Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model

Non-Invasive and Quantitative Estimation of Left Atrial Fibrosis Based on P Waves of the 12-Lead ECG-A Large-Scale Computational Study Covering Anatomical Variability

The arrhythmogenesis of atrial fibrillation is associated with the presence of fibrotic atrial tissue. Not only fibrosis but also physiological anatomical variability of the atria and the thorax reflect in altered morphology of the P wave in the 12-lead electrocardiogram (ECG). Distinguishing between the effects on the P wave induced by local atrial substrate changes and those caused by healthy anatomical variations is important to gauge the potential of the 12-lead ECG as a non-invasive and cost-effective tool for the early detection of fibrotic atrial cardiomyopathy to stratify atrial fibrillation propensity. In this work, we realized 54,000 combinations of different atria and thorax geometries from statistical shape models capturing anatomical variability in the general population. For each atrial model, 10 different volume fractions (0-45%) were defined as fibrotic. Electrophysiological simulations in sinus rhythm were conducted for each model combination and the respective 12-lead ECGs were computed. P wave features (duration, amplitude, dispersion, terminal force in V1) were extracted and compared between the healthy and the diseased model cohorts. All investigated feature values systematically in- or decreased with the left atrial volume fraction covered by fibrotic tissue, however value ranges overlapped between the healthy and the diseased cohort. Using all extracted P wave features as input values, the amount of the fibrotic left atrial volume fraction was estimated by a neural network with an absolute root mean square error of 8.78%. Our simulation results suggest that although all investigated P wave features highly vary for different anatomical properties, the combination of these features can contribute to non-invasively estimate the volume fraction of atrial fibrosis using ECG-based machine learning approaches.

Personalising left-ventricular biophysical models of the heart using parametric physics-informed neural networks

We present a parametric physics-informed neural network for the simulation of personalised left-ventricular biomechanics. The neural network is constrained to the biophysical problem in two ways: (i) the network output is restricted to a subspace built from radial basis functions capturing characteristic deformations of left ventricles and (ii) the cost function used for training is the energy potential functional specifically tailored for hyperelastic, anisotropic, nearly-incompressible active materials. The radial bases are generated from the results of a nonlinear Finite Element model coupled with an anatomical shape model derived from high-resolution cardiac images. We show that, by coupling the neural network with a simplified circulation model, we can efficiently generate computationally inexpensive estimations of cardiac mechanics. Our model is 30 times faster than the reference Finite Element model used, including training time, while yielding satisfactory average errors in the predictions of ejection fraction (-3%), peak systolic pressure (7%), stroke work (4%) and myocardial strains (14%). This physics-informed neural network is well suited to efficiently augment cardiac images with functional data and to generate large sets of synthetic cases for training deep network classifiers while it provides efficient personalization to the specific patient of interest with a high level of detail.

Linking statistical shape models and simulated function in the healthy adult human heart

Cardiac anatomy plays a crucial role in determining cardiac function. However, there is a poor understanding of how specific and localised anatomical changes affect different cardiac functional outputs. In this work, we test the hypothesis that in a statistical shape model (SSM), the modes that are most relevant for describing anatomy are also most important for determining the output of cardiac electromechanics simulations. We made patient-specific four-chamber heart meshes (n = 20) from cardiac CT images in asymptomatic subjects and created a SSM from 19 cases. Nine modes captured 90% of the anatomical variation in the SSM. Functional simulation outputs correlated best with modes 2, 3 and 9 on average (R = 0.49 ± 0.17, 0.37 ± 0.23 and 0.34 ± 0.17 respectively). We performed a global sensitivity analysis to identify the different modes responsible for different simulated electrical and mechanical measures of cardiac function. Modes 2 and 9 were the most important for determining simulated left ventricular mechanics and pressure-derived phenotypes. Mode 2 explained 28.56 ± 16.48% and 25.5 ± 20.85, and mode 9 explained 12.1 ± 8.74% and 13.54 ± 16.91% of the variances of mechanics and pressure-derived phenotypes, respectively. Electrophysiological biomarkers were explained by the interaction of 3 ± 1 modes. In the healthy adult human heart, shape modes that explain large portions of anatomical variance do not explain equivalent levels of electromechanical functional variation. As a result, in cardiac models, representing patient anatomy using a limited number of modes of anatomical variation can cause a loss in accuracy of simulated electromechanical function.

Combining endocardial mapping and electrocardiographic imaging (ECGI) for improving PVC localization: A feasibility study

INTRODUCTION

Accurate reconstruction of cardiac activation wavefronts is crucial for clinical diagnosis, management, and treatment of cardiac arrhythmias. Furthermore, reconstruction of activation profiles within the intramural myocardium has long been impossible because electrical mapping was only performed on the endocardial surface. Recent advancements in electrocardiographic imaging (ECGI) have made endocardial and epicardial activation mapping possible. We propose a novel approach to use both endocardial and epicardial mapping in a combined approach to reconstruct intramural activation times.

OBJECTIVE

To implement and validate a combined epicardial/endocardial intramural activation time reconstruction technique.

METHODS

We used 11 simulations of ventricular activation paced from sites throughout myocardial wall and extracted endocardial and epicardial activation maps at approximate clinical resolution. From these maps, we interpolated the activation times through the myocardium using thin-plate-spline radial basis functions. We evaluated activation time reconstruction accuracy using root-mean-squared error (RMSE) of activation times and the percent of nodes within 1 ms of the ground truth.

RESULTS

Reconstructed intramural activation times showed an RMSE and percentage of nodes within 1 ms of the ground truth simulations of 3 ms and 70%, respectively. In the worst case, the RMSE and percentage of nodes were 4 ms and 60%, respectively.

CONCLUSION

We showed that a simple, yet effective combination of clinical endocardial and epicardial activation maps can accurately reconstruct intramural wavefronts. Furthermore, we showed that this approach provided robust reconstructions across multiple intramural stimulation sites.

An Inverse Eikonal Method for Identifying Ventricular Activation Sequences from Epicardial Activation Maps

A key mechanism controlling cardiac function is the electrical activation sequence of the heart's main pumping chambers termed the ventricles. As such, personalization of the ventricular activation sequences is of pivotal importance for the clinical utility of computational models of cardiac electrophysiology. However, a direct observation of the activation sequence throughout the ventricular volume is virtually impossible. In this study, we report on a novel method for identification of activation sequences from activation maps measured at the outer surface of the heart termed the epicardium. Conceptually, the method attempts to identify the key factors governing the ventricular activation sequence - the timing of earliest activation sites (EAS) and the velocity tensor field within the ventricular walls - from sparse and noisy activation maps sampled from the epicardial surface and fits an Eikonal model to the observations. Regularization methods are first investigated to overcome the severe ill-posedness of the inverse problem in a simplified 2D example. These methods are then employed in an anatomically accurate biventricular model with two realistic activation models of varying complexity - a simplified trifascicular model (3F) and a topologically realistic model of the His-Purkinje system (HPS). Using epicardial activation maps at full resolution, we first demonstrate that reconstructing the volumetric activation sequence is, in principle, feasible under the assumption of known location of EAS and later evaluate robustness of the method against noise and reduced spatial resolution of observations. Our results suggest that the FIMIN algorithm is able to robustly recover the full 3D activation sequence using epicardial activation maps at a spatial resolution achievable with current mapping systems and in the presence of noise. Comparing the accuracy achieved in the reconstructed activation maps with clinical data uncertainties suggests that the FIMIN method may be suitable for the patient- specific parameterization of activation models.

Integration of activation maps of epicardial veins in computational cardiac electrophysiology

In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac electro-physiology of the left ventricle. To this aim, we consider four patients who suffered from Left Bundle Branch Block (LBBB). We use activation maps performed at the septum as input data for the model and maps at the epicardial veins for the validation. In particular, a first set (half) of the latter are used to estimate the conductivities of the patient and a second set (the remaining half) to compute the errors of the numerical simulations. We find an excellent agreement between measures and numerical results. Our validated computational tool could be used to accurately predict activation times at the epicardial veins with a short mapping, i.e. by using only a part (the most proximal) of the standard acquisition points, thus reducing the invasive procedure and exposure to radiation.

Using cardiac ionic cell models to interpret clinical data

For over 100 years cardiac electrophysiology has been measured in the clinic. The electrical signals that can be measured span from noninvasive ECG and body surface potentials measurements through to detailed invasive measurements of local tissue electrophysiology. These electrophysiological measurements form a crucial component of patient diagnosis and monitoring; however, it remains challenging to quantitatively link changes in clinical electrophysiology measurements to biophysical cellular function. Multi-scale biophysical computational models represent one solution to this problem. These models provide a formal framework for linking cellular function through to emergent whole organ function and routine clinical diagnostic signals. In this review, we describe recent work on the use of computational models to interpret clinical electrophysiology signals. We review the simulation of human cardiac myocyte electrophysiology in the atria and the ventricles and how these models are being used to link organ scale function to patient disease mechanisms and therapy response in patients receiving implanted defibrillators, \cardiac resynchronisation therapy or suffering from atrial fibrillation and ventricular tachycardia. There is a growing use of multi-scale biophysical models to interpret clinical data. This allows cardiologists to link clinical observations with cellular mechanisms to better understand cardiopathophysiology and identify novel treatment strategies. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Deep learning-based reduced order models in cardiac electrophysiology

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters), as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach relying on deep learning (DL) algorithms—such as deep feedforward neural networks and convolutional autoencoders—to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate four challenging test cases in cardiac electrophysiology, thus demonstrating that DL-ROM outperforms classical projection-based ROMs.

A publicly available virtual cohort of four-chamber heart meshes for cardiac electro-mechanics simulations

Computational models of the heart are increasingly being used in the development of devices, patient diagnosis and therapy guidance. While software techniques have been developed for simulating single hearts, there remain significant challenges in simulating cohorts of virtual hearts from multiple patients. To facilitate the development of new simulation and model analysis techniques by groups without direct access to medical data, image analysis techniques and meshing tools, we have created the first publicly available virtual cohort of twenty-four four-chamber hearts. Our cohort was built from heart failure patients, age 67±14 years. We segmented four-chamber heart geometries from end-diastolic (ED) CT images and generated linear tetrahedral meshes with an average edge length of 1.1±0.2mm. Ventricular fibres were added in the ventricles with a rule-based method with an orientation of -60° and 80° at the epicardium and endocardium, respectively. We additionally refined the meshes to an average edge length of 0.39±0.10mm to show that all given meshes can be resampled to achieve an arbitrary desired resolution. We ran simulations for ventricular electrical activation and free mechanical contraction on all 1.1mm-resolution meshes to ensure that our meshes are suitable for electro-mechanical simulations. Simulations for electrical activation resulted in a total activation time of 149±16ms. Free mechanical contractions gave an average left ventricular (LV) and right ventricular (RV) ejection fraction (EF) of 35±1% and 30±2%, respectively, and a LV and RV stroke volume (SV) of 95±28mL and 65±11mL, respectively. By making the cohort publicly available, we hope to facilitate large cohort computational studies and to promote the development of cardiac computational electro-mechanics for clinical applications.

Personalization of electro-mechanical models of the pressure-overloaded left ventricle: fitting of Windkessel-type afterload models

Computer models of left ventricular (LV) electro-mechanics (EM) show promise as a tool for assessing the impact of increased afterload upon LV performance. However, the identification of unique afterload model parameters and the personalization of EM LV models remains challenging due to significant clinical input uncertainties. Here, we personalized a virtual cohort of N = 17 EM LV models under pressure overload conditions. A global-local optimizer was developed to uniquely identify parameters of a three-element Windkessel (Wk3) afterload model. The sensitivity of Wk3 parameters to input uncertainty and of the EM LV model to Wk3 parameter uncertainty was analysed. The optimizer uniquely identified Wk3 parameters, and outputs of the personalized EM LV models showed close agreement with clinical data in all cases. Sensitivity analysis revealed a strong dependence of Wk3 parameters on input uncertainty. However, this had limited impact on outputs of EM LV models. A unique identification of Wk3 parameters from clinical data appears feasible, but it is sensitive to input uncertainty, thus depending on accurate invasive measurements. By contrast, the EM LV model outputs were less sensitive, with errors of less than 8.14% for input data errors of 10%, which is within the bounds of clinical data uncertainty. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

The impact of wall thickness and curvature on wall stress in patient-specific electromechanical models of the left atrium

The left atrium (LA) has a complex anatomy with heterogeneous wall thickness and curvature. The anatomy plays an important role in determining local wall stress; however, the relative contribution of wall thickness and curvature in determining wall stress in the LA is unknown. We have developed electromechanical finite element (FE) models of the LA using patient-specific anatomical FE meshes with rule-based myofiber directions. The models of the LA were passively inflated to 10mmHg followed by simulation of the contraction phase of the atrial cardiac cycle. The FE models predicted maximum LA volumes of 156.5 mL, 99.3 mL and 83.4 mL and ejection fractions of 36.9%, 32.0% and 25.2%. The median wall thickness in the 3 cases was calculated as [Formula: see text] mm, [Formula: see text] mm, and [Formula: see text] mm. The median curvature was determined as [Formula: see text] [Formula: see text], [Formula: see text], and [Formula: see text]. Following passive inflation, the correlation of wall stress with the inverse of wall thickness and curvature was 0.55-0.62 and 0.20-0.25, respectively. At peak contraction, the correlation of wall stress with the inverse of wall thickness and curvature was 0.38-0.44 and 0.16-0.34, respectively. In the LA, the 1st principal Cauchy stress is more dependent on wall thickness than curvature during passive inflation and both correlations decrease during active contraction. This emphasizes the importance of including the heterogeneous wall thickness in electromechanical FE simulations of the LA. Overall, simulation results and sensitivity analyses show that in complex atrial anatomy it is unlikely that a simple anatomical-based law can be used to estimate local wall stress, demonstrating the importance of FE analyses.

Left ventricular endocardial pacing is less arrhythmogenic than conventional epicardial pacing when pacing in proximity to scar

Background

Epicardial pacing increases risk of ventricular tachycardia (VT) in patients with ischemic cardiomyopathy (ICM) when pacing in proximity to scar. Endocardial pacing may be less arrhythmogenic as it preserves the physiological sequences of activation and repolarization.

Objective

The purpose of this study was to determine the relative arrhythmogenic risk of endocardial compared to epicardial pacing, and the role of the transmural gradient of action potential duration (APD) and pacing location relative to scar on arrhythmogenic risk during endocardial pacing.

Methods

Computational models of ICM patients (n = 24) were used to simulate left ventricular (LV) epicardial and endocardial pacing 0.2–3.5 cm from a scar. Mechanisms were investigated in idealized models of the ventricular wall and scar. Simulations were run with/without a 20-ms transmural APD gradient in the physiological direction and with the gradient inverted. Dispersion of repolarization was computed as a surrogate of VT risk.

Results

Patient-specific models with a physiological APD gradient predict that endocardial pacing decreases VT risk (34%; P <.05) compared to epicardial pacing when pacing in proximity to scar (0.2 cm). Endocardial pacing location does not significantly affect VT risk, but epicardial pacing at 0.2 cm compared to 3.5 cm from scar increases it (P <.05). Inverting the transmural APD gradient reverses this trend. Idealized models predict that propagation in the direction opposite to APD gradient decreases VT risk.

Conclusion

Endocardial pacing is less arrhythmogenic than epicardial pacing when pacing proximal to scar and is less susceptible to pacing location relative to scar. The physiological repolarization sequence during endocardial pacing mechanistically explains reduced VT risk compared to epicardial pacing.

Validation of Intramural Wavefront Reconstruction and Estimation of 3D Conduction Velocity

INTRODUCTION

Changes in conduction velocity are indicative of a wide variety of cardiac abnormalities yet measuring conduction velocity is challenging, especially within the myocardial volume. In this study we investigated a novel technique to reconstruct activation fronts and estimate three-dimensional (3D) conduction velocity (CV) from experimental intramural recordings.

METHODS

From the intermittently sampled electrograms we both reconstruct the activation profile and compute the reciprocal of the gradient of activation times and a series of streamlines that allows for the CV estimation.

RESULTS

The reconstructed activation times agreed closely with simulated values, with 50% to 70% of the nodes ≤ 1ms of absolute error. We found close agreement between the CVs calculated using reconstructed versus simulated activation times. Across the reconstructed stimulation sites we saw that the reconstructed CV was on average 3.8% different than the ground truth CV.

DISCUSSION

This study used simulated datasets to validate our methods for reconstructing 3D activation fronts and estimating conduction velocities. Our results indicate that our method allows accurate reconstructions from sparse measurements, thus allowing us to examine changes in activation induced by experimental interventions such as acute ischemia, ectopic pacing, or drugs.

Simulating ventricular systolic motion in a four-chamber heart model with spatially varying robin boundary conditions to model the effect of the pericardium

The pericardium affects cardiac motion by limiting epicardial displacement normal to the surface. In computational studies, it is important for the model to replicate realistic motion, as this affects the physiological fidelity of the model. Previous computational studies showed that accounting for the effect of the pericardium allows for a more realistic motion simulation. In this study, we describe the mechanism through which the pericardium causes improved cardiac motion. We simulated electrical activation and contraction of the ventricles on a four-chamber heart in the presence and absence of the effect of the pericardium. We simulated the mechanical constraints imposed by the pericardium by applying normal Robin boundary conditions on the ventricular epicardium. We defined a regional scaling of normal springs stiffness based on image-derived motion from CT images. The presence of the pericardium reduced the error between simulated and image-derived end-systolic configurations from 12.8±4.1 mm to 5.7±2.5 mm. First, the pericardium prevents the ventricles from spherising during isovolumic contraction, reducing the outward motion of the free walls normal to the surface and the upwards motion of the apex. Second, by restricting the inward motion of the free and apical walls of the ventricles the pericardium increases atrioventricular plane displacement by four folds during ejection. Our results provide a mechanistic explanation of the importance of the pericardium in physiological simulations of electromechanical cardiac function.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

How personalized heart modeling can help treatment of lethal arrhythmias: A focus on ventricular tachycardia ablation strategies in post-infarction patients

Precision Cardiology is a targeted strategy for cardiovascular disease prevention and treatment that accounts for individual variability. Computational heart modeling is one of the novel approaches that have been developed under the umbrella of Precision Cardiology. Personalized computational modeling of patient hearts has made strides in the development of models that incorporate the individual geometry and structure of the heart as well as other patient-specific information. Of these developments, one of the potentially most impactful is the research aimed at noninvasively predicting the targets of ablation of lethal arrhythmia, ventricular tachycardia (VT), using patient-specific models. The approach has been successfully applied to patients with ischemic cardiomyopathy in proof-of-concept studies. The goal of this paper is to review the strategies for computational VT ablation guidance in ischemic cardiomyopathy patients, from model developments to the intricacies of the actual clinical application. To provide context in describing the road these computational modeling applications have undertaken, we first review the state of the art in VT ablation in the clinic, emphasizing the benefits that personalized computational prediction of ablation targets could bring to the clinical electrophysiology practice. This article is characterized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Translational, Genomic, and Systems Medicine > Translational Medicine.

Automating image-based mesh generation and manipulation tasks in cardiac modeling workflows using Meshtool

Advanced cardiac modeling studies rely on the ability to generate and functionalize personalized in silico models from tomographic multi-label image stacks. Eventually, this is used for building virtual cohorts that capture the variability in size, shape, and morphology of individual hearts. Typical modeling workflows involve a multitude of interactive mesh manipulation steps, rendering model generation expensive. Meshtool is software specifically designed for automating all complex mesh manipulation tasks emerging in such workflows by implementing algorithms for tasks describable as operations on label fields and/or geometric features. We illustrate how Meshtool increases efficiency and reduces costs by offering an automatable, high performance mesh manipulation toolbox.

Curved surface geometry-induced topological change of an excitable planar wavefront

On the curved surfaces of living and nonliving materials, planar excitable wavefronts frequently exhibit a directional change and subsequently undergo a discontinuous (topological) change; i.e., a series of wavefront dynamics from collision, annihilation to splitting. Theoretical studies have shown that excitable planar stable waves change their topology significantly depending on the initial conditions on flat surfaces, whereas the directional change of the waves occurs based on the geometry of curved surfaces. However, it is not clear if the geometry of curved surfaces induces this topological change. In this study, we first demonstrated that the curved surface geometry induces bending, collision, and splitting of a planar stable wavefront by numerically solving an excitable reaction-diffusion equation on a bell-shaped surface. We determined two necessary conditions for inducing the topological change: the characteristic length of the curved surface (i.e., the height of the bell-shaped structure) should be greater than the width of the wave, and the ratio of the height to the width of the bell shape should be greater than a threshold. As for the geometrical mechanism of the latter, we found that a bifurcation of the geodesics on the curved surface provides the alternative minimal paths of the wavefront, which circumvent the surface region with a high local curvature, thereby resulting in the topological change. These conditions imply that the topological change of the wavefront can be predicted on the basis of the curved surfaces, whose structures are larger than the wave width.

Sex-Dependent QRS Guidelines for Cardiac Resynchronization Therapy Using Computer Model Predictions

Cardiac resynchronization therapy (CRT) is an important treatment for heart failure. Low female enrollment in clinical trials means that current CRT guidelines may be biased toward males. However, females have higher response rates at lower QRS duration (QRSd) thresholds. Sex differences in the left ventricle (LV) size could provide an explanation for the improved female response at lower QRSd. We aimed to test if sex differences in CRT response at lower QRSd thresholds are explained by differences in LV size and hence predict sex-specific guidelines for CRT. We investigated the effect that LV size sex difference has on QRSd between male and females in 1093 healthy individuals and 50 CRT patients using electrophysiological computer models of the heart. Simulations on the healthy mean shape models show that LV size sex difference can account for 50–100% of the sex difference in baseline QRSd in healthy individuals. In the CRT patient cohort, model simulations predicted female-specific guidelines for CRT, which were 9–13 ms lower than current guidelines. Sex differences in the LV size are able to account for a significant proportion of the sex difference in QRSd and provide a mechanistic explanation for the sex difference in CRT response. Simulations accounting for the smaller LV size in female CRT patients predict 9–13 ms lower QRSd thresholds for female CRT guidelines.

MRI-Based Computational Torso/Biventricular Multiscale Models to Investigate the Impact of Anatomical Variability on the ECG QRS Complex

AIMS

Patient-to-patient anatomical differences are an important source of variability in the electrocardiogram, and they may compromise the identification of pathological electrophysiological abnormalities. This study aims at quantifying the contribution of variability in ventricular and torso anatomies to differences in QRS complexes of the 12-lead ECG using computer simulations.

METHODS

A computational pipeline is presented that enables computer simulations using human torso/biventricular anatomically based electrophysiological models from clinically standard magnetic resonance imaging (MRI). The ventricular model includes membrane kinetics represented by the biophysically detailed O'Hara Rudy model modified for tissue heterogeneity and includes fiber orientation based on the Streeter rule. A population of 265 torso/biventricular models was generated by combining ventricular and torso anatomies obtained from clinically standard MRIs, augmented with a statistical shape model of the body. 12-lead ECGs were simulated on the 265 human torso/biventricular electrophysiology models, and QRS morphology, duration and amplitude were quantified in each ECG lead for each of the human torso-biventricular models.

RESULTS

QRS morphologies in limb leads are mainly determined by ventricular anatomy, while in the precordial leads, and especially V1 to V4, they are determined by heart position within the torso. Differences in ventricular orientation within the torso can explain morphological variability from monophasic to biphasic QRS complexes. QRS duration is mainly influenced by myocardial volume, while it is hardly affected by the torso anatomy or position. An average increase of 0.12 ± 0.05 ms in QRS duration is obtained for each cm3 of myocardial volume across all the leads while it hardly changed due to changes in torso volume.

CONCLUSION

Computer simulations using populations of human torso/biventricular models based on clinical MRI enable quantification of anatomical causes of variability in the QRS complex of the 12-lead ECG. The human models presented also pave the way toward their use as testbeds in silico clinical trials.

A rule-based method for predicting the electrical activation of the heart with cardiac resynchronization therapy from non-invasive clinical data

Background

Cardiac Resynchronization Therapy (CRT) is one of the few effective treatments for heart failure patients with ventricular dyssynchrony. The pacing location of the left ventricle is indicated as a determinant of CRT outcome.

Objective

Patient specific computational models allow the activation pattern following CRT implant to be predicted and this may be used to optimize CRT lead placement.

Methods

In this study, the effects of heterogeneous cardiac substrate (scar, fast endocardial conduction, slow septal conduction, functional block) on accurately predicting the electrical activation of the LV epicardium were tested to determine the minimal detail required to create a rule based model of cardiac electrophysiology. Non-invasive clinical data (CT or CMR images and 12 lead ECG) from eighteen patients from two centers were used to investigate the models.

Results

Validation with invasive electro-anatomical mapping data identified that computer models with fast endocardial conduction were able to predict the electrical activation with a mean distance errors of 9.2 ± 0.5 mm (CMR data) or (CT data) 7.5 ± 0.7 mm.

Conclusion

This study identified a simple rule-based fast endocardial conduction model, built using non-invasive clinical data that can be used to rapidly and robustly predict the electrical activation of the heart. Pre-procedural prediction of the latest electrically activating region to identify the optimal LV pacing site could potentially be a useful clinical planning tool for CRT procedures.

Pacing in proximity to scar during cardiac resynchronization therapy increases local dispersion of repolarization and susceptibility to ventricular arrhythmogenesis

BACKGROUND

Cardiac resynchronization therapy (CRT) increases the risk of ventricular tachycardia (VT) in patients with ischemic cardiomyopathy (ICM) when the left ventricular (LV) epicardial lead is implanted in proximity to scar.

OBJECTIVE

The purpose of this study was to determine the mechanisms underpinning this risk by investigating the effects of pacing on local electrophysiology (EP) in relation to scar that provides a substrate for VT in ICM patients undergoing CRT.

METHODS

Imaging data from ICM patients (n = 24) undergoing CRT were used to create patient-specific LV anatomic computational models including scar morphology. Simulations of LV epicardial pacing at 0.2-4.5 cm from the scar were performed using EP models of chronic infarct and heart failure (HF). Dispersion of repolarization and the vulnerable window were computed as surrogates for VT risk.

RESULTS

Simulations predict that pacing in proximity to scar (0.2 cm) compared to more distant pacing to a scar (4.5 cm) significantly (P <.01) increased dispersion of repolarization in the vicinity of the scar and widened (P <.01) the vulnerable window, increasing the likelihood of unidirectional block. Moreover, slow conduction during HF further increased dispersion (∼194%). Analysis of variance and post hoc tests show significantly (P <.01) reduced repolarization dispersion when pacing ≥3.5 cm from the scar compared to pacing at 0.2 cm.

CONCLUSION

Increased dispersion of repolarization in the vicinity of the scar and widening of the vulnerable window when pacing in proximity to scar provides a mechanistic explanation for VT induction in ICM-CRT with lead placement proximal to scar. Pacing 3.5 cm or more from scar may avoid increasing VT risk in ICM-CRT patients.

Patient-Specific Identification of Atrial Flutter Vulnerability-A Computational Approach to Reveal Latent Reentry Pathways

Atypical atrial flutter (AFlut) is a reentrant arrhythmia which patients frequently develop after ablation for atrial fibrillation (AF). Indeed, substrate modifications during AF ablation can increase the likelihood to develop AFlut and it is clinically not feasible to reliably and sensitively test if a patient is vulnerable to AFlut. Here, we present a novel method based on personalized computational models to identify pathways along which AFlut can be sustained in an individual patient. We build a personalized model of atrial excitation propagation considering the anatomy as well as the spatial distribution of anisotropic conduction velocity and repolarization characteristics based on a combination of a priori knowledge on the population level and information derived from measurements performed in the individual patient. The fast marching scheme is employed to compute activation times for stimuli from all parts of the atria. Potential flutter pathways are then identified by tracing loops from wave front collision sites and constricting them using a geometric snake approach under consideration of the heterogeneous wavelength condition. In this way, all pathways along which AFlut can be sustained are identified. Flutter pathways can be instantiated by using an eikonal-diffusion phase extrapolation approach and a dynamic multifront fast marching simulation. In these dynamic simulations, the initial pattern eventually turns into the one driven by the dominant pathway, which is the only pathway that can be observed clinically. We assessed the sensitivity of the flutter pathway maps with respect to conduction velocity and its anisotropy. Moreover, we demonstrate the application of tailored models considering disease-specific repolarization properties (healthy, AF-remodeled, potassium channel mutations) as well as applicabiltiy on a clinical dataset. Finally, we tested how AFlut vulnerability of these substrates is modulated by exemplary antiarrhythmic drugs (amiodarone, dronedarone). Our novel method allows to assess the vulnerability of an individual patient to develop AFlut based on the personal anatomical, electrophysiological, and pharmacological characteristics. In contrast to clinical electrophysiological studies, our computational approach provides the means to identify all possible AFlut pathways and not just the currently dominant one. This allows to consider all relevant AFlut pathways when tailoring clinical ablation therapy in order to reduce the development and recurrence of AFlut.

Assessment of wall stresses and mechanical heart power in the left ventricle: Finite element modeling versus Laplace analysis

INTRODUCTION

Stenotic aortic valve disease (AS) causes pressure overload of the left ventricle (LV) that may trigger adverse remodeling and precipitate progression towards heart failure (HF). As myocardial energetics can be impaired during AS, LV wall stresses and biomechanical power provide a complementary view of LV performance that may aide in better assessing the state of disease.

OBJECTIVES

Using a high-resolution electro-mechanical (EM) in silico model of the LV as a reference, we evaluated clinically feasible Laplace-based methods for assessing global LV wall stresses and biomechanical power.

METHODS

We used N = 4 in silico finite element (FE) EM models of LV and aorta of patients suffering from AS. All models were personalized with clinical data under pretreatment conditions. Left ventricle wall stresses and biomechanical power were computed accurately from FE kinematic data and compared with Laplace-based estimation methods, which were applied to the same FE model data.

RESULTS AND CONCLUSION

Laplace estimates of LV wall stress are able to provide a rough approximation of global mean stress in the circumferential-longitudinal plane of the LV. However, according to FE results, spatial heterogeneity of stresses in the LV wall is significant, leading to major discrepancies between local stresses and global mean stress. Assessment of mechanical power with Laplace methods is feasible, but these are inferior in accuracy compared with FE models. The accurate assessment of stress and power density distribution in the LV wall is only feasible based on patient-specific FE modeling.

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed-point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium-Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases.

Towards a Computational Framework for Modeling the Impact of Aortic Coarctations Upon Left Ventricular Load

Computational fluid dynamics (CFD) models of blood flow in the left ventricle (LV) and aorta are important tools for analyzing the mechanistic links between myocardial deformation and flow patterns. Typically, the use of image-based kinematic CFD models prevails in applications such as predicting the acute response to interventions which alter LV afterload conditions. However, such models are limited in their ability to analyze any impacts upon LV load or key biomarkers known to be implicated in driving remodeling processes as LV function is not accounted for in a mechanistic sense. This study addresses these limitations by reporting on progress made toward a novel electro-mechano-fluidic (EMF) model that represents the entire physics of LV electromechanics (EM) based on first principles. A biophysically detailed finite element (FE) model of LV EM was coupled with a FE-based CFD solver for moving domains using an arbitrary Eulerian-Lagrangian (ALE) formulation. Two clinical cases of patients suffering from aortic coarctations (CoA) were built and parameterized based on clinical data under pre-treatment conditions. For one patient case simulations under post-treatment conditions after geometric repair of CoA by a virtual stenting procedure were compared against pre-treatment results. Numerical stability of the approach was demonstrated by analyzing mesh quality and solver performance under the significantly large deformations of the LV blood pool. Further, computational tractability and compatibility with clinical time scales were investigated by performing strong scaling benchmarks up to 1536 compute cores. The overall cost of the entire workflow for building, fitting and executing EMF simulations was comparable to those reported for image-based kinematic models, suggesting that EMF models show potential of evolving into a viable clinical research tool.

Conduction in the Heart Wall: Helicoidal Fibers Minimize Diffusion Bias

The mammalian heart must function as an efficient pump while simultaneously conducting electrical signals to drive the contraction process. In the ventricles, electrical activation begins at the insertion points of the Purkinje network in the endocardium. How does the diffusion component of the subsequent excitation wave propagate from the endocardium in a healthy heart wall without creating directional biases? We show that this is a consequence of the particular geometric organization of myocytes in the heart wall. Using a generalized helicoid to model fiber orientation, we treat the myocardium as a curved space via Riemannian geometry, and then use stochastic calculus to model local signal diffusion. Our analysis shows that the helicoidal arrangement of myocytes minimizes the directional biases that could lead to aberrant propagation, thereby explaining how electrophysiological principles are consistent with local measurements of cardiac fiber geometry. We discuss our results in the context of the need to balance electrical and mechanical requirements for heart function.

Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart

Realistic electrocardiogram (ECG) simulation with numerical models is important for research linking cellular and molecular physiology to clinically observable signals, and crucial for patient tailoring of numerical heart models. However, ECG simulation with a realistic torso model is computationally much harder than simulation of cardiac activity itself, so that many studies with sophisticated heart models have resorted to crude approximations of the ECG. This paper shows how the classical concept of electrocardiographic lead fields can be used for an ECG simulation method that matches the realism of modern heart models. The accuracy and resource requirements were compared to those of a full-torso solution for the potential and scaling was tested up to 14,336 cores with a heart model consisting of 11 million nodes. Reference ECGs were computed on a 3.3 billion-node heart-torso mesh at 0.2 mm resolution. The results show that the lead-field method is more efficient than a full-torso solution when the number of simulated samples is larger than the number of computed ECG leads. While the initial computation of the lead fields remains a hard and poorly scalable problem, the ECG computation itself scales almost perfectly and, even for several hundreds of ECG leads, takes much less time than the underlying simulation of cardiac activity.

A conduction velocity adapted eikonal model for electrophysiology problems with re-excitability evaluation

Computational models of heart electrophysiology achieved a considerable interest in the medical community as they represent a novel framework for the study of the mechanisms underpinning heart pathologies. The high demand of computational resources and the long computational time required to evaluate the model solution hamper the use of detailed computational models in clinical applications. In this paper, we present a multi-front eikonal algorithm that adapts the conduction velocity (CV) to the activation frequency of the tissue substrate. We then couple the eikonal new algorithm with the Mitchell-Schaeffer (MS) ionic model to determine the tissue electrical state. Compared to the standard eikonal model, this model introduces three novelties: first, it evaluates the local value of the transmembrane potential and of the ionic variable solving an ionic model; second, it computes the action potential duration (APD) and the diastolic interval (DI) from the solution of the MS model and uses them to determine if the tissue is locally re-excitable; third, it adapts the CV to the underpinning electrophysiological state through an analytical expression of the CV restitution and the computed local DI. We conduct series of simulations on a 3D tissue slab and on a realistic heart geometry and compare the solutions with those obtained solving the monodomain equation. Our results show that the new model is significantly more accurate than the standard eikonal model. The proposed model enables the numerical simulation of the heart electrophysiology on a clinical time scale and thus constitutes a viable model candidate for computer-guided radio-frequency ablation.