Image-based models of cardiac structure with applications in arrhythmia and defibrillation studies

Personalized biomechanical insights in atrial fibrillation: opportunities & challenges

INTRODUCTION

Atrial fibrillation (AF) is an increasingly prevalent and significant worldwide health problem. Manifested as an irregular atrial electrophysiological activation, it is associated with many serious health complications. AF affects the biomechanical function of the heart as contraction follows the electrical activation, subsequently leading to reduced blood flow. The underlying mechanisms behind AF are not fully understood, but it is known that AF is highly correlated with the presence of atrial fibrosis, and with a manifold increase in risk of stroke.

AREAS COVERED

In this review, we focus on biomechanical aspects in atrial fibrillation, current and emerging use of clinical images, and personalized computational models. We also discuss how these can be used to provide patient-specific care.

EXPERT OPINION

Understanding the connection betweenatrial fibrillation and atrial remodeling might lead to valuable understanding of stroke and heart failure pathophysiology. Established and emerging imaging modalities can bring us closer to this understanding, especially with continued advancements in processing accuracy, reproducibility, and clinical relevance of the associated technologies. Computational models of cardiac electromechanics can be used to glean additional insights on the roles of AF and remodeling in heart function.

Cardiac biophysical detailed synergetic modality rendering and visible correlation

The heart is a vital organ in the human body. Research and treatment for the heart have made remarkable progress, and the functional mechanisms of the heart have been simulated and rendered through the construction of relevant models. The current methods for rendering cardiac functional mechanisms only consider one type of modality, which means they cannot show how different types of modality, such as physical and physiological, work together. To realistically represent the three-dimensional synergetic biological modality of the heart, this paper proposes a WebGL-based cardiac synergetic modality rendering framework to visualize the cardiac physical volume data and present synergetic correspondence rendering of the cardiac electrophysiological modality. By constructing the biological detailed interactive histogram, users can implement local details rendering for the heart, which could reveal the cardiac biology details more clearly. We also present cardiac physical-physiological correlation visualization to explore cardiac biological association characteristics. Experimental results show that the proposed framework can provide favorable cardiac biological detailed synergetic modality rendering results in terms of both effectiveness and efficiency. Compared with existing methods, the framework can facilitate the study of the internal mechanism of the heart and subsequently deduce the process of initiation, development, and transformation from a healthy heart to an ill one, and thereby improve the diagnosis and treatment of cardiac disorders.

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

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

Computational analysis of the effect of KCNH2 L532P mutation on ventricular electromechanical behaviors

The KCNH2 L532P mutation is an alteration in the I_Kr channel that is associated with short QT syndrome and atrial fibrillation in zebrafish. In preliminary studies, the electrophysiological effects of the hERG L532P mutation were investigated using a mathematical model in a single-cell and 2D sheet medium. The objective of this study was to quantify the effects of the KCNH2 L532P mutation on the 3D ventricular electrophysiological behavior and the mechanical pumping responses. We used a realistic three-dimensional ventricular electrophysiological-mechanical model, which was adjusted into two conditions: the wild-type (WT) condition, i.e., the original case of the Tusscher et al. model, and the L532P mutation condition, with modification of the original I_Kr equation. The action potential duration (APD) in the mutant ventricle was reduced by 73% owing to the significant increase of the I_Kr current density. In the 3D simulation, the L532P mutation maintained the sustainability of reentrant waves; however, the reentry was terminated in the WT condition. The contractility of the ventricle with L532P mutation was significantly reduced compared with that in WT which results in sustain shivering heart during reentry condition. The reduction of the contractility was associated with the shortening APD which simultaneously shortened the duration of the Ca²⁺ channel opening. In conclusion, the ventricle with KCNH2 L532P mutation is prone to reentry generation with a sustained chaotic condition, and the mutation significantly reduced the pumping performance of the ventricles.

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

Preprocedure Application of Machine Learning and Mechanistic Simulations Predicts Likelihood of Paroxysmal Atrial Fibrillation Recurrence Following Pulmonary Vein Isolation

BACKGROUND

Pulmonary vein isolation (PVI) is an effective treatment strategy for patients with atrial fibrillation (AF), but many experience AF recurrence and require repeat ablation procedures. The goal of this study was to develop and evaluate a methodology that combines machine learning (ML) and personalized computational modeling to predict, before PVI, which patients are most likely to experience AF recurrence after PVI.

METHODS

This single-center retrospective proof-of-concept study included 32 patients with documented paroxysmal AF who underwent PVI and had preprocedural late gadolinium enhanced magnetic resonance imaging. For each patient, a personalized computational model of the left atrium simulated AF induction via rapid pacing. Features were derived from pre-PVI late gadolinium enhanced magnetic resonance images and from results of simulations of AF induction. The most predictive features were used as input to a quadratic discriminant analysis ML classifier, which was trained, optimized, and evaluated with 10-fold nested cross-validation to predict the probability of AF recurrence post-PVI.

RESULTS

In our cohort, the ML classifier predicted probability of AF recurrence with an average validation sensitivity and specificity of 82% and 89%, respectively, and a validation area under the curve of 0.82. Dissecting the relative contributions of simulations of AF induction and raw images to the predictive capability of the ML classifier, we found that when only features from simulations of AF induction were used to train the ML classifier, its performance remained similar (validation area under the curve, 0.81). However, when only features extracted from raw images were used for training, the validation area under the curve significantly decreased (0.47).

CONCLUSIONS

ML and personalized computational modeling can be used together to accurately predict, using only pre-PVI late gadolinium enhanced magnetic resonance imaging scans as input, whether a patient is likely to experience AF recurrence following PVI, even when the patient cohort is small.

Computational prediction of the effect of D172N KCNJ2 mutation on ventricular pumping during sinus rhythm and reentry

The understanding of cardiac arrhythmia under genetic mutations has grown in interest among researchers. Previous studies focused on the effect of the D172N mutation on electrophysiological behavior. In this study, we analyzed not only the electrophysiological activity but also the mechanical responses during normal sinus rhythm and reentry conditions by using computational modeling. We simulated four different ventricular conditions including normal case of ten Tusscher model 2006 (TTM), wild-type (WT), heterozygous (WT/D172N), and homozygous D172N mutation. The 2D simulation result (in wire-shaped mesh) showed the WT/D172N and D172N mutation shortened the action potential duration by 14%, and by 23%, respectively. The 3D electrophysiological simulation results showed that the electrical wavelength between TTM and WT conditions were identical. Under sinus rhythm condition, the WT/D172N and D172N reduced the pumping efficacy with a lower left ventricle (LV) and aortic pressures, stroke volume, ejection fraction, and cardiac output. Under the reentry conditions, the WT condition has a small probability of reentry. However, in the event of reentry, WT has shown the most severe condition. Furthermore, we found that the position of the rotor or the scroll wave substantially influenced the ventricular pumping efficacy during arrhythmia. If the rotor stays in the LV, it will cause very poor pumping performance. Graphical Abstract A model of a ventricular electromechanical system. This whole model was established to observe the effect of D172N KCNJ2 mutation on ventricular pumping behavior during sinus rhythm and reentry conditions. The model consists of two components; electrical component and mechanical component. The electrophysiological model based on ten Tusscher et al. with the IK1 D172N KCNJ2 mutation, and the myofilament dynamic (cross-bridge) model based on Rice et al. study. The 3D electrical component is a ventricular geometry based on MRI which composed of nodes representing single-cell with electrophysiological activation. The 3D ventricular mechanic is a finite element mesh composed of single-cells myofilament dynamic model. Both components were coupled with Ca2+ concentration. We used Gaussian points for the calcium interpolation from the electrical mesh to the mechanical mesh.

Computationally guided personalized targeted ablation of persistent atrial fibrillation

Atrial fibrillation (AF) — the most common arrhythmia — significantly increases the risk of stroke and heart failure. Although catheter ablation can restore normal heart rhythms, patients with persistent AF who develop atrial fibrosis often undergo multiple failed ablations and thus increased procedural risks. Here, we present personalized computational modelling for the reliable predetermination of ablation targets, which are then used to guide the ablation procedure in patients with persistent AF and atrial fibrosis. We first show that a computational model of the atria of patients identifies fibrotic tissue that if ablated will not sustain AF. We then integrated the target-ablation sites in a clinical-mapping system, and tested its feasibility in 10 patients with persistent AF. The computational prediction of ablation targets avoids lengthy electrical mapping and could improve the accuracy and efficacy of targeted AF ablation in patients whilst eliminating the need for repeat procedures.

Effect of myocardial heterogeneity on ventricular electro-mechanical responses: a computational study

BACKGROUND

The heart wall exhibits three layers of different thicknesses: the outer epicardium, mid-myocardium, and inner endocardium. Among these layers, the mid-myocardium is typically the thickest. As indicated by preliminary studies, heart-wall layers exhibit various characteristics with regard to electrophysiology, pharmacology, and pathology. Construction of an accurate three-dimensional (3D) model of the heart is important for predicting physiological behaviors. However, the wide variability of myocardial shapes and the unclear edges between the epicardium and soft tissues are major challenges in the 3D model segmentation approach for identifying the boundaries of the epicardium, mid-myocardium, and endocardium. Therefore, this results in possible variations in the heterogeneity ratios between the epicardium, mid-myocardium, and endocardium. The objective of this study was to observe the effects of different thickness ratios of the epicardium, mid-myocardium, and endocardium on cardiac arrhythmogenesis, reentry instability, and mechanical responses during arrhythmia.

METHODS

We used a computational method and simulated three heterogeneous ventricular models: Model 1 had the thickest M cell layer and thinnest epicardium and endocardium. Model 2 had intermediate layer thicknesses. Model 3 exhibited the thinnest mid-myocardium and thickest epicardium and endocardium. Electrical and mechanical simulations of the three heterogeneous models were performed under normal sinus rhythm and reentry conditions.

RESULTS

Model 1 exhibited the highest probability of terminating reentrant waves, and Model 3 exhibited to experience greater cardiac arrhythmia. In the reentry simulation, at 8 s, Model 3 generated the largest number of rotors (eight), while Models 1 and 2 produced five and seven rotors, respectively. There was no significant difference in the cardiac output obtained during the sinus rhythm. Under the reentry condition, the highest cardiac output was generated by Model 1 (19 mL/s), followed by Model 2 (9 mL/s) and Model 3 (7 mL/s).

CONCLUSIONS

A thicker mid-myocardium led to improvements in the pumping efficacy and contractility and reduced the probability of cardiac arrhythmia. Conversely, thinner M cell layers generated more unstable reentrant spiral waves and hindered the ventricular pumping.

Semi-implicit Non-conforming Finite-Element Schemes for Cardiac Electrophysiology: A Framework for Mesh-Coarsening Heart Simulations

The field of computational cardiology has steadily progressed toward reliable and accurate simulations of the heart, showing great potential in clinical applications such as the optimization of cardiac interventions and the study of pro-arrhythmic effects of drugs in humans, among others. However, the computational effort demanded by in-silico studies of the heart remains challenging, highlighting the need of novel numerical methods that can improve the efficiency of simulations while targeting an acceptable accuracy. In this work, we propose a semi-implicit non-conforming finite-element scheme (SINCFES) suitable for cardiac electrophysiology simulations. The accuracy and efficiency of the proposed scheme are assessed by means of numerical simulations of the electrical excitation and propagation in regular and biventricular geometries. We show that the SINCFES allows for coarse-mesh simulations that reduce the computation time when compared to fine-mesh models while delivering wavefront shapes and conduction velocities that are more accurate than those predicted by traditional finite-element formulations based on the same coarse mesh, thus improving the accuracy-efficiency trade-off of cardiac simulations.

The Fibrotic Substrate in Persistent Atrial Fibrillation Patients: Comparison Between Predictions From Computational Modeling and Measurements From Focal Impulse and Rotor Mapping

Focal impulse and rotor mapping (FIRM) involves intracardiac detection and catheter ablation of re-entrant drivers (RDs), some of which may contribute to arrhythmia perpetuation in persistent atrial fibrillation (PsAF). Patient-specific computational models derived from late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) has the potential to non-invasively identify all areas of the fibrotic substrate where RDs could potentially be sustained, including locations where RDs may not manifest during mapped AF episodes. The objective of this study was to carry out multi-modal assessment of the arrhythmogenic propensity of the fibrotic substrate in PsAF patients by comparing locations of RD-harboring regions found in simulations and detected by FIRM (RD_sim and RD_FIRM) and analyze implications for ablation strategies predicated on targeting RDs. For 11 PsAF patients who underwent pre-procedure LGE-MRI and FIRM-guided ablation, we retrospectively simulated AF in individualized atrial models, with geometry and fibrosis distribution reconstructed from pre-ablation LGE-MRI scans, and identified RD_sim sites. Regions harboring RD_sim and RD_FIRM were compared. RD_sim were found in 38 atrial regions (median [inter-quartile range (IQR)] = 4 [3; 4] per model). RD_FIRM were identified and subsequently ablated in 24 atrial regions (2 [1; 3] per patient), which was significantly fewer than the number of RD_sim-harboring regions in corresponding models (p < 0.05). Computational modeling predicted RD_sim in 20 of 24 (83%) atrial regions identified as RD_FIRM-harboring during clinical mapping. In a large number of cases, we uncovered RD_sim-harboring regions in which RD_FIRM were never observed (18/22 regions that differed between the two modalities; 82%); we termed such cases “latent” RD_sim sites. During follow-up (230 [180; 326] days), AF recurrence occurred in 7/11 (64%) individuals. Interestingly, latent RD_sim sites were observed in all seven computational models corresponding to patients who experienced recurrent AF (2 [2; 2] per patient); in contrast, latent RD_sim sites were only discovered in two of four patients who were free from AF during follow-up (0.5 [0; 1.5] per patient; p < 0.05 vs. patients with AF recurrence). We conclude that substrate-based ablation based on computational modeling could improve outcomes.

Computational techniques for ECG analysis and interpretation in light of their contribution to medical advances

Widely developed for clinical screening, electrocardiogram (ECG) recordings capture the cardiac electrical activity from the body surface. ECG analysis can therefore be a crucial first step to help diagnose, understand and predict cardiovascular disorders responsible for 30% of deaths worldwide. Computational techniques, and more specifically machine learning techniques and computational modelling are powerful tools for classification, clustering and simulation, and they have recently been applied to address the analysis of medical data, especially ECG data. This review describes the computational methods in use for ECG analysis, with a focus on machine learning and 3D computer simulations, as well as their accuracy, clinical implications and contributions to medical advances. The first section focuses on heartbeat classification and the techniques developed to extract and classify abnormal from regular beats. The second section focuses on patient diagnosis from whole recordings, applied to different diseases. The third section presents real-time diagnosis and applications to wearable devices. The fourth section highlights the recent field of personalized ECG computer simulations and their interpretation. Finally, the discussion section outlines the challenges of ECG analysis and provides a critical assessment of the methods presented. The computational methods reported in this review are a strong asset for medical discoveries and their translation to the clinical world may lead to promising advances.

Patient-specific computational modeling of cortical spreading depression via diffusion tensor imaging

Cortical spreading depression, a depolarization wave originating in the visual cortex and traveling towards the frontal lobe, is commonly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in supporting or contrasting the propagation of cortical spreading depression. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisation in the grey matter. In this paper, we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from diffusion tensor imaging data.

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.

Analysis of Microstructure of the Cardiac Conduction System Based on Three-Dimensional Confocal Microscopy

The specialised conducting tissues present in the ventricles are responsible for the fast distribution of the electrical impulse from the atrio-ventricular node to regions in the subendocardial myocardium. Characterisation of anatomical features of the specialised conducting tissues in the ventricles is highly challenging, in particular its most distal section, which is connected to the working myocardium via Purkinje-myocardial junctions. The goal of this work is to characterise the architecture of the distal section of the Purkinje network by differentiating Purkinje cells from surrounding tissue, performing a segmentation of Purkinje fibres at cellular scale, and mathematically describing its morphology and interconnections. Purkinje cells from rabbit hearts were visualised by confocal microscopy using wheat germ agglutinin labelling. A total of 16 3D stacks including labeled Purkinje cells were collected, and semi-automatically segmented. State-of-the-art graph metrics were applied to estimate regional and global features of the Purkinje network complexity. Two types of cell types, tubular and star-like, were characterised from 3D segmentations. The analysis of 3D imaging data confirms the previously suggested presence of two types of Purkinje-myocardium connections, a 2D interconnection sheet and a funnel one, in which the narrow side of a Purkinje fibre connect progressively to muscle fibres. The complex network analysis of interconnected Purkinje cells showed no small-world connectivity or assortativity properties. These results might help building more realistic computational PK systems at high resolution levels including different cell configurations and shapes. Better knowledge on the organisation of the network might help in understanding the effects that several treatments such as radio-frequency ablation might have when the PK system is disrupted locally.

Optogenetic defibrillation terminates ventricular arrhythmia in mouse hearts and human simulations

Ventricular arrhythmias are among the most severe complications of heart disease and can result in sudden cardiac death. Patients at risk currently receive implantable defibrillators that deliver electrical shocks to terminate arrhythmias on demand. However, strong electrical shocks can damage the heart and cause severe pain. Therefore, we have tested optogenetic defibrillation using expression of the light-sensitive channel channelrhodopsin-2 (ChR2) in cardiac tissue. Epicardial illumination effectively terminated ventricular arrhythmias in hearts from transgenic mice and from WT mice after adeno-associated virus-based gene transfer of ChR2. We also explored optogenetic defibrillation for human hearts, taking advantage of a recently developed, clinically validated in silico approach for simulating infarct-related ventricular tachycardia (VT). Our analysis revealed that illumination with red light effectively terminates VT in diseased, ChR2-expressing human hearts. Mechanistically, we determined that the observed VT termination is due to ChR2-mediated transmural depolarization of the myocardium, which causes a block of voltage-dependent Na+ channels throughout the myocardial wall and interrupts wavefront propagation into illuminated tissue. Thus, our results demonstrate that optogenetic defibrillation is highly effective in the mouse heart and could potentially be translated into humans to achieve nondamaging and pain-free termination of ventricular arrhythmia.

Comparison of Detailed and Simplified Models of Human Atrial Myocytes to Recapitulate Patient Specific Properties

Computer studies are often used to study mechanisms of cardiac arrhythmias, including atrial fibrillation (AF). A crucial component in these studies is the electrophysiological model that describes the membrane potential of myocytes. The models vary from detailed, describing numerous ion channels, to simplified, grouping ionic channels into a minimal set of variables. The parameters of these models, however, are determined across different experiments in varied species. Furthermore, a single set of parameters may not describe variations across patients, and models have rarely been shown to recapitulate critical features of AF in a given patient. In this study we develop physiologically accurate computational human atrial models by fitting parameters of a detailed and of a simplified model to clinical data for five patients undergoing ablation therapy. Parameters were simultaneously fitted to action potential (AP) morphology, action potential duration (APD) restitution and conduction velocity (CV) restitution curves in these patients. For both models, our fitting procedure generated parameter sets that accurately reproduced clinical data, but differed markedly from published sets and between patients, emphasizing the need for patient-specific adjustment. Both models produced two-dimensional spiral wave dynamics for that were similar for each patient. These results show that simplified, computationally efficient models are an attractive choice for simulations of human atrial electrophysiology in spatially extended domains. This study motivates the development and validation of patient-specific model-based mechanistic studies to target therapy.

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.

Simulation of Cardiac Arrhythmias Using a 2D Heterogeneous Whole Heart Model

Simulation studies of cardiac arrhythmias at the whole heart level with electrocardiogram (ECG) gives an understanding of how the underlying cell and tissue level changes manifest as rhythm disturbances in the ECG. We present a 2D whole heart model (WHM2D) which can accommodate variations at the cellular level and can generate the ECG waveform. It is shown that, by varying cellular-level parameters like the gap junction conductance (GJC), excitability, action potential duration (APD) and frequency of oscillations of the auto-rhythmic cell in WHM2D a large variety of cardiac arrhythmias can be generated including sinus tachycardia, sinus bradycardia, sinus arrhythmia, sinus pause, junctional rhythm, Wolf Parkinson White syndrome and all types of AV conduction blocks. WHM2D includes key components of the electrical conduction system of the heart like the SA (Sino atrial) node cells, fast conducting intranodal pathways, slow conducting atriovenctricular (AV) node, bundle of His cells, Purkinje network, atrial, and ventricular myocardial cells. SA nodal cells, AV nodal cells, bundle of His cells, and Purkinje cells are represented by the Fitzhugh-Nagumo (FN) model which is a reduced model of the Hodgkin-Huxley neuron model. The atrial and ventricular myocardial cells are modeled by the Aliev-Panfilov (AP) two-variable model proposed for cardiac excitation. WHM2D can prove to be a valuable clinical tool for understanding cardiac arrhythmias.

A New MRI-Based Model of Heart Function with Coupled Hemodynamics and Application to Normal and Diseased Canine Left Ventricles

A methodology for the simulation of heart function that combines an MRI-based model of cardiac electromechanics (CE) with a Navier–Stokes-based hemodynamics model is presented. The CE model consists of two coupled components that simulate the electrical and the mechanical functions of the heart. Accurate representations of ventricular geometry and fiber orientations are constructed from the structural magnetic resonance and the diffusion tensor MR images, respectively. The deformation of the ventricle obtained from the electromechanical model serves as input to the hemodynamics model in this one-way coupled approach via imposed kinematic wall velocity boundary conditions and at the same time, governs the blood flow into and out of the ventricular volume. The time-dependent endocardial surfaces are registered using a diffeomorphic mapping algorithm, while the intraventricular blood flow patterns are simulated using a sharp-interface immersed boundary method-based flow solver. The utility of the combined heart-function model is demonstrated by comparing the hemodynamic characteristics of a normal canine heart beating in sinus rhythm against that of the dyssynchronously beating failing heart. We also discuss the potential of coupled CE and hemodynamics models for various clinical applications.

Estimation of Purkinje trees from electro-anatomical mapping of the left ventricle using minimal cost geodesics

The electrical activation of the heart is a complex physiological process that is essential for the understanding of several cardiac dysfunctions, such as ventricular tachycardia (VT). Nowadays, patient-specific activation times on ventricular chambers can be estimated from electro-anatomical maps, providing crucial information to clinicians for guiding cardiac radio-frequency ablation treatment. However, some relevant electrical pathways such as those of the Purkinje system are very difficult to interpret from these maps due to sparsity of data and the limited spatial resolution of the system. We present here a novel method to estimate these fast electrical pathways from the local activations maps (LATs) obtained from electro-anatomical maps. The location of Purkinje-myocardial junctions (PMJs) is estimated considering them as critical points of a distance map defined by the activation maps, and then minimal cost geodesic paths are computed on the ventricular surface between the detected junctions. Experiments to validate the proposed method have been carried out in simplified and realistic simulated data, showing good performance on recovering the main characteristics of simulated Purkinje networks (e.g. PMJs). A feasibility study with real cases of fascicular VT was also performed, showing promising results.

Computational modeling of cardiac optogenetics: Methodology overview & review of findings from simulations

Cardiac optogenetics is emerging as an exciting new potential avenue to enable spatiotemporally precise control of excitable cells and tissue in the heart with low-energy optical stimuli. This approach involves the expression of exogenous light-sensitive proteins (opsins) in target heart tissue via viral gene or cell delivery. Preliminary experiments in optogenetically-modified cells, tissue, and organisms have made great strides towards demonstrating the feasibility of basic applications, including the use of light stimuli to pace or disrupt reentrant activity. However, it remains unknown whether techniques based on this intriguing technology could be scaled up and used in humans for novel clinical applications, such as pain-free optical defibrillation or dynamic modulation of action potential shape. A key step towards answering such questions is to explore potential optogenetics-based therapies using sophisticated computer simulation tools capable of realistically representing opsin delivery and light stimulation in biophysically detailed, patient-specific models of the human heart. This review provides (1) a detailed overview of the methodological developments necessary to represent optogenetics-based solutions in existing virtual heart platforms and (2) a survey of findings that have been derived from such simulations and a critical assessment of their significance with respect to the progress of the field.

Three-dimensional cardiac computational modelling: methods, features and applications

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

Fitting C² continuous parametric surfaces to frontiers delimiting physiologic structures

We present a technique to fit C(2) continuous parametric surfaces to scattered geometric data points forming frontiers delimiting physiologic structures in segmented images. Such mathematical representation is interesting because it facilitates a large number of operations in modeling. While the fitting of C(2) continuous parametric curves to scattered geometric data points is quite trivial, the fitting of C(2) continuous parametric surfaces is not. The difficulty comes from the fact that each scattered data point should be assigned a unique parametric coordinate, and the fit is quite sensitive to their distribution on the parametric plane. We present a new approach where a polygonal (quadrilateral or triangular) surface is extracted from the segmented image. This surface is subsequently projected onto a parametric plane in a manner to ensure a one-to-one mapping. The resulting polygonal mesh is then regularized for area and edge length. Finally, from this point, surface fitting is relatively trivial. The novelty of our approach lies in the regularization of the polygonal mesh. Process performance is assessed with the reconstruction of a geometric model of mouse heart ventricles from a computerized tomography scan. Our results show an excellent reproduction of the geometric data with surfaces that are C(2) continuous.

Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology

We study the numerical accuracy and computational efficiency of alternative formulations of the finite element solution procedure for the monodomain equations of cardiac electrophysiology, focusing on the interaction of spatial quadrature implementations with operator splitting and examining both nodal and Gauss quadrature methods and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of 'lumped' approximations of consistent capacitance and mass matrices. Most generally, we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally, we illustrate some of the physiological consequences of discretization error in electrophysiological simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce nonuniform meshes having a large distribution of element sizes.

A framework for myoarchitecture analysis of high resolution cardiac MRI and comparison with diffusion tensor MRI

The ventricular myocardium has a structure of branching laminae through which course regularly orientated myofibers, an architecture important in excitation and contraction. Quantifying this architecture is vital for understanding normal and disease states in the heart and for assessing their impact on electrical function. These data are also highly important in the construction of scientifically and clinically useful computer models of cardiac electrical behavior. Detailed structural information has previously been obtained from serial imaging. In this work we assess the potential for high-resolution (HR) MRI as a means to furnish useful myoarchitecture and compare and contrast this approach with the growing use of DT. Using rat hearts, we conclude that both approaches have strengths and weaknesses, however, HR-MRI may provide a consistently more robust picture of the myoarchitecture in small hearts.

Optimisation of ionic models to fit tissue action potentials: application to 3D atrial modelling

A 3D model of atrial electrical activity has been developed with spatially heterogeneous electrophysiological properties. The atrial geometry, reconstructed from the male Visible Human dataset, included gross anatomical features such as the central and peripheral sinoatrial node (SAN), intra-atrial connections, pulmonary veins, inferior and superior vena cava, and the coronary sinus. Membrane potentials of myocytes from spontaneously active or electrically paced in vitro rabbit cardiac tissue preparations were recorded using intracellular glass microelectrodes. Action potentials of central and peripheral SAN, right and left atrial, and pulmonary vein myocytes were each fitted using a generic ionic model having three phenomenological ionic current components: one time-dependent inward, one time-dependent outward, and one leakage current. To bridge the gap between the single-cell ionic models and the gross electrical behaviour of the 3D whole-atrial model, a simplified 2D tissue disc with heterogeneous regions was optimised to arrive at parameters for each cell type under electrotonic load. Parameters were then incorporated into the 3D atrial model, which as a result exhibited a spontaneously active SAN able to rhythmically excite the atria. The tissue-based optimisation of ionic models and the modelling process outlined are generic and applicable to image-based computer reconstruction and simulation of excitable tissue.

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

BACKGROUND

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

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

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

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

Characterization and modeling of the peripheral cardiac conduction system

The development of biophysical models of the heart has the potential to get insights in the patho-physiology of the heart, which requires to accurately modeling anatomy and function. The electrical activation sequence of the ventricles depends strongly on the cardiac conduction system (CCS). Its morphology and function cannot be observed in vivo, and therefore data available come from histological studies. We present a review on data available of the peripheral CCS including new experiments. In order to build a realistic model of the CCS we designed a procedure to extract morphological characteristics of the CCS from stained calf tissue samples. A CCS model personalized with our measurements has been built using L-systems. The effect of key unknown parameters of the model in the electrical activation of the left ventricle has been analyzed. The CCS models generated share the main characteristics of observed stained Purkinje networks. The timing of the simulated electrical activation sequences were in the physiological range for CCS models that included enough density of PMJs. These results show that this approach is a potential methodology for collecting knowledge-domain data and build improved CCS models of the heart automatically.

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.

Patient-specific identification of optimal ubiquitous electrocardiogram (U-ECG) placement using a three-dimensional model of cardiac electrophysiology

A bipolar mini-ECG for ubiquitous healthcare (U-ECG) has been introduced, and various studies using the U-ECG device are in progress. Because it uses two electrodes within a small torso surface area, the design of the U-ECG must be suitable for detecting ECG signals. Using a 3-D model of cardiac electrophysiology, we have developed a simulation method for identifying the optimal placement of U-ECG electrodes on the torso surface. We simulated the heart-torso model to obtain a body surface potential map and ECG waveforms, which were compared with the empirical data. Using this model, we determined the optimal placement of the two U-ECG electrodes, spaced 5 cm apart, for detecting the P, R, and T waves. The ECG data, obtained using the optimal U-ECG placement for a specific wave, showed a clear shape for the target wave, but equivocal shapes for the other waves. The present study provides an efficient simulation method to identify the optimal attachment position and direction of the U-ECG electrodes on the surface of the torso.

Predicting the optimal position and direction of a ubiquitous ECG using a multi-scale model of cardiac electrophysiology

In this study, we determined the optimal position and direction of a one-channel bipolar electrocardiogram (ECG), used ubiquitously in healthcare. To do this, we developed a three-dimensional (3D) electrophysiological model of the heart coupled with a torso model that can generate a virtual body surface potential map (BSPM). Finite element models of the atria and ventricles incorporated the electrophysiological dynamics of atrial and ventricular myocytes, respectively. The torso model, in which the electric wave pattern on the cardiac tissue is reflected onto the body surface, was implemented using a boundary element method. Using the model, we derived the optimal positions of two electrodes, 5 cm apart, of the bipolar ubiquitous ECG (U-ECG) for detecting the P, R, and T waves. This model can be used as a simulation tool to design U-ECG device for use for various arrhythmia and normal patients.

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

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

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

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

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.

Construction of 3D MR image-based computer models of pathologic hearts, augmented with histology and optical fluorescence imaging to characterize action potential propagation

Cardiac computer models can help us understand and predict the propagation of excitation waves (i.e., action potential, AP) in healthy and pathologic hearts. Our broad aim is to develop accurate 3D MR image-based computer models of electrophysiology in large hearts (translatable to clinical applications) and to validate them experimentally. The specific goals of this paper were to match models with maps of the propagation of optical AP on the epicardial surface using large porcine hearts with scars, estimating several parameters relevant to macroscopic reaction-diffusion electrophysiological models. We used voltage-sensitive dyes to image AP in large porcine hearts with scars (three specimens had chronic myocardial infarct, and three had radiofrequency RF acute scars). We first analyzed the main AP waves' characteristics: duration (APD) and propagation under controlled pacing locations and frequencies as recorded from 2D optical images. We further built 3D MR image-based computer models that have information derived from the optical measures, as well as morphologic MRI data (i.e., myocardial anatomy, fiber directions and scar definition). The scar morphology from MR images was validated against corresponding whole-mount histology. We also compared the measured 3D isochronal maps of depolarization to simulated isochrones (the latter replicating precisely the experimental conditions), performing model customization and 3D volumetric adjustments of the local conductivity. Our results demonstrated that mean APD in the border zone (BZ) of the infarct scars was reduced by ~13% (compared to ~318 ms measured in normal zone, NZ), but APD did not change significantly in the thin BZ of the ablation scars. A generic value for velocity ratio (1:2.7) in healthy myocardial tissue was derived from measured values of transverse and longitudinal conduction velocities relative to fibers direction (22 cm/s and 60 cm/s, respectively). The model customization and 3D volumetric adjustment reduced the differences between measurements and simulations; for example, from one pacing location, the adjustment reduced the absolute error in local depolarization times by a factor of 5 (i.e., from 58 ms to 11 ms) in the infarcted heart, and by a factor of 6 (i.e., from 60 ms to 9 ms) in the heart with the RF scar. Moreover, the sensitivity of adjusted conductivity maps to different pacing locations was tested, and the errors in activation times were found to be of approximately 10-12 ms independent of pacing location used to adjust model parameters, suggesting that any location can be used for model predictions.

Unstable QT interval dynamics precedes ventricular tachycardia onset in patients with acute myocardial infarction: a novel approach to detect instability in QT interval dynamics from clinical ECG

BACKGROUND

Instability in ventricular repolarization in the presence of premature activations (PA) plays an important role in arrhythmogenesis. However, such instability cannot be detected clinically. This study developed a methodology for detecting QT interval (QTI) dynamics instability from the ECG and explored the contribution of PA and QTI instability to ventricular tachycardia (VT) onset.

METHODS AND RESULTS

To examine the contribution of PAs and QTI instability to VT onset, ECGs of 24 patients with acute myocardial infarction, 12 of whom had sustained VT (VT) and 12 nonsustained VT (NSVT), were used. From each patient ECG, 2 10-minute-long ECG recordings were extracted, 1 right before VT onset (onset epoch) and 1 at least 1 hour before it (control epoch). To ascertain how PA affects QTI dynamics stability, pseudo-ECGs were calculated from an MRI-based human ventricular model. Clinical and pseudo-ECGs were subdivided into 1-minute recordings (minECGs). QTI dynamics stability of each minECG was assessed with a novel approach. Frequency of PAs (f(PA)) and the number of minECGs with unstable QTI dynamics (N(us)) were determined for each patient. In the VT group, f(PA) and N(us) of the onset epoch were larger than in control. Positive regression relationships between f(PA) and N(us) were identified in both groups. The simulations showed that both f(PA) and the PA degree of prematurity contribute to QTI dynamics instability.

CONCLUSIONS

Increased PA frequency and QTI dynamics instability precede VT onset in patients with acute myocardial infarction, as determined by novel methodology for detecting instability in QTI dynamics from clinical ECGs.

Susceptibility to arrhythmia in the infarcted heart depends on myofibroblast density

Fibroblasts are electrophysiologically quiescent in the healthy heart. Evidence suggests that remodeling following myocardial infarction may include coupling of myofibroblasts (Mfbs) among themselves and with myocytes via gap junctions. We use a magnetic resonance imaging-based, three-dimensional computational model of the chronically infarcted rabbit ventricles to characterize the arrhythmogenic substrate resulting from Mfb infiltration as a function of Mfb density. Mfbs forming gap junctions were incorporated into both infarct regions, the periinfarct zone (PZ) and the scar; six scenarios were modeled: 0%, 10%, and 30% Mfbs in the PZ, with either 80% or 0% Mfbs in the scar. Ionic current remodeling in PZ was also included. All preparations exhibited elevated resting membrane potential within and near the PZ and action potential duration shortening throughout the ventricles. The unique combination of PZ ionic current remodeling and different degrees of Mfb infiltration in the infarcted ventricles determines susceptibility to arrhythmia. At low densities, Mfbs do not alter arrhythmia propensity; the latter arises predominantly from ionic current remodeling in PZ. At intermediate densities, Mfbs cause additional action potential shortening and exacerbate arrhythmia propensity. At high densities, Mfbs protect against arrhythmia by causing resting depolarization and blocking propagation, thus overcoming the arrhythmogenic effects of PZ ionic current remodeling.

Correspondence between simple 3-D MRI-based computer models and in-vivo EP measurements in swine with chronic infarctions

The aim of this paper was to compare several in-vivo electrophysiological (EP) characteristics measured in a swine model of chronic infarct, with those predicted by simple 3-D MRI-based computer models built from ex-vivo scans (voxel size <1  mm(3)). Specifically, we recorded electroanatomical voltage maps (EAVM) in six animals, and ECG waves during induction of arrhythmia in two of these cases. The infarct heterogeneities (dense scar and border zone) as well as fiber directions were estimated using diffusion weighted DW-MRI. We found a good correspondence (r = 0.9) between scar areas delineated on the EAVM and MRI maps. For theoretical predictions, we used a simple two-variable macroscopic model and computed the propagation of action potential after application of a train of stimuli, with location and timing replicating the stimulation protocol used in the in-vivo EP study. Simulation results are exemplified for two hearts: one with noninducible ventricular tachycardia (VT), and another with a macroreentrant VT (for the latter, the average predicted VT cycle length was 273  ms, compared to a recorded VT of 250  ms).

Construction of a computational anatomical model of the peripheral cardiac conduction system

A methodology is presented here for automatic construction of a ventricular model of the cardiac conduction system (CCS), which is currently a missing block in many multiscale cardiac electromechanic models. It includes the His bundle, left bundle branches, and the peripheral CCS. The algorithm is fundamentally an enhancement of a rule-based method known as the Lindenmayer systems (L-systems). The generative procedure has been divided into three consecutive independent stages, which subsequently build the CCS from proximal to distal sections. Each stage is governed by a set of user parameters together with anatomical and physiological constrains to direct the generation process and adhere to the structural observations derived from histology studies. Several parameters are defined using statistical distributions to introduce stochastic variability in the models. The CCS built with this approach can generate electrical activation sequences with physiological characteristics.

Rabbit-specific ventricular model of cardiac electrophysiological function including specialized conduction system

The function of the ventricular specialized conduction system in the heart is to ensure the coordinated electrical activation of the ventricles. It is therefore critical to the overall function of the heart, and has also been implicated as an important player in various diseases, including lethal ventricular arrhythmias such as ventricular fibrillation and drug-induced torsades de pointes. However, current ventricular models of electrophysiology usually ignore, or include highly simplified representations of the specialized conduction system. Here, we describe the development of an image-based, species-consistent, anatomically-detailed model of rabbit ventricular electrophysiology that incorporates a detailed description of the free-running part of the specialized conduction system. Techniques used for the construction of the geometrical model of the specialized conduction system from a magnetic resonance dataset and integration of the system model into a ventricular anatomical model, developed from the same dataset, are described. Computer simulations of rabbit ventricular electrophysiology are conducted using the novel anatomical model and rabbit-specific membrane kinetics to investigate the importance of the components and properties of the conduction system in determining ventricular function under physiological conditions. Simulation results are compared to panoramic optical mapping experiments for model validation and results interpretation. Full access is provided to the anatomical models developed in this study.

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

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

Electromechanical models of the ventricles

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

Integrated approach for the study of anatomical variability in the cardiac Purkinje system: from high resolution MRI to electrophysiology simulation

The ordered electrical stimulation of the ventricles is achieved by a specialized network of fibres known as the Purkinje system. The gross anatomy and basic functional role of the Purkinje system is well understood. However, very little is known about the detailed anatomy of the Purkinje system, its inter-individual variability and the implications of the variability in ventricular function, in part due to limitations in experimental techniques. In this study, we aim to provide new insight into the inter-individual variability of the free running Purkinje system anatomy and its impact on ventricular electrophysiological function. As a first step towards achieving this aim, high resolution magnetic resonance imaging (MRI) datasets of rat and the rabbit ventricles are obtained and analysed using a novel semi-automatic image processing algorithm for segmentation of the free-running Purkinje system. Segmented geometry from the MRI datasets is used to construct a computational model of the Purkinje system, which is incorporated in to an anatomically-based ventricular geometry to simulate ventricular electrophysiological activity.

Estimation of local orientations in fibrous structures with applications to the Purkinje system

The extraction of the cardiac Purkinje system (PS) from intensity images is a critical step toward the development of realistic structural models of the heart. Such models are important for uncovering the mechanisms of cardiac disease and improving its treatment and prevention. Unfortunately, the manual extraction of the PS is a challenging and error-prone task due to the presence of image noise and numerous fiber junctions. To deal with these challenges, we propose a framework that estimates local fiber orientations with high accuracy and reconstructs the fibers via tracking. Our key contribution is the development of a descriptor for estimating the orientation distribution function (ODF), a spherical function encoding the local geometry of the fibers at a point of interest. The fiber/branch orientations are identified as the modes of the ODFs via spherical clustering and guide the extraction of the fiber centerlines. Experiments on synthetic data evaluate the sensitivity of our approach to image noise, width of the fiber, and choice of the mode detection strategy, and show its superior performance compared to those of the existing descriptors. Experiments on the free-running PS in an MR image also demonstrate the accuracy of our method in reconstructing such sparse fibrous structures.

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.