Tunnel propagation of postshock activations as a hypothesis for fibrillation induction and isoelectric window

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.

The role of conductivity discontinuities in design of cardiac defibrillation

Fibrillation is an erratic electrical state of the heart, of rapid twitching rather than organized contractions. Ventricular fibrillation is fatal if not treated promptly. The standard treatment, defibrillation, is a strong electrical shock to reinitialize the electrical dynamics and allow a normal heart beat. Both the normal and the fibrillatory electrical dynamics of the heart are organized into moving wave fronts of changing electrical signals, especially in the transmembrane voltage, which is the potential difference between the cardiac cellular interior and the intracellular region of the heart. In a normal heart beat, the wave front motion is from bottom to top and is accompanied by the release of Ca ions to induce contractions and pump the blood. In a fibrillatory state, these wave fronts are organized into rotating scroll waves, with a centerline known as a filament. Treatment requires altering the electrical state of the heart through an externally applied electrical shock, in a manner that precludes the existence of the filaments and scroll waves. Detailed mechanisms for the success of this treatment are partially understood, and involve local shock-induced changes in the transmembrane potential, known as virtual electrode alterations. These transmembrane alterations are located at boundaries of the cardiac tissue, including blood vessels and the heart chamber wall, where discontinuities in electrical conductivity occur. The primary focus of this paper is the defibrillation shock and the subsequent electrical phenomena it induces. Six partially overlapping causal factors for defibrillation success are identified from the literature. We present evidence in favor of five of these and against one of them. A major conclusion is that a dynamically growing wave front starting at the heart surface appears to play a primary role during defibrillation by critically reducing the volume available to sustain the dynamic motion of scroll waves; in contrast, virtual electrodes occurring at the boundaries of small, isolated blood vessels only cause minor effects. As a consequence, we suggest that the size of the heart (specifically, the surface to volume ratio) is an important defibrillation variable.

Bidomain Predictions of Virtual Electrode-Induced Make and Break Excitations around Blood Vessels

Introduction and background

Virtual electrodes formed by field stimulation during defibrillation of cardiac tissue play an important role in eliciting activations. It has been suggested that the coronary vasculature is an important source of virtual electrodes, especially during low-energy defibrillation. This work aims to further the understanding of how virtual electrodes from the coronary vasculature influence defibrillation outcomes.

Methods

Using the bidomain model, we investigated how field stimulation elicited activations from virtual electrodes around idealized intramural blood vessels. Strength–interval curves, which quantify the stimulus strength required to elicit wavefront propagation from the vessels at different states of tissue refractoriness, were computed for each idealized geometry.

Results

Make excitations occurred at late diastolic intervals, originating from regions of depolarization around the vessel. Break excitations occurred at early diastolic intervals, whereby the vessels were able to excite surrounding refractory tissue due to the local restoration of excitability by virtual electrode-induced hyperpolarizations. Overall, strength–interval curves had similar morphologies and underlying excitation mechanisms compared with previous experimental and numerical unipolar stimulation studies of cardiac tissue. Including the presence of the vessel wall increased the field strength required for make excitations but decreased the field strength required for break excitations, and the field strength at which break excitations occurred was generally greater than 5 V/cm. Finally, in a more realistic ventricular slice geometry, the proximity of virtual electrodes around subepicardial vessels was seen to cause break excitations in the form of propagating unstable wavelets to the subepicardial layer.

Conclusion

Representing the blood vessel wall microstructure in computational bidomain models of defibrillation is recommended as it significantly alters the electrophysiological response of the vessel to field stimulation. Although vessels may facilitate excitation of relatively refractory tissue via break excitations, the field strength required for this is generally greater than those used in the literature on low-energy defibrillation. However, the high-intensity shocks used in standard defibrillation may elicit break excitation propagation from the coronary vasculature.

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.

The Relationship Between Cardiac Vulnerability and Restitution Properties of the Ventricular Activation Recovery Interval

INTRODUCTION

The restitution of the action potential duration (APD) is an important contributor to ventricular fibrillation (VF) initiation by a single critically timed ectopic beat. We hypothesized that a steep slope of the activation recovery interval restitution curve was related to the upper limit of vulnerability (ULV).

METHODS AND RESULTS

Fifty-four consecutive patients with implantable cardioverter defibrillators (ICDs) implanted between April 2012 and July 2013 were included. At the implantation, pacing from the right ventricular (RV) coil to an indifferent electrode inserted in the ICD pocket was performed, and the unipolar electrograms from the RV coil were simultaneously recorded. We assessed the standard restitution by introducing extra-stimuli, while measuring the activation recovery interval (ARI). Our protocol for the vulnerability test consisted of delivering three 15 J shocks on the T-peak and within ±20 milliseconds of it. If VF was not induced by that procedure, a ULV of ≤15 J was defined. The relationship between the ULV and maximum slope of the restitution curve was analyzed. A restitution curve could finally be obtained in a total of 40 patients. The background characteristics were similar between the two groups. The maximum slope of the restitution curve was steeper in the ULV > 15 J group than ULV ≤ 15 J group (1.55 ± 0.45 vs. 0.91 ± 0.64, P < 0.05). A maximum slope exceeding 1.0 was the optimal point for discriminating patients with a ULV > 15 J from a ULV ≤ 15 J (sensitivity 61.5% and specificity 96.3%).

CONCLUSION

The maximum slope of the restitution curve was significantly related to the ULV. High defibrillation threshold patients could be detected by the ARI dynamics.

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.

Advances in modeling ventricular arrhythmias: from mechanisms to the clinic

Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.

Diastolic field stimulation: the role of shock duration in epicardial activation and propagation

Detailed knowledge of tissue response to both systolic and diastolic shock is critical for understanding defibrillation. Diastolic field stimulation has been much less studied than systolic stimulation, particularly regarding transient virtual anodes. Here we investigated high-voltage-induced polarization and activation patterns in response to strong diastolic shocks of various durations and of both polarities, and tested the hypothesis that the activation versus shock duration curve contains a local minimum for moderate shock durations, and it grows for short and long durations. We found that 0.1-0.2-ms shocks produced slow and heterogeneous activation. During 0.8-1 ms shocks, the activation was very fast and homogeneous. Further shock extension to 8 ms delayed activation from 1.55 ± 0.27 ms and 1.63 ± 0.21 ms at 0.8 ms shock to 2.32 ± 0.41 ms and 2.37 ± 0.3 ms (N = 7) for normal and opposite polarities, respectively. The traces from hyperpolarized regions during 3-8 ms shocks exhibited four different phases: beginning negative polarization, fast depolarization, slow depolarization, and after-shock increase in upstroke velocity. Thus, the shocks of >3 ms in duration created strong hyperpolarization associated with significant delay (P < 0.05) in activation compared with moderate shocks of 0.8 and 1 ms. This effect appears as a dip in the activation-versus-shock-duration curve.

Placement of implantable cardioverter-defibrillators in paediatric and congenital heart defect patients: a pipeline for model generation and simulation prediction of optimal configurations

There is currently no reliable way of predicting the optimal implantable cardioverter-defibrillator (ICD) placement in paediatric and congenital heart defect (CHD) patients. This study aimed to: (1) develop a new image processing pipeline for constructing patient-specific heart-torso models from clinical magnetic resonance images (MRIs); (2) use the pipeline to determine the optimal ICD configuration in a paediatric tricuspid valve atresia patient; (3) establish whether the widely used criterion of shock-induced extracellular potential (Φe) gradients ≥5 V cm(-1) in ≥95% of ventricular volume predicts defibrillation success. A biophysically detailed heart-torso model was generated from patient MRIs. Because transvenous access was impossible, three subcutaneous and three epicardial lead placement sites were identified along with five ICD scan locations. Ventricular fibrillation was induced, and defibrillation shocks were applied from 11 ICD configurations to determine defibrillation thresholds (DFTs). Two configurations with epicardial leads resulted in the lowest DFTs overall and were thus considered optimal. Three configurations shared the lowest DFT among subcutaneous lead ICDs. The Φe gradient criterion was an inadequate predictor of defibrillation success, as defibrillation failed in numerous instances even when 100% of the myocardium experienced such gradients. In conclusion, we have developed a new image processing pipeline and applied it to a CHD patient to construct the first active heart-torso model from clinical MRIs.

Terminating ventricular tachyarrhythmias using far-field low-voltage stimuli: mechanisms and delivery protocols

BACKGROUND

Low-voltage termination of ventricular tachycardia (VT) and atrial fibrillation has shown promising results; however, the mechanisms and full range of applications remain unexplored.

OBJECTIVES

To elucidate the mechanisms for low-voltage cardioversion and defibrillation and to develop an optimal low-voltage defibrillation protocol.

METHODS

We developed a detailed magnetic resonance imaging-based computational model of the rabbit right ventricular wall. We applied multiple low-voltage far-field stimuli of various strengths (≤1 V/cm) and stimulation rates in VT and ventricular fibrillation (VF).

RESULTS

Of the 5 stimulation rates tested, stimuli applied at 16% or 88% of the VT cycle length (CL) were most effective in cardioverting VT, the mechanism being consecutive excitable gap decreases. Stimuli given at 88% of the VF CL defibrillated successfully, whereas a faster stimulation rate (16%) often failed because the fast stimuli did not capture enough tissue. In this model, defibrillation threshold energy for multiple low-voltage stimuli at 88% of VF CL was 0.58% of the defibrillation threshold energy for a single strong biphasic shock. Based on the simulation results, a novel 2-stage defibrillation protocol was proposed. The first stage converted VF into VT by applying low-voltage stimuli at times of maximal excitable gap, capturing large tissue volume and synchronizing depolarization; the second stage terminated VT. The energy required for successful defibrillation using this protocol was 57.42% of the energy for low-voltage defibrillation when stimulating at 88% of VF CL.

CONCLUSIONS

A novel 2-stage low-voltage defibrillation protocol using the excitable gap extent to time multiple stimuli defibrillated VF with the least energy by first converting VF into VT and then terminating VT.

Computational cardiology: how computer simulations could be used to develop new therapies and advance existing ones

This article reviews the latest developments in computational cardiology. It focuses on the contribution of cardiac modelling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modelling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.

The effect of pinacidil on postshock activation and ventricular defibrillation threshold in canine hearts

AIM

To determine the postshock activation patterns with both successful and failed shocks in a canine model of ventricular fibrillation, and whether piniacidil, an early after-depolarization (EAD) inhibitor, altered the defibrillation threshold (DFT) and postshock activation patterns.

METHODS

In 6 beagles, a basket catheter with 64 unipolar electrodes was placed in the LV for global endocardial mapping, a monophasic action potential catheter was inserted into the LV apex, and a catheter with the negative electrode in the right ventricle and the positive electrode in the superior vena cava was inserted for defibrillation. The DFT, 90% action potential duration (APD(90)) and activation recovery interval (ARI) were evaluated before and after pinacidil administration (loading dosage 0.5 mg/kg and maintenance dosage 0.5 mg·kg(-1)·h(-1), iv). Electrical heterogeneities were defined with the dispersion of ARI. After successful and failed shocks with near-DFT strength, the earliest postshock activation patterns (focal or nonfocal endocardial activation), interval and location were detected.

RESULTS

Pinacidil significantly decreased APD(90) (from 178±16 ms to 168±18 ms) and ARI from (152±10 ms to 143±10 ms) at pacing cycle length of 300 ms. The drug significantly increased VF activation rate (from 10.0±1.9 Hz to 10.8±2.0 Hz). The drug did not affect the dispersion of ARI, neither it changed DFT (baseline: 480±110 V; pinacidil: 425±55 V, P>0.05). The earliest postshock activation arose locally on the LV apical endocardium before and after the drug treatment. Pinacidil significantly prolonged the postshock cycle length of cycles 2 to 5 for the successful episodes but not for the failed episodes.

CONCLUSION

Pinacidil increases the postshock cycle length suggesting that EAD may play a role in postshock activation, while it fails to alter DFT suggesting that EAD produced by shock does not determine a defibrillation success or failure.

Computational cardiology: the heart of the matter

This paper reviews the newest developments in computational cardiology. It focuses on the contribution of cardiac modeling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modeling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.

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.

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.

Reversible cardiac conduction block and defibrillation with high-frequency electric field

Electrical impulse propagation is an essential function in cardiac, skeletal muscle, and nervous tissue. Abnormalities in cardiac impulse propagation underlie lethal reentrant arrhythmias, including ventricular fibrillation. Temporary propagation block throughout the ventricular myocardium could possibly terminate these arrhythmias. Electrical stimulation has been applied to nervous tissue to cause reversible conduction block, but has not been explored sufficiently in cardiac tissue. We show that reversible propagation block can be achieved in cardiac tissue by holding myocardial cells in a refractory state for a designated period of time by applying a sustained sinusoidal high-frequency alternating current (HFAC); in doing so, reentrant arrhythmias are terminated. We demonstrate proof of concept using several models, including optically mapped monolayers of neonatal rat ventricular cardiomyocytes, Langendorff-perfused guinea pig and rabbit hearts, intact anesthetized adult rabbits, and computer simulations of whole-heart impulse propagation. HFAC may be an effective and potentially safer alternative to direct current application, currently used to treat ventricular fibrillation.

Propagating unstable wavelets in cardiac tissue

Solitonlike propagating modes have been proposed for excitable tissue, but have never been measured in cardiac tissue. In this study, we simulate an experimental protocol to elicit these propagating unstable wavelets (PUWs) in a detailed three-dimensional ventricular wedge preparation. PUWs appear as fixed-shape wavelets that propagate only in the direction of cardiac fibers, with conduction velocity approximately 40% slower than normal action potential excitation. We investigate their properties, demonstrating that PUWs are not true solitons. The range of stimuli for which PUWs were elicited was very narrow (several orders of magnitude lower than the stimulus strength itself), but increased with reduced sodium conductance and reduced coupling in nonlongitudinal directions. We show that the phenomenon does not depend on the particular membrane representation used or the shape of the stimulating electrode.

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.

Image-based models of cardiac structure in health and disease

Computational approaches to investigating the electromechanics of healthy and diseased hearts are becoming essential for the comprehensive understanding of cardiac function. In this article, we first present a brief review of existing image-based computational models of cardiac structure. We then provide a detailed explanation of a processing pipeline which we have recently developed for constructing realistic computational models of the heart from high resolution structural and diffusion tensor (DT) magnetic resonance (MR) images acquired ex vivo. The presentation of the pipeline incorporates a review of the methodologies that can be used to reconstruct models of cardiac structure. In this pipeline, the structural image is segmented to reconstruct the ventricles, normal myocardium, and infarct. A finite element mesh is generated from the segmented structural image, and fiber orientations are assigned to the elements based on DTMR data. The methods were applied to construct seven different models of healthy and diseased hearts. These models contain millions of elements, with spatial resolutions in the order of hundreds of microns, providing unprecedented detail in the representation of cardiac structure for simulation studies.

Mechanisms of defibrillation

Electrical shock has been the one effective treatment for ventricular fibrillation for several decades. With the advancement of electrical and optical mapping techniques, histology, and computer modeling, the mechanisms responsible for defibrillation are now coming to light. In this review, we discuss recent work that demonstrates the various mechanisms responsible for defibrillation. On the cellular level, membrane depolarization and electroporation affect defibrillation outcome. Cell bundles and collagenous septae are secondary sources and cause virtual electrodes at sites far from shocking electrodes. On the whole-heart level, shock field gradient and critical points determine whether a shock is successful or whether reentry causes initiation and continuation of fibrillation.

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.

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.

Tunnel propagation following defibrillation with ICD shocks: hidden postshock activations in the left ventricular wall underlie isoelectric window

BACKGROUND

After near-defibrillation threshold (DFT) shocks from an implantable cardioverter-defibrillator (ICD), the first postshock activation that leads to defibrillation failure arises focally after an isoelectric window (IW). The mechanisms underlying the IW remain incompletely understood.

OBJECTIVE

The goal of this study was to provide mechanistic insight into the origins of postshock activations and IW after ICD shocks, and to link shock outcome to the preshock state of the ventricles. We hypothesized that the nonuniform ICD field results in the formation of an intramural excitable area (tunnel) only in the left ventricular (LV) free wall, through which both pre-existing and new shock-induced wavefronts propagate during the IW.

METHODS

Simulations were conducted using a realistic three dimensional (3D) model of defibrillation in the rabbit ventricles. Biphasic ICD shocks of varying strengths were delivered to 27 different fibrillatory states.

RESULTS

After near-DFT shocks, regardless of preshock state, the main postshock excitable area was always located within LV free wall, creating an intramural tunnel. Either pre-existing fibrillatory or shock-induced wavefronts propagated during the IW (duration of up to 74 ms) in this tunnel and emerged as breakthroughs on LV epicardium. Preshock activity within the LV played a significant role in shock outcome: a large number of preshock filaments resulted in an IW associated with tunnel propagation of pre-existing rather than shock-induced wavefronts. Furthermore, shocks were more likely to succeed if the LV excitable area was smaller.

CONCLUSION

The LV intramural excitable area is the primary reason for near-DFT failure. Any intervention that decreases the extent of this area will improve the likelihood of defibrillation success.

Purkinje activation precedes myocardial activation following defibrillation after long-duration ventricular fibrillation

BACKGROUND

While reentry within the ventricular myocardium (VM) is responsible for the maintenance of short-duration ventricular fibrillation (SDVF; VF duration <1 minute), Purkinje fibers (PFs) are important in the maintenance of long-duration ventricular fibrillation (LDVF; VF duration >1 minute).

OBJECTIVE

The purpose of this study was to test the hypothesis that the mechanisms of defibrillation may also be different for SDVF and LDVF.

METHODS

A multielectrode basket catheter was deployed in the left ventricle of eight beagles. External defibrillation shocks were delivered with a ramp-up protocol after SDVF (20 seconds) and LDVF (150 seconds). Earliest VM and PF activations were identified after the highest energy shock that failed to terminate VF and the successful shock.

RESULTS

Defibrillation was successful after 36 +/- 12 and 181 +/- 14 seconds for SDVF and LDVF, respectively. The time after shock delivery until earliest activation was detected for failed shocks and was significantly longer after LDVF (138.7 +/- 24.1 ms) than after SDVF (75.6 +/- 8.7 ms). Earliest postshock activation after SDVF typically initiated in the VM (14 of 16 episodes), while it always initiated in the PF (16 of 16 episodes) after LDVF. Sites of earliest activity during sinus rhythm correlated with sites of earliest postshock activation for PF-led cycles but not for VM-led cycles.

CONCLUSION

Earliest recorded postshock activation is in the Purkinje system after LDVF but not after SDVF. This difference raises the possibility that the optimal defibrillation strategy is different for SDVF and LDVF.

Development of an anatomically detailed MRI-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function

Recent advances in magnetic resonance (MR) imaging technology have unveiled a wealth of information regarding cardiac histoanatomical complexity. However, methods to faithfully translate this level of fine-scale structural detail into computational whole ventricular models are still in their infancy, and, thus, the relevance of this additional complexity for simulations of cardiac function has yet to be elucidated. Here, we describe the development of a highly detailed finite-element computational model (resolution: approximately 125 microm) of rabbit ventricles constructed from high-resolution MR data (raw data resolution: 43 x 43 x 36 microm), including the processes of segmentation (using a combination of level-set approaches), identification of relevant anatomical features, mesh generation, and myocyte orientation representation (using a rule-based approach). Full access is provided to the completed model and MR data. Simulation results were compared with those from a simplified model built from the same images but excluding finer anatomical features (vessels/endocardial structures). Initial simulations showed that the presence of trabeculations can provide shortcut paths for excitation, causing regional differences in activation after pacing between models. Endocardial structures gave rise to small-scale virtual electrodes upon the application of external field stimulation, which appeared to protect parts of the endocardium in the complex model from strong polarizations, whereas intramural virtual electrodes caused by blood vessels and extracellular cleft spaces appeared to reduce polarization of the epicardium. Postshock, these differences resulted in the genesis of new excitation wavefronts that were not observed in more simplified models. Furthermore, global differences in the stimulus recovery rates of apex/base regions were observed, causing differences in the ensuing arrhythmogenic episodes. In conclusion, structurally simplified models are well suited for a large range of cardiac modeling applications. However, important differences are seen when behavior at microscales is relevant, particularly when examining the effects of external electrical stimulation on tissue electrophysiology and arrhythmia induction. This highlights the utility of histoanatomically detailed models for investigations of cardiac function, in particular for future patient-specific modeling.

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.

Arrhythmogenic mechanisms of the Purkinje system during electric shocks: a modeling study

BACKGROUND

The function of the Purkinje system (PS) is to ensure fast and uniform activation of the heart. Although this vital role during sinus rhythm is well understood, this is not the case when shocks are applied to the heart, especially in the case of failed defibrillation. The PS activates differently from the myocardium, has different electrophysiological properties, and provides alternate propagation pathways; thus, there are many ways in which it can contribute to postshock behavior.

OBJECTIVE

The purpose of this study was to elucidate the role of the PS in the initiation and maintenance of postshock arrhythmias.

METHODS

A computer model of the ventricles including the PS was subjected to different reentry induction protocols.

RESULTS

The PS facilitated reentry induction at relatively weaker shocks. Disconnecting the PS from the ventricles during the postshock interval revealed that the PS helps stabilize early-stage reentry by providing focal breakthroughs. During later stages, the PS contributed to reentry by leading to higher frequency rotors. The PS also promoted wave front splitting during reentry due to electrotonic coupling, which prolongs action potential durations at PS-myocyte junctions. The presence of a PS results in the anchoring of reentrant activations that propagate through the pathways provided by the PS.

CONCLUSIONS

The PS is proarrhythmic in that it provides pathways that prolong activity, and it plays a supplementary role in maintaining the later stages of reentry (>800 ms).

Generation of histo-anatomically representative models of the individual heart: tools and application

This paper presents methods to build histo-anatomically detailed individualized cardiac models. The models are based on high-resolution three-dimensional anatomical and/or diffusion tensor magnetic resonance images, combined with serial histological sectioning data, and are used to investigate individualized cardiac function. The current state of the art is reviewed, and its limitations are discussed. We assess the challenges associated with the generation of histo-anatomically representative individualized in silico models of the heart. The entire processing pipeline including image acquisition, image processing, mesh generation, model set-up and execution of computer simulations, and the underlying methods are described. The multifaceted challenges associated with these goals are highlighted, suitable solutions are proposed, and an important application of developed high-resolution structure-function models in elucidating the effect of individual structural heterogeneity upon wavefront dynamics is demonstrated.

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 meta-analysis of cardiac electrophysiology computational models

Computational models of cardiac electrophysiology are exemplar demonstrations of the integration of multiple data sets into a consistent biophysical framework. These models encapsulate physiological understanding to provide quantitative predictions of function. The combination or extension of existing models within a common framework allows integrative phenomena in larger systems to be investigated. This methodology is now routinely applied, as demonstrated by the increasing number of studies which use or extend previously developed models. In this study, we present a meta-analysis of this model re-use for two leading models of cardiac electrophysiology in the form of parameter inheritance trees, a sensitivity analysis and a comparison of the functional significance of the sodium potassium pump for defining restitution curves. These results indicate that even though the models aim to represent the same physiological system, both the sources of parameter values and the function of equivalent components are significantly different.

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

Computer simulations of electrical behaviour in the whole ventricles have become commonplace during the last few years. The goals of this article are (i) to review the techniques that are currently employed to model cardiac electrical activity in the heart, discussing the strengths and weaknesses of the various approaches, and (ii) to implement a novel modelling approach, based on physiological reasoning, that lifts some of the restrictions imposed by current state-of-the-art ionic models. To illustrate the latter approach, the present study uses a recently developed ionic model of the ventricular myocyte that incorporates an excitation-contraction coupling and mitochondrial energetics model. A paradigm to bridge the vastly disparate spatial and temporal scales, from subcellular processes to the entire organ, and from sub-microseconds to minutes, is presented. Achieving sufficient computational efficiency is the key to success in the quest to develop multiscale realistic models that are expected to lead to better understanding of the mechanisms of arrhythmia induction following failure at the organelle level, and ultimately to the development of novel therapeutic applications.

Panoramic imaging reveals basic mechanisms of induction and termination of ventricular tachycardia in rabbit heart with chronic infarction: implications for low-voltage cardioversion

BACKGROUND

Sudden cardiac death due to arrhythmia in the settings of chronic myocardial infarction (MI) is an important clinical problem. Arrhythmic risk post-MI continues indefinitely even if heart failure and acute ischemia are not present due to the anatomic substrate of the scar and border zone (BZ) tissue.

OBJECTIVE

The purpose of this study was to determine mechanisms of arrhythmia initiation and termination in a rabbit model of chronic MI.

METHODS

Ligation of the lateral division of the left circumflex artery was performed 72 +/- 29 days before acute experiments (n = 11). Flecainide (2.13 +/- 0.64 microM) was administered to promote sustained arrhythmias, which were induced with burst pacing or a multiple shock protocol (four pulses, 140-200 ms coupling interval).

RESULTS

Panoramic optical mapping with blebbistatin (5 microM) revealed monomorphic ventricular tachycardia (VT) maintained by a single mother rotor (cycle length [CL] = 174.7 +/- 38.4 ms) as the primary mechanism of arrhythmia. Mother rotors were anchored to the scar or BZ for 16 of the 19 rotor locations recorded. Cardioversion thresholds (CVTs) were determined at various phases throughout the VT CL from external shock electrodes. CVTs were found to be phase dependent, and the maximum versus minimum CVT was 7.8 +/- 1.9 vs. 4.1 +/- 1.6 V/cm, respectively (P = .005). Antitachycardia pacing was found to be effective in only 2.7% of cases in this model.

CONCLUSIONS

These results indicate that scar and BZ tissue heterogeneity provide the substrate for VT by attracting and stabilizing rotors. Additionally, a significant reduction in CVT may be achieved by appropriately timed shocks in which the shock-induced virtual electrode polarization interacts with the rotor to destabilize VT.

Polarity reversal lowers activation time during diastolic field stimulation of the rabbit ventricles: insights into mechanisms

To fully characterize the mechanisms of defibrillation, it is necessary to understand the response, within the three-dimensional (3D) volume of the ventricles, to shocks given in diastole. Studies that have examined diastolic responses conducted measurements on the epicardium or on a transmural surface of the left ventricular (LV) wall only. The goal of this study was to use optical imaging experiments and 3D bidomain simulations, including a model of optical mapping, to ascertain the shock-induced virtual electrode and activation patterns throughout the rabbit ventricles following diastolic shocks. We tested the hypothesis that the locations of shock-induced regions of hyperpolarization govern the different diastolic activation patterns for shocks of reversed polarity. In model and experiment, uniform-field monophasic shocks of reversed polarities (cathode over the right ventricle is RV-, reverse polarity is LV-) were applied to the ventricles in diastole. Experiments and simulations revealed that RV- shocks resulted in longer activation times compared with LV- shocks of the same strength. 3D simulations demonstrated that RV- shocks induced a greater volume of hyperpolarization at shock end compared with LV- shocks; most of these hyperpolarized regions were located in the LV. The results of this study indicate that ventricular geometry plays an important role in both the location and size of the shock-induced virtual anodes that determine activation delay during the shock and subsequently affect shock-induced propagation. If regions of hyperpolarization that develop during the shock are sufficiently large, activation delay may persist until shock end.