Simulating human cardiac electrophysiology on clinical time-scales

Evaluating computational efforts and physiological resolution of mathematical models of cardiac tissue

Computational techniques have significantly advanced our understanding of cardiac electrophysiology, yet they have predominantly concentrated on averaged models that do not represent the intricate dynamics near individual cardiomyocytes. Recently, accurate models representing individual cells have gained popularity, enabling analysis of the electrophysiology at the micrometer level. Here, we evaluate five mathematical models to determine their computational efficiency and physiological fidelity. Our findings reveal that cell-based models introduced in recent literature offer both efficiency and precision for simulating small tissue samples (comprising thousands of cardiomyocytes). Conversely, the traditional bidomain model and its simplified counterpart, the monodomain model, are more appropriate for larger tissue masses (encompassing millions to billions of cardiomyocytes). For simulations requiring detailed parameter variations along individual cell membranes, the EMI model emerges as the only viable choice. This model distinctively accounts for the extracellular (E), membrane (M), and intracellular (I) spaces, providing a comprehensive framework for detailed studies. Nonetheless, the EMI model's applicability to large-scale tissues is limited by its substantial computational demands for subcellular resolution.

The simplified Kirchhoff network model (SKNM): a cell-based reaction-diffusion model of excitable tissue

Cell-based models of excitable tissues offer the advantage of cell-level precision, which cannot be achieved using traditional homogenized electrophysiological models. However, this enhanced accuracy comes at the cost of increased computational demands, necessitating the development of efficient cell-based models. The widely-accepted bidomain model serves as the standard in computational cardiac electrophysiology, and under certain anisotropy ratio conditions, it is well known that it can be reduced to the simpler monodomain model. Recently, the Kirchhoff Network Model (KNM) was developed as a cell-based counterpart to the bidomain model. In this paper, we aim to demonstrate that KNM can be simplified using the same steps employed to derive the monodomain model from the bidomain model. We present the cell-based Simplified Kirchhoff Network Model (SKNM), which produces results closely aligned with those of KNM while requiring significantly less computational resources.

Efficient, cell-based simulations of cardiac electrophysiology; The Kirchhoff Network Model (KNM)

Mathematical models based on homogenized representation of cardiac tissue have greatly improved our understanding of cardiac electrophysiology. However, these models are too coarse to investigate the dynamics at the level of the myocytes since the cells are not present in homogenized models. Recently, fine scale models have been proposed to allow for cell-level resolution of the dynamics, but these models are too computationally expensive to be used in applications like whole heart simulations of large animals. To address this issue, we propose a model that balances computational demands and physiological accuracy. The model is founded on Kirchhoff's current law, and represents every myocyte in the tissue. This allows specific properties to be assigned to individual cardiomyocytes, and other cell types like fibroblasts can be added to the model in an accurate manner while keeping the computing efforts reasonable.

An inner-outer subcycling algorithm for parallel cardiac electrophysiology simulations

This paper explores cardiac electrophysiological simulations of the monodomain equations and introduces a novel subcycling time integration algorithm to exploit the structure of the ionic model. The aim of this work is to improve upon the efficiency of parallel cardiac monodomain simulations by using our subcycling algorithm in the computation of the ionic model to handle the local sharp changes of the solution. This will reduce the turnaround time for the simulation of basic cardiac electrical function on both idealized and patient-specific geometry. Numerical experiments show that the proposed approach is accurate and also has close to linear parallel scalability on a computer with more than 1000 processor cores. Ultimately, the reduction in simulation time can be beneficial in clinical applications, where multiple simulations are often required to tune a model to match clinical measurements.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

An automated near-real time computational method for induction and treatment of scar-related ventricular tachycardias

Catheter ablation is currently the only curative treatment for scar-related ventricular tachycardias (VTs). However, not only are ablation procedures long, with relatively high risk, but success rates are punitively low, with frequent VT recurrence. Personalized in-silico approaches have the opportunity to address these limitations. However, state-of-the-art reaction diffusion (R-D) simulations of VT induction and subsequent circuits used for in-silico ablation target identification require long execution times, along with vast computational resources, which are incompatible with the clinical workflow. Here, we present the Virtual Induction and Treatment of Arrhythmias (VITA), a novel, rapid and fully automated computational approach that uses reaction-Eikonal methodology to induce VT and identify subsequent ablation targets. The rationale for VITA is based on finding isosurfaces associated with an activation wavefront that splits in the ventricles due to the presence of an isolated isthmus of conduction within the scar; once identified, each isthmus may be assessed for their vulnerability to sustain a reentrant circuit, and the corresponding exit site automatically identified for potential ablation targeting. VITA was tested on a virtual cohort of 7 post-infarcted porcine hearts and the results compared to R-D simulations. Using only a standard desktop machine, VITA could detect all scar-related VTs, simulating activation time maps and ECGs (for clinical comparison) as well as computing ablation targets in 48 minutes. The comparable VTs probed by the R-D simulations took 68.5 hours on 256 cores of high-performance computing infrastructure. The set of lesions computed by VITA was shown to render the ventricular model VT-free. VITA could be used in near real-time as a complementary modality aiding in clinical decision-making in the treatment of post-infarction VTs.

Resource-Efficient Use of Modern Processor Architectures For Numerically Solving Cardiac Ionic Cell Models

A central component in simulating cardiac electrophysiology is the numerical solution of nonlinear ordinary differential equations, also called cardiac ionic cell models, that describe cross-cell-membrane ion transport. Biophysically detailed cell models often require a considerable amount of computation, including calls to special mathematical functions. This paper systematically studies how to efficiently use modern multicore CPUs for this costly computational task. We start by investigating the code restructurings needed to effectively enable compiler-supported SIMD vectorisation, which is the most important performance booster in this context. It is found that suitable OpenMP directives are sufficient for achieving both vectorisation and parallelisation. We then continue with an evaluation of the performance optimisation technique of using lookup tables. Due to increased challenges for automated vectorisation, the obtainable benefits of lookup tables are dependent on the hardware platforms chosen. Throughout the study, we report detailed time measurements obtained on Intel Xeon, Xeon Phi, AMD Epyc and two ARM processors including Fujitsu A64FX, while attention is also paid to the impact of SIMD vectorisation and lookup tables on the computational accuracy. As a realistic example, the benefits of performance enhancement are demonstrated by a 109-run ensemble on the Oakforest-PACS system, where code restructurings and SIMD vectorisation yield an 84% reduction in computing time, corresponding to 63,270 node hours.

Arrhythmogenic influence of mutations in a myocyte-based computational model of the pulmonary vein sleeve

In the heart, electrophysiological dysregulation arises from defects at many biological levels (from point mutations in ion channel proteins to gross structural abnormalities). These defects disrupt the normal pattern of electrical activation, producing ectopic activity and reentrant arrhythmia. To interrogate mechanisms that link these primary biological defects to macroscopic electrophysiologic dysregulation most prior computational studies have utilized either (i) detailed models of myocyte ion channel dynamics at limited spatial scales, or (ii) homogenized models of action potential conduction that reproduce arrhythmic activity at tissue and organ levels. Here we apply our recent model (EMI), which integrates electrical activation and propagation across these scales, to study human atrial arrhythmias originating in the pulmonary vein (PV) sleeves. These small structures initiate most supraventricular arrhythmias and include pronounced myocyte-to-myocyte heterogeneities in ion channel expression and intercellular coupling. To test EMI's cell-based architecture in this physiological context we asked whether ion channel mutations known to underlie atrial fibrillation are capable of initiating arrhythmogenic behavior via increased excitability or reentry in a schematic PV sleeve geometry. Our results illustrate that EMI's improved spatial resolution can directly interrogate how electrophysiological changes at the individual myocyte level manifest in tissue and as arrhythmia in the PV sleeve.

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

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

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

From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.

POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.

The openCARP simulation environment for cardiac electrophysiology

BACKGROUND AND OBJECTIVE

Cardiac electrophysiology is a medical specialty with a long and rich tradition of computational modeling. Nevertheless, no community standard for cardiac electrophysiology simulation software has evolved yet. Here, we present the openCARP simulation environment as one solution that could foster the needs of large parts of this community.

METHODS AND RESULTS

openCARP and the Python-based carputils framework allow developing and sharing simulation pipelines which automate in silico experiments including all modeling and simulation steps to increase reproducibility and productivity. The continuously expanding openCARP user community is supported by tailored infrastructure. Documentation and training material facilitate access to this complementary research tool for new users. After a brief historic review, this paper summarizes requirements for a high-usability electrophysiology simulator and describes how openCARP fulfills them. We introduce the openCARP modeling workflow in a multi-scale example of atrial fibrillation simulations on single cell, tissue, organ and body level and finally outline future development potential.

CONCLUSION

As an open simulator, openCARP can advance the computational cardiac electrophysiology field by making state-of-the-art simulations accessible. In combination with the carputils framework, it offers a tailored software solution for the scientific community and contributes towards increasing use, transparency, standardization and reproducibility of in silico experiments.

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.

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.

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

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

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.

Creation and application of virtual patient cohorts of heart models

Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Accelerating simulations of cardiac electrical dynamics through a multi-GPU platform and an optimized data structure

Simulations of cardiac electrophysiological models in tissue, particularly in 3D require the solutions of billions of differential equations even for just a couple of milliseconds, thus highly demanding in computational resources. In fact, even studies in small domains with very complex models may take several hours to reproduce seconds of electrical cardiac behavior. Today's Graphics Processor Units (GPUs) are becoming a way to accelerate such simulations, and give the added possibilities to run them locally without the need for supercomputers. Nevertheless, when using GPUs, bottlenecks related to global memory access caused by the spatial discretization of the large tissue domains being simulated, become a big challenge. For simulations in a single GPU, we propose a strategy to accelerate the computation of the diffusion term through a data-structure and memory access pattern designed to maximize coalescent memory transactions and minimize branch divergence, achieving results approximately 1.4 times faster than a standard GPU method. We also combine this data structure with a designed communication strategy to take advantage in the case of simulations in multi-GPU platforms. We demonstrate that, in the multi-GPU approach performs, simulations in 3D tissue can be just 4× slower than real time.

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.

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.

Differential effect with septal and apical RV pacing on ventricular activation in patients with left bundle branch block assessed by non-invasive electrical imaging and in silico modelling

Purpose

It is uncertain whether right ventricular (RV) lead position in cardiac resynchronization therapy impacts response. There has been little detailed analysis of the activation patterns in RV septal pacing (RVSP), especially in the CRT population. We compare left bundle branch block (LBBB) activation patterns with RV pacing (RVP) within the same patients with further comparison between RV apical pacing (RVAP) and RVSP.

Methods

Body surface mapping was undertaken in 14 LBBB patients after CRT implantation. Nine patients had RVAP, 5 patients had RVSP. Activation parameters included left ventricular total activation time (LVtat), biventricular total activation time (VVtat), interventricular electrical synchronicity (VVsync), and dispersion of left ventricular activation times (LVdisp). The direction of activation wave front was also compared in each patient (wave front angle (WFA)). In silico computer modelling was applied to assess the effect of RVAP and RVSP in order to validate the clinical results.

Results

Patients were aged 64.6 ± 12.2 years, 12 were male, 8 were ischemic. Baseline QRS durations were 157 ± 18 ms. There was no difference in VVtat between RVP and LBBB but a longer LVtat in RVP (102.8 ± 19.6 vs. 87.4 ± 21.1 ms, p = 0.046). VVsync was significantly greater in LBBB (45.1 ± 20.2 vs. 35.9 ± 17.1 ms, p = 0.01) but LVdisp was greater in RVP (33.4 ± 5.9 vs. 27.6 ± 6.9 ms, p = 0.025). WFA did rotate clockwise with RVP vs. LBBB (82.5 ± 25.2 vs. 62.1 ± 31.7 ^op = 0.026). None of the measurements were different to LBBB with RVSP; however, the differences were preserved with RVAP for VVsync, LVdisp, and WFA. In silico modelling corroborated these results.

Conclusions

RVAP activation differs from LBBB where RVSP appears similar.

Trial registration

(ClinicalTrials.gov identifier: NCT01831518)

Electronic supplementary material

The online version of this article (10.1007/s10840-019-00567-2) contains supplementary material, which is available to authorized users.

The Left and Right Ventricles Respond Differently to Variation of Pacing Delays in Cardiac Resynchronization Therapy: A Combined Experimental- Computational Approach

Introduction: Timing of atrial, right (RV), and left ventricular (LV) stimulation in cardiac resynchronization therapy (CRT) is known to affect electrical activation and pump function of the LV. In this study, we used computer simulations, with input from animal experiments, to investigate the effect of varying pacing delays on both LV and RV electrical dyssynchrony and contractile function.

Methods: A pacing protocol was performed in dogs with atrioventricular block (N = 6), using 100 different combinations of atrial (A)-LV and A-RV pacing delays. Regional LV and RV electrical activation times were measured using 112 electrodes and LV and RV pressures were measured with catheter-tip micromanometers. Contractile response to a pacing delay was defined as relative change of the maximum rate of LV and RV pressure rise (dP/dt_max) compared to RV pacing with an A-RV delay of 125 ms. The pacing protocol was simulated in the CircAdapt model of cardiovascular system dynamics, using the experimentally acquired electrical mapping data as input.

Results: Ventricular electrical activation changed with changes in the amount of LV or RV pre-excitation. The resulting changes in dP/dt_max differed markedly between the LV and RV. Pacing the LV 10–50 ms before the RV led to the largest increases in LV dP/dt_max. In contrast, RV dP/dt_max was highest with RV pre-excitation and decreased up to 33% with LV pre-excitation. These opposite patterns of changes in RV and LV dP/dt_max were reproduced by the simulations. The simulations extended these observations by showing that changes in steady-state biventricular cardiac output differed from changes in both LV and RV dP/dt_max. The model allowed to explain the discrepant changes in dP/dt_max and cardiac output by coupling between atria and ventricles as well as between the ventricles.

Conclusion: The LV and the RV respond in a opposite manner to variation in the amount of LV or RV pre-excitation. Computer simulations capture LV and RV behavior during pacing delay variation and may be used in the design of new CRT optimization studies.

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.

A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

A work flow to build and validate patient specific left atrium electrophysiology models from catheter measurements

Biophysical models of the atrium provide a physically constrained framework for describing the current state of an atrium and allow predictions of how that atrium will respond to therapy. We propose a work flow to simulate patient specific electrophysiological heterogeneity from clinical data and validate the resulting biophysical models. In 7 patients, we recorded the atrial anatomy with an electroanatomical mapping system (St Jude Velocity); we then applied an S1-S2 electrical stimulation protocol from the coronary sinus (CS) and the high right atrium (HRA) whilst recording the activation patterns using a PentaRay catheter with 10 bipolar electrodes at 12 ± 2 sites across the atrium. Using only the activation times measured with a PentaRay catheter and caused by a stimulus applied in the CS with a remote catheter we fitted the four parameters for a modified Mitchell-Schaeffer model and the tissue conductivity to the recorded local conduction velocity restitution curve and estimated local effective refractory period. Model parameters were then interpolated across each atrium. The fitted model recapitulated the S1-S2 activation times for CS pacing giving a correlation ranging between 0.81 and 0.98. The model was validated by comparing simulated activations times with the independently recorded HRA pacing S1-S2 activation times, giving a correlation ranging between 0.65 and 0.96. The resulting work flow provides the first validated cohort of models that capture clinically measured patient specific electrophysiological heterogeneity.

Fast uncertainty quantification of activation sequences in patient-specific cardiac electrophysiology meeting clinical time constraints

We present a fast, patient-specific methodology for uncertainty quantification in electrophysiology, aimed at meeting the time constraints of clinical practitioners. We focus on computing the statistics of the activation map, given the uncertainties associated with the conductivity tensor modeling the fiber orientation in the heart. We use a fast parallel solution method implemented on a graphics processing unit for the eikonal approximation, in order to compute the activation map and to sample the random fiber field with correlation on the basis of geodesic distances. While this enables to perform uncertainty quantification studies with a manageable computational effort, the required time frame still exceeds clinically suitable time expectations. In order to reduce it further by 2 orders of magnitude, we rely on Bayesian multifidelity methods. In particular, we propose a low-fidelity model that is patient-specific and free from the additional training cost associated with reduced models. This is achieved by a sound physics-based simplification of the full eikonal model. The low-fidelity output is then corrected by the standard multifidelity framework. In practice, the complete procedure only requires approximately 100 new runs of our eikonal graphics processing unit solver for producing the sought estimates and their associated credible intervals, enabling a full online analysis in less than 5 minutes.

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.

Comparing two sequential Monte Carlo samplers for exact and approximate Bayesian inference on biological models

Bayesian methods are advantageous for biological modelling studies due to their ability to quantify and characterize posterior variability in model parameters. When Bayesian methods cannot be applied, due either to non-determinism in the model or limitations on system observability, approximate Bayesian computation (ABC) methods can be used to similar effect, despite producing inflated estimates of the true posterior variance. Owing to generally differing application domains, there are few studies comparing Bayesian and ABC methods, and thus there is little understanding of the properties and magnitude of this uncertainty inflation. To address this problem, we present two popular strategies for ABC sampling that we have adapted to perform exact Bayesian inference, and compare them on several model problems. We find that one sampler was impractical for exact inference due to its sensitivity to a key normalizing constant, and additionally highlight sensitivities of both samplers to various algorithmic parameters and model conditions. We conclude with a study of the O'Hara-Rudy cardiac action potential model to quantify the uncertainty amplification resulting from employing ABC using a set of clinically relevant biomarkers. We hope that this work serves to guide the implementation and comparative assessment of Bayesian and ABC sampling techniques in biological models.

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.

Computational Modeling for Cardiac Resynchronization Therapy

Cardiac resynchronization therapy (CRT) is an effective treatment for heart failure (HF) patients with an electrical substrate pathology causing ventricular dyssynchrony. However 40-50% of patients do not respond to treatment. Cardiac modeling of the electrophysiology, electromechanics, and hemodynamics of the heart has been used to study mechanisms behind HF pathology and CRT response. Recently, multi-scale dyssynchronous HF models have been used to study optimal device settings and optimal lead locations, investigate the underlying cardiac pathophysiology, as well as investigate emerging technologies proposed to treat cardiac dyssynchrony. However the breadth of patient and experimental data required to create and parameterize these models and the computational resources required currently limits the use of these models to small patient numbers. In the future, once these technical challenges are overcome, biophysically based models of the heart have the potential to become a clinical tool to aid in the diagnosis and treatment of HF.

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

Anatomically accurate and biophysically detailed bidomain models of the human heart have proven a powerful tool for gaining quantitative insight into the links between electrical sources in the myocardium and the concomitant current flow in the surrounding medium as they represent their relationship mechanistically based on first principles. Such models are increasingly considered as a clinical research tool with the perspective of being used, ultimately, as a complementary diagnostic modality. An important prerequisite in many clinical modeling applications is the ability of models to faithfully replicate potential maps and electrograms recorded from a given patient. However, while the personalization of electrophysiology models based on the gold standard bidomain formulation is in principle feasible, the associated computational expenses are significant, rendering their use incompatible with clinical time frames. In this study we report on the development of a novel computationally efficient reaction-eikonal (R-E) model for modeling extracellular potential maps and electrograms. Using a biventricular human electrophysiology model, which incorporates a topologically realistic His-Purkinje system (HPS), we demonstrate by comparing against a high-resolution reaction-diffusion (R-D) bidomain model that the R-E model predicts extracellular potential fields, electrograms as well as ECGs at the body surface with high fidelity and offers vast computational savings greater than three orders of magnitude. Due to their efficiency R-E models are ideally suitable for forward simulations in clinical modeling studies which attempt to personalize electrophysiological model features.

Analysis of lead placement optimization metrics in cardiac resynchronization therapy with computational modelling

AIMS

The efficacy of cardiac resynchronization therapy (CRT) is known to vary considerably with pacing location, however the most effective set of metrics by which to select the optimal pacing site is not yet well understood. Computational modelling offers a powerful methodology to comprehensively test the effect of pacing location in silico and investigate how to best optimize therapy using clinically available metrics for the individual patient.

METHODS AND RESULTS

Personalized computational models of cardiac electromechanics were used to perform an in silico left ventricle (LV) pacing site optimization study as part of biventricular CRT in three patient cases. Maps of response to therapy according to changes in total activation time (ΔTAT) and acute haemodynamic response (AHR) were generated and compared with preclinical metrics of electrical function, strain, stress, and mechanical work to assess their suitability for selecting the optimal pacing site. In all three patients, response to therapy was highly sensitive to pacing location, with laterobasal locations being optimal. ΔTAT and AHR were found to be correlated (ρ < -0.80), as were AHR and the preclinical activation time at the pacing site (ρ ≥ 0.73), however pacing in the last activated site did not result in the optimal response to therapy in all cases.

CONCLUSION

This computational modelling study supports pacing in laterobasal locations, optimizing pacing site by minimizing paced QRS duration and pacing in regions activated late at sinus rhythm. Results demonstrate information content is redundant using multiple preclinical metrics. Of significance, the correlation of AHR with ΔTAT indicates that minimization of QRSd is a promising metric for optimization of lead placement.

Biophysical Modeling to Determine the Optimization of Left Ventricular Pacing Site and AV/VV Delays in the Acute and Chronic Phase of Cardiac Resynchronization Therapy

BACKGROUND

Cardiac anatomy and function adapt in response to chronic cardiac resynchronization therapy (CRT). The effects of these changes on the optimal left ventricle (LV) lead location and timing delay settings have yet to be fully explored.

OBJECTIVE

To predict the effects of chronic CRT on the optimal LV lead location and device timing settings over time.

METHODS

Biophysical computational cardiac models were generated for 3 patients, immediately post-implant (ACUTE) and after at least 6 months of CRT (CHRONIC). Optimal LV pacing area and device settings were predicted by pacing the ACUTE and CHRONIC models across the LV epicardium (49 sites each) with a range of 9 pacing settings and simulating the acute hemodynamic response (AHR) of the heart.

RESULTS

There were statistically significant differences between the distribution of the AHR in the ACUTE and CHRONIC models (P < 0.0005 in all cases). The site delivering the maximal AHR shifted location between the ACUTE and CHRONIC models but provided a negligible improvement (<2%). The majority of the acute optimal LV pacing regions (76-100%) and device settings (76-91%) remained optimal chronically.

CONCLUSION

Optimization of the LV pacing location and device settings were important at the time of implant, with a reduced benefit over time, where the majority of the acute optimal LV pacing region and device settings remained optimal with chronic CRT.

Using physiologically based models for clinical translation: predictive modelling, data interpretation or something in-between?

Heart disease continues to be a significant clinical problem in Western society. Predictive models and simulations that integrate physiological understanding with patient information derived from clinical data have huge potential to contribute to improving our understanding of both the progression and treatment of heart disease. In particular they provide the potential to improve patient selection and optimisation of cardiovascular interventions across a range of pathologies. Currently a significant proportion of this potential is still to be realised. In this paper we discuss the opportunities and challenges associated with this realisation. Reviewing the successful elements of model translation for biophysically based models and the emerging supporting technologies, we propose three distinct modes of clinical translation. Finally we outline the challenges ahead that will be fundamental to overcome if the ultimate goal of fully personalised clinical cardiac care is to be achieved.

Space-discretization error analysis and stabilization schemes for conduction velocity in cardiac electrophysiology

In cardiac electrophysiology, the propagation of the action potential may be described by a set of reaction-diffusion equations known as the bidomain model. The shape of the solution is determined by a balance of a strong reaction and a relatively weak diffusion, which leads to steep variations in space and time. From a numerical point of view, the sharp spatial gradients may be seen as particularly problematic, because computational grid resolution on the order of 0.1 mm or less is required, yielding considerable computational efforts on human geometries. In this paper, we discuss a number of well-known numerical schemes for the bidomain equation and show how the quality of the solution is affected by the spatial discretization. In particular, we study in detail the effect of discretization on the conduction velocity (CV), which is an important quantity from a physiological point of view. We show that commonly applied finite element techniques tend to overestimate the CV on coarse grids, while it tends to be underestimated by finite difference schemes. Furthermore, the choice of interpolation and discretization scheme for the nonlinear reaction term has a strong impact on the CV. Finally, we exploit the results of the error analysis to propose improved numerical methods, including a stabilized scheme that tends to correct the CV on coarse grids but converges to the correct solution as the grid is refined. Copyright © 2016 John Wiley & Sons, Ltd.

A two-variable model robust to pacemaker behaviour for the dynamics of the cardiac action potential

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Simplified cardiomyocyte electrophysiology model optimised for patient specific modelling.

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Modified Mitchell and Schaeffer model.

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No spurious pacemaker behaviour.

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Suitable for parameter fitting.

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Consistent leading order APD approximation.

Ionic models with two state variables are routinely used in patient specific electro-physiology simulations due to the small number of parameters to be constrained and their computational tractability. Among these models, the Mitchell and Schaeffer (MS) action potential model is often used in ventricle electro-physiology due to its ability to reproduce the shape of the action potential and its restitution properties. However, for some choices of parameters characterising this ionic model, unwanted pacemaker behaviour is present. The absence of any a priori criterion to exclude unstable parameter combinations affects parameter fitting algorithms, as unphysiological solutions can only be discarded a posteriori. In this paper we propose an adaptation of the MS model that does not exhibit pacemaker behaviour for any combination of the parameters. The robustness to pacemaker behaviour makes this model suitable for inverse problem applications.

PDE constrained optimization of electrical defibrillation in a 3D ventricular slice geometry

A computational study of an optimal control approach for cardiac defibrillation in a 3D geometry is presented. The cardiac bioelectric activity at the tissue and bath volumes is modeled by the bidomain model equations. The model includes intramural fiber rotation, axially symmetric around the fiber direction, and anisotropic conductivity coefficients, which are extracted from a histological image. The dynamics of the ionic currents are based on the regularized Mitchell-Schaeffer model. The controls enter in the form of electrodes, which are placed at the boundary of the bath volume with the goal of dampening undesired arrhythmias. The numerical optimization is based on Newton techniques. We demonstrated the parallel architecture environment for the computation of potentials on multidomains and for the higher order optimization techniques.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

Parallel Optimization of 3D Cardiac Electrophysiological Model Using GPU

Large-scale 3D virtual heart model simulations are highly demanding in computational resources. This imposes a big challenge to the traditional computation resources based on CPU environment, which already cannot meet the requirement of the whole computation demands or are not easily available due to expensive costs. GPU as a parallel computing environment therefore provides an alternative to solve the large-scale computational problems of whole heart modeling. In this study, using a 3D sheep atrial model as a test bed, we developed a GPU-based simulation algorithm to simulate the conduction of electrical excitation waves in the 3D atria. In the GPU algorithm, a multicellular tissue model was split into two components: one is the single cell model (ordinary differential equation) and the other is the diffusion term of the monodomain model (partial differential equation). Such a decoupling enabled realization of the GPU parallel algorithm. Furthermore, several optimization strategies were proposed based on the features of the virtual heart model, which enabled a 200-fold speedup as compared to a CPU implementation. In conclusion, an optimized GPU algorithm has been developed that provides an economic and powerful platform for 3D whole heart simulations.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

Beneficial Effect on Cardiac Resynchronization From Left Ventricular Endocardial Pacing Is Mediated by Early Access to High Conduction Velocity Tissue: Electrophysiological Simulation Study

BACKGROUND

Cardiac resynchronization therapy (CRT) delivered via left ventricular (LV) endocardial pacing (ENDO-CRT) is associated with improved acute hemodynamic response compared with LV epicardial pacing (EPI-CRT). The role of cardiac anatomy and physiology in this improved response remains controversial. We used computational electrophysiological models to quantify the role of cardiac geometry, tissue anisotropy, and the presence of fast endocardial conduction on myocardial activation during ENDO-CRT and EPI-CRT.

METHODS AND RESULTS

Cardiac activation was simulated using the monodomain tissue excitation model in 2-dimensional (2D) canine and human and 3D canine biventricular models. The latest activation times (LATs) for LV endocardial and biventricular epicardial tissue were calculated (LVLAT and TLAT), as well the percentage decrease in LATs for endocardial (en) versus epicardial (ep) LV pacing (defined as %dLV=100×(LVLATep-LVLATen)/LVLATep and %dT=100×(TLATep-TLATen)/TLATep, respectively). Normal canine cardiac anatomy is responsible for %dLV and %dT values of 7.4% and 5.5%, respectively. Concentric and eccentric remodeled anatomies resulted in %dT values of 15.6% and 1.3%, respectively. The 3D biventricular-paced canine model resulted in %dLV and %dT values of -7.1% and 1.5%, in contrast to the experimental observations of 16% and 11%, respectively. Adding fast endocardial conduction to this model altered %dLV and %dT to 13.1% and 10.1%, respectively.

CONCLUSIONS

Our results provide a physiological explanation for improved response to ENDO-CRT. We predict that patients with viable fast-conducting endocardial tissue or distal Purkinje network or both, as well as concentric remodeling, are more likely to benefit from reduced ATs and increased synchrony arising from endocardial pacing.

Three-dimensional atrial wall thickness maps to inform catheter ablation procedures for atrial fibrillation

AIMS

Transmural lesion formation is critical to success in atrial fibrillation ablation and is dependent on left atrial wall thickness (LAWT). Pre- and peri-procedural planning may benefit from LAWT measurements.

METHODS AND RESULTS

To calculate the LAWT, the Laplace equation was solved over a finite element mesh of the left atrium derived from the segmented computed tomographic angiography (CTA) dataset. Local LAWT was then calculated from the length of field lines derived from the Laplace solution that spanned the wall from the endocardium or epicardium. The method was validated on an atrium phantom and retrospectively applied to 10 patients who underwent routine coronary CTA for standard clinical indications at our institute. The Laplace wall thickness algorithm was validated on the left atrium phantom. Wall thickness measurements had errors of <0.2 mm for thicknesses of 0.5-5.0 mm that are attributed to image resolution and segmentation artefacts. Left atrial wall thickness measurements were performed on 10 patients. Successful comprehensive LAWT maps were generated in all patients from the coronary CTA images. Mean LAWT measurements ranged from 0.6 to 1.0 mm and showed significant inter and intra patient variability.

CONCLUSIONS

Left atrial wall thickness can be measured robustly and efficiently across the whole left atrium using a solution of the Laplace equation over a finite element mesh of the left atrium. Further studies are indicated to determine whether the integration of LAWT maps into pre-existing 3D anatomical mapping systems may provide important anatomical information for guiding radiofrequency ablation.

Increased cell membrane capacitance is the dominant mechanism of stretch-dependent conduction slowing in the rabbit heart: a computational study

Volume loading of the cardiac ventricles is known to slow electrical conduction in the rabbit heart, but the mechanisms remain unclear. Previous experimental and modeling studies have investigated some of these mechanisms, including stretch-activated membrane currents, reduced gap junctional conductance, and altered cell membrane capacitance. In order to quantify the relative contributions of these mechanisms, we combined a monomain model of rabbit ventricular electrophysiology with a hyperelastic model of passive ventricular mechanics. First, a simplified geometric model with prescribed homogeneous deformation was used to fit model parameters and characterize individual MEF mechanisms, and showed good qualitative agreement with experimentally measured strain-CV relations. A 3D model of the rabbit left and right ventricles was then compared with experimental measurements from optical electrical mapping studies in the isolated rabbit heart. The model was inflated to an end-diastolic pressure of 30 mmHg, resulting in epicardial strains comparable to those measured in the anterior left ventricular free wall. While the effects of stretch activated channels did alter epicardial conduction velocity, an increase in cellular capacitance was required to explain previously reported experimental results. The new results suggest that for large strains, various mechanisms can combine and produce a biphasic relationship between strain and conduction velocity. However, at the moderate strains generated by high end-diastolic pressure, a stretch-induced increase in myocyte membrane capacitance is the dominant driver of conduction slowing during ventricular volume loading.

Imaging of Ventricular Fibrillation and Defibrillation: The Virtual Electrode Hypothesis

Ventricular fibrillation is the major underlying cause of sudden cardiac death. Understanding the complex activation patterns that give rise to ventricular fibrillation requires high resolution mapping of localized activation. The use of multi-electrode mapping unraveled re-entrant activation patterns that underlie ventricular fibrillation. However, optical mapping contributed critically to understanding the mechanism of defibrillation, where multi-electrode recordings could not measure activation patterns during and immediately after a shock. In addition, optical mapping visualizes the virtual electrodes that are generated during stimulation and defibrillation pulses, which contributed to the formulation of the virtual electrode hypothesis. The generation of virtual electrode induced phase singularities during defibrillation is arrhythmogenic and may lead to the induction of fibrillation subsequent to defibrillation. Defibrillating with low energy may circumvent this problem. Therefore, the current challenge is to use the knowledge provided by optical mapping to develop a low energy approach of defibrillation, which may lead to more successful defibrillation.