Generating Purkinje networks in the human heart

Effects of cardiac growth on electrical dyssynchrony in the single ventricle patient

Single ventricle patients, including those with hypoplastic left heart syndrome (HLHS), typically undergo three palliative heart surgeries culminating in the Fontan procedure. HLHS is associated with high rates of morbidity and mortality, and many patients develop arrhythmias, electrical dyssynchrony, and eventually ventricular failure. However, the correlation between ventricular enlargement and electrical dysfunction in HLHS physiology remains poorly understood. Here we characterize the relationship between growth and electrophysiology in HLHS using computational modeling. We integrate a personalized finite element model, a volumetric growth model, and a personalized electrophysiology model to perform controlled in silico experiments. We show that right ventricle enlargement negatively affects QRS duration and interventricular dyssynchrony. Conversely, left ventricle enlargement can partially compensate for this dyssynchrony. These findings have potential implications on our understanding of the origins of electrical dyssynchrony and, ultimately, the treatment of HLHS patients.

Assessing Post-TAVR Cardiac Conduction Abnormalities Risk Using a Digital Twin of a Beating Heart

Transcatheter aortic valve replacement (TAVR) has rapidly displaced surgical aortic valve replacement (SAVR). However, certain post-TAVR complications persist, with cardiac conduction abnormalities (CCA) being one of the major ones. The elevated pressure exerted by the TAVR stent onto the conduction fibers situated between the aortic annulus and the His bundle, in proximity to the atrioventricular (AV) node, may disrupt the cardiac conduction leading to the emergence of CCA. In his study, an in-silico framework was developed to assess the CCA risk, incorporating the effect of a dynamic beating heart and pre-procedural parameters such as implantation depth and preexisting cardiac asynchrony in the new onset of post-TAVR CCA. A self-expandable TAVR device deployment was simulated inside an electro-mechanically coupled beating heart model in five patient scenarios, including three implantation depths, and two preexisting cardiac asynchronies: (i) a right bundle branch block (RBBB) and (ii) a left bundle branch block (LBBB). Subsequently, several biomechanical parameters were analyzed to assess the post-TAVR CCA risk. The results manifested a lower cumulative contact pressure on the conduction fibers following TAVR for aortic deployment (0.018 MPa) compared to baseline (0.29 MPa) and ventricular deployment (0.52 MPa). Notably, the preexisting RBBB demonstrated a higher cumulative contact pressure (0.34 MPa) compared to the baseline and preexisting LBBB (0.25 MPa). Deeper implantation and preexisting RBBB cause higher stresses and contact pressure on the conduction fibers leading to an increased risk of post-TAVR CCA. Conversely, implantation above the MS landmark and preexisting LBBB reduces the risk.

Branched Latent Neural Maps

We introduce Branched Latent Neural Maps (BLNMs) to learn finite dimensional input-output maps encoding complex physical processes. A BLNM is defined by a simple and compact feedforward partially-connected neural network that structurally disentangles inputs with different intrinsic roles, such as the time variable from model parameters of a differential equation, while transferring them into a generic field of interest. BLNMs leverage latent outputs to enhance the learned dynamics and break the curse of dimensionality by showing excellent in-distribution generalization properties with small training datasets and short training times on a single processor. Indeed, their in-distribution generalization error remains comparable regardless of the adopted discretization during the testing phase. Moreover, the partial connections, in place of a fully-connected structure, significantly reduce the number of tunable parameters. We show the capabilities of BLNMs in a challenging test case involving biophysically detailed electrophysiology simulations in a biventricular cardiac model of a pediatric patient with hypoplastic left heart syndrome. The model includes a 1D Purkinje network for fast conduction and a 3D heart-torso geometry. Specifically, we trained BLNMs on 150 in silico generated 12-lead electrocardiograms (ECGs) while spanning 7 model parameters, covering cell-scale, organ-level and electrical dyssynchrony. Although the 12-lead ECGs manifest very fast dynamics with sharp gradients, after automatic hyperparameter tuning the optimal BLNM, trained in less than 3 hours on a single CPU, retains just 7 hidden layers and 19 neurons per layer. The resulting mean square error is on the order of 10 - 4 on an independent test dataset comprised of 50 additional electrophysiology simulations. In the online phase, the BLNM allows for 5000x faster real-time simulations of cardiac electrophysiology on a single core standard computer and can be employed to solve inverse problems via global optimization in a few seconds of computational time. This paper provides a novel computational tool to build reliable and efficient reduced-order models for digital twinning in engineering applications. The Julia implementation is publicly available under MIT License at https://github.com/StanfordCBCL/BLNM.jl.

Digital twinning of cardiac electrophysiology for congenital heart disease

In recent years, blending mechanistic knowledge with machine learning has had a major impact in digital healthcare. In this work, we introduce a computational pipeline to build certified digital replicas of cardiac electrophysiology in pediatric patients with congenital heart disease. We construct the patient-specific geometry by means of semi-automatic segmentation and meshing tools. We generate a dataset of electrophysiology simulations covering cell-to-organ level model parameters and utilizing rigorous mathematical models based on differential equations. We previously proposed Branched Latent Neural Maps (BLNMs) as an accurate and efficient means to recapitulate complex physical processes in a neural network. Here, we employ BLNMs to encode the parametrized temporal dynamics of in silico 12-lead electrocardiograms (ECGs). BLNMs act as a geometry-specific surrogate model of cardiac function for fast and robust parameter estimation to match clinical ECGs in pediatric patients. Identifiability and trustworthiness of calibrated model parameters are assessed by sensitivity analysis and uncertainty quantification.

Computational Modelling Enabling In Silico Trials for Cardiac Physiologic Pacing

Conduction system pacing (CSP) has the potential to achieve physiological-paced activation by pacing the ventricular conduction system. Before CSP is adopted in standard clinical practice, large, randomised, and multi-centre trials are required to investigate CSP safety and efficacy compared to standard biventricular pacing (BVP). Furthermore, there are unanswered questions about pacing thresholds required to achieve optimal pacing delivery while preventing device battery draining, and about which patient groups are more likely to benefit from CSP rather than BVP. In silico studies have been increasingly used to investigate mechanisms underlying changes in cardiac function in response to pathologies and treatment. In the context of CSP, they have been used to improve our understanding of conduction system capture to optimise CSP delivery and battery life, and noninvasively compare different pacing methods on different patient groups. In this review, we discuss the in silico studies published to date investigating different aspects of CSP delivery.

Enhanced optimization-based method for the generation of patient-specific models of Purkinje networks

Cardiac Purkinje networks are a fundamental part of the conduction system and are known to initiate a variety of cardiac arrhythmias. However, patient-specific modeling of Purkinje networks remains a challenge due to their high morphological complexity. This work presents a novel method based on optimization principles for the generation of Purkinje networks that combines geometric and activation accuracy in branch size, bifurcation angles, and Purkinje-ventricular-junction activation times. Three biventricular meshes with increasing levels of complexity are used to evaluate the performance of our approach. Purkinje-tissue coupled monodomain simulations are executed to evaluate the generated networks in a realistic scenario using the most recent Purkinje/ventricular human cellular models and physiological values for the Purkinje-ventricular-junction characteristic delay. The results demonstrate that the new method can generate patient-specific Purkinje networks with controlled morphological metrics and specified local activation times at the Purkinje-ventricular junctions.

Combination of personalized computational modeling and machine learning for optimization of left ventricular pacing site in cardiac resynchronization therapy

Introduction: The 30-50% non-response rate to cardiac resynchronization therapy (CRT) calls for improved patient selection and optimized pacing lead placement. The study aimed to develop a novel technique using patient-specific cardiac models and machine learning (ML) to predict an optimal left ventricular (LV) pacing site (ML-PS) that maximizes the likelihood of LV ejection fraction (LVEF) improvement in a given CRT candidate. To validate the approach, we evaluated whether the distance D_PS between the clinical LV pacing site (ref-PS) and ML-PS is associated with improved response rate and magnitude. Materials and methods: We reviewed retrospective data for 57 CRT recipients. A positive response was defined as a more than 10% LVEF improvement. Personalized models of ventricular activation and ECG were created from MRI and CT images. The characteristics of ventricular activation during intrinsic rhythm and biventricular (BiV) pacing with ref-PS were derived from the models and used in combination with clinical data to train supervised ML classifiers. The best logistic regression model classified CRT responders with a high accuracy of 0.77 (ROC AUC = 0.84). The LR classifier, model simulations and Bayesian optimization with Gaussian process regression were combined to identify an optimal ML-PS that maximizes the ML-score of CRT response over the LV surface in each patient. Results: The optimal ML-PS improved the ML-score by 17 ± 14% over the ref-PS. Twenty percent of the non-responders were reclassified as positive at ML-PS. Selection of positive patients with a max ML-score >0.5 demonstrated an improved clinical response rate. The distance D_PS was shorter in the responders. The max ML-score and D_PS were found to be strong predictors of CRT response (ROC AUC = 0.85). In the group with max ML-score > 0.5 and D_PS< 30 mm, the response rate was 83% compared to 14% in the rest of the cohort. LVEF improvement in this group was higher than in the other patients (16 ± 8% vs. 7 ± 8%). Conclusion: A new technique combining clinical data, personalized heart modelling and supervised ML demonstrates the potential for use in clinical practice to assist in optimizing patient selection and predicting optimal LV pacing lead position in HF candidates for CRT.

Transmural fibre orientations based on Laplace-Dirichlet-Rule-Based-Methods and their influence on human heart simulations

It is well known that the orthotropic tissue structure decisively influences the mechanical and electrical properties of the heart. Numerous approaches to compute the orthotropic tissue structure in computational heart models have been developed in the past decades. In this study, we investigate to what extent different Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) influence the local orthotropic tissue structure and thus the electromechanical behaviour of the subsequent cardiac simulation. In detail, we are utilising three Laplace-Dirichlet-Rule-Based-Methods and compare: (i) the local myofibre orientation; (ii) important global characteristics (ejection fraction, peak pressure, apex shortening, myocardial volume reduction, fractional wall thickening); (iii) local characteristics (active fibre stress, fibre strain). We observe that the orthotropic tissue structures for the three LDRBMs show significant differences in the local myofibre orientation. The global characteristics myocardial volume reduction and peak pressure are rather insensitive to a change in local myofibre orientation, while the ejection fraction is moderately influenced by the different LDRBMs. Moreover, the apical shortening and fractional wall thickening exhibit a sensitive behaviour to a change in the local myofibre orientation. The highest sensitivity can be observed for the local characteristics.

Comparison of novel ventricular pacing strategies using an electro-mechanical simulation platform

AIMS

Focus of pacemaker therapy is shifting from right ventricular (RV) apex pacing (RVAP) and biventricular pacing (BiVP) to conduction system pacing. Direct comparison between the different pacing modalities and their consequences to cardiac pump function is difficult, due to the practical implications and confounding variables. Computational modelling and simulation provide the opportunity to compare electrical, mechanical, and haemodynamic consequences in the same virtual heart.

METHODS AND RESULTS

Using the same single cardiac geometry, electrical activation maps following the different pacing strategies were calculated using an Eikonal model on a three-dimensional geometry, which were then used as input for a lumped mechanical and haemodynamic model (CircAdapt). We then compared simulated strain, regional myocardial work, and haemodynamic function for each pacing strategy. Selective His-bundle pacing (HBP) best replicated physiological electrical activation and led to the most homogeneous mechanical behaviour. Selective left bundle branch (LBB) pacing led to good left ventricular (LV) function but significantly increased RV load. RV activation times were reduced in non-selective LBB pacing (nsLBBP), reducing RV load but increasing heterogeneity in LV contraction. LV septal pacing led to a slower LV and more heterogeneous LV activation than nsLBBP, while RV activation was similar. BiVP led to a synchronous LV-RV, but resulted in a heterogeneous contraction. RVAP led to the slowest and most heterogeneous contraction. Haemodynamic differences were small compared to differences in local wall behaviour.

CONCLUSION

Using a computational modelling framework, we investigated the mechanical and haemodynamic outcome of the prevailing pacing strategies in hearts with normal electrical and mechanical function. For this class of patients, nsLBBP was the best compromise between LV and RV function if HBP is not possible.

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

How viscous is the beating heart?: Insights from a computational study

Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress-relaxation curves, pressure-volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic.

Patient-specific finite element analysis of heart failure and the impact of surgical intervention in pulmonary hypertension secondary to mitral valve disease

Pulmonary hypertension (PH), a chronic and complex medical condition affecting 1% of the global population, requires clinical evaluation of right ventricular maladaptation patterns under various conditions. A particular challenge for clinicians is a proper quantitative assessment of the right ventricle (RV) owing to its intimate coupling to the left ventricle (LV). We, thus, proposed a patient-specific computational approach to simulate PH caused by left heart disease and its main adverse functional and structural effects on the whole heart. Information obtained from both prospective and retrospective studies of two patients with severe PH, a 72-year-old female and a 61-year-old male, is used to present patient-specific versions of the Living Heart Human Model (LHHM) for the pre-operative and post-operative cardiac surgery. Our findings suggest that before mitral and tricuspid valve repair, the patients were at risk of right ventricular dilatation which may progress to right ventricular failure secondary to their mitral valve disease and left ventricular dysfunction. Our analysis provides detailed evidence that mitral valve replacement and subsequent chamber pressure unloading are associated with a significant decrease in failure risk post-operatively in the context of pulmonary hypertension. In particular, right-sided strain markers, such as tricuspid annular plane systolic excursion (TAPSE) and circumferential and longitudinal strains, indicate a transition from a range representative of disease to within typical values after surgery. Furthermore, the wall stresses across the RV and the interventricular septum showed a notable decrease during the systolic phase after surgery, lessening the drive for further RV maladaptation and significantly reducing the risk of RV failure.

Rate dependence of early afterdepolarizations in the His-Purkinje system: A simulation study

BACKGROUND AND OBJECTIVE

Early afterdepolarizations (EADs) are associated with a variety of arrhythmias and have the property of rate dependence. EADs can occur in Purkinje cells while the effect of rate dependence of EADs in the His-Purkinje system has not been fully investigated. In order to reveal the rate dependence of EADs in the His-Purkinje system and its effect on ventricular electrical activities, the simulation research was carried out in this manuscript.

METHODS

This manuscript first studied the relationship between the occurrence of EADs and stimulation cycle length on the DiFranNoble cell model. Then, the relationship between the rate dependence of EADs and the conduction block of the His-Purkinje system at slow heart rates was studied on the rabbit whole ventricular model including the His-Purkinje system, and its mechanism was analyzed from multiple angles.

RESULTS

① The rate dependence of EADs is related to the inconsistency of EADs occurrence in the His-Purkinje system. When the stimulation cycle length is long or short enough, EADs either occur or not occur stably in the His-Purkinje system, while in a certain stimulation cycle length window, the chaotic state of EADs will be observed. ② The key subcellular factors x-gate is an important mechanism involved to the rate dependence of EADs in the His-Purkinje system. ③ The discrete distribution of x-gate values and the "source-sink" mechanism lead to the inconsistency of EADs in the His-Purkinje system. The prolonged action potential duration caused by EADs can lead to conduction block at slow heart rates.

CONCLUSION

The rate dependence of EADs in Purkinje system can lead to disordered ventricular electrical activity.

Machine Learning Prediction of Cardiac Resynchronisation Therapy Response From Combination of Clinical and Model-Driven Data

Background: Up to 30–50% of chronic heart failure patients who underwent cardiac resynchronization therapy (CRT) do not respond to the treatment. Therefore, patient stratification for CRT and optimization of CRT device settings remain a challenge.

Objective: The main goal of our study is to develop a predictive model of CRT outcome using a combination of clinical data recorded in patients before CRT and simulations of the response to biventricular (BiV) pacing in personalized computational models of the cardiac electrophysiology.

Materials and Methods: Retrospective data from 57 patients who underwent CRT device implantation was utilized. Positive response to CRT was defined by a 10% increase in the left ventricular ejection fraction in a year after implantation. For each patient, an anatomical model of the heart and torso was reconstructed from MRI and CT images and tailored to ECG recorded in the participant. The models were used to compute ventricular activation time, ECG duration and electrical dyssynchrony indices during intrinsic rhythm and BiV pacing from the sites of implanted leads. For building a predictive model of CRT response, we used clinical data recorded before CRT device implantation together with model-derived biomarkers of ventricular excitation in the left bundle branch block mode of activation and under BiV stimulation. Several Machine Learning (ML) classifiers and feature selection algorithms were tested on the hybrid dataset, and the quality of predictors was assessed using the area under receiver operating curve (ROC AUC). The classifiers on the hybrid data were compared with ML models built on clinical data only.

Results: The best ML classifier utilizing a hybrid set of clinical and model-driven data demonstrated ROC AUC of 0.82, an accuracy of 0.82, sensitivity of 0.85, and specificity of 0.78, improving quality over that of ML predictors built on clinical data from much larger datasets by more than 0.1. Distance from the LV pacing site to the post-infarction zone and ventricular activation characteristics under BiV pacing were shown as the most relevant model-driven features for CRT response classification.

Conclusion: Our results suggest that combination of clinical and model-driven data increases the accuracy of classification models for CRT outcomes.

The Purkinje network plays a major role in low-energy ventricular defibrillation

BACKGROUND

During ventricular fibrillation (VF), targeting the excitable gap (EG) of reentry throughout the myocardium with low-energy surface stimulation shows promise for painless defibrillation. However, the Purkinje network may provide alternative pathways for reentry to evade termination. This study investigates the role of the Purkinje network in painless defibrillation.

METHODS

In a computational human biventricular model featuring a Purkinje network, VF was initiated with 4 Hz epicardial pacing. Defibrillation was attempted by stimulating myocardial surface EG with a low-energy 2 ms duration pulse at 2x stimulus capture, which was administered at coupling intervals incremented by 0.25 s between 0.25 and 5 s after VF initiation. Defibrillation was accomplished if reentry ceased ≤ 1 s after the defibrillation pulse. The protocol was repeated with the Purkinje network and myocardial surface EG stimulated simultaneously, and again after uncoupling the Purkinje network from the myocardium.

RESULTS

VF with the Purkinje network coupled and uncoupled had comparable dominant frequency in the left (3.81 ± 0.44 versus 3.77 ± 0.53 Hz) and right (3.80 ± 0.37 versus 3.76 ± 0.48 Hz) ventricles. When uncoupling the Purkinje network, myocardial surface EG stimulation terminated VF for all defibrillation pulses. When coupled, myocardial EG surface stimulation terminated VF for only 55% of the defibrillation pulses, but improved to 100% when stimulated simultaneously with Purkinje network EG. Defibrillation failures were attributed to EG evading stimulation in the Purkinje network.

CONCLUSIONS

Defibrillation that exclusively targets myocardium can fail due to accessory pathways in the Purkinje network that allow for reentrant activity to evade termination and maintain VF. Painless defibrillation strategies should be adapted to include the Purkinje network.

Automated Framework for the Inclusion of a His-Purkinje System in Cardiac Digital Twins of Ventricular Electrophysiology

Personalized models of cardiac electrophysiology (EP) that match clinical observation with high fidelity, referred to as cardiac digital twins (CDTs), show promise as a tool for tailoring cardiac precision therapies. Building CDTs of cardiac EP relies on the ability of models to replicate the ventricular activation sequence under a broad range of conditions. Of pivotal importance is the His-Purkinje system (HPS) within the ventricles. Workflows for the generation and incorporation of HPS models are needed for use in cardiac digital twinning pipelines that aim to minimize the misfit between model predictions and clinical data such as the 12 lead electrocardiogram (ECG). We thus develop an automated two stage approach for HPS personalization. A fascicular-based model is first introduced that modulates the endocardial Purkinje network. Only emergent features of sites of earliest activation within the ventricular myocardium and a fast-conducting sub-endocardial layer are accounted for. It is then replaced by a topologically realistic Purkinje-based representation of the HPS. Feasibility of the approach is demonstrated. Equivalence between both HPS model representations is investigated by comparing activation patterns and 12 lead ECGs under both sinus rhythm and right-ventricular apical pacing. Predominant ECG morphology is preserved by both HPS models under sinus conditions, but elucidates differences during pacing.

Image-based Cardiac Electrophysiology Simulation through the Meshfree Mixed Collocation Method

State-of-the-art solvers for in silico cardiac electro-physiology employ the Finite Element Method to solve complex anatomical models. While this is a robust and accurate tech-nique, it requires a high-quality mesh to prevent its accuracy from being severely deteriorated. The generation of a good quality mesh for realistic anatomical models can be very time-consuming, making the translation to the clinics challenging, especially if we try to use patient-specific geometries.Aiming to tackle this challenge, we propose an image-based model generation approach based on the meshfree Mixed Col-location Method. The flexibility provided by this method during model generation allows building meshfree models directly from the image data in an automatic procedure. Furthermore, this approach allows interpreting the simulation results directly in the voxel coordinates system of the image.We simulate electrical propagation in a porcine biventricular model with the proposed method and we compare the results with those obtained using the Finite Element Method. We conclude that the proposed method can generate results that are in good agreement with the Finite Element Method solution, alleviating the requirement of a mesh and user-input during modeling with only minimum efficiency overhead.

Sex Differences in Drug-Induced Arrhythmogenesis

The electrical activity in the heart varies significantly between men and women and results in a sex-specific response to drugs. Recent evidence suggests that women are more than twice as likely as men to develop drug-induced arrhythmia with potentially fatal consequences. Yet, the sex-specific differences in drug-induced arrhythmogenesis remain poorly understood. Here we integrate multiscale modeling and machine learning to gain mechanistic insight into the sex-specific origin of drug-induced cardiac arrhythmia at differing drug concentrations. To quantify critical drug concentrations in male and female hearts, we identify the most important ion channels that trigger male and female arrhythmogenesis, and create and train a sex-specific multi-fidelity arrhythmogenic risk classifier. Our study reveals that sex differences in ion channel activity, tissue conductivity, and heart dimensions trigger longer QT-intervals in women than in men. We quantify the critical drug concentration for dofetilide, a high risk drug, to be seven times lower for women than for men. Our results emphasize the importance of including sex as an independent biological variable in risk assessment during drug development. Acknowledging and understanding sex differences in drug safety evaluation is critical when developing novel therapeutic treatments on a personalized basis. The general trends of this study have significant implications on the development of safe and efficacious new drugs and the prescription of existing drugs in combination with other drugs.

GEASI: Geodesic-based earliest activation sites identification in cardiac models

The identification of the initial ventricular activation sequence is a critical step for the correct personalization of patient-specific cardiac models. In healthy conditions, the Purkinje network is the main source of the electrical activation, but under pathological conditions the so-called earliest activation sites (EASs) are possibly sparser and more localized. Yet, their number, location and timing may not be easily inferred from remote recordings, such as the epicardial activation or the 12-lead electrocardiogram (ECG), due to the underlying complexity of the model. In this work, we introduce GEASI (Geodesic-based Earliest Activation Sites Identification) as a novel approach to simultaneously identify all EASs. To this end, we start from the anisotropic eikonal equation modeling cardiac electrical activation and exploit its Hamilton-Jacobi formulation to minimize a given objective function, for example, the quadratic mismatch to given activation measurements. This versatile approach can be extended to estimate the number of activation sites by means of the topological gradient, or fitting a given ECG. We conducted various experiments in 2D and 3D for in-silico models and an in-vivo intracardiac recording collected from a patient undergoing cardiac resynchronization therapy. The results demonstrate the clinical applicability of GEASI for potential future personalized models and clinical intervention.

Estimation of Personalized Minimal Purkinje Systems From Human Electro-Anatomical Maps

The Purkinje system is a heart structure responsible for transmitting electrical impulses through the ventricles in a fast and coordinated way to trigger mechanical contraction. Estimating a patient-specific compatible Purkinje Network from an electro-anatomical map is a challenging task, that could help to improve models for electrophysiology simulations or provide aid in therapy planning, such as radiofrequency ablation. In this study, we present a methodology to inversely estimate a Purkinje network from a patient's electro-anatomical map. First, we carry out a simulation study to assess the accuracy of the method for different synthetic Purkinje network morphologies and myocardial junction densities. Second, we estimate the Purkinje network from a set of 28 electro-anatomical maps from patients, obtaining an optimal conduction velocity in the Purkinje network of 1.95 ± 0.25 m/s, together with the location of their Purkinje-myocardial junctions, and Purkinje network structure. Our results showed an average local activation time error of 6.8±2.2 ms in the endocardium. Finally, using the personalized Purkinje network, we obtained correlations higher than 0.85 between simulated and clinical 12-lead ECGs.

A dual adaptive explicit time integration algorithm for efficiently solving the cardiac monodomain equation

The monodomain model is widely used in in-silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so that they can be solved separately. Commonly, the diffusion term is solved implicitly with a large time step while the reaction term is solved by using an explicit method with adaptive time stepping. In this work, we propose a fully explicit method for the solution of the decoupled monodomain model. In contrast to semi-implicit methods, fully explicit methods present lower memory footprint and higher scalability. However, such methods are only conditionally stable. We overcome the conditional stability limitation by proposing a dual adaptive explicit method in which adaptive time integration is applied for the solution of both the reaction and diffusion terms. We perform a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions. Results show that the proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting-based methods.

Multiphysics computational modelling of the cardiac ventricles

Development of cardiac multiphysics models has progressed significantly over the decades and simulations combining multiple physics interactions have become increasingly common. In this review, we summarise the progress in this field focusing on various approaches of integrating ventricular structures. electrophysiological properties, myocardial mechanics, as well as incorporating blood hemodynamics and the circulatory system. Common coupling approaches are discussed and compared, including the advantages and shortcomings of each. Currently used strategies for patient-specific implementations are highlighted and potential future improvements considered.

A Framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs

Cardiac digital twins (Cardiac Digital Twin (CDT)s) of human electrophysiology (Electrophysiology (EP)) are digital replicas of patient hearts derived from clinical data that match like-for-like all available clinical observations. Due to their inherent predictive potential, CDTs show high promise as a complementary modality aiding in clinical decision making and also in the cost-effective, safe and ethical testing of novel EP device therapies. However, current workflows for both the anatomical and functional twinning phases within CDT generation, referring to the inference of model anatomy and parameters from clinical data, are not sufficiently efficient, robust and accurate for advanced clinical and industrial applications. Our study addresses three primary limitations impeding the routine generation of high-fidelity CDTs by introducing; a comprehensive parameter vector encapsulating all factors relating to the ventricular EP; an abstract reference frame within the model allowing the unattended manipulation of model parameter fields; a novel fast-forward electrocardiogram (Electrocardiogram (ECG)) model for efficient and bio-physically-detailed simulation required for parameter inference. A novel workflow for the generation of CDTs is then introduced as an initial proof of concept. Anatomical twinning was performed within a reasonable time compatible with clinical workflows (<4h) for 12 subjects from clinically-attained magnetic resonance images. After assessment of the underlying fast forward ECG model against a gold standard bidomain ECG model, functional twinning of optimal parameters according to a clinically-attained 12 lead ECG was then performed using a forward Saltelli sampling approach for a single subject. The achieved results in terms of efficiency and fidelity demonstrate that our workflow is well-suited and viable for generating biophysically-detailed CDTs at scale.

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.

Precision medicine in human heart modeling : Perspectives, challenges, and opportunities

Precision medicine is a new frontier in healthcare that uses scientific methods to customize medical treatment to the individual genes, anatomy, physiology, and lifestyle of each person. In cardiovascular health, precision medicine has emerged as a promising paradigm to enable cost-effective solutions that improve quality of life and reduce mortality rates. However, the exact role in precision medicine for human heart modeling has not yet been fully explored. Here, we discuss the challenges and opportunities for personalized human heart simulations, from diagnosis to device design, treatment planning, and prognosis. With a view toward personalization, we map out the history of anatomic, physical, and constitutive human heart models throughout the past three decades. We illustrate recent human heart modeling in electrophysiology, cardiac mechanics, and fluid dynamics and highlight clinically relevant applications of these models for drug development, pacing lead failure, heart failure, ventricular assist devices, edge-to-edge repair, and annuloplasty. With a view toward translational medicine, we provide a clinical perspective on virtual imaging trials and a regulatory perspective on medical device innovation. We show that precision medicine in human heart modeling does not necessarily require a fully personalized, high-resolution whole heart model with an entire personalized medical history. Instead, we advocate for creating personalized models out of population-based libraries with geometric, biological, physical, and clinical information by morphing between clinical data and medical histories from cohorts of patients using machine learning. We anticipate that this perspective will shape the path toward introducing human heart simulations into precision medicine with the ultimate goals to facilitate clinical decision making, guide treatment planning, and accelerate device design.

OPTIMIZATION OF RABBIT VENTRICULAR ELECTROPHYSIOLOGICAL MODEL AND SIMULATION OF SYNTHETIC ELECTROCARDIOGRAM

This study aimed to use computer simulation method to study the mechanism of cardiac electrical activities. We optimized an electrophysiological rabbit ventricular model, including myocardial segmentation, heterogeneity and a realistic His-Purkinje network. Simulations of normal state, several types of ventricular premature contractions (VPC), conduction system pacing and right ventricular apical pacing were performed and the detailed cardiac electrical activities were studied from cell level to electrocardiogram (ECG) level. A detailed multiscale optimized ventricular model was obtained. The model effectively simulated various types of electrical activities. The synthetic ECG results were very similar to the real clinical ECG. The duration of QRS of typical VPC is 58[Formula: see text]ms, 71% longer than that of a normal-state synthetic QRS and the amplitude of the QRS is 35% larger, while the QRS duration and amplitude of the real clinical ECG of typical VPC are 69% longer and 36% larger than those of the real normal QRS. The duration of QRS of ventricular fusion beat is 31[Formula: see text]ms, 91% of that of a normal-state synthetic QRS and the amplitude of the QRS is 36% larger, while the QRS duration of the real clinical ECG of a ventricular fusion beat is 92% of the real normal QRS and the amplitude is 37% larger. Therefore, the results indicate that this model is effective and reliable in studying the detailed process of cardiac excitation and pacing.

A Simulation Study on the Pacing and Driving of the Biological Pacemaker

The research on the biological pacemaker has been very active in recent years. And turning nonautomatic ventricular cells into pacemaking cells is believed to hold the key to making a biological pacemaker. In the study, the inward-rectifier K⁺ current (I_K1) is depressed to induce the automaticity of the ventricular myocyte, and then, the effects of the other membrane ion currents on the automaticity are analyzed. It is discovered that the L-type calcium current (I_CaL) plays a major part in the rapid depolarization of the action potential (AP). A small enough I_CaL would lead to the failure of the automaticity of the ventricular myocyte. Meanwhile, the background sodium current (I_bNa), the background calcium current (I_bCa), and the Na⁺/Ca²⁺ exchanger current (I_NaCa) contribute significantly to the slow depolarization, indicating that these currents are the main supplementary power of the pacing induced by depressing I_K1, while in the 2D simulation, we find that the weak electrical coupling plays a more important role in the driving of a biological pacemaker.

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.

Classifying Drugs by their Arrhythmogenic Risk Using Machine Learning

All medications have adverse effects. Among the most serious of these are cardiac arrhythmias. Current paradigms for drug safety evaluation are costly, lengthy, conservative, and impede efficient drug development. Here, we combine multiscale experiment and simulation, high-performance computing, and machine learning to create a risk estimator to stratify new and existing drugs according to their proarrhythmic potential. We capitalize on recent developments in machine learning and integrate information across 10 orders of magnitude in space and time to provide a holistic picture of the effects of drugs, either individually or in combination with other drugs. We show, both experimentally and computationally, that drug-induced arrhythmias are dominated by the interplay between two currents with opposing effects: the rapid delayed rectifier potassium current and the L-type calcium current. Using Gaussian process classification, we create a classifier that stratifies drugs into safe and arrhythmic domains for any combinations of these two currents. We demonstrate that our classifier correctly identifies the risk categories of 22 common drugs exclusively on the basis of their concentrations at 50% current block. Our new risk assessment tool explains under which conditions blocking the L-type calcium current can delay or even entirely suppress arrhythmogenic events. Using machine learning in drug safety evaluation can provide a more accurate and comprehensive mechanistic assessment of the proarrhythmic potential of new drugs. Our study paves the way toward establishing science-based criteria to accelerate drug development, design safer drugs, and reduce heart rhythm disorders.

R-From-T as a Common Mechanism of Arrhythmia Initiation in Long QT Syndromes

BACKGROUND

Long QT syndromes (LQTS) arise from many genetic and nongenetic causes with certain characteristic ECG features preceding polymorphic ventricular tachyarrhythmias (PVTs). However, how the many molecular causes result in these characteristic ECG patterns and how these patterns are mechanistically linked to the spontaneous initiation of PVT remain poorly understood.

METHODS

Anatomic human ventricle and simplified tissue models were used to investigate the mechanisms of spontaneous initiation of PVT in LQTS.

RESULTS

Spontaneous initiation of PVT was elicited by gradually ramping up ICa,L to simulate the initial phase of a sympathetic surge or by changing the heart rate, reproducing the different genotype-dependent clinical ECG features. In LQTS type 2 (LQT2) and LQTS type 3 (LQT3), T-wave alternans was observed followed by premature ventricular complexes (PVCs). Compensatory pauses occurred resulting in short-long-short sequences. As ICa,L increased further, PVT episodes occurred, always preceded by a short-long-short sequence. However, in LQTS type 1 (LQT1), once a PVC occurred, it always immediately led to an episode of PVT. Arrhythmias in LQT2 and LQT3 were bradycardia dependent, whereas those in LQT1 were not. In all 3 genotypes, PVCs always originated spontaneously from the steep repolarization gradient region and manifested on ECG as R-on-T. We call this mechanism R-from-T, to distinguish it from the classic explanation of R-on-T arrhythmogenesis in which an exogenous PVC coincidentally encounters a repolarizing region. In R-from-T, the PVC and the T wave are causally related, where steep repolarization gradients combined with enhanced ICa,L lead to PVCs emerging from the T wave. Since enhanced ICa,L was required for R-from-T to occur, suppressing window ICa,L effectively prevented arrhythmias in all 3 genotypes.

CONCLUSIONS

Despite the complex molecular causes, these results suggest that R-from-T is likely a common mechanism for PVT initiation in LQTS. Targeting ICa,L properties, such as suppressing window ICa,L or preventing excessive ICa,L increase, could be an effective unified therapy for arrhythmia prevention in LQTS.

Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study

In this paper, we are investigating the interaction between different passive material models and the mechano-electrical feedback (MEF) in cardiac modeling. Various types of passive mechanical laws (nearly incompressible/compressible, polynomial/exponential-type, transversally isotropic/orthotropic material models) are integrated in a fully coupled electromechanical model in order to study their specific influence on the overall MEF behavior. Our computational model is based on a three-dimensional (3D) geometry of a healthy rat left ventricle reconstructed from magnetic resonance imaging (MRI). The electromechanically coupled problem is solved using a fully implicit finite element-based approach. The effects of different passive material models on the MEF are studied with the help of numerical examples. It turns out that there is a significant difference between the behavior of the MEF for compressible and incompressible material models. Numerical results for the incompressible models exhibit that a change in the electrophysiology can be observed such that the transmembrane potential (TP) is unable to reach the resting state in the repolarization phase, and this leads to non-zero relaxation deformations. The most significant and strongest effects of the MEF on the rat cardiac muscle response are observed for the exponential passive material law.

Predicting critical drug concentrations and torsadogenic risk using a multiscale exposure-response simulator

Torsades de pointes is a serious side effect of many drugs that can trigger sudden cardiac death, even in patients with structurally normal hearts. Torsadogenic risk has traditionally been correlated with the blockage of a specific potassium channel and a prolonged recovery period in the electrocardiogram. However, the precise mechanisms by which single channel block translates into heart rhythm disorders remain incompletely understood. Here we establish a multiscale exposure-response simulator that converts block-concentration characteristics from single cell recordings into three-dimensional excitation profiles and electrocardiograms to rapidly assess torsadogenic risk. For the drug dofetilide, we characterize the QT interval and heart rate at different drug concentrations and identify the critical concentration at the onset of torsades de pointes: For dofetilide concentrations of 2x, 3x, and 4x, as multiples of the free plasma concentration Cmax = 2.1 nM, the QT interval increased by +62.0%, +71.2%, and +82.3% compared to baseline, and the heart rate changed by -21.7%, -23.3%, and +88.3%. The last number indicates that, at the critical concentration of 4x, the heart spontaneously developed an episode of a torsades-like arrhythmia. Strikingly, this critical drug concentration is higher than the concentration estimated from early afterdepolarizations in single cells and lower than in one-dimensional cable models. Our results highlight the importance of whole heart modeling and explain, at least in part, why current regulatory paradigms often fail to accurately quantify the pro-arrhythmic potential of a drug. Our exposure-response simulator could provide a more mechanistic assessment of pro-arrhythmic risk and help establish science-based guidelines to reduce rhythm disorders, design safer drugs, and accelerate drug development.

A comprehensive, multiscale framework for evaluation of arrhythmias arising from cell therapy in the whole post-myocardial infarcted heart

Direct remuscularization approaches to cell-based heart repair seek to restore ventricular contractility following myocardial infarction (MI) by introducing new cardiomyocytes (CMs) to replace lost or injured ones. However, despite promising improvements in cardiac function, high incidences of ventricular arrhythmias have been observed in animal models of MI injected with pluripotent stem cell-derived cardiomyocytes (PSC-CMs). The mechanisms of arrhythmogenesis remain unclear. Here, we present a comprehensive framework for computational modeling of direct remuscularization approaches to cell therapy. Our multiscale 3D whole-heart modeling framework integrates realistic representations of cell delivery and transdifferentiation therapy modalities as well as representation of spatial distributions of engrafted cells, enabling simulation of clinical therapy and the prediction of emergent electrophysiological behavior and arrhythmogenensis. We employ this framework to explore how varying parameters of cell delivery and transdifferentiation could result in three mechanisms of arrhythmogenesis: focal ectopy, heart block, and reentry.

Linking microvascular collapse to tissue hypoxia in a multiscale model of pressure ulcer initiation

Pressure ulcers are devastating injuries that disproportionately affect the older adult population. The initiating factor of pressure ulcers is local ischemia, or lack of perfusion at the microvascular level, following tissue compression against bony prominences. In turn, lack of blood flow leads to a drop in oxygen concentration, i.e, hypoxia, that ultimately leads to cell death, tissue necrosis, and disruption of tissue continuity. Despite our qualitative understanding of the initiating mechanisms of pressure ulcers, we are lacking quantitative knowledge of the relationship between applied pressure, skin mechanical properties as well as structure, and tissue hypoxia. This gap in our understanding is, at least in part, due to the limitations of current imaging technologies that cannot simultaneously image the microvascular architecture, while quantifying tissue deformation. We overcome this limitation in our work by combining realistic microvascular geometries with appropriate mechanical constitutive models into a microscale finite element model of the skin. By solving boundary value problems on a representative volume element via the finite element method, we can predict blood volume fractions in response to physiological skin loading conditions (i.e., shear and compression). We then use blood volume fraction as a homogenized variable to couple tissue-level skin mechanics to an oxygen diffusion model. With our model, we find that moderate levels of pressure applied to the outer skin surface lead to oxygen concentration contours indicative of tissue hypoxia. For instance, we show that applying a pressure of 60 kPa at the skin surface leads to a decrease in oxygen partial pressure from a physiological value of 65 mmHg to a hypoxic level of 31 mmHg. Additionally, we explore the sensitivity of local oxygen concentration to skin thickness and tissue stiffness, two age-related skin parameters. We find that, for a given pressure, oxygen concentration decreases with decreasing skin thickness and skin stiffness. Future work will include rigorous calibration and validation of this model, which may render our work an important tool toward developing better prevention and treatment tools for pressure ulcers specifically targeted toward the older adult patient population.

Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification

Prolonged QT intervals are a major risk factor for ventricular arrhythmias and a leading cause of sudden cardiac death. Various drugs are known to trigger QT interval prolongation and increase the proarrhythmic potential. Yet, how precisely the action of drugs on the cellular level translates into QT interval prolongation on the whole organ level remains insufficiently understood. Here we use machine learning techniques to systematically characterize the effect of 30 common drugs on the QT interval. We combine information from high fidelity three-dimensional human heart simulations with low fidelity one-dimensional cable simulations to build a surrogate model for the QT interval using multi-fidelity Gaussian process regression. Once trained and cross-validated, we apply our surrogate model to perform sensitivity analysis and uncertainty quantification. Our sensitivity analysis suggests that compounds that block the rapid delayed rectifier potassium current I Kr have the greatest prolonging effect of the QT interval, and that blocking the L-type calcium current I CaL and late sodium current I NaL shortens the QT interval. Our uncertainty quantification allows us to propagate the experimental variability from individual block-concentration measurements into the QT interval and reveals that QT interval uncertainty is mainly driven by the variability in I Kr block. In a final validation study, we demonstrate an excellent agreement between our predicted QT interval changes and the changes observed in a randomized clinical trial for the drugs dofetilide, quinidine, ranolazine, and verapamil. We anticipate that both the machine learning methods and the results of this study will have great potential in the efficient development of safer drugs.

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.

Predicting drug-induced arrhythmias by multiscale modeling

Drugs often have undesired side effects. In the heart, they can induce lethal arrhythmias such as torsades de pointes. The risk evaluation of a new compound is costly and can take a long time, which often hinders the development of new drugs. Here, we establish a high-resolution, multiscale computational model to quickly assess the cardiac toxicity of new and existing drugs. The input of the model is the drug-specific current block from single cell electrophysiology; the output is the spatio-temporal activation profile and the associated electrocardiogram. We demonstrate the potential of our model for a low-risk drug, ranolazine, and a high-risk drug, quinidine: For ranolazine, our model predicts a prolonged QT interval of 19.4% compared with baseline and a regular sinus rhythm at 60.15 beats per minute. For quinidine, our model predicts a prolonged QT interval of 78.4% and a spontaneous development of torsades de pointes both in the activation profile and in the electrocardiogram. Our model reveals the mechanisms by which electrophysiological abnormalities propagate across the spatio-temporal scales, from specific channel blockage, via altered single cell action potentials and prolonged QT intervals, to the spontaneous emergence of ventricular tachycardia in the form of torsades de pointes. Our model could have important implications for researchers, regulatory agencies, and pharmaceutical companies on rationalizing safe drug development and reducing the time-to-market of new drugs.

Efficient Computational Modeling of Human Ventricular Activation and Its Electrocardiographic Representation: A Sensitivity Study

Patient-specific models of the ventricular myocardium, combined with the computational power to run rapid simulations, are approaching the level where they could be used for personalized cardiovascular medicine. A major remaining challenge is determining model parameters from available patient data, especially for models of the Purkinje-myocardial junctions (PMJs): the sites of initial ventricular electrical activation. There are no non-invasive methods for localizing PMJs in patients, and the relationship between the standard clinical ECG and PMJ model parameters is underexplored. Thus, this study aimed to determine the sensitivity of the QRS complex of the ECG to the anatomical location and regional number of PMJs. The QRS complex was simulated using an image-based human torso and biventricular model, and cardiac electrophysiology was simulated using Cardioid. The PMJs were modeled as discrete current injection stimuli, and the location and number of stimuli were varied within initial activation regions based on published experiments. Results indicate that the QRS complex features were most sensitive to the presence or absence of four “seed” stimuli, and adjusting locations of nearby “regional” stimuli provided finer tuning. Decreasing number of regional stimuli by an order of magnitude resulted in virtually no change in the QRS complex. Thus, a minimal 12-stimuli configuration was identified that resulted in physiological excitation, defined by QRS complex feature metrics and ventricular excitation pattern. Overall, the sensitivity results suggest that parameterizing PMJ location, rather than number, be given significantly higher priority in future studies creating personalized ventricular models from patient-derived ECGs.

Interpreting Activation Mapping of Atrial Fibrillation: A Hybrid Computational/Physiological Study

Atrial fibrillation is the most common rhythm disorder of the heart associated with a rapid and irregular beating of the upper chambers. Activation mapping remains the gold standard to diagnose and interpret atrial fibrillation. However, fibrillatory activation maps are highly sensitive to far-field effects, and often disagree with other optical mapping modalities. Here we show that computational modeling can identify spurious non-local components of atrial fibrillation electrograms and improve activation mapping. We motivate our approach with a cohort of patients with potential drivers of persistent atrial fibrillation. In a computational study using a monodomain Maleckar model, we demonstrate that in organized rhythms, electrograms successfully track local activation, whereas in atrial fibrillation, electrograms are sensitive to spiral wave distance and number, spiral tip trajectories, and effects of fibrosis. In a clinical study, we analyzed n = 15 patients with persistent atrial fibrillation that was terminated by limited ablation. In five cases, traditional activation maps revealed a spiral wave at sites of termination; in ten cases, electrogram timings were ambiguous and activation maps showed incomplete reentry. By adjusting electrogram timing through computational modeling, we found rotational activation, which was undetectable with conventional methods. Our results demonstrate that computational modeling can identify non-local deflections to improve activation mapping and explain how and where ablation can terminate persistent atrial fibrillation. Our hybrid computational/physiological approach has the potential to optimize map-guided ablation and improve ablation therapy in atrial fibrillation.

Predicting the cardiac toxicity of drugs using a novel multiscale exposure-response simulator

A common but serious side effect of many drugs is torsades de pointes, a rhythm disorder that can have fatal consequences. Torsadogenic risk has traditionally been associated with blockage of a specific potassium channel and an increased recovery period in the electrocardiogram. However, the mechanisms that trigger torsades de pointes remain incompletely understood. Here we establish a computational model to explore how drug-induced effects propagate from the single channel, via the single cell, to the whole heart level. Our mechanistic exposure-response simulator translates block-concentration characteristics for arbitrary drugs into three-dimensional excitation profiles and electrocardiogram recordings to rapidly assess torsadogenic risk. For the drug of dofetilide, we show that this risk is highly dose-dependent: at a concentration of 1x, QT prolongation is 55% but the heart maintains its regular sinus rhythm; at 5.7x, QT prolongation is 102% and the heart spontaneously transitions into torsades de points; at 30x, QT prolongation is 132% and the heart adapts a quasi-depolarized state with numerous rapidly flickering local excitations. Our simulations suggest that neither potassium channel blockage nor QT interval prolongation alone trigger torsades de pointes. The underlying mechanism predicted by our model is early afterdepolarization, which translates into pronounced U waves in the electrocardiogram, a signature that is correctly predicted by our model. Beyond the risk assessment of existing drugs, our exposure-response simulator can become a powerful tool to optimize the co-administration of drugs and, ultimately, guide the design of new drugs toward reducing life threatening drug-induced rhythm disorders in the heart.

Inverse estimation of cardiac activation times via gradient-based optimization

Computational modeling may provide a quantitative framework for integrating multiscale data to gain insight into mechanisms of heart disease, identify and test pharmacological and electrical therapy and interventions, and support clinical decisions. Patient-specific computational cardiac models can help guide such procedures, and cardiac inverse modeling is a promising alternative to adequately personalize these models. Indeed, full cardiac inverse modeling is currently becoming computationally feasible; however, fundamental work to assess the feasibility of emerging techniques is still needed. In this study, we use a partial differential equation-constrained optimal control approach to numerically investigate the identifiability of an initial activation sequence from synthetic (partial) observations of the extracellular potential using the bidomain approximation and 2D representations of cardiac tissue. Our results demonstrate that activation times and duration of several stimuli can be recovered even with high levels of noise, that it is sufficient to sample the observations at the electrocardiogram-relevant sampling frequency of 1 kHz, and that spatial resolutions that are coarser than the standard in electrophysiological simulations can be used. The optimization of activation times is still effective when synthetic data are generated with a different cell membrane kinetics model than optimized for. The findings thus indicate that the presented approach has potential for finding activation sequences from clinical data modalities, as an extension to existing cardiac imaging approaches.

Uncertainty quantification of 2 models of cardiac electromechanics

Computational models of the heart have reached a maturity level that render them useful for in silico studies of arrhythmia and other cardiac diseases. However, the translation to the clinic of cardiac simulations critically depends on demonstrating the accuracy, robustness, and reliability of the underlying computational models under the presence of uncertainties. In this work, we study for the first time the effect of parameter uncertainty on 2 state-of-the-art coupled models of excitation-contraction of cardiac tissue. To this end, we perform forward uncertainty propagation and sensitivity analyses to understand how variability in key maximal conductances affect selected quantities of interest, such as the action potential duration (APD₉₀ ), maximum intracellular calcium concentration, cardiac stretch, and stress. Our results suggest a strong linear relationship between selected maximal conductances and quantities of interest for a variability in parameters up to 25%, which justifies the construction of linear response surfaces that are used to compute the empirical probability density functions of all the quantities of interest under study. For both electromechanical models analyzed, uncertainty in the material parameters associated to the passive mechanical response of cardiac tissue does not affect the duration of action potentials, neither the amplitude of intracellular calcium concentrations. Our results confirm the poor mechanoelectric feedback that classical models of cardiac electromechanics have, even under the presence of parameter uncertainty.

Sensitivity analysis of ventricular activation and electrocardiogram in tailored models of heart-failure patients

Cardiac resynchronization therapy is not effective in a variable proportion of heart failure patients. An accurate knowledge of each patient's electroanatomical features could be helpful to determine the most appropriate treatment. The goal of this study was to analyze and quantify the sensitivity of left ventricular (LV) activation and the electrocardiogram (ECG) to changes in 39 parameters used to tune realistic anatomical-electrophysiological models of the heart. Electrical activity in the ventricles was simulated using a reaction-diffusion equation. To simulate cellular electrophysiology, the Ten Tusscher-Panfilov 2006 model was used. Intracardiac electrograms and 12-lead ECGs were computed by solving the bidomain equation. Parameters showing the highest sensitivity values were similar in the six patients studied. QRS complex and LV activation times were modulated by the sodium current, the cell surface-to-volume ratio in the LV, and tissue conductivities. The T-wave was modulated by the calcium and rectifier-potassium currents, and the cell surface-to-volume ratio in both ventricles. We conclude that homogeneous changes in ionic currents entail similar effects in all ECG leads, whereas the effects of changes in tissue properties show larger inter-lead variability. The effects of parameter variations are highly consistent between patients and most of the model tuning could be performed with only ~10 parameters.

Human ventricular activation sequence and the simulation of the electrocardiographic QRS complex and its variability in healthy and intraventricular block conditions

Aims

To investigate how variability in activation sequence and passive conduction properties translates into clinical variability in QRS biomarkers, and gain novel physiological knowledge on the information contained in the human QRS complex.

Methods and results

Multiscale bidomain simulations using a detailed heart-torso human anatomical model are performed to investigate the impact of activation sequence characteristics on clinical QRS biomarkers. Activation sequences are built and validated against experimentally-derived ex vivo and in vivo human activation data. R-peak amplitude exhibits the largest variability in terms of QRS morphology, due to its simultaneous modulation by activation sequence speed, myocardial intracellular and extracellular conductivities, and propagation through the human torso. QRS width, however, is regulated by endocardial activation speed and intracellular myocardial conductivities, whereas QR intervals are only affected by the endocardial activation profile. Variability in the apico-basal location of activation sites on the anterior and posterior left ventricular wall is associated with S-wave progression in limb and precordial leads, respectively, and occasional notched QRS complexes in precordial derivations. Variability in the number of early activation sites successfully reproduces pathological abnormalities of the human conduction system in the QRS complex.

Conclusion

Variability in activation sequence and passive conduction properties captures and explains a large part of the clinical variability observed in the human QRS complex. Our physiological insights allow for a deeper interpretation of human QRS biomarkers in terms of QRS morphology and location of early endocardial activation sites. This might be used to attain a better patient-specific knowledge of activation sequence from routine body-surface electrocardiograms.

The importance of mechano-electrical feedback and inertia in cardiac electromechanics

In the past years, a number cardiac electromechanics models have been developed to better understand the excitation-contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechanoelectrical feedback and inertia in cardiac electromechanics.

The fractal heart - embracing mathematics in the cardiology clinic

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.