Upper limit of vulnerability in a defibrillation model of the rabbit ventricles

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Personalized Imaging and Modeling Strategies for Arrhythmia Prevention and Therapy

The goal of this article is to review advances in computational modeling of the heart, with a focus on recent non-invasive clinical imaging- and simulation-based strategies aimed at improving the diagnosis and treatment of patients with arrhythmias and structural heart disease. Following a brief overview of the field of computational cardiology, we present recent applications of the personalized virtual-heart approach in predicting the optimal targets for infarct-related ventricular tachycardia and atrial fibrillation ablation, and in determining risk of sudden cardiac death in myocardial infarction patients. The hope is that with such models at the patient bedside, therapies could be improved, invasiveness of diagnostic procedures minimized, and health-care costs reduced.

Light-based Approaches to Cardiac Arrhythmia Research: From Basic Science to Translational Applications

Light has long been used to image the heart, but now it can be used to modulate its electrophysiological function. Imaging modalities and techniques have long constituted an indispensable part of arrhythmia research and treatment. Recently, advances in the fields of optogenetics and photodynamic therapy have provided scientists with more effective approaches for probing, studying and potentially devising new treatments for cardiac arrhythmias. This article is a review of research toward the application of these techniques. It contains (a) an overview of advancements in technology and research that have contributed to light-based cardiac applications and (b) a summary of current and potential future applications of light-based control of cardiac cells, including modulation of heart rhythm, manipulation of cardiac action potential morphology, quantitative analysis of arrhythmias, defibrillation and cardiac ablation.

Computational rabbit models to investigate the initiation, perpetuation, and termination of ventricular arrhythmia

Current understanding of cardiac electrophysiology has been greatly aided by computational work performed using rabbit ventricular models. This article reviews the contributions of multiscale models of rabbit ventricles in understanding cardiac arrhythmia mechanisms. This review will provide an overview of multiscale modeling of the rabbit ventricles. It will then highlight works that provide insights into the role of the conduction system, complex geometric structures, and heterogeneous cellular electrophysiology in diseased and healthy rabbit hearts to the initiation and maintenance of ventricular arrhythmia. Finally, it will provide an overview on the contributions of rabbit ventricular modeling on understanding the mechanisms underlying shock-induced defibrillation.

How computer simulations of the human heart can improve anti-arrhythmia therapy

Over the last decade, the state-of-the-art in cardiac computational modelling has progressed rapidly. The electrophysiological function of the heart can now be simulated with a high degree of detail and accuracy, opening the doors for simulation-guided approaches to anti-arrhythmic drug development and patient-specific therapeutic interventions. In this review, we outline the basic methodology for cardiac modelling, which has been developed and validated over decades of research. In addition, we present several recent examples of how computational models of the human heart have been used to address current clinical problems in cardiac electrophysiology. We will explore the use of simulations to improve anti-arrhythmic pacing and defibrillation interventions; to predict optimal sites for clinical ablation procedures; and to aid in the understanding and selection of arrhythmia risk markers. Together, these studies illustrate how the tremendous advances in cardiac modelling are poised to revolutionize medical treatment and prevention of arrhythmia.

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.

New insights into defibrillation of the heart from realistic simulation studies

Cardiac defibrillation, as accomplished nowadays by automatic, implantable devices, constitutes the most important means of combating sudden cardiac death. Advancing our understanding towards a full appreciation of the mechanisms by which a shock interacts with the heart, particularly under diseased conditions, is a promising approach to achieve an optimal therapy. The aim of this article is to assess the current state-of-the-art in whole-heart defibrillation modelling, focusing on major insights that have been obtained using defibrillation models, primarily those of realistic heart geometry and disease remodelling. The article showcases the contributions that modelling and simulation have made to our understanding of the defibrillation process. The review thus provides an example of biophysically based computational modelling 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.

Defibrillation success with high frequency electric fields is related to degree and location of conduction block

BACKGROUND

We recently demonstrated that high frequency alternating current (HFAC) electric fields can reversibly block propagation in the heart by inducing an oscillating, elevated transmembrane potential (Vm) that maintains myocytes in a refractory state for the field duration and can terminate arrhythmias, including ventricular fibrillation (VF).

OBJECTIVES

To quantify and characterize conduction block (CB) induced by HFAC fields and to determine whether the degree of CB can be used to predict defibrillation success.

METHODS

Optical mapping was performed in adult guinea pig hearts (n = 14), and simulations were performed in an anatomically accurate rabbit ventricular model. HFAC fields (50-500 Hz) were applied to the ventricles. A novel power spectrum metric of CB-the loss of spectral power in the 1-30 Hz range, termed loss of conduction power (LCP)-was assessed during the HFAC field and compared with defibrillation success and VF vulnerability.

RESULTS

LCP increased with field strength and decreased with frequency. Optical mapping experiments conducted on the epicardial surface showed that LCP and the size of CB regions were significantly correlated with VF initiation and termination. In simulations, subsurface myocardial LCP and CB sizes were more closely correlated with VF termination than surface values. Multilinear regression analysis of simulation results revealed that while CB on both the surface and the subsurface myocardium was predictive, subsurface myocardial CB was the better predictor of defibrillation success.

CONCLUSIONS

HFAC fields induce a field-dependent state of CB, and defibrillation success is related to the degree and location of the CB.

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.

ANALYSIS OF THE VIRTUAL ELECTRODE PHENOMENA USING BIDOMAIN MODEL: BASIC CHARACTERISTICS FOR PASSIVE MEMBRANE

The virtual electrode (VE) has been recognized as an important factor for success or failure of cardiac defibrillation. Many researches have been performed to study characteristics of the VE. However, there are some questions which remain unanswered. In this study, we developed a simulator to solve a three-dimensional bidomain model and performed several simulations to elucidate the basic characteristics of VE in a simplified cardiac tissue with passive membrane when a constant unipolar cathodal stimulus was applied. The results showed that for smaller electrodes, VE has a typical dog-bone shaped virtual cathode (VC) and two egg-shaped virtual anodes (VAs). The distributions both in intra- and extracellular potentials have concentric ellipsoidal isosurfaces, but their ellipticities are subtly different, producing VE. For larger electrodes, VC becomes larger and has a flat-dish shape rather than dog-bone, and VA becomes smaller and also flattens and collapses. The peak values of VE are larger for smaller electrodes, but their time courses show similar tendency among the different sized electrodes. The change of stimulus strength and polarity only affects the magnitude of VE in a linear manner and the distribution pattern is unchanged. These results provide us fundamental knowledge about VE.

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.

Shock-induced arrhythmogenesis in the human heart: A computational modelling study

Electrical defibrillation by application of a strong shock to the heart is the only effective treatment against lethal cardiac arrhythmias such as ventricular fibrillation. A large body of experimental and computational research has been devoted to understanding shock-induced effects on the heart in an attempt to improve defibrillation efficacy. However, most of the research has been performed in small animal hearts, and in particular rabbits. The difference in size between rabbits and humans might limit the extrapolation of the results to the clinical setting. In this paper, we present, for the first time, computer simulations of shock-induced effects on a human ventricular model with realistic ion channel dynamics and fibre architecture. Bidomain simulations using the human ventricular model were performed using the Chaste open source simulation package. The parallel performance of the software package was highly improved in order to meet the computational requirements of these kind of studies.

How hyperpolarization and the recovery of excitability affect propagation through a virtual anode in the heart

Researchers have suggested that the fate of a shock-induced wave front at the edge of a "virtual anode" (a region hyperpolarized by the shock) is a key factor determining success or failure during defibrillation of the heart. In this paper, we use a simple one-dimensional computer model to examine propagation speed through a hyperpolarized region. Our goal is to test the hypothesis that rapid propagation through a virtual anode can cause failure of propagation at the edge of the virtual anode. The calculations support this hypothesis and suggest that the time constant of the sodium inactivation gate is an important parameter. These results may be significant in understanding the mechanism of the upper limit of vulnerability.

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.

Cilostazol attenuates ventricular arrhythmia induction and improves defibrillation efficacy in swine

Previous reports demonstrated that cilostazol, a phosphodiesterase 3 inhibitor, affected cellular electrophysiology and reduced episodes of ventricular fibrillation (VF) in patients with Brugada syndrome. However, its effects on VF induction and defibrillation efficacy have never been investigated. We tested the hypothesis that cilostazol increases the VF threshold (VFT) and decreases the upper limit of vulnerability (ULV) and the defibrillation threshold (DFT). A total of 48 pigs were randomly assigned to defibrillation and VF induction studies. The diastolic pacing threshold (DPT), VFT, ULV, DFT, and effective refractory period were determined before and after the infusion of cilostazol at 6 mg/kg, 3 mg/kg, or vehicle. The DPT was significantly increased after administration of 3 and 6 mg/kg cilostazol. The ULV and DFT were significantly decreased after administration of 6 mg/kg cilostazol only. The ULV in the 6 mg/kg group had 12% lower peak voltage and 25% lower total energy, and the DFT had 13% lower peak voltage and 25% lower total energy. The VFT was not altered in any experimental group. This study shows that cilostazol administration significantly increased the DPT, which was associated with significantly reduced DFT and ULV.

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.

Towards predictive modelling of the electrophysiology of the heart

The simulation of cardiac electrical function is an example of a successful integrative multiscale modelling approach that is directly relevant to human disease. Today we stand at the threshold of a new era, in which anatomically detailed, tomographically reconstructed models are being developed that integrate from the ion channel to the electromechanical interactions in the intact heart. Such models hold high promise for interpretation of clinical and physiological measurements, for improving the basic understanding of the mechanisms of dysfunction in disease, such as arrhythmias, myocardial ischaemia and heart failure, and for the development and performance optimization of medical devices. The goal of this article is to present an overview of current state-of-art advances towards predictive computational modelling of the heart as developed recently by the authors of this article. We first outline the methodology for constructing electrophysiological models of the heart. We then provide three examples that demonstrate the use of these models, focusing specifically on the mechanisms for arrhythmogenesis and defibrillation in the heart. These include: (1) uncovering the role of ventricular structure in defibrillation; (2) examining the contribution of Purkinje fibres to the failure of the shock; and (3) using magnetic resonance imaging reconstructed heart models to investigate the re-entrant circuits formed in the presence of an infarct scar.

A mechanism for the upper limit of vulnerability

BACKGROUND

The strongest shock that induces reentry in the heart is the upper limit of vulnerability (ULV). In order to understand defibrillation, one must know what causes the ULV.

OBJECTIVE

The goal of this study was to examine the mechanism of the upper limit of vulnerability.

METHODS

Numerical simulations of cardiac tissue were performed using the bidomain model. An S2 shock was applied during the refractory period of the S1 action potential, and results using a smooth curving fiber geometry were compared with results using a smooth plus random fiber geometry.

RESULTS

When using a smooth fiber geometry only, no ULV was observed. However, when a random fiber geometry was included, the ULV was present. The difference arises from the fate of the shock-induced break wave front when it reaches the edge of the tissue hyperpolarized by the shock (the virtual anode).

CONCLUSION

Our numerical simulations suggest that local heterogeneities throughout the tissue may be crucial for determining the fate of the shock-induced wave front at the edge of the virtual anode, and therefore play an important role in the mechanism underlying the ULV.

Multiscale modelling of drug-induced effects on cardiac electrophysiological activity

Many drugs fail in the clinical trials and therefore do not reach the market due to adverse effects on cardiac electrical function. This represents a growing concern for both regulatory and pharmaceutical agencies as it translates into important socio-economic costs. Drugs affecting cardiac activity come from diverse pharmacological groups and their interaction with cardiac electrophysiology can result in increased risk of potentially life threatening arrhythmias, such as Torsade de Pointes. The mechanisms of drug interaction with the heart are very complex and the effects span from the ion channel to the whole organ level. This makes their investigation using solely experimental in vitro and in vivo techniques very difficult. Computational modelling of cardiac electrophysiological behaviour has provided insight into the mechanisms of cardiac arrhythmogenesis, with high spatio-temporal resolution, from the ion channel to the whole organ level. It therefore represents a powerful tool in investigating mechanisms of drug-induced changes in cardiac behaviour and in their pro-arrhythmic potential. This article presents a comprehensive review of the recent advances in detailed models of drug action on cardiac electrophysiological activity.

Mechanistic investigation into the arrhythmogenic role of transmural heterogeneities in regional ischaemia phase 1A

AIMS

Studies of arrhythmogenesis during ischemia have focused primarily on reentrant mechanisms manifested on the epicardial surface. The goal of this study was to use a physiologically-accurate model of acute regional ischemia phase 1A to determine the contribution of ischaemia-induced transmural electrophysiological heterogeneities to arrhythmogenesis following left anterior descending artery occlusion.

METHODS AND RESULTS

A slice through a geometrical model of the rabbit ventricles was extracted and a model of regional ischaemia developed. The model included a central ischaemic zone incorporating transmural gradients of I(K(ATP)) activation and [K+]o, surrounded by ischaemic border zones (BZs), with the degree of ischaemic effects varied to represent progression of ischaemia 2-10 min post-occlusion. Premature stimulation was applied over a range of coupling intervals to induce re-entry. The presence of ischaemic BZs and a transmural gradient in I(K(ATP)) activation provided the substrate for re-entrant arrhythmias. Increased dispersion of refractoriness and conduction velocity in the BZs with time post-occlusion led to a progressive increase in arrhythmogenesis. In the absence of a transmural gradient of I(K(ATP)) activation, re-entry was rarely sustained.

CONCLUSION

Knowledge of the mechanism by which specific electrophysiological heterogeneities underlie arrhythmogenesis during acute ischaemia could be useful in developing preventative treatments for patients at risk of coronary vascular disease.

Modulation of shock-end virtual electrode polarisation as a direct result of 3D fluorescent photon scattering

Due to the large transmural variation in transmembrane potential following the application of strong electric shocks, it is thought that fluorescent photon scattering from depth plays a significant role in optical signal modulation at shock-end. For the first time, a model of photon scattering is used to accurately synthesize fluorescent signals over the irregular geometry of the rabbit ventricles following the application of such strong shocks. A bidomain representation of electrical activity is combined with finite element solutions to the photon diffusion equation, simulating both the excitation and emission processes, over an anatomically-based model of rabbit ventricular geometry and fiber orientation. Photon scattering from within a 3D volume beneath the epicardial optical recording site is shown to transduce differences in transmembrane potential within this volume through the myocardial wall. This leads directly to a significantly modulated optical signal response with respect to that predicted by the bidomain simulations, distorting epicardial virtual electrode polarization produced at shock-end. Furthermore, we show that this degree of distortion is very sensitive to the optical properties of the tissue, an important variable to consider during experimental mapping set-ups. These findings provide an essential first-step in aiding the interpretation of experimental optical mapping recordings following strong defibrillation shocks.

The role of mechanoelectric feedback in vulnerability to electric shock

Experimental and clinical studies have shown that ventricular dilatation is associated with increased arrhythmogenesis and elevated defibrillation threshold; however, the underlying mechanisms remain poorly understood. The goal of the present study was to test the hypothesis that (1) stretch-activated channel (SAC) recruitment and (2) geometrical deformations in organ shape and fiber architecture lead to increased arrhythmogenesis by electric shocks following acute ventricular dilatation. To elucidate the contribution of these two factors, the study employed, for the first time, a combined electro-mechanical simulation approach. Acute dilatation was simulated in a model of rabbit ventricular mechanics by raising the LV end-diastolic pressure from 0.6 (control) to 4.2 kPa (dilated). The output of the mechanics model was used in the electrophysiological model. Vulnerability to shocks was examined in the control, the dilated ventricles, and in the dilated ventricles that also incorporated currents through SAC as a function of local strain, by constructing vulnerability grids. Results showed that dilatation-induced deformation alone decreased upper limit of vulnerability (ULV) slightly and did not result in increased vulnerability. With SAC recruitment in the dilated ventricles, the number of shock-induced arrhythmia episodes increased by 37% (from 41 to 56) and the lower limit of vulnerability (LLV) decreased from 9 to 7 V/cm, while ULV did not change. The heterogeneous activation of SAC caused by the heterogeneous fiber strain in the ventricular walls was the main reason for increased vulnerability to electric shocks since it caused dispersion of electrophysiological properties in the tissue, resulting in postshock unidirectional block and establishment of reentry.

The pinwheel experiment revisited: effects of cellular electrophysiological properties on vulnerability to cardiac reentry

In normal heart, ventricular fibrillation can be induced by a single properly timed strong electrical or mechanical stimulus. A mechanism first proposed by Winfree and coined the “pinwheel experiment” emphasizes the timing and strength of the stimulus in inducing figure-of-eight reentry. However, the effects of cellular electrophysiological properties on vulnerability to reentry in the pinwheel scenario have not been investigated. In this study, we extend Winfree's pinwheel experiment to show how the vulnerability to reentry is affected by the graded action potential responses induced by a strong premature stimulus, action potential duration (APD), and APD restitution in simulated monodomain homogeneous two-dimensional tissue. We find that a larger graded response, longer APD, or steeper APD restitution slope reduces the vulnerable window of reentry. Strong graded responses and long APD promote tip-tip interactions at long coupling intervals, causing the two initiated spiral wave tips to annihilate. Steep APD restitution promotes wave front-wave back interaction, causing conduction block in the central common pathway of figure-of-eight reentry. We derive an analytical treatment that shows good agreement with numerical simulation results.

Reduced-order preconditioning for bidomain simulations

Simulations of the bidomain equations involve solving large, sparse, linear systems of the form Ax = b. Being an initial value problems, it is solved at every time step. Therefore, efficient solvers are essential to keep simulations tractable. Iterative solvers, especially the preconditioned conjugate gradient (PCG) method, are attractive since memory demands are minimized compared to direct methods, albeit at the cost of solution speed. However, a proper preconditioner can drastically speed up the solution process by reducing the number of iterations. In this paper, a novel preconditioner for the PCG method based on system order reduction using the Arnoldi method (A-PCG) is proposed. Large order systems, generated during cardiac bidomain simulations employing a finite element method formulation, are solved with the A-PCG method. Its performance is compared with incomplete LU (ILU) preconditioning. Results indicate that the A-PCG estimates an approximate solution considerably faster than the ILU, often within a single iteration. To reduce the computational demands in terms of memory and run time, the use of a cascaded preconditioner was suggested. The A-PCG was applied to quickly obtain an approximate solution, and subsequently a cheap iterative method such as successive overrelaxation (SOR) is applied to further refine the solution to arrive at a desired accuracy. The memory requirements are less than those of direct LU but more than ILU method. The proposed scheme is shown to yield significant speedups when solving time evolving systems.

Arnoldi preconditioning for solving large linear biomedical systems

Simulations of biomedical systems often involve solving large, sparse, linear systems of the form Ax = b. In initial value problems, this system is solved at every time step, so a quick solution is essential for tractability. Iterative solvers, especially preconditioned conjugate gradient, are attractive since memory demands are minimized compared to direct methods, albeit at a cost of solution speed. A proper preconditioner can drastically reduce computation and remains an area of active research. In this paper, we propose a novel preconditioner based on system order reduction using the Arnoldi method. Systems of orders up to a million, generated from a finite element method formulation of the elliptic portion of the bidomain equations, are solved with the new preconditioner and performance is compared with that of other preconditioners. Results indicate that the new method converges considerably faster, often within a single iteration. It also uses less memory than an incomplete LU decomposition (ILU). For solving a system repeatedly, the Arnoldi transformation must be continually recomputed, unlike ILU, but this can be done quickly. In conclusion, for solving a system once, the Arnoldi preconditioner offers a greatly reduced solution time, and for repeated solves, will still be faster than an ILU preconditioner.

Modeling cardiac ischemia

Myocardial ischemia is one of the main causes of sudden cardiac death, with 80% of victims suffering from coronary heart disease. In acute myocardial ischemia, the obstruction of coronary flow leads to the interruption of oxygen flow, glucose, and washout in the affected tissue. Cellular metabolism is impaired and severe electrophysiological changes in ionic currents and concentrations ensue, which favor the development of lethal cardiac arrhythmias such as ventricular fibrillation. Due to the burden imposed by ischemia in our societies, a large body of research has attempted to unravel the mechanisms of initiation, sustenance, and termination of cardiac arrhythmias in acute ischemia, but the rapidity and complexity of ischemia-induced changes as well as the limitations in current experimental techniques have hampered evaluation of ischemia-induced alterations in cardiac electrical activity and understanding of the underlying mechanisms. Over the last decade, computer simulations have demonstrated the ability to provide insight, with high spatiotemporal resolution, into ischemic abnormalities in cardiac electrophysiological behavior from the ionic channel to the whole organ. This article aims to review and summarize the results of these studies and to emphasize the role of computer simulations in improving the understanding of ischemia-related arrhythmias and how to efficiently terminate them.

Myocardial ischemia lowers precordial thump efficacy: an inquiry into mechanisms using three-dimensional simulations

BACKGROUND

Precordial thump is the first International Liaison Committee on Resuscitation-prescribed procedure for advanced life support in witnessed cardiac arrest. Success rates vary and, according to clinical evidence, are significantly reduced under ischemic conditions.

OBJECTIVES

The purpose of this study was to elucidate the mechanisms involved in termination of ventricular tachycardia (VT) by precordial thump and its decreased rate of success in ischemia using a three-dimensional realistic model of electrical behavior in the rabbit ventricles.

METHODS

The electrophysiologic effect of precordial thump was represented by recruitment of mechanosensitive channels in the regions affected by precordial thump. In normoxia, precordial thump opened cation nonselective stretch-activated channels (SAC-NS, reversal potential -20 mV). In ischemia, precordial thump was assumed to additionally activate ATP-sensitive K+ (K(ATP)) channels (reversal potential -95 mV). Ten randomly selected cases of VT were used, and for each case the effect of precordial thump on VT was examined for normoxia and under ischemic conditions of varying severity.

RESULTS

Precordial thump was found to have a 60% success rate in normoxia and 30% in ischemia. Results demonstrate that precordial thump-induced SAC-NS opening in normoxia reduced heterogeneity in transmembrane potential by partially repolarizing excited tissue and depolarizing resting myocardium, potentially causing foci of excitation that eradicate the excitable gap, thus facilitating VT termination. Decreased precordial thump efficacy in ischemia was caused by recruitment of K(ATP), which diminished the depolarizing effect of SAC-NS on resting tissue and caused pronounced action potential shortening, thus facilitating establishment of reentry.

CONCLUSION

This study provides mechanistic insight into precordial thump mechanisms and its reduced clinical utility in patients with myocardial ischemia.

The effect of the fiber curvature gradient on break excitation in cardiac tissue

BACKGROUND

Break excitation has been hypothesized as a mechanism for the initiation of reentry in cardiac tissue. One way break excitation can occur is by virtual electrodes formed due to a curving fiber geometry. In this article, we are concerned with the relationship between the peak gradient of fiber curvature and the threshold for break stimulation and the initiation of reentry.

METHODS

We calculate the maximum gradient of fiber curvature for different scales of fiber geometry in a constant tissue size (20x20 mm), and also examine the mechanisms by which reentry initiation fails.

RESULTS

For small peak gradients, reentry fails because break excitation does not occur. For larger peak gradients, reentry fails because break excitation fails to develop into full-scale reentry. For strong stimuli above the upper limit of vulnerability, reentry fails because the break excitation propagates through the hyperpolarized region and then encounters refractory tissue, causing the wave front to die.

Defibrillation of the heart: insights into mechanisms from modelling studies

Despite its critical role in restoring cardiac rhythm and thus in saving human life, cardiac defibrillation remains poorly understood. Further mechanistic inquiry is hampered by the inability of presently available experimental techniques to resolve, with sufficient accuracy, electrical behaviour confined to the depth of the ventricles. The objective of this review article is to demonstrate that realistic 3-D simulations of the ventricular defibrillation process in close conjunction with experimental observations are capable of bringing a new level of understanding of the electrical events that ensue from the interaction between fibrillating myocardium and applied shock. The article does this by reviewing the results of two studies, one on vulnerability to electric shocks and another on defibrillation. An overview of the modelling tools used in these studies is also provided.

Accelerating large cardiac bidomain simulations by arnoldi preconditioning

Bidomain simulations of cardiac systems often in volve solving large, sparse, linear systems of the form Ax=b. These simulations are computationally very expensive in terms of run time and memory requirements. Therefore, efficient solvers are essential to keep simulations tractable. In this paper, an efficient preconditioner for the conjugate gradient (CG) method based on system order reduction using the Arnoldi method (A-PCG) is explained. Large order systems generated during cardiac bidomain simulations using a finite element method formulation, are solved using the A-PCG method. Its performance is compared with incomplete LU (ILU) preconditioning. Results indicate that the A-PCG estimates an approximate solution considerably faster than the ILU, often within a single iteration. To reduce the computational demands in terms of memory and run time, the use of a cascaded preconditioner is suggested. The A-PCG can be applied to quickly obtain an approximate solution, subsequently a cheap iterative method such as successive overrelaxation (SOR) is applied to further refine the solution to arrive at a desired accuracy. The memory requirements are less than direct LU but more than ILU method. The proposed scheme is shown to yield significant speedups when solving time evolving systems.

How the spatial frequency of polarization influences the induction of reentry in cardiac tissue

Influences of spatial frequency of polarization.

INTRODUCTION

The mechanism by which an electric field induces a rotor during cross-field stimulation of cardiac tissue is not entirely known. Different heterogeneous aspects of cardiac tissue have been offered as possible theories, a prominent one being fiber curvature. The polarization produced when an electric field is applied to a sheet of tissue is varied over many spatial frequencies, depending upon the fiber angle. This article compares the effect of high and low spatial frequencies of polarization on reentry induction.

METHODS AND RESULTS

We incorporate a randomized fiber angle geometry into a two-dimensional active cardiac tissue model with unequal anisotropy ratios already exhibiting smooth, curving fibers. We simulate cross-field stimulation to initiate reentry in the tissue model, and compare the electric field thresholds at different S1-S2 intervals for tissue with randomized fiber angles, tissue with a smooth fiber geometry, and tissue with randomized fiber angles plus smooth, curving fibers. The tissue with both small, random fiber angles and curving fibers has a significantly lower threshold for reentry at certain intervals on the strength-interval curve than for the two cases individually.

CONCLUSION

Cardiac tissue exhibiting a random fiber geometry in conjunction with a smooth fiber geometry includes high and low spatial frequencies of polarization that may have an effect on the mechanism for reentry at certain S1-S2 intervals. Low spatial frequency regions of hyperpolarization carve out excitable pathways, and high spatial frequency regions provide the large gradient of transmembrane potential required to initiate break excitation.

Functionally and structurally integrated computational modeling of ventricular physiology

Computational biology is integrative in several ways. Functionally, computational models are valuable for integrating the many interacting processes within biochemical networks and the many interacting physiological subsystems within the cell. Structurally detailed models provide a way of integrating across scales of biological organization from molecule to organism. Data integration across diverse laboratory and clinical measurements is another unique strength of computational biology. We describe examples of all three categories of integration by using recent advances in modeling cardiac excitation-contraction coupling and whole-heart electromechanics in health and disease.

Cardiac vulnerability to electric shocks during phase 1A of acute global ischemia

OBJECTIVES

The purpose of this study is to characterize the changes in vulnerability to electric shocks during phase 1A of global ischemia in the rabbit ventricles and to determine the mechanisms responsible for these changes.

BACKGROUND

Mechanisms responsible for the changes in cardiac vulnerability over the course of ischemia phase 1A remain poorly understood. The lack of understanding results from the rapid ischemic change in cardiac electrophysiologic properties, which renders experimental evaluation of vulnerability difficult.

METHODS

To examine dynamic changes in vulnerability to electric shocks over the course of acute global ischemia phase 1A, this study used a three-dimensional anatomically accurate bidomain model of ischemic rabbit ventricles. Monophasic shocks are applied at various coupling intervals to construct vulnerability grids in normoxia and at various stages of ischemia phase 1A.

RESULTS

Our simulations demonstrate that 2 to 3 minutes after the onset of ischemia, the upper limit of vulnerability remains at its normoxic value (12.75 V/cm); however, arrhythmias are induced at shorter coupling intervals. As ischemia progresses, the upper limit of vulnerability decreases, reaching 6.4 V/cm in the advanced stage of ischemia phase 1A, and the vulnerable window shifts towards longer coupling intervals.

CONCLUSIONS

Changes in the upper limit of vulnerability result from an increase in the spatial extent of the shock-end excitation wavefronts and the slower recovery from shock-induced positive polarization. Shifts in the vulnerable window stem from decreases in local repolarization times and the occurrence of postshock conduction failure caused by prolonged postrepolarization refractoriness.

Differences between left and right ventricular chamber geometry affect cardiac vulnerability to electric shocks

Although effects of shock strength and waveform on cardiac vulnerability to electric shocks have been extensively documented, the contribution of ventricular anatomy to shock-induced polarization and postshock propagation and thus, to shock outcome, has never been quantified; this is caused by lack of experimental methodology capable of mapping 3-D electrical activity. The goal of this study was to use optical imaging experiments and 3-D bidomain simulations to investigate the role of structural differences between left and right ventricles in vulnerability to electric shocks in rabbit hearts. The ventricles were paced apically, and uniform-field, truncated-exponential, monophasic shocks of reversed polarity were applied over a range of coupling intervals (CIs) in experiment and model. Experiments and simulations revealed that reversing the direction of externally-applied field (RV- or LV- shocks) alters the shape of the vulnerability area (VA), the 2-D grid encompassing episodes of arrhythmia induction. For RV- shocks, VA was nearly rectangular indicating little dependence of postshock arrhythmogenesis on CI. For LV- shocks, the probability of arrhythmia induction was higher for longer than for shorter CIs. The 3-D simulations demonstrated that these effects stem from the fact that reversal of field direction results in relocation of the main postshock excitable area from LV wall (RV- shocks) to septum (LV- shocks). Furthermore, the effect of septal (but not LV) excitable area in postshock propagation was found to strongly depend on preshock state. Knowledge regarding the location of the main postshock excitable area within the 3-D ventricular volume could be important for improving defibrillation efficacy.

Induction of ventricular arrhythmias following mechanical impact: a simulation study in 3D

Commotio cordis, mechanical induction of heart rhythm disturbances, including sudden cardiac death, in the absence of corresponding structural damage, has been reported with increasing frequency in young individuals participating in sporting activities. Recently, the electrophysiological changes during c. cordis have been attributed to mechano-electric feedback, and particularly, to the recruitment of stretch-activated ion channels. The underlying mechanisms, however, by which a mechanical impact results in ventricular fibrillation, remain unknown. This study employs a 3D realistic model of rabbit ventricular geometry and fiber orientation to elucidate the electrophysiological mechanisms involved in arrhythmia induction following acute mechanical stimulation of the heart. Impact effects are modeled through stretch-activated ion channel activation in a 3D region of the ventricles representing the impact profile. Both cation-nonselective and potassium-selective stretch-activated ion channels are recruited upon mechanical impact. The impact is administered at various coupling intervals following pacing at the apex. To aid in the interpretation of results, the effect of mechanical stimulation on single cell action potentials is also examined. The results demonstrate that the region of impact is characterized by different types of cellular responses, including generation of a new action potential, shortening, or lengthening of action potential duration. The impact induces sustained reentry only when (1) a new activation is elicited by mechanical stimulation (caused by activation of cation-nonselective stretch-activated ion channels), and (2) upon return to the original region of impact, this activation does not encounter an extension of action potential duration (prevented by activation of potassium-selective stretch-activated ion channels).

Computer simulations of successful defibrillation in decoupled and non-uniform cardiac tissue

Aim

The aim of the present study is to investigate the origin and effect of virtual electrode polarization in uniform, decoupled and non-uniform cardiac tissue during field stimulation.

Methods

A discrete bidomain model with active membrane behaviour was used to simulate normal cardiac tissue as well as cardiac tissue that is decoupled due to fibrosis and gap junction remodelling. Various uniform and non-uniform electric fields were applied to the external domain of uniform, decoupled and non-uniform resting cardiac tissue as well as cardiac tissue in which spiral waves were induced.

Results

Field stimulation applied on non-uniform tissue results in more virtual electrodes compared with uniform tissue. The spiral waves were terminated in decoupled tissue, but not in uniform, homogeneous tissue. By gradually increasing local differences in intracellular conductivities, the amount and spread of virtual electrodes increased and the spiral waves were terminated.

Conclusion

Fast depolarization of the tissue after field stimulation may be explained by intracellular decoupling and spatial heterogeneity present in normal and pathological cardiac tissue. We demonstrated that termination of spiral waves by means of field stimulation can be achieved when the tissue is modelled as a non-uniform, anisotropic bidomain with active membrane behaviour.