Cardiac bidomain bath-loading effects during arrhythmias: interaction with anatomical heterogeneity

Impact of electrode orientation, myocardial wall thickness, and myofiber direction on intracardiac electrograms: numerical modeling and analytical solutions

Intracardiac electrograms (iEGMs) are time traces of the electrical potential recorded close to the heart muscle. We calculate unipolar and bipolar iEGMs analytically for a myocardial slab with parallel myofibers and validate them against numerical bidomain simulations. The analytical solution obtained via the method of mirrors is an infinite series of arctangents. It goes beyond the solid angle theory and is in good agreement with the simulations, even though bath loading effects were not accounted for in the analytical calculation. At a large distance from the myocardium, iEGMs decay as 1/R (unipolar), 1/R ² (bipolar and parallel), and 1/R ³ (bipolar and perpendicular to the endocardium). At the endocardial surface, there is a mathematical branch cut. Here, we show how a thicker myocardium generates iEGMs with larger amplitudes and how anisotropy affects the iEGM width and amplitude. If only the leading-order term of our expansion is retained, it can be determined how the conductivities of the bath, torso, myocardium, and myofiber direction together determine the iEGM amplitude. Our results will be useful in the quantitative interpretation of iEGMs, the selection of thresholds to characterize viable tissues, and for future inferences of tissue parameters.

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.

Parameter variations in personalized electrophysiological models of human heart ventricles

The objectives of this study were to evaluate the accuracy of personalized numerical simulations of the electrical activity in human ventricles by comparing simulated electrocardiograms (ECGs) with real patients’ ECGs and analyzing the sensitivity of the model output to variations in the model parameters. We used standard 12-lead ECGs and up to 224 unipolar body-surface ECGs to record three patients with cardiac resynchronization therapy devices and three patients with focal ventricular tachycardia. Patient-tailored geometrical models of the ventricles, atria, large vessels, liver, and spine were created using computed tomography data. Ten cases of focal ventricular activation were simulated using the bidomain model and the TNNP 2006 cellular model. The population-based values of electrical conductivities and other model parameters were used for accuracy analysis, and their variations were used for sensitivity analysis. The mean correlation coefficient between the simulated and real ECGs varied significantly (from r = 0.29 to r = 0.86) among the simulated cases. A strong mean correlation (r > 0.7) was found in eight of the ten model cases. The accuracy of the ECG simulation varied widely in the same patient depending on the localization of the excitation origin. The sensitivity analysis revealed that variations in the anisotropy ratio, blood conductivity, and cellular apicobasal heterogeneity had the strongest influence on transmembrane potential, while variation in lung conductivity had the greatest influence on body-surface ECGs. Futhermore, the anisotropy ratio predominantly affected the latest activation time and repolarization time dispersion, while the cellular apicobasal heterogeneity mainly affected the dispersion of action potential duration, and variation in lung conductivity mainly led to changes in the amplitudes of ECGs and cardiac electrograms. We also found that the effects of certain parameter variations had specific regional patterns on the cardiac and body surfaces. These observations are useful for further developing personalized cardiac models.

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.

Muscle Thickness and Curvature Influence Atrial Conduction Velocities

Electroanatomical mapping is currently used to provide clinicians with information about the electrophysiological state of the heart and to guide interventions like ablation. These maps can be used to identify ectopic triggers of an arrhythmia such as atrial fibrillation (AF) or changes in the conduction velocity (CV) that have been associated with poor cell to cell coupling or fibrosis. Unfortunately, many factors are known to affect CV, including membrane excitability, pacing rate, wavefront curvature, and bath loading, making interpretation challenging. In this work, we show how endocardial conduction velocities are also affected by the geometrical factors of muscle thickness and wall curvature. Using an idealized three-dimensional strand, we show that transverse conductivities and boundary conditions can slow down or speed up signal propagation, depending on the curvature of the muscle tissue. In fact, a planar wavefront that is parallel to a straight line normal to the mid-surface does not remain normal to the mid-surface in a curved domain. We further demonstrate that the conclusions drawn from the idealized test case can be used to explain spatial changes in conduction velocities in a patient-specific reconstruction of the left atrial posterior wall. The simulations suggest that the widespread assumption of treating atrial muscle as a two-dimensional manifold for electrophysiological simulations will not accurately represent the endocardial conduction velocities in regions of the heart thicker than 0.5 mm with significant wall curvature.

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.

Bidomain Predictions of Virtual Electrode-Induced Make and Break Excitations around Blood Vessels

Introduction and background

Virtual electrodes formed by field stimulation during defibrillation of cardiac tissue play an important role in eliciting activations. It has been suggested that the coronary vasculature is an important source of virtual electrodes, especially during low-energy defibrillation. This work aims to further the understanding of how virtual electrodes from the coronary vasculature influence defibrillation outcomes.

Methods

Using the bidomain model, we investigated how field stimulation elicited activations from virtual electrodes around idealized intramural blood vessels. Strength–interval curves, which quantify the stimulus strength required to elicit wavefront propagation from the vessels at different states of tissue refractoriness, were computed for each idealized geometry.

Results

Make excitations occurred at late diastolic intervals, originating from regions of depolarization around the vessel. Break excitations occurred at early diastolic intervals, whereby the vessels were able to excite surrounding refractory tissue due to the local restoration of excitability by virtual electrode-induced hyperpolarizations. Overall, strength–interval curves had similar morphologies and underlying excitation mechanisms compared with previous experimental and numerical unipolar stimulation studies of cardiac tissue. Including the presence of the vessel wall increased the field strength required for make excitations but decreased the field strength required for break excitations, and the field strength at which break excitations occurred was generally greater than 5 V/cm. Finally, in a more realistic ventricular slice geometry, the proximity of virtual electrodes around subepicardial vessels was seen to cause break excitations in the form of propagating unstable wavelets to the subepicardial layer.

Conclusion

Representing the blood vessel wall microstructure in computational bidomain models of defibrillation is recommended as it significantly alters the electrophysiological response of the vessel to field stimulation. Although vessels may facilitate excitation of relatively refractory tissue via break excitations, the field strength required for this is generally greater than those used in the literature on low-energy defibrillation. However, the high-intensity shocks used in standard defibrillation may elicit break excitation propagation from the coronary vasculature.

Virtual electrodes around anatomical structures and their roles in defibrillation

BACKGROUND

Virtual electrodes from structural/conductivity heterogeneities are known to elicit wavefront propagation, upon field-stimulation, and are thought to be important for defibrillation. In this work we investigate how the constitutive and geometrical parameters associated with such anatomical heterogeneities, represented by endo/epicardial surfaces and intramural surfaces in the form of blood-vessels, affect the virtual electrode patterns produced.

METHODS AND RESULTS

The steady-state bidomain model is used to obtain, using analytical and numerical methods, the virtual electrode patterns created around idealized endocardial trabeculations and blood-vessels. The virtual electrode pattern around blood-vessels is shown to be composed of two dominant effects; current traversing the vessel surface and conductivity heterogeneity from the fibre-architecture. The relative magnitudes of these two effects explain the swapping of the virtual electrode polarity observed, as a function of the vessel radius, and aid in the understanding of the virtual electrode patterns predicted by numerical bidomain modelling. The relatively high conductivity of blood, compared to myocardium, is shown to cause stronger depolarizations in the endocardial trabeculae grooves than the protrusions.

CONCLUSIONS

The results provide additional quantitative understanding of the virtual electrodes produced by small-scale ventricular anatomy, and highlight the importance of faithfully representing the physiology and the physics in the context of computational modelling of field stimulation.

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.

Asymptotic wave propagation in excitable media

Wave shape and velocity are important issues in reaction-diffusion systems, and are often the result of competition in media with heterogeneous conduction properties. Asymptotic wave front propagation at maximal conduction velocity has been previously reported in the context of anisotropic cardiac tissue, but it is unknown whether this is a universal property of excitable tissues where conduction velocity can be locally modulated by mechanisms other than anisotropy. Here, we investigate the impact of conduction heterogeneities and boundary effects on wave propagation in excitable media. Following a theoretical analysis, we find that wave-front cusps occur where local velocity is reduced and that asymptotic wave fronts propagate at the maximal translational conduction velocity. Simulations performed in different reaction-diffusion systems, including cardiac tissue, confirm our theoretical findings. We conclude that this property can be found in a wide range of reaction-diffusion systems with excitable dynamics and that asymptotic wave-front shapes can be predicted.

Structural heterogeneity modulates effective refractory period: a mechanism of focal arrhythmia initiation

Reductions in electrotonic loading around regions of structural and electrophysiological heterogeneity may facilitate capture of focal triggered activity, initiating reentrant arrhythmias. How electrotonic loading, refractoriness and capture of focal ectopics depend upon the intricate nature of physiological structural anatomy, as well as pathological tissue remodelling, however, is not well understood. In this study, we performed computational bidomain simulations with anatomically-detailed models representing the rabbit left ventricle. We used these models to quantify the relationship between local structural anatomy and spatial heterogeneity in action potential (AP) characteristics, electrotonic currents and effective refractory periods (ERPs) under pacing and restitution protocols. Regions surrounding vessel cavities, in addition to tissue surfaces, had significantly lower peak downstream electrotonic currents than well coupled myocardium ( vs A/cm²), with faster maximum AP upstroke velocities ( vs mV/ms), although noticeably very similar APDs ( vs ms) and AP restitution properties. Despite similarities in APDs, ERPs in regions of low electrotonic load in the vicinity of surfaces, intramural vessel cavities and endocardial structures were up to ms shorter compared to neighbouring well-coupled tissue, leading to regions of sharp ERP gradients. Consequently, focal extra-stimuli timed within this window of ERP heterogeneity between neighbouring regions readily induced uni-directional block, inducing reentry. Most effective induction sites were within channels of low ERPs between large vessels and epicardium. Significant differences in ERP driven by reductions in electrotonic loading due to fine-scale physiological structural heterogeneity provides an important mechanism of capture of focal activity and reentry induction. Application to pathological ventricles, particularly myocardial infarction, will have important implications in anti-arrhythmia therapy.

Simulating photon scattering effects in structurally detailed ventricular models using a Monte Carlo approach

Light scattering during optical imaging of electrical activation within the heart is known to significantly distort the optically-recorded action potential (AP) upstroke, as well as affecting the magnitude of the measured response of ventricular tissue to strong electric shocks. Modeling approaches based on the photon diffusion equation have recently been instrumental in quantifying and helping to understand the origin of the resulting distortion. However, they are unable to faithfully represent regions of non-scattering media, such as small cavities within the myocardium which are filled with perfusate during experiments. Stochastic Monte Carlo (MC) approaches allow simulation and tracking of individual photon “packets” as they propagate through tissue with differing scattering properties. Here, we present a novel application of the MC method of photon scattering simulation, applied for the first time to the simulation of cardiac optical mapping signals within unstructured, tetrahedral, finite element computational ventricular models. The method faithfully allows simulation of optical signals over highly-detailed, anatomically-complex MR-based models, including representations of fine-scale anatomy and intramural cavities. We show that optical action potential upstroke is prolonged close to large subepicardial vessels than further away from vessels, at times having a distinct “humped” morphology. Furthermore, we uncover a novel mechanism by which photon scattering effects around vessels cavities interact with “virtual-electrode” regions of strong de-/hyper-polarized tissue surrounding cavities during shocks, significantly reducing the apparent optically-measured epicardial polarization. We therefore demonstrate the importance of this novel optical mapping simulation approach along with highly anatomically-detailed models to fully investigate electrophysiological phenomena driven by fine-scale structural heterogeneity.

The role of Purkinje-myocardial coupling during ventricular arrhythmia: a modeling study

The Purkinje system is the fast conduction network of the heart which couples to the myocardium at discrete sites called Purkinje-Myocyte Junctions (PMJs). However, the distribution and number of PMJs remains elusive, as does whether a particular PMJ is functional. We hypothesized that the Purkinje system plays a role during reentry and that the number of functional PMJs affect reentry dynamics. We used a computer finite element model of rabbit ventricles in which we varied the number of PMJs. Sustained, complex reentry was induced by applying an electric shock and the role of the Purkinje system in maintaining the arrhythmia was assessed by analyzing phase singularities, frequency of activation, and bidirectional propagation at PMJs. For larger junctional resistances, increasing PMJ density increased the mean firing rate in the Purkinje system, the percentage of successful retrograde conduction at PMJs, and the incidence of wave break on the epicardium. However, the mean firing of the ventricles was not affected. Furthermore, increasing PMJ density above 13/ did not alter reentry dynamics. For lower junctional resistances, the trend was not as clear. We conclude that Purkinje system topology affects reentry dynamics and conditions which alter PMJ density can alter reentry dynamics.

Advances in modeling ventricular arrhythmias: from mechanisms to the clinic

Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.

Electrophysiological and structural determinants of electrotonic modulation of repolarization by the activation sequence

Spatial dispersion of repolarization is known to play an important role in arrhythmogenesis. Electrotonic modulation of repolarization by the activation sequence has been observed in some species and tissue preparations, but to varying extents. Our study sought to determine the mechanisms underlying species- and tissue-dependent electrotonic modulation of repolarization in ventricles. Epi-fluorescence optical imaging of whole rat hearts and pig left ventricular wedges were used to assess epicardial spatial activation and repolarization characteristics. Experiments were supported by computer simulations using realistic geometries. Tight coupling between activation times (AT) and action potential duration (APD) were observed in rat experiments but not in pig. Linear correlation analysis found slopes of −1.03 ± 0.59 and −0.26 ± 0.13 for rat and pig, respectively (p < 0.0001). In rat, maximal dispersion of APD was 11.0 ± 3.1 ms but dispersion of repolarization time (RT) was relatively homogeneous (8.2 ± 2.7, p < 0.0001). However, in pig no such difference was observed between the dispersion of APD and RT (17.8 ± 6.1 vs. 17.7 ± 6.5, respectively). Localized elevations of APD (12.9 ± 8.3%) were identified at ventricular insertion sites of rat hearts both in experiments and simulations. Tissue geometry and action potential (AP) morphology contributed significantly to determining influence of electrotonic modulation. Simulations of a rat AP in a pig geometry decreased the slope of AT and APD relationships by 70.6% whereas slopes were increased by 75.0% when implementing a pig AP in a rat geometry. A modified pig AP, shortened to match the rat APD, showed little coupling between AT and APD with greatly reduced slope compared to the rat AP. Electrotonic modulation of repolarization by the activation sequence is especially pronounced in small hearts with murine-like APs. Tissue architecture and AP morphology play an important role in electrotonic modulation of repolarization.

The functional role of electrophysiological heterogeneity in the rabbit ventricle during rapid pacing and arrhythmias

Electrophysiological heterogeneity in action potential recordings from healthy intact hearts remains highly variable and, where present, is almost entirely abolished at fast pacing rates. Consequently, the functional importance of intrinsic action potential duration (APD) heterogeneity in healthy ventricles, and particularly its role during rapidly activating reentrant arrhythmias, remain poorly understood. By incorporating both transmural and apicobasal APD heterogeneity within a biventricular rabbit computational model and comparing with an equivalent homogeneous model, we directly investigated the functional importance of intrinsic APD heterogeneity under fast pacing and arrhythmogenic protocols. Although differences in APD were significantly modulated at the tissue level during pacing and further reduced as pacing frequency increased, small differences were still noticeable. Such differences were further marginally accentuated/attenuated via electrotonic effects relative to wavefront propagation directions. The remaining small levels of APD heterogeneity under the fastest pacing frequencies resulted in arrhythmia initiation via heterogeneous conduction block, in contrast to complete block in the homogeneous model. Such induction mechanisms were more evident during premature stimuli at slower paced rhythms where intrinsic heterogeneity remained to a greater degree. During sustained arrhythmias, however, intrinsic heterogeneity made little difference to overall reentrant behavior, either visually, or in terms of duration, metrics quantifying filament/phase singularity dynamics, and global electrocardiogram characteristics. These findings suggest that, despite being important during arrhythmia initiation, intrinsic electrophysiological heterogeneity plays little functional role during rapid pacing and sustained arrhythmia dynamics in the healthy ventricle and thus questions the need to incorporate such detail in computational models when simulating rapid arrhythmias.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

The role of fine-scale anatomical structure in the dynamics of reentry in computational models of the rabbit ventricles

Fine-scale anatomical structures in the heart may play an important role in sustaining cardiac arrhythmias. However, the extent of this role and how it may differ between species are not fully understood. In this study we used computational modelling to assess the impact of anatomy upon arrhythmia maintenance in the rabbit ventricles. Specifically, we quantified the dynamics of excitation wavefronts during episodes of simulated tachyarrhythmias and fibrillatory arrhythmias, defined as being respectively characterised by relatively low and high spatio-temporal disorganisation.Two computational models were used: a highly anatomically detailed MR-derived rabbit ventricular model (representing vasculature, endocardial structures) and a simplified equivalent model, constructed from the same MR-data but lacking such fine-scale anatomical features. During tachyarrhythmias, anatomically complex and simplified models showed very similar dynamics; however, during fibrillatory arrhythmias, as activation wavelength decreased, the presence of fine-scale anatomical details appeared to marginally increase disorganisation of wavefronts during arrhythmias in the complex model. Although a small amount of clustering of reentrant rotor centres (filaments) around endocardial structures was witnessed in follow-up analysis (which slightly increased during fibrillation as rotor size decreased), this was significantly less than previously reported in large animals. Importantly, no anchoring of reentrant rotors was visibly identifiable in arrhythmia movies. These differences between tachy- and fibrillatory arrhythmias suggest that the relative size of reentrant rotors with respect to anatomical obstacles governs the influence of fine-scale anatomy in the maintenance of ventricular arrhythmias in the rabbit. In conclusion, our simulations suggest that fine-scale anatomical features play little apparent role in the maintenance of tachyarrhythmias in the rabbit ventricles and, contrary to experimental reports in larger animals, appear to play only a minor role in the maintenance of fibrillatory arrhythmias. These findings also have important implications in optimising the level of detail required in anatomical computational meshes frequently used in arrhythmia investigations.