Modeling defibrillation of the heart: approaches and insights

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.

Low-energy defibrillation using a base-apex epicardial electrode

BACKGROUND

Current implantable cardioverter defibrillators (ICDs) require electric conduction with high voltage and high energy, which can impair cardiac function and induce another malignant arrhythmia. As a result, there has been a demand for an ICD that can effectively operate with lower energy to mitigate the risks of a strong electric shock.

METHODS

A pair of sheet-shaped electrodes covering the heart were analyzed in three configurations (top-bottom, left-right, and front-back) using a heart simulator. We also varied the distance between the two electrodes (clearance) to identify the electrode shape with the lowest defibrillation threshold (DFT). We also investigated the ICD shock waveform, shock direction, and the effect of the backside insulator of the electrode.

RESULTS

The DFT was high when the clearance was too small and the DFT was high even when the clearance was too large, suggesting that an optimal value clearance. The top-bottom electrodes with optimal clearance showed the lowest DFT when the biphasic shocks set the top electrode to a high potential first and then the bottom electrode was set to a high potential. An interval between a first shock waveform and a second shock waveform should be provided for low-energy defibrillation. Because the insulator prevents unnecessary current flow to the backside, the DFT of the electrodes with insulators is less than those without insulators.

CONCLUSION

Painless defibrillation using sheet-shaped electrodes on the epicardium is predicated on the basis of results using a heart simulator.

Optimising low-energy defibrillation in 2D cardiac tissue with a genetic algorithm

Sequences of low-energy electrical pulses can effectively terminate ventricular fibrillation (VF) and avoid the side effects of conventional high-energy electrical defibrillation shocks, including tissue damage, traumatic pain, and worsening of prognosis. However, the systematic optimisation of sequences of low-energy pulses remains a major challenge. Using 2D simulations of homogeneous cardiac tissue and a genetic algorithm, we demonstrate the optimisation of sequences with non-uniform pulse energies and time intervals between consecutive pulses for efficient VF termination. We further identify model-dependent reductions of total pacing energy ranging from ∼4% to ∼80% compared to reference adaptive-deceleration pacing (ADP) protocols of equal success rate (100%).

A smoothed boundary bidomain model for cardiac simulations in anatomically detailed geometries

This manuscript presents a novel finite difference method to solve cardiac bidomain equations in anatomical models of the heart. The proposed method employs a smoothed boundary approach that represents the boundaries between the heart and the surrounding medium as a spatially diffuse interface of finite thickness. The bidomain boundary conditions are implicitly implemented in the smoothed boundary bidomain equations presented in the manuscript without the need of a structured mesh that explicitly tracks the heart-torso boundaries. We reported some significant examples assessing the method's accuracy using nontrivial test geometries and demonstrating the applicability of the method to complex anatomically detailed human cardiac geometries. In particular, we showed that our approach could be employed to simulate cardiac defibrillation in a human left ventricle comprising fiber architecture. The main advantage of the proposed method is the possibility of implementing bidomain boundary conditions directly on voxel structures, which makes it attractive for three dimensional, patient specific simulations based on medical images. Moreover, given the ease of implementation, we believe that the proposed method could provide an interesting and feasible alternative to finite element methods, and could find application in future cardiac research guiding electrotherapy with computational models.

Deriving the Bidomain Model of Cardiac Electrophysiology From a Cell-Based Model; Properties and Comparisons

The bidomain model is considered to be the gold standard for numerical simulation of the electrophysiology of cardiac tissue. The model provides important insights into the conduction properties of the electrochemical wave traversing the cardiac muscle in every heartbeat. However, in normal resolution, the model represents the average over a large number of cardiomyocytes, and more accurate models based on representations of all individual cells have therefore been introduced in order to gain insight into the conduction properties close to the myocytes. The more accurate model considered here is referred to as the EMI model since both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model. Here, we show that the bidomain model can be derived from the cell-based EMI model and we thus reveal the close relation between the two models, and obtain an indication of the error introduced in the approximation. Also, we present numerical simulations comparing the results of the two models and thereby highlight both similarities and differences between the models. We observe that the deviations between the solutions of the models become larger for larger cell sizes. Furthermore, we observe that the bidomain model provides solutions that are very similar to the EMI model when conductive properties of the tissue are in the normal range, but large deviations are present when the resistance between cardiomyocytes is increased.

Computational Model for Therapy Optimization of Wearable Cardioverter Defibrillator: Shockable Rhythm Detection and Optimal Electrotherapy

Wearable cardioverter defibrillator (WCD) is a life saving, wearable, noninvasive therapeutic device that prevents fatal ventricular arrhythmic propagation that leads to sudden cardiac death (SCD). WCD are frequently prescribed to patients deemed to be at high arrhythmic risk but the underlying pathology is potentially reversible or to those who are awaiting an implantable cardioverter-defibrillator. WCD is programmed to detect appropriate arrhythmic events and generate high energy shock capable of depolarizing the myocardium and thus re-initiating the sinus rhythm. WCD guidelines dictate very high reliability and accuracy to deliver timely and optimal therapy. Computational model-based process validation can verify device performance and benchmark the device setting to suit personalized requirements. In this article, we present a computational pipeline for WCD validation, both in terms of shock classification and shock optimization. For classification, we propose a convolutional neural network-"Long Short Term Memory network (LSTM) full form" (Convolutional neural network- Long short term memory network (CNN-LSTM)) based deep neural architecture for classifying shockable rhythms like Ventricular Fibrillation (VF), Ventricular Tachycardia (VT) vs. other kinds of non-shockable rhythms. The proposed architecture has been evaluated on two open access ECG databases and the classification accuracy achieved is in adherence to American Heart Association standards for WCD. The computational model developed to study optimal electrotherapy response is an in-silico cardiac model integrating cardiac hemodynamics functionality and a 3D volume conductor model encompassing biophysical simulation to compute the effect of shock voltage on myocardial potential distribution. Defibrillation efficacy is simulated for different shocking electrode configurations to assess the best defibrillator outcome with minimal myocardial damage. While the biophysical simulation provides the field distribution through Finite Element Modeling during defibrillation, the hemodynamic module captures the changes in left ventricle functionality during an arrhythmic event. The developed computational model, apart from acting as a device validation test-bed, can also be used for the design and development of personalized WCD vests depending on subject-specific anatomy and pathology.

Effect of Shock Vector Orientation in Modulating and Terminating Rotors - a Simulation Study

The main treatment option for Ventricular Fibrillation (VF), especially in out-of-hospital cardiac arrests (OHCA) is defibrillation. Typically, the survival-to-discharge rates are very poor for OHCA. Existing studies have shown that rotors may be the sources of arrhythmia and ablating them could modulate or terminate VF. However, tracking rotors and ablating them is not a feasible solution in a OHCA scenario. Hence, if the sources (or rotors) can be regionally localized non-invasively and this information can be used to direct the orientation of the shock vectors, it may aid the termination of rotors and defibrillation success. In this work, using computational modeling, we present our initial results on testing the effect of shock vector orientation on modulating (or) terminating rotors. A combination of Sovilj's and Aliev Panfilov's monodomain cardiac models were used in inducing rotors and testing the effect of shock vector magnitude and direction. Based on our simulation results on an average with four experimental trials, a shock vector directed in the perpendicular direction along the axis of the rotor terminated the rotor with 16% lesser magnitude than parallel direction and 38% lesser magnitude than in oblique direction.Clinical Relevance- A rotor localization dependent defibrillation strategy may aid the defibrillation protocol procedures to improve the survival rates. Based on the four experimental trials, the results indicate shock vectors oriented perpendicular to the axis of the rotors were efficient in modulating or terminating rotors with lower magnitude than other directions.

Data integration for the numerical simulation of cardiac electrophysiology

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing therapies and interventions. In this direction, mathematical and numerical models provide a complementary relevant tool, able not only to reproduce patient-specific clinical indicators but also to predict and explore unseen scenarios. With this goal, clinical data are processed and provided as inputs to the mathematical model, which quantitatively describes the physical processes that occur in the cardiac tissue. In this paper, the process of integration of clinical data and mathematical models is discussed. Some challenges and contributions in the field of cardiac electrophysiology are reported.

Cardiac computational modelling

Cardiovascular diseases currently have a major social and economic impact, constituting one of the leading causes of mortality and morbidity. Personalized computational models of the heart are demonstrating their usefulness both to help understand the mechanisms underlying cardiac disease, and to optimize their treatment and predict the patient's response. Within this framework, the Spanish Research Network for Cardiac Computational Modelling (VHeart-SN) has been launched. The general objective of the VHeart-SN network is the development of an integrated, modular and multiscale multiphysical computational model of the heart. This general objective is addressed through the following specific objectives: a) to integrate the different numerical methods and models taking into account the specificity of patients; b) to assist in advancing knowledge of the mechanisms associated with cardiac and vascular diseases; and c) to support the application of different personalized therapies. This article presents the current state of cardiac computational modelling and different scientific works conducted by the members of the network to gain greater understanding of the characteristics and usefulness of these models.

Stabilized hybrid discontinuous Galerkin finite element method for the cardiac monodomain equation

Numerical methods for solving the cardiac electrophysiology model, which describes the electrical activity in the heart, are proposed. The model problem consists of a nonlinear reaction-diffusion partial differential equation coupled to systems of ordinary differential equations that describes electrochemical reactions in cardiac cells. The proposed methods combine an operator splitting technique for the reaction-diffusion equation with primal hybrid methods for spatial discretization considering continuous or discontinuous approximations for the Lagrange multiplier. A static condensation is adopted to form a reduced global system in terms of the multiplier only. Convergence studies exhibit optimal rates of convergence and numerical experiments show that the proposed schemes can be more efficient than standard numerical techniques commonly used in this context when preconditioned iterative methods are used for the solution of linear systems.

Effects of high-frequency biphasic shocks on ventricular vulnerability and defibrillation outcomes through synchronized virtual electrode responses

Electrical defibrillation is a well-established treatment for cardiac dysrhythmias. Studies have suggested that shock-induced spatial sawtooth patterns and virtual electrodes are responsible for defibrillation efficacy. We hypothesize that high-frequency shocks enhance defibrillation efficacy by generating temporal sawtooth patterns and using rapid virtual electrodes synchronized with shock frequency. High-speed optical mapping was performed on isolated rat hearts at 2000 frames/s. Two defibrillation electrodes were placed on opposite sides of the ventricles. An S1-S2 pacing protocol was used to induce ventricular tachyarrhythmia (VTA). High-frequency shocks of equal energy but varying frequencies of 125–1000 Hz were used to evaluate VTA vulnerability and defibrillation success rate. The 1000-Hz shock had the highest VTA induction rate in the shorter S1-S2 intervals (50 and 100 ms) and the highest VTA defibrillation rate (70%) among all frequencies. Temporal sawtooth patterns and synchronous shock-induced virtual electrode responses could be observed with frequencies of up to 1000 Hz. The improved defibrillation outcome with high-frequency shocks suggests a lower energy requirement than that of low-frequency shocks for successful ventricular defibrillation.

BeatBox-HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology

The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.

Anti-arrhythmic strategies for atrial fibrillation: The role of computational modeling in discovery, development, and optimization

Atrial fibrillation (AF), the most common cardiac arrhythmia, is associated with increased risk of cerebrovascular stroke, and with several other pathologies, including heart failure. Current therapies for AF are targeted at reducing risk of stroke (anticoagulation) and tachycardia-induced cardiomyopathy (rate or rhythm control). Rate control, typically achieved by atrioventricular nodal blocking drugs, is often insufficient to alleviate symptoms. Rhythm control approaches include antiarrhythmic drugs, electrical cardioversion, and ablation strategies. Here, we offer several examples of how computational modeling can provide a quantitative framework for integrating multiscale data to: (a) gain insight into multiscale mechanisms of AF; (b) identify and test pharmacological and electrical therapy and interventions; and (c) support clinical decisions. We review how modeling approaches have evolved and contributed to the research pipeline and preclinical development and discuss future directions and challenges in the field.

A shocking past: a walk through generations of defibrillation development

Defibrillation is one of the most successful and widely recognized applications of electrotherapy. Yet the historical road to its first successful application in a patient and the innovative adaptation to an implantable device is marred with unexpected turns, political and personal setbacks, and public and scientific condemnation at each new idea. Driven by dedicated scientists and ever-advancing creative applications of new technologies, from electrocardiography to high density mapping and computational simulations, the field of defibrillation persevered and continued to evolve to the life-saving tool it is today. In addition to critical technological advances, the history of defibrillation is also marked by the plasticity of the theory of defibrillation. The advancing theories of success have propelled the campaign for reducing the defibrillation energy requirement, instilling hope in the development of a painless and harmless electrical defibrillation strategy.

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.

Shock-induced termination of reentrant cardiac arrhythmias: comparing monophasic and biphasic shock protocols

In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one-dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 10(6) simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.

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.

Modeling for cardiac excitation propagation based on the Nernst-Planck equation and homogenization

The bidomain model is a commonly used mathematical model of the electrical properties of the cardiac muscle that takes into account the anisotropy of both the intracellular and extracellular spaces. However, the equations contain self-contradiction such that the update of ion concentrations does not consider intracellular or extracellular ion movements due to the gradient of electric potential and the membrane charge as capacitive currents in spite of the fact that those currents are taken into account in forming Kirchhoff's first law. To overcome this problem, we start with the Nernst-Planck equation, the ionic conservation law, and the electroneutrality condition at the cellular level, and by introducing a homogenization method and assuming uniformity of variables at the microscopic scale, we derive rational bidomain equations at the macroscopic level.

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.