scenarios. This work addresses these situations and explains the measurement bias by adapting existing theoretical expressions of the electrogram to represent practical experimental recording configurations. A new analytic expression for the electrogram's local component is derived, which identifies the source of measurement bias for positive T waves. A computer implementation of the new analytic model confirms our hypothesis that the bias is systematically dependent on the electrode configuration. These results provide an aid to electrogram interpretation in general, and this work's outcomes are used to make recommendations on how to minimize measurement error.

Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach

Under diseased conditions, remodeling of the cardiac tissue properties (“passive properties”) takes place; these are aspects of electrophysiological behavior that are not associated with active ion transport across cell membranes. Remodeling of the passive electrophysiological properties most often results from structural remodeling, such as gap junction down-regulation and lateralization, fibrotic growth infiltrating the myocardium, or the development of an infarct scar. Such structural remodeling renders atrial or ventricular tissue as a major substrate for arrhythmias. The current review focuses on these aspects of cardiac arrhythmogenesis. Due to the inherent complexity of cardiac arrhythmias, computer simulations have provided means to elucidate interactions pertinent to this spatial scale. Here we review the current state-of-the-art in modeling atrial and ventricular arrhythmogenesis as arising from the disease-induced changes in the passive tissue properties, as well as the contributions these modeling studies have made to our understanding of the mechanisms of arrhythmias in the heart. Because of the rapid advance of structural imaging methodologies in cardiac electrophysiology, we chose to present studies that have used such imaging methodologies to construct geometrically realistic models of cardiac tissue, or the organ itself, where the regional remodeling properties of the myocardium can be represented in a realistic way. We emphasize how the acquired knowledge can be used to pave the way for clinical applications of cardiac organ modeling under the conditions of structural remodeling.

Mitochondrial depolarization and electrophysiological changes during ischemia in the rabbit and human heart

Instability of the inner mitochondrial membrane potential (ΔΨm) has been implicated in electrical dysfunction, including arrhythmogenesis during ischemia-reperfusion. Monitoring ΔΨm has led to conflicting results, where depolarization has been reported as sporadic and as a propagating wave. The present study was designed to resolve the aforementioned difference and determine the unknown relationship between ΔΨm and electrophysiology. We developed a novel imaging modality for simultaneous optical mapping of ΔΨm and transmembrane potential (Vm). Optical mapping was performed using potentiometric dyes on preparations from 4 mouse hearts, 14 rabbit hearts, and 7 human hearts. Our data showed that during ischemia, ΔΨm depolarization is sporadic and changes asynchronously with electrophysiological changes. Spatially, ΔΨm depolarization was associated with action potential duration shortening but not conduction slowing. Analysis of focal activity indicated that ΔΨm is not different within the myocardium where the focus originates compared with normal ventricular tissue. Overall, our data suggest that during ischemia, mitochondria maintain their function at the expense of sarcolemmal electrophysiology, but ΔΨm depolarization does not have a direct association to ischemia-induced arrhythmias.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

A heterogeneous coupled oscillator model for simulation of ECG signals

We present a novel model of cardiac conduction system including main pacemakers and heart muscles. Sinoatrial node, atrioventricular node and His-Purkinje system are represented by modified van der Pol-type oscillators connected with time-delay velocity coupling. For description of atrial and ventricular muscles, where depolarization and repolarization processes are considered as separate waves, we use modified FitzHugh-Nagumo model. In this work, we obtained synthetic ECG as a combined signal of atrial and ventricular muscles and reproduced several normal and pathological rhythms. Inclusion of cardiac muscle response allows to investigate interactions between pacemakers and resulting global heartbeat dynamics by means of clinically comparable realistic ECG signals. This feature distinguishes our model from existing cardiac oscillator models. To solve the system of differential equations describing the proposed heterogeneous coupled oscillator model we developed a software in MATLAB environment utilizing special DDE23 function.

Effects of fibrosis morphology on reentrant ventricular tachycardia inducibility and simulation fidelity in patient-derived models

Myocardial fibrosis detected via delayed-enhanced magnetic resonance imaging (MRI) has been shown to be a strong indicator for ventricular tachycardia (VT) inducibility. However, little is known regarding how inducibility is affected by the details of the fibrosis extent, morphology, and border zone configuration. The objective of this article is to systematically study the arrhythmogenic effects of fibrosis geometry and extent, specifically on VT inducibility and maintenance. We present a set of methods for constructing patient-specific computational models of human ventricles using in vivo MRI data for patients suffering from hypertension, hypercholesterolemia, and chronic myocardial infarction. Additional synthesized models with morphologically varied extents of fibrosis and gray zone (GZ) distribution were derived to study the alterations in the arrhythmia induction and reentry patterns. Detailed electrophysiological simulations demonstrated that (1) VT morphology was highly dependent on the extent of fibrosis, which acts as a structural substrate, (2) reentry tended to be anchored to the fibrosis edges and showed transmural conduction of activations through narrow channels formed within fibrosis, and (3) increasing the extent of GZ within fibrosis tended to destabilize the structural reentry sites and aggravate the VT as compared to fibrotic regions of the same size and shape but with lower or no GZ. The approach and findings represent a significant step toward patient-specific cardiac modeling as a reliable tool for VT prediction and management of the patient. Sensitivities to approximation nuances in the modeling of structural pathology by image-based reconstruction techniques are also implicated.

Methodology for image-based reconstruction of ventricular geometry for patient-specific modeling of cardiac electrophysiology

Patient-specific modeling of ventricular electrophysiology requires an interpolated reconstruction of the 3-dimensional (3D) geometry of the patient ventricles from the low-resolution (Lo-res) clinical images. The goal of this study was to implement a processing pipeline for obtaining the interpolated reconstruction, and thoroughly evaluate the efficacy of this pipeline in comparison with alternative methods. The pipeline implemented here involves contouring the epi- and endocardial boundaries in Lo-res images, interpolating the contours using the variational implicit functions method, and merging the interpolation results to obtain the ventricular reconstruction. Five alternative interpolation methods, namely linear, cubic spline, spherical harmonics, cylindrical harmonics, and shape-based interpolation were implemented for comparison. In the thorough evaluation of the processing pipeline, Hi-res magnetic resonance (MR), computed tomography (CT), and diffusion tensor (DT) MR images from numerous hearts were used. Reconstructions obtained from the Hi-res images were compared with the reconstructions computed by each of the interpolation methods from a sparse sample of the Hi-res contours, which mimicked Lo-res clinical images. Qualitative and quantitative comparison of these ventricular geometry reconstructions showed that the variational implicit functions approach performed better than others. Additionally, the outcomes of electrophysiological simulations (sinus rhythm activation maps and pseudo-ECGs) conducted using models based on the various reconstructions were compared. These electrophysiological simulations demonstrated that our implementation of the variational implicit functions-based method had the best accuracy.

An efficient finite element approach for modeling fibrotic clefts in the heart

Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify microstructural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method, this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.

Reduction in dynamin-2 is implicated in ischaemic cardiac arrhythmias

Ischaemic cardiac arrhythmias cause a large proportion of sudden cardiac deaths worldwide. The ischaemic arrhythmogenesis is primarily because of the dysfunction and adverse remodelling of sarcolemma ion channels. However, the potential regulators of sarcolemma ion channel turnover and function in ischaemic cardiac arrhythmias remains unknown. Our previous studies indicate that dynamin-2 (DNM2), a cardiac membrane-remodelling GTPase, modulates ion channels membrane trafficking in the cardiomyocytes. Here, we have found that DNM2 plays an important role in acute ischaemic arrhythmias. In rat ventricular tissues and primary cardiomyocytes subjected to acute ischaemic stress, the DNM2 protein and transcription levels were markedly down-regulated. This DNM2 reduction was coupled with severe ventricular arrhythmias. Moreover, we identified that the down-regulation of DNM2 within cardiomyocytes increases the action potential amplitude and prolongs the re-polarization duration by depressing the retrograde trafficking of Nav1.5 and Kir2.1 channels. These effects are likely to account for the DNM2 defect-induced arrhythmogenic potentials. These results suggest that DNM2, with its multi-ion channel targeting properties, could be a promising target for novel antiarrhythmic therapies.

Mathematical approaches to understanding and imaging atrial fibrillation: significance for mechanisms and management

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This article aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention.

Effects of regional mitochondrial depolarization on electrical propagation: implications for arrhythmogenesis

BACKGROUND

Sudden cardiac death often involves arrhythmias triggered by metabolic stress. Loss of mitochondrial function is thought to contribute to the arrhythmogenic substrate, but how mitochondria contribute to uncoordinated electrical activity is poorly understood. It has been proposed that the formation of metabolic current sinks, caused by the nonuniform collapse of mitochondrial inner membrane potential (ΔΨm), contributes to re-entrant arrhythmias because ΔΨm depolarization is tightly coupled to the activation of sarcolemmal ATP-sensitive K(+) channels, hastening action potential repolarization and shortening the refractory period.

METHODS AND RESULTS

Here, we use computational and experimental methods to investigate how ΔΨm instability can induce re-entrant arrhythmias. We develop the first tissue-level model of cardiac electrical propagation incorporating cellular electrophysiology, excitation-contraction coupling, mitochondrial energetics, and reactive oxygen species balance. Simulations show that re-entry and fibrillation can be initiated by regional ΔΨm loss because of the disparity of refractory periods inside and outside the metabolic sink. Computational results are compared with the effects of a metabolic sink generated experimentally by local perfusion of a mitochondrial uncoupler in a monolayer of cardiac myocytes.

CONCLUSIONS

The results demonstrate that regional mitochondrial depolarization triggered by oxidative stress activates sarcolemmal ATP-sensitive K(+) currents to form a metabolic sink. Consequent shortening of the action potential inside, but not outside, the sink increases the propensity for re-entry. ΔΨm recovery during pacing can lead to novel mechanisms of ectopic activation. The findings highlight the importance of mitochondria as potential therapeutic targets for sudden death associated with cardiovascular disease.

Modeling the dispersion in electromechanically coupled myocardium

We present an approach to model the dispersion of fiber and sheet orientations in the myocardium. By utilizing structure parameters, an existing orthotropic and invariant-based constitutive model developed to describe the passive behavior of the myocardium is augmented. Two dispersion parameters are fitted to experimentally observed angular dispersion data of the myocardial tissue. Computations are performed on a unit myocardium tissue cube and on a slice of the left ventricle indicating that the dispersion parameter has an effect on the myocardial deformation and stress development. The use of fiber dispersions relating to a pathological myocardium had a rather big effect. The final example represents an ellipsoidal model of the left ventricle indicating the influence of fiber and sheet dispersions upon contraction over a cardiac cycle. Although only a minor shift in the pressure-volume (PV) loops between the cases with no dispersions and with fiber and sheet dispersions for a healthy myocardium was observed, a remarkably different behavior is obtained with a fiber dispersion relating to a diseased myocardium. In future simulations, this dispersion model for myocardial tissue may advantageously be used together with models of, for example, growth and remodeling of various cardiac diseases.

Tachycardia in post-infarction hearts: insights from 3D image-based ventricular models

Ventricular tachycardia, a life-threatening regular and repetitive fast heart rhythm, frequently occurs in the setting of myocardial infarction. Recently, the peri-infarct zones surrounding the necrotic scar (termed gray zones) have been shown to correlate with ventricular tachycardia inducibility. However, it remains unknown how the latter is determined by gray zone distribution and size. The goal of this study is to examine how tachycardia circuits are maintained in the infarcted heart and to explore the relationship between the tachycardia organizing centers and the infarct gray zone size and degree of heterogeneity. To achieve the goals of the study, we employ a sophisticated high-resolution electrophysiological model of the infarcted canine ventricles reconstructed from imaging data, representing both scar and gray zone. The baseline canine ventricular model was also used to generate additional ventricular models with different gray zone sizes, as well as models in which the gray zone was represented as different heterogeneous combinations of viable tissue and necrotic scar. The results of the tachycardia induction simulations with a number of high-resolution canine ventricular models (22 altogether) demonstrated that the gray zone was the critical factor resulting in arrhythmia induction and maintenance. In all models with inducible arrhythmia, the scroll-wave filaments were contained entirely within the gray zone, regardless of its size or the level of heterogeneity of its composition. The gray zone was thus found to be the arrhythmogenic substrate that promoted wavebreak and reentry formation. We found that the scroll-wave filament locations were insensitive to the structural composition of the gray zone and were determined predominantly by the gray zone morphology and size. The findings of this study have important implications for the advancement of improved criteria for stratifying arrhythmia risk in post-infarction patients and for the development of new approaches for determining the ablation targets of infarct-related tachycardia.

Feasibility of image-based simulation to estimate ablation target in human ventricular arrhythmia

BACKGROUND

Previous studies suggest that magnetic resonance imaging with late gadolinium enhancement (LGE) may identify slowly conducting tissues in scar-related ventricular tachycardia (VT).

OBJECTIVE

To test the feasibility of image-based simulation based on LGE to estimate ablation targets in VT.

METHODS

We conducted a retrospective study in 13 patients who had preablation magnetic resonance imaging for scar-related VT ablation. We used image-based simulation to induce VT and estimate target regions according to the simulated VT circuit. The estimated target regions were coregistered with the LGE scar map and the ablation sites from the electroanatomical map in the standard ablation approach.

RESULTS

In image-based simulation, VT was inducible in 12 (92.3%) patients. All VTs showed macroreentrant propagation patterns, and the narrowest width of estimated target region that an ablation line should span to prevent VT recurrence was 5.0 ± 3.4 mm. Of 11 patients who underwent ablation, the results of image-based simulation and the standard approach were consistent in 9 (82%) patients, where ablation within the estimated target region was associated with acute success (n = 8) and ablation outside the estimated target region was associated with failure (n = 1). In 1 (9%) case, the results of image-based simulation and the standard approach were inconsistent, where ablation outside the estimated target region was associated with acute success.

CONCLUSIONS

The image-based simulation can be used to estimate potential ablation targets of scar-related VT. The image-based simulation may be a powerful noninvasive tool for preprocedural planning of ablation procedures to potentially reduce the procedure time and complication rates.

Effects of mechano-electric feedback on scroll wave stability in human ventricular fibrillation

Recruitment of stretch-activated channels, one of the mechanisms of mechano-electric feedback, has been shown to influence the stability of scroll waves, the waves that underlie reentrant arrhythmias. However, a comprehensive study to examine the effects of recruitment of stretch-activated channels with different reversal potentials and conductances on scroll wave stability has not been undertaken; the mechanisms by which stretch-activated channel opening alters scroll wave stability are also not well understood. The goals of this study were to test the hypothesis that recruitment of stretch-activated channels affects scroll wave stability differently depending on stretch-activated channel reversal potential and channel conductance, and to uncover the relevant mechanisms underlying the observed behaviors. We developed a strongly-coupled model of human ventricular electromechanics that incorporated human ventricular geometry and fiber and sheet orientation reconstructed from MR and diffusion tensor MR images. Since a wide variety of reversal potentials and channel conductances have been reported for stretch-activated channels, two reversal potentials, −60 mV and −10 mV, and a range of channel conductances (0 to 0.07 mS/µF) were implemented. Opening of stretch-activated channels with a reversal potential of −60 mV diminished scroll wave breakup for all values of conductances by flattening heterogeneously the action potential duration restitution curve. Opening of stretch-activated channels with a reversal potential of −10 mV inhibited partially scroll wave breakup at low conductance values (from 0.02 to 0.04 mS/µF) by flattening heterogeneously the conduction velocity restitution relation. For large conductance values (>0.05 mS/µF), recruitment of stretch-activated channels with a reversal potential of −10 mV did not reduce the likelihood of scroll wave breakup because Na channel inactivation in regions of large stretch led to conduction block, which counteracted the increased scroll wave stability due to an overall flatter conduction velocity restitution.

Electroanatomical characterization of atrial microfibrosis in a histologically detailed computer model

Fibrosis is thought to play an important role in the formation and maintenance of atrial fibrillation (AF). The propensity of fibrosis to increase AF vulnerability depends not only on its amount, its texture plays a crucial role as well. While the detection of fibrotic tissue patches in the atria with extracellular recordings is feasible based on the analysis of electrogram fractionation, as used in clinical practice to identify ablation targets, the classification of fibrotic texture is a more challenging problem. This study seeks to establish a method for the electroanatomical characterization of the fibrotic textures based on the analysis of electrogram fractionation. The proposed method exploits the dependence of fractionation patterns on the incidence direction of wavefronts which differs significantly as a function of texture. A histologically detailed computer model of the right atrial isthmus was developed for testing the method. A stimulation protocol was conceived which generated various incidence directions for any given recording site where electrograms were computed. A classification method is derived then for discriminating three types of fibrosis, no fibrosis (control), diffuse, and patchy fibrosis. Simulation results showed that electrogram fractionation and amplitudes and their dependence upon incidence direction allow a robust discrimination between different classes of fibrosis. Finally, to minimize the technical effort, sensitivity analysis was performed to identify a minimum number of incidence directions required for robust classification.

The force-frequency relationship: insights from mathematical modeling

The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by β-adrenergic stimulation, and, in a coordinated way, the neurohumoral state alters both frequency (acting on the sinoatrial node) as well as force generation (modifying ventricular myocytes). This synchronized tuning is needed to meet new metabolic demands. Cardiac modelers have already linked mechanical and electrical activity in their formulations and showed how those activities feedback on each other. However, now it is necessary to include neurological control to have a complete description of heart performance, especially when changes in frequency are involved. Study of arrhythmias (or antiarrhythmic drugs) based on mathematical models should incorporate this effect to make useful predictions or point out potential pharmaceutical targets.

Patient-specific modeling of the heart: estimation of ventricular fiber orientations

Patient-specific simulations of heart (dys)function aimed at personalizing cardiac therapy are hampered by the absence of in vivo imaging technology for clinically acquiring myocardial fiber orientations. The objective of this project was to develop a methodology to estimate cardiac fiber orientations from in vivo images of patient heart geometries. An accurate representation of ventricular geometry and fiber orientations was reconstructed, respectively, from high-resolution ex vivo structural magnetic resonance (MR) and diffusion tensor (DT) MR images of a normal human heart, referred to as the atlas. Ventricular geometry of a patient heart was extracted, via semiautomatic segmentation, from an in vivo computed tomography (CT) image. Using image transformation algorithms, the atlas ventricular geometry was deformed to match that of the patient. Finally, the deformation field was applied to the atlas fiber orientations to obtain an estimate of patient fiber orientations. The accuracy of the fiber estimates was assessed using six normal and three failing canine hearts. The mean absolute difference between inclination angles of acquired and estimated fiber orientations was 15.4 °. Computational simulations of ventricular activation maps and pseudo-ECGs in sinus rhythm and ventricular tachycardia indicated that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.The new insights obtained from the project will pave the way for the development of patient-specific models of the heart that can aid physicians in personalized diagnosis and decisions regarding electrophysiological interventions.

Methodology for patient-specific modeling of atrial fibrosis as a substrate for atrial fibrillation

Personalized computational cardiac models are emerging as an important tool for studying cardiac arrhythmia mechanisms, and have the potential to become powerful instruments for guiding clinical anti-arrhythmia therapy. In this article, we present the methodology for constructing a patient-specific model of atrial fibrosis as a substrate for atrial fibrillation. The model is constructed from high-resolution late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) images acquired in vivo from a patient suffering from persistent atrial fibrillation, accurately capturing both the patient's atrial geometry and the distribution of the fibrotic regions in the atria. Atrial fiber orientation is estimated using a novel image-based method, and fibrosis is represented in the patient-specific fibrotic regions as incorporating collagenous septa, gap junction remodeling, and myofibroblast proliferation. A proof-of-concept simulation result of reentrant circuits underlying atrial fibrillation in the model of the patient's fibrotic atrium is presented to demonstrate the completion of methodology development.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Modeling defibrillation of the heart: approaches and insights

Cardiac defibrillation, as accomplished nowadays by automatic, implantable devices (ICDs), constitutes the most important means of combating sudden cardiac death. While ICD therapy has proved to be efficient and reliable, defibrillation is a traumatic experience. Thus, research on defibrillation mechanisms, particularly aimed at lowering defibrillation voltage, remains an important topic. Advancing our understanding towards a full appreciation of the mechanisms by which a shock interacts with the heart is the most promising approach to achieve this goal. The aim of this paper is to assess the current state-of-the-art in ventricular defibrillation modeling, focusing on both numerical modeling approaches and major insights that have been obtained using defibrillation models, primarily those of realistic ventricular geometry. The paper showcases the contributions that modeling and simulation have made to our understanding of the defibrillation process. The review thus provides an example of biophysically based computational modeling of the heart (i.e., cardiac defibrillation) that has advanced the understanding of cardiac electrophysiological interaction at the organ level and has the potential to contribute to the betterment of the clinical practice of defibrillation.

Accelerating cardiac bidomain simulations using graphics processing units

Anatomically realistic and biophysically detailed multiscale computer models of the heart are playing an increasingly important role in advancing our understanding of integrated cardiac function in health and disease. Such detailed simulations, however, are computationally vastly demanding, which is a limiting factor for a wider adoption of in-silico modeling. While current trends in high-performance computing (HPC) hardware promise to alleviate this problem, exploiting the potential of such architectures remains challenging since strongly scalable algorithms are necessitated to reduce execution times. Alternatively, acceleration technologies such as graphics processing units (GPUs) are being considered. While the potential of GPUs has been demonstrated in various applications, benefits in the context of bidomain simulations where large sparse linear systems have to be solved in parallel with advanced numerical techniques are less clear. In this study, the feasibility of multi-GPU bidomain simulations is demonstrated by running strong scalability benchmarks using a state-of-the-art model of rabbit ventricles. The model is spatially discretized using the finite element methods (FEM) on fully unstructured grids. The GPU code is directly derived from a large pre-existing code, the Cardiac Arrhythmia Research Package (CARP), with very minor perturbation of the code base. Overall, bidomain simulations were sped up by a factor of 11.8 to 16.3 in benchmarks running on 6-20 GPUs compared to the same number of CPU cores. To match the fastest GPU simulation which engaged 20 GPUs, 476 CPU cores were required on a national supercomputing facility.

Three-dimensional mechanisms of increased vulnerability to electric shocks in myocardial infarction: altered virtual electrode polarizations and conduction delay in the peri-infarct zone

Defibrillation efficacy is decreased in infarcted hearts, but the mechanisms by which infarcted hearts are more vulnerable to electric shocks than healthy hearts remain poorly understood. The goal of this study was to provide insight into the 3D mechanisms for the increased vulnerability to electric shocks in infarcted hearts. We hypothesized that changes in virtual electrode polarizations (VEPs) and propagation delay through the peri-infarct zone (PZ) were responsible. We developed a micro anatomically detailed rabbit ventricular model with chronic myocardial infarction from magnetic resonance imaging and enriched the model with data from optical mapping experiments. We further developed a control model without the infarct. The simulation protocol involved apical pacing followed by biphasic shocks. Simulation results from both models were compared.The upper limit of vulnerability(ULV) was 8 V cm(-1) in the infarction model and 4 V cm(-1) in the control model. VEPs were less pronounced in the infarction model, providing a larger excitable area for postshock propagation but smaller transmembrane potential gradients to initiate new wavefronts. Initial post-shock transmural activation occurred at a later time in the infarction model, and the PZ served to delay propagation in subsequent beats. The presence of the PZ was found to be responsible for the increased vulnerability.

Image-based estimation of ventricular fiber orientations for personalized modeling of cardiac electrophysiology

Technological limitations pose a major challenge to acquisition of myocardial fiber orientations for patient-specific modeling of cardiac (dys)function and assessment of therapy. The objective of this project was to develop a methodology to estimate cardiac fiber orientations from in vivo images of patient heart geometries. An accurate representation of ventricular geometry and fiber orientations was reconstructed, respectively, from high-resolution ex vivo structural magnetic resonance (MR) and diffusion tensor (DT) MR images of a normal human heart, referred to as the atlas. Ventricular geometry of a patient heart was extracted, via semiautomatic segmentation, from an in vivo computed tomography (CT) image. Using image transformation algorithms, the atlas ventricular geometry was deformed to match that of the patient. Finally, the deformation field was applied to the atlas fiber orientations to obtain an estimate of patient fiber orientations. The accuracy of the fiber estimates was assessed using six normal and three failing canine hearts. The mean absolute difference between inclination angles of acquired and estimated fiber orientations was 15.4°. Computational simulations of ventricular activation maps and pseudo-ECGs in sinus rhythm and ventricular tachycardia indicated that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.

Influence of ischemic core muscle fibers on surface depolarization potentials in superfused cardiac tissue preparations: a simulation study

Thin-walled cardiac tissue samples superfused with oxygenated solutions are widely used in experimental studies. However, due to decreased oxygen supply and insufficient wash out of waste products in the inner layers of such preparations, electrophysiological functions could be compromised. Although the cascade of events triggered by cutting off perfusion is well known, it remains unclear as to which degree electrophysiological function in viable surface layers is affected by pathological processes occurring in adjacent tissue. Using a 3D numerical bidomain model, we aim to quantify the impact of superfusion-induced heterogeneities occurring in the depth of the tissue on impulse propagation in superficial layers. Simulations demonstrated that both the pattern of activation as well as the distribution of extracellular potentials close to the surface remain essentially unchanged. This was true also for the electrophysiological properties of cells in the surface layer, where most relevant depolarization parameters varied by less than 5.5 %. The main observed effect on the surface was related to action potential duration that shortened noticeably by 53 % as hypoxia deteriorated. Despite the known limitations of such experimental methods, we conclude that superfusion is adequate for studying impulse propagation and depolarization whereas repolarization studies should consider the influence of pathological processes taking place at the core of tissue sample.

Electromechanical wave imaging for noninvasive mapping of the 3D electrical activation sequence in canines and humans in vivo

Cardiovascular diseases rank as America's primary killer, claiming the lives of over 41% of more than 2.4 million Americans. One of the main reasons for this high death toll is the severe lack of effective imaging techniques for screening, early detection and localization of an abnormality detected on the electrocardiogram (ECG). The two most widely used imaging techniques in the clinic are CT angiography and echocardiography with limitations in speed of application and reliability, respectively. It has been established that the mechanical and electrical properties of the myocardium change dramatically as a result of ischemia, infarction or arrhythmia; both at their onset and after survival. Despite these findings, no imaging technique currently exists that is routinely used in the clinic and can provide reliable, non-invasive, quantitative mapping of the regional, mechanical, and electrical function of the myocardium. Electromechanical Wave Imaging (EWI) is an ultrasound-based technique that utilizes the electromechanical coupling and its associated resulting strain to infer to the underlying electrical function of the myocardium. The methodology of EWI is first described and its fundamental performance is presented. Subsequent in vivo canine and human applications are provided that demonstrate the applicability of Electromechanical Wave Imaging in differentiating between sinus rhythm and induced pacing schemes as well as mapping arrhythmias. Preliminary validation with catheter mapping is also provided and transthoracic electromechanical mapping in all four chambers of the human heart is also presented demonstrating the potential of this novel methodology to noninvasively infer to both the normal and pathological electrical conduction of the heart.

Image-based estimation of ventricular fiber orientations for patient-specific simulations

Patient-specific simulation of heart (dys)function aimed at personalizing cardiac therapy are hampered by the absence of in vivo imaging technology for clinically acquiring myocardial fiber orientations. In this research, we develop a methodology to predict ventricular fiber orientations of a patient heart, given the geometry of the heart and an atlas. We test the methodology by comparing the estimated fiber orientations with measured ones, and by quantifying the effect of the estimation error on outcomes of electrophysiological simulations, in normal and failing canine hearts. The new insights obtained from the project will pave the way for the development of patient-specific models of the heart that can aid physicians in personalized diagnosis and decisions regarding electrophysiological interventions.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

Modeling of mitochondria bioenergetics using a composable chemiosmotic energy transduction rate law: theory and experimental validation

Mitochondrial bioenergetic processes are central to the production of cellular energy, and a decrease in the expression or activity of enzyme complexes responsible for these processes can result in energetic deficit that correlates with many metabolic diseases and aging. Unfortunately, existing computational models of mitochondrial bioenergetics either lack relevant kinetic descriptions of the enzyme complexes, or incorporate mechanisms too specific to a particular mitochondrial system and are thus incapable of capturing the heterogeneity associated with these complexes across different systems and system states. Here we introduce a new composable rate equation, the chemiosmotic rate law, that expresses the flux of a prototypical energy transduction complex as a function of: the saturation kinetics of the electron donor and acceptor substrates; the redox transfer potential between the complex and the substrates; and the steady-state thermodynamic force-to-flux relationship of the overall electro-chemical reaction. Modeling of bioenergetics with this rate law has several advantages: (1) it minimizes the use of arbitrary free parameters while featuring biochemically relevant parameters that can be obtained through progress curves of common enzyme kinetics protocols; (2) it is modular and can adapt to various enzyme complex arrangements for both in vivo and in vitro systems via transformation of its rate and equilibrium constants; (3) it provides a clear association between the sensitivity of the parameters of the individual complexes and the sensitivity of the system's steady-state. To validate our approach, we conduct in vitro measurements of ETC complex I, III, and IV activities using rat heart homogenates, and construct an estimation procedure for the parameter values directly from these measurements. In addition, we show the theoretical connections of our approach to the existing models, and compare the predictive accuracy of the rate law with our experimentally fitted parameters to those of existing models. Finally, we present a complete perturbation study of these parameters to reveal how they can significantly and differentially influence global flux and operational thresholds, suggesting that this modeling approach could help enable the comparative analysis of mitochondria from different systems and pathological states. The procedures and results are available in Mathematica notebooks at http://www.igb.uci.edu/tools/sb/mitochondria-modeling.html.

Cardiac electromechanical models: from cell to organ

The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computational physiology and medicine. This review focuses on electromechanical (EM) models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single-cell models and the second half addresses organ models. At the subcellular level, myofilament models represent actin–myosin interaction and Ca-based activation. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered to be the cellular basis of the Frank–Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of the field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction–diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and defibrillation.

Bidomain ECG simulations using an augmented monodomain model for the cardiac source

The electrocardiogram (ECG) is an essential clinical tool for the non-invasive assessment of cardiac function. Computational simulations of ECGs using bidomain models are considered the biophysically most detailed approach, but computational costs are significant. Alternatively, pseudo-bidomain formulations can be used, combining a monodomain model with an infrequent bidomain solve to obtain full extracellular potential (φ(e)) distributions and traces. However, previous attempts at such approaches did not see the expected significant decrease in compute time and did not include important effects of bath-loading on activation wavefront morphology (present in full bidomain models), representing a less accurate source term for φ(e) solution. ECG traces can also be derived from computationally cheaper φ(e) recovery techniques, whereby the time-course of φ(e) is approximated at a particular point using the monodomain transmembrane potential as source term. However, φ(e) recovery methods also assume tissue to be immersed in an unbounded conductive medium; not the case in most practical scenarios. We recently demonstrated how bath-loading effects in bidomain simulations could be replicated using an augmented monodomain model, faithfully reproducing bidomain wavefront shapes and activation patterns. Here, a computationally-efficient pseudobidomain formulation is suggested which combines the advantages of an augmented monodomain method with an infrequent bidomain solve, providing activation sequences, ECG traces and φ(e) distributions in a bounded medium surrounding the heart which closely match those of the full bidomain, but at ≈ 10% the computational cost. We demonstrate the important impact of both bath-loading and a finite surrounding bath on spatiotemporal φ(e) distributions, thus demonstrating the utility of our novel pseudo-bidomain model in ECG computation with respect to previous pseudo-bidomain and φ(e) recovery approaches.

Models of cardiac electromechanics based on individual hearts imaging data: image-based electromechanical models of the heart

Current multi-scale computational models of ventricular electromechanics describe the full process of cardiac contraction on both the micro- and macro- scales including: the depolarization of cardiac cells, the release of calcium from intracellular stores, tension generation by cardiac myofilaments, and mechanical contraction of the whole heart. Such models are used to reveal basic mechanisms of cardiac contraction as well as the mechanisms of cardiac dysfunction in disease conditions. In this paper, we present a methodology to construct finite element electromechanical models of ventricular contraction with anatomically accurate ventricular geometry based on magnetic resonance and diffusion tensor magnetic resonance imaging of the heart. The electromechanical model couples detailed representations of the cardiac cell membrane, cardiac myofilament dynamics, electrical impulse propagation, ventricular contraction, and circulation to simulate the electrical and mechanical activity of the ventricles. The utility of the model is demonstrated in an example simulation of contraction during sinus rhythm using a model of the normal canine ventricles.

Orthogonal recursive bisection as data decomposition strategy for massively parallel cardiac simulations

We present the orthogonal recursive bisection algorithm that hierarchically segments the anatomical model structure into subvolumes that are distributed to cores. The anatomy is derived from the Visible Human Project, with electrophysiology based on the FitzHugh-Nagumo (FHN) and ten Tusscher (TT04) models with monodomain diffusion. Benchmark simulations with up to 16,384 and 32,768 cores on IBM Blue Gene/P and L supercomputers for both FHN and TT04 results show good load balancing with almost perfect speedup factors that are close to linear with the number of cores. Hence, strong scaling is demonstrated. With 32,768 cores, a 1000 ms simulation of full heart beat requires about 6.5 min of wall clock time for a simulation of the FHN model. For the largest machine partitions, the simulations execute at a rate of 0.548 s (BG/P) and 0.394 s (BG/L) of wall clock time per 1 ms of simulation time. To our knowledge, these simulations show strong scaling to substantially higher numbers of cores than reported previously for organ-level simulation of the heart, thus significantly reducing run times. The ability to reduce runtimes could play a critical role in enabling wider use of cardiac models in research and clinical applications.

Electromechanical models of the ventricles

Computational modeling has traditionally played an important role in dissecting the mechanisms for cardiac dysfunction. Ventricular electromechanical models, likely the most sophisticated virtual organs to date, integrate detailed information across the spatial scales of cardiac electrophysiology and mechanics and are capable of capturing the emergent behavior and the interaction between electrical activation and mechanical contraction of the heart. The goal of this review is to provide an overview of the latest advancements in multiscale electromechanical modeling of the ventricles. We first detail the general framework of multiscale ventricular electromechanical modeling and describe the state of the art in computational techniques and experimental validation approaches. The powerful utility of ventricular electromechanical models in providing a better understanding of cardiac function is then demonstrated by reviewing the latest insights obtained by these models, focusing primarily on the mechanisms by which mechanoelectric coupling contributes to ventricular arrythmogenesis, the relationship between electrical activation and mechanical contraction in the normal heart, and the mechanisms of mechanical dyssynchrony and resynchronization in the failing heart. Computational modeling of cardiac electromechanics will continue to complement basic science research and clinical cardiology and holds promise to become an important clinical tool aiding the diagnosis and treatment of cardiac disease.

Simulating human cardiac electrophysiology on clinical time-scales

In this study, the feasibility of conducting in silico experiments in near-realtime with anatomically realistic, biophysically detailed models of human cardiac electrophysiology is demonstrated using a current national high-performance computing facility. The required performance is achieved by integrating and optimizing load balancing and parallel I/O, which lead to strongly scalable simulations up to 16,384 compute cores. This degree of parallelization enables computer simulations of human cardiac electrophysiology at 240 times slower than real time and activation times can be simulated in approximately 1 min. This unprecedented speed suffices requirements for introducing in silico experimentation into a clinical workflow.

Whole-heart modeling: applications to cardiac electrophysiology and electromechanics

Recent developments in cardiac simulation have rendered the heart the most highly integrated example of a virtual organ. We are on the brink of a revolution in cardiac research, one in which computational modeling of proteins, cells, tissues, and the organ permit linking genomic and proteomic information to the integrated organ behavior, in the quest for a quantitative understanding of the functioning of the heart in health and disease. The goal of this review is to assess the existing state-of-the-art in whole-heart modeling and the plethora of its applications in cardiac research. General whole-heart modeling approaches are presented, and the applications of whole-heart models in cardiac electrophysiology and electromechanics research are reviewed. The article showcases the contributions that whole-heart modeling and simulation have made to our understanding of the functioning of the heart. A summary of the future developments envisioned for the field of cardiac simulation and modeling is also presented. Biophysically based computational modeling of the heart, applied to human heart physiology and the diagnosis and treatment of cardiac disease, has the potential to dramatically change 21st century cardiac research and the field of cardiology.

Efficient computational methods for strongly coupled cardiac electromechanics

Strongly coupled cardiac electromechanical models can further our understanding of the relative importance of feedback mechanisms in the heart, but computational challenges currently remain a major obstacle, which limit their widespread use. To address this issue, we present a set of efficient computational methods including an efficient adaptive cell model integration scheme and a solution method for the monodomain equations that maintains high conduction velocity for time steps greater than 0.1 ms. We also present a novel method for increasing the efficiency of simulating electromechanical coupling, which shows a significant reduction in computational cost of the mechanical component on a personalized left ventricular geometry with an active contraction cell model reparametrized for human cells.

A macro finite-element formulation for cardiac electrophysiology simulations using hybrid unstructured grids

Electrical activity in cardiac tissue can be described by the bidomain equations whose solution for large-scale simulations still remains a computational challenge. Therefore, improvements in the discrete formulation of the problem, which decrease computational and/or memory demands are highly desirable. In this study, we propose a novel technique for computing shape functions of finite elements (FEs). The technique generates macro FEs (MFEs) based on the local decomposition of elements into tetrahedral subelements with linear shape functions. Such an approach necessitates the direct use of hybrid meshes (HMs) composed of different types of elements. MFEs are compared to classic standard FEs with respect to accuracy and RAM memory usage under different scenarios of cardiac modeling, including bidomain and monodomain simulations in 2-D and 3-D for simple and complex tissue geometries. In problems with analytical solutions, MFEs displayed the same numerical accuracy of standard linear triangular and tetrahedral elements. In propagation simulations, conduction velocity and activation times agreed very well with those computed with standard FEs. However, MFEs offer a significant decrease in memory requirements. We conclude that HMs composed of MFEs are well suited for solving problems in cardiac computational electrophysiology.

From isolated to networked: a paradigmatic shift in mitochondrial physiology

A new paradigm of mitochondrial function in networks is emerging which includes, without undermining, the glorious and still useful paradigm of the isolated mitochondrion. The mitochondrial network paradigm introduces new concepts, tools, and analytical techniques. Among them is that mitochondrial function in networks exhibits interdependence and multiplicative effects based on synchronization mechanisms, which involve communication between mitochondrial neighbors. The collective dynamics of these networks become advantageous for coordinating function spanning from the cell, to the tissue, and the organ. However, under severely stressful conditions the network behavior of mitochondria may become life threatening.

Models of cardiac tissue electrophysiology: progress, challenges and open questions

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

Near-real-time simulations of biolelectric activity in small mammalian hearts using graphical processing units

Simulations of cardiac bioelectric phenomena remain a significant challenge despite continual advancements in computational machinery. Spanning large temporal and spatial ranges demands millions of nodes to accurately depict geometry, and a comparable number of timesteps to capture dynamics. This study explores a new hardware computing paradigm, the graphics processing unit (GPU), to accelerate cardiac models, and analyzes results in the context of simulating a small mammalian heart in real time. The ODEs associated with membrane ionic flow were computed on traditional CPU and compared to GPU performance, for one to four parallel processing units. The scalability of solving the PDE responsible for tissue coupling was examined on a cluster using up to 128 cores. Results indicate that the GPU implementation was between 9 and 17 times faster than the CPU implementation and scaled similarly. Solving the PDE was still 160 times slower than real time.

[Multiscale modeling of cardiac electrical activity]

Models of cardiac electrical activity cover a wide range of spatial scales, from the genesis of the ionic currents in individual cardiomyocytes to the generation of electrocardiograms on the torso. The level of detail that is appropriate and practicable depends on the problem investigated and the scope of the computations that are required. We briefly present three examples of modelling: the dynamics of the entrainment of a single cell, the impact of fibrosis on electrical propagation in a piece of tissue and the generation of ECG in human. In each case, the methods, results and limitations are discussed.

Multi-scale modelling in computational biomedicine

The inherent complexity of biomedical systems is well recognized; they are multi-scale, multi-science systems, bridging a wide range of temporal and spatial scales. This article reviews the currently emerging field of multi-scale modelling in computational biomedicine. Many exciting multi-scale models exist or are under development. However, an underpinning multi-scale modelling methodology seems to be missing. We propose a direction that complements the classic dynamical systems approach and introduce two distinct case studies, transmission of resistance in human immunodeficiency virus spreading and in-stent restenosis in coronary artery disease.

Cross-bridge cycling gives rise to spatiotemporal heterogeneity of dynamic subcellular mechanics in cardiac myocytes probed with atomic force microscopy

To study how the dynamic subcellular mechanical properties of the heart relate to the fundamental underlying process of actin-myosin cross-bridge cycling, we developed a novel atomic force microscope elastography technique for mapping spatiotemporal stiffness of isolated, spontaneously beating neonatal rat cardiomyocytes. Cells were indented repeatedly at a rate close but unequal to their contractile frequency. The resultant changes in pointwise apparent elastic modulus cycled at a predictable envelope frequency between a systolic value of 26.2 +/- 5.1 kPa and a diastolic value of 7.8 +/- 4.1 kPa at a representative depth of 400 nm. In cells probed along their major axis, spatiotemporal changes in systolic stiffness displayed a heterogeneous pattern, reflecting the banded sarcomeric structure of underlying myofibrils. Treatment with blebbistatin eliminated contractile activity and resulted in a uniform apparent modulus of 6.5 +/- 4.8 kPa. This study represents the first quantitative dynamic mechanical mapping of beating cardiomyocytes. The technique provides a means of probing the micromechanical effects of disease processes and pharmacological treatments on beating cardiomyocytes, providing new insights and relating subcellular cardiac structure and function.

Mitochondria in cardiomyocyte Ca2+ signaling

Ca(2+) signaling is of vital importance to cardiac cell function and plays an important role in heart failure. It is based on sarcolemmal, sarcoplasmic reticulum and mitochondrial Ca(2+) cycling. While the first two are well characterized, the latter remains unclear, controversial and technically challenging. In mammalian cardiac myocytes, Ca(2+) influx through L-type calcium channels in the sarcolemmal membrane triggers Ca(2+) release from the nearby junctional sarcoplasmic reticulum to produce Ca(2+) sparks. When this triggering is synchronized by the cardiac action potential, a global [Ca(2+)](i) transient arises from coordinated Ca(2+) release events. The ends of intermyofibrillar mitochondria are located within 20 nm of the junctional sarcoplasmic reticulum and thereby experience a high local [Ca(2+)] during the Ca(2+) release process. Both local and global Ca(2+) signals may thus influence calcium signaling in mitochondria and, reciprocally, mitochondria may contribute to the local control of calcium signaling. In addition to the intermyofibrillar mitochondria, morphologically distinct mitochondria are also located in the perinuclear and subsarcolemmal regions of the cardiomyocyte and thus experience a different local [Ca(2+)]. Here we review the literature in regard to several issues of broad interest: (1) the ultrastructural basis for mitochondrion - sarcoplasmic reticulum cross-signaling; (2) mechanisms of sarcoplasmic reticulum signaling; (3) mitochondrial calcium signaling; and (4) the possible interplay of calcium signaling between the sarcoplasmic reticulum and adjacent mitochondria. Finally, this review discusses experimental findings and mathematical models of cardiac calcium signaling between the sarcoplasmic reticulum and mitochondria, identifies weaknesses in these models, and suggests strategies and approaches for future investigations.

Integrative computational models of cardiac arrhythmias -- simulating the structurally realistic heart

Simulation of cardiac electrical function, and specifically, simulation aimed at understanding the mechanisms of cardiac rhythm disorders, represents an example of a successful integrative multiscale modeling approach, uncovering emergent behavior at the successive scales in the hierarchy of structural complexity. The goal of this article is to present a review of the integrative multiscale models of realistic ventricular structure used in the quest to understand and treat ventricular arrhythmias. It concludes with the new advances in image-based modeling of the heart and the promise it holds for the development of individualized models of ventricular function in health and disease.