Representing cardiac bidomain bath-loading effects by an augmented monodomain approach: application to complex ventricular models

Effect of excitation sequence of myocardial contraction on the mechanical response of the left ventricle

In the past two decades there has been rapid development in the field of computational cardiac models. These have included either (i) mechanical models that assumed simultaneous myocardial activation, or (ii) electromechanical models that assumed time-varying myocardial activation. The influence of these modelling assumptions of myocardial activation on clinically relevant metrics, like myocardial strain, commonly used for validation of cardiac models has yet to be systematically examined, leading to uncertainty over their influence on the predictions of these models. This study examined the effects of simultaneous (mechanical), uniform endocardial, 3-patch endocardial (simulating the fascicles of the His-Purkinje system) and 1-patch endocardial (simulating the atrioventricular node) excitation sequences on the mechanical response of a synthetic human left ventricular model. The influence of the duration of the activation and time-to-peak contraction was also investigated. The electromechanical and mechanical models produced different strain distributions in early systole. However, these differences decayed as systole progressed. Using the same activation duration (74 ms) the average peak-systolic circumferential strain difference between the models was 0.65±0.37 %. A slightly prolonged activation duration (134 ms) resulted in no substantial difference increase (0.76±0.47 %). Differences up to 3.5 % were observed for prolonged activation durations (200 ms). Endocardial excitation produced non-physiological cumulative activation time distributions compared to the other models. Septal 1-patch excitation resulted in early systolic strain response that resembled pathological left bundle branch block. Decreased time-to-peak contraction exaggerated the effects of electrophysiology. The study found that excitation sequence minimally affects strain distributions at peak systole for physiological and even slightly pathological activation durations. However, electromechanical models with (patho)physiologically informed activation sequences are important for the accurate prediction of early systolic and pathological late systolic responses.

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

ForCEPSS-A framework for cardiac electrophysiology simulations standardization

BACKGROUND AND OBJECTIVE

Simulation of cardiac electrophysiology (CEP) is an important research tool that is increasingly being adopted in industrial and clinical applications. Typical workflows for CEP simulation consist of a sequence of processing stages starting with building an anatomical model and then calibrating its electrophysiological properties to match observable data. While the calibration stages are common and generalizable, most CEP studies re-implement these steps in complex and highly variable workflows. This lack of standardization renders the execution of computational CEP studies in an efficient, robust, and reproducible manner a significant challenge. Here, we propose ForCEPSS as an efficient and robust, yet flexible, software framework for standardizing CEP simulation studies.

METHODS AND RESULTS

Key processing stages of CEP simulation studies are identified and implemented in a standardized workflow that builds on openCARP1 Plank et al. (2021) and the Python-based carputils2 framework. Stages include (i) the definition and initialization of action potential phenotypes, (ii) the tissue scale calibration of conduction properties, (iii) the functional initialization to approximate a limit cycle corresponding to the dynamic reference state according to an experimental protocol, and, (iv) the execution of the CEP study where the electrophysiological response to a perturbation of the limit cycle is probed. As an exemplar application, we employ ForCEPSS to prepare a CEP study according to the Virtual Arrhythmia Risk Prediction protocol used for investigating the arrhythmogenic risk of developing infarct-related ventricular tachycardia (VT) in ischemic cardiomyopathy patients. We demonstrate that ForCEPSS enables a fully automated execution of all stages of this complex protocol.

CONCLUSION

ForCEPSS offers a novel comprehensive, standardized, and automated CEP simulation workflow. The high degree of automation accelerates the execution of CEP simulation studies, reduces errors, improves robustness, and makes CEP studies reproducible. Verification of simulation studies within the CEP modeling community is thus possible. As such, ForCEPSS makes an important contribution towards increasing transparency, standardization, and reproducibility of in silico CEP experiments.

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.

Credibility assessment of patient-specific computational modeling using patient-specific cardiac modeling as an exemplar

Reliable and robust simulation of individual patients using patient-specific models (PSMs) is one of the next frontiers for modeling and simulation (M&S) in healthcare. PSMs, which form the basis of digital twins, can be employed as clinical tools to, for example, assess disease state, predict response to therapy, or optimize therapy. They may also be used to construct virtual cohorts of patients, for in silico evaluation of medical product safety and/or performance. Methods and frameworks have recently been proposed for evaluating the credibility of M&S in healthcare applications. However, such efforts have generally been motivated by models of medical devices or generic patient models; how best to evaluate the credibility of PSMs has largely been unexplored. The aim of this paper is to understand and demonstrate the credibility assessment process for PSMs using patient-specific cardiac electrophysiological (EP) modeling as an exemplar. We first review approaches used to generate cardiac PSMs and consider how verification, validation, and uncertainty quantification (VVUQ) apply to cardiac PSMs. Next, we execute two simulation studies using a publicly available virtual cohort of 24 patient-specific ventricular models, the first a multi-patient verification study, the second investigating the impact of uncertainty in personalized and non-personalized inputs in a virtual cohort. We then use the findings from our analyses to identify how important characteristics of PSMs can be considered when assessing credibility with the approach of the ASME V&V40 Standard, accounting for PSM concepts such as inter- and intra-user variability, multi-patient and “every-patient” error estimation, uncertainty quantification in personalized vs non-personalized inputs, clinical validation, and others. The results of this paper will be useful to developers of cardiac and other medical image based PSMs, when assessing PSM credibility.

Patient-specific models are computational models that have been personalized using data from a patient. After decades of research, recent computational, data science and healthcare advances have opened the door to the fulfilment of the enormous potential of such models, from truly personalized medicine to efficient and cost-effective testing of new medical products. However, reliability (credibility) of patient-specific models is key to their success, and there are currently no general guidelines for evaluating credibility of patient-specific models. Here, we consider how frameworks and model evaluation activities that have been developed for generic (not patient-specific) computational models, can be extended to patient specific models. We achieve this through a detailed analysis of the activities required to evaluate cardiac electrophysiological models, chosen as an exemplar field due to its maturity and the complexity of such models. This is the first paper on the topic of reliability of patient-specific models and will help pave the way to reliable and trusted patient-specific modeling across healthcare applications.

A personalized real-time virtual model of whole heart electrophysiology

Computer models capable of representing the intrinsic personal electrophysiology (EP) of the heart in silico are termed virtual heart technologies. When anatomy and EP are tailored to individual patients within the model, such technologies are promising clinical and industrial tools. Regardless of their vast potential, few virtual technologies simulating the entire organ-scale EP of all four-chambers of the heart have been reported and widespread clinical use is limited due to high computational costs and difficulty in validation. We thus report on the development of a novel virtual technology representing the electrophysiology of all four-chambers of the heart aiming to overcome these limitations. In our previous work, a model of ventricular EP embedded in a torso was constructed from clinical magnetic resonance image (MRI) data and personalized according to the measured 12 lead electrocardiogram (ECG) of a single subject under normal sinus rhythm. This model is then expanded upon to include whole heart EP and a detailed representation of the His-Purkinje system (HPS). To test the capacities of the personalized virtual heart technology to replicate standard clinical morphological ECG features under such conditions, bundle branch blocks within both the right and the left ventricles under two different conduction velocity settings are modeled alongside sinus rhythm. To ensure clinical viability, model generation was completely automated and simulations were performed using an efficient real-time cardiac EP simulator. Close correspondence between the measured and simulated 12 lead ECG was observed under normal sinus conditions and all simulated bundle branch blocks manifested relevant clinical morphological features.

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.

A Review of Healthy and Fibrotic Myocardium Microstructure Modeling and Corresponding Intracardiac Electrograms

Computational simulations of cardiac electrophysiology provide detailed information on the depolarization phenomena at different spatial and temporal scales. With the development of new hardware and software, in silico experiments have gained more importance in cardiac electrophysiology research. For plane waves in healthy tissue, in vivo and in silico electrograms at the surface of the tissue demonstrate symmetric morphology and high peak-to-peak amplitude. Simulations provided insight into the factors that alter the morphology and amplitude of the electrograms. The situation is more complex in remodeled tissue with fibrotic infiltrations. Clinically, different changes including fractionation of the signal, extended duration and reduced amplitude have been described. In silico, numerous approaches have been proposed to represent the pathological changes on different spatial and functional scales. Different modeling approaches can reproduce distinct subsets of the clinically observed electrogram phenomena. This review provides an overview of how different modeling approaches to incorporate fibrotic and structural remodeling affect the electrogram and highlights open challenges to be addressed in future research.

Modelling the interaction between stem cells derived cardiomyocytes patches and host myocardium to aid non-arrhythmic engineered heart tissue design

Application of epicardial patches constructed from human-induced pluripotent stem cell- derived cardiomyocytes (hiPSC-CMs) has been proposed as a long-term therapy to treat scarred hearts post myocardial infarction (MI). Understanding electrical interaction between engineered heart tissue patches (EHT) and host myocardium represents a key step toward a successful patch engraftment. EHT retain different electrical properties with respect to the host heart tissue due to the hiPSC-CMs immature phenotype, which may lead to increased arrhythmia risk. We developed a modelling framework to examine the influence of patch design on electrical activation at the engraftment site. We performed an in silico investigation of different patch design approaches to restore pre-MI activation properties and evaluated the associated arrhythmic risk. We developed an in silico cardiac electrophysiology model of a transmural cross section of host myocardium. The model featured an infarct region, an epicardial patch spanning the infarct region and a bath region. The patch is modelled as a layer of hiPSC-CM, combined with a layer of conductive polymer (CP). Tissue and patch geometrical dimensions and conductivities were incorporated through 10 modifiable model parameters. We validated our model against 4 independent experimental studies and showed that it can qualitatively reproduce their findings. We performed a global sensitivity analysis (GSA) to isolate the most important parameters, showing that the stimulus propagation is mainly governed by the scar depth, radius and conductivity when the scar is not transmural, and by the EHT patch conductivity when the scar is transmural. We assessed the relevance of small animal studies to humans by comparing simulations of rat, rabbit and human myocardium. We found that stimulus propagation paths and GSA sensitivity indices are consistent across species. We explored which EHT design variables have the potential to restore physiological propagation. Simulations predict that increasing EHT conductivity from 0.28 to 1-1.1 S/m recovered physiological activation in rat, rabbit and human. Finally, we assessed arrhythmia risk related to increasing EHT conductivity and tested increasing the EHT Na+ channel density as an alternative strategy to match healthy activation. Our results revealed a greater arrhythmia risk linked to increased EHT conductivity compared to increased Na+ channel density. We demonstrated that our modeling framework could capture the interaction between host and EHT patches observed in in vitro experiments. We showed that large (patch and tissue dimensions) and small (cardiac myocyte electrophysiology) scale differences between small animals and humans do not alter EHT patch effect on infarcted tissue. Our model revealed that only when the scar is transmural do EHT properties impact activation times and isolated the EHT conductivity as the main parameter influencing propagation. We predicted that restoring physiological activation by tuning EHT conductivity is possible but may promote arrhythmic behavior. Finally, our model suggests that acting on hiPSC-CMs low action potential upstroke velocity and lack of IK1 may restore pre-MI activation while not promoting arrhythmia.

Whole-heart ventricular arrhythmia modeling moving forward: Mechanistic insights and translational applications

Ventricular arrhythmias are the primary cause of sudden cardiac death and one of the leading causes of mortality worldwide. Whole-heart computational modeling offers a unique approach for studying ventricular arrhythmias, offering vast potential for developing both a mechanistic understanding of ventricular arrhythmias and clinical applications for treatment. In this review, the fundamentals of whole-heart ventricular modeling and current methods of personalizing models using clinical data are presented. From this foundation, the authors summarize recent advances in whole-heart ventricular arrhythmia modeling. Efforts in gaining mechanistic insights into ventricular arrhythmias are discussed, in addition to other applications of models such as the assessment of novel therapeutics. The review emphasizes the unique benefits of computational modeling that allow for insights that are not obtainable by contemporary experimental or clinical means. Additionally, the clinical impact of modeling is explored, demonstrating how patient care is influenced by the information gained from ventricular arrhythmia models. The authors conclude with future perspectives about the direction of whole-heart ventricular arrhythmia modeling, outlining how advances in neural network methodologies hold the potential to reduce computational expense and permit for efficient whole-heart modeling.

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.

Using Machine Learning to Characterize Atrial Fibrotic Substrate From Intracardiac Signals With a Hybrid in silico and in vivo Dataset

In patients with atrial fibrillation, intracardiac electrogram signal amplitude is known to decrease with increased structural tissue remodeling, referred to as fibrosis. In addition to the isolation of the pulmonary veins, fibrotic sites are considered a suitable target for catheter ablation. However, it remains an open challenge to find fibrotic areas and to differentiate their density and transmurality. This study aims to identify the volume fraction and transmurality of fibrosis in the atrial substrate. Simulated cardiac electrograms, combined with a generalized model of clinical noise, reproduce clinically measured signals. Our hybrid dataset approach combines in silico and clinical electrograms to train a decision tree classifier to characterize the fibrotic atrial substrate. This approach captures different in vivo dynamics of the electrical propagation reflected on healthy electrogram morphology and synergistically combines it with synthetic fibrotic electrograms from in silico experiments. The machine learning algorithm was tested on five patients and compared against clinical voltage maps as a proof of concept, distinguishing non-fibrotic from fibrotic tissue and characterizing the patient's fibrotic tissue in terms of density and transmurality. The proposed approach can be used to overcome a single voltage cut-off value to identify fibrotic tissue and guide ablation targeting fibrotic areas.

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.

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.

Assessing the ability of substrate mapping techniques to guide ventricular tachycardia ablation using computational modelling

BACKGROUND

Identification of targets for ablation of post-infarction ventricular tachycardias (VTs) remains challenging, often requiring arrhythmia induction to delineate the reentrant circuit. This carries a risk for the patient and may not be feasible. Substrate mapping has emerged as a safer strategy to uncover arrhythmogenic regions. However, VT recurrence remains common.

GOAL

To use computer simulations to assess the ability of different substrate mapping approaches to identify VT exit sites.

METHODS

A 3D computational model of the porcine post-infarction heart was constructed to simulate VT and paced rhythm. Electroanatomical maps were constructed based on endocardial electrogram features and the reentry vulnerability index (RVI - a metric combining activation (AT) and repolarization timings to identify tissue susceptibility to reentry). Since scar transmurality in our model was not homogeneous, parameters derived from all signals (including dense scar regions) were used in the analysis. Potential ablation targets obtained from each electroanatomical map during pacing were compared to the exit site detected during VT mapping.

RESULTS

Simulation data showed that voltage cut-offs applied to bipolar electrograms could delineate the scar, but not the VT circuit. Electrogram fractionation had the highest correlation with scar transmurality. The RVI identified regions closest to VT exit site but was outperformed by AT gradients combined with voltage cut-offs. The performance of all metrics was affected by pacing location.

CONCLUSIONS

Substrate mapping could provide information about the infarct, but the directional dependency on activation should be considered. Activation-repolarization metrics have utility in safely identifying VT targets, even with non-transmural scars.

Factors Promoting Conduction Slowing as Substrates for Block and Reentry in Infarcted Hearts

The development of effective and safe therapies for scar-related ventricular tachycardias requires a detailed understanding of the mechanisms underlying the conduction block that initiates electrical re-entries associated with these arrhythmias. Conduction block has been often associated with electrophysiological changes that prolong action potential duration (APD) within the border zone (BZ) of chronically infarcted hearts. However, experimental evidence suggests that remodeling processes promoting conduction slowing as opposed to APD prolongation mark the chronic phase. In this context, the substrate for the initial block at the mouth of an isthmus/diastolic channel leading to ventricular tachycardia is unclear. The goal of this study was to determine whether electrophysiological parameters associated with conduction slowing can cause block and re-entry in the BZ. In silico experiments were conducted on two-dimensional idealized infarct tissue as well as on a cohort of postinfarction porcine left ventricular models constructed from ex vivo magnetic resonance imaging scans. Functional conduction slowing in the BZ was modeled by reducing sodium current density, whereas structural conduction slowing was represented by decreasing tissue conductivity and including fibrosis. The arrhythmogenic potential of APD prolongation was also tested as a basis for comparison. Within all models, the combination of reduced sodium current with structural remodeling more often degenerated into re-entry and, if so, was more likely to be sustained for more cycles. Although re-entries were also detected in experiments with prolonged APD, they were often not sustained because of the subsequent block caused by long-lasting repolarization. Functional and structural conditions associated with slow conduction rather than APD prolongation form a potent substrate for arrhythmogenesis at the isthmus/BZ of chronically infarcted hearts. Reduced excitability led to block while slow conduction shortened the wavelength of propagation, facilitating the sustenance of re-entries. These findings provide important insights for models of patient-specific risk stratification and therapy planning.

Characterizing the clinical implementation of a novel activation-repolarization metric to identify targets for catheter ablation of ventricular tachycardias using computational models

Identification of targets for catheter ablation of ventricular tachycardias (VTs) remains a significant challenge. VTs are often driven by re-entrant circuits resulting from a complex interaction between the front (activation) and tail (repolarization) of the electrical wavefront. Most mapping techniques do not take into account the tissue repolarization which may hinder the detection of ablation targets. The re-entry vulnerability index (RVI), a recently proposed mapping procedure, incorporates both activation and repolarization times to uncover VT circuits. The method showed potential in a series of experiments, but it still requires further development to enable its incorporation into a clinical protocol. Here, in-silico experiments were conducted to thoroughly assess RVI maps constructed under clinically-relevant mapping conditions. Within idealized as well as anatomically realistic infarct models, we show that parameters of the algorithm such as the search radius can significantly alter the specificity and sensitivity of the RVI maps. When constructed on sparse grids obtained following various placements of clinical recording catheters, RVI maps can identify vulnerable regions as long as two electrodes were placed on both sides of the line of block. Moreover, maps computed during pacing without inducing VT can reveal areas of abnormal repolarization and slow conduction but not directly vulnerability. In conclusion, the RVI algorithm can detect re-entrant circuits during VT from low resolution mapping grids resembling the clinical setting. Furthermore, RVI maps may provide information about the underlying tissue electrophysiology to guide catheter ablation without the need of inducing potentially harmful VT during the clinical procedure. Finally, the ability of the RVI maps to identify vulnerable regions with specificity in high resolution computer models could potentially improve the prediction of optimal ablation targets of simulation-based strategies.

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Safe and accurate detection of targets for catheter ablation remains a challenge.

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We conducted a thorough assessment of the Re-entry Vulnerability Index (RVI).

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Parameters of the algorithm can alter the specificity and sensitivity of RVI maps.

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When constructed on sparse grids RVI maps could still detect arrhythmogenic sites.

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In absence of arrhythmia, RVI maps revealed abnormal sites, but not vulnerability.

A technique for measuring anisotropy in atrial conduction to estimate conduction velocity and atrial fibre direction

BACKGROUND

Cardiac conduction properties exhibit large variability, and affect patient-specific arrhythmia mechanisms. However, it is challenging to clinically measure conduction velocity (CV), anisotropy and fibre direction. Our aim is to develop a technique to estimate conduction anisotropy and fibre direction from clinically available electrical recordings.

METHODS

We developed and validated automated algorithms for estimating cardiac CV anisotropy, from any distribution of recording locations on the atrial surface. The first algorithm is for elliptical wavefront fitting to a single activation map (method 1), which works well close to the pacing location, but decreases in accuracy further from the pacing location (due to spatial heterogeneity in the conductivity and fibre fields). As such, we developed a second methodology for measuring local conduction anisotropy, using data from two or three activation maps (method 2: ellipse fitting to wavefront propagation velocity vectors from multiple activation maps).

RESULTS

Ellipse fitting to CV vectors from two activation maps (method 2) leads to an improved estimation of longitudinal and transverse CV compared to method 1, but fibre direction estimation is still relatively poor. Using three activation maps with method 2 provides accurate estimation, with approximately 70% of atrial fibres estimated within 20∘. We applied the technique to clinical activation maps to demonstrate the presence of heterogeneous conduction anisotropy, and then tested the effects of this conduction anisotropy on predicted arrhythmia dynamics using computational simulation.

CONCLUSIONS

We have developed novel algorithms for calculating CV and measuring the direction dependency of atrial activation to estimate atrial fibre direction, without the need for specialised pacing protocols, using clinically available electrical recordings.

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.

Reducing Error in ECG Forward Simulations With Improved Source Sampling

A continuing challenge in validating electrocardiographic imaging (ECGI) is the persistent error in the associated forward problem observed in experimental studies. One possible cause of this error is insufficient representation of the cardiac sources; cardiac source measurements often sample only the ventricular epicardium, ignoring the endocardium and the atria. We hypothesize that measurements that completely cover the pericardial surface are required for accurate forward solutions. In this study, we used simulated and measured cardiac potentials to test the effect of different levels of spatial source sampling on the forward simulation. Not surprisingly, increasing the source sampling over the atria reduced the average error of the forward simulations, but some sampling strategies were more effective than others. Uniform and random distributions of samples across the atrial surface were the most efficient strategies in terms of lowest error with the fewest sampling locations, whereas “single direction” strategies, i.e., adding to the atrioventricular (AV) plane or atrial roof only, were the least efficient. Complete sampling of the atria is needed to eliminate errors from missing cardiac sources, but while high density sampling that covers the entire atria yields the best results, adding as few as 11 electrodes on the atria can significantly reduce these errors. Future validation studies of the ECG forward simulations should use a cardiac source sampling that takes these considerations into account, which will, in turn, improve validation and understanding of ECGI.

The role of conductivity discontinuities in design of cardiac defibrillation

Fibrillation is an erratic electrical state of the heart, of rapid twitching rather than organized contractions. Ventricular fibrillation is fatal if not treated promptly. The standard treatment, defibrillation, is a strong electrical shock to reinitialize the electrical dynamics and allow a normal heart beat. Both the normal and the fibrillatory electrical dynamics of the heart are organized into moving wave fronts of changing electrical signals, especially in the transmembrane voltage, which is the potential difference between the cardiac cellular interior and the intracellular region of the heart. In a normal heart beat, the wave front motion is from bottom to top and is accompanied by the release of Ca ions to induce contractions and pump the blood. In a fibrillatory state, these wave fronts are organized into rotating scroll waves, with a centerline known as a filament. Treatment requires altering the electrical state of the heart through an externally applied electrical shock, in a manner that precludes the existence of the filaments and scroll waves. Detailed mechanisms for the success of this treatment are partially understood, and involve local shock-induced changes in the transmembrane potential, known as virtual electrode alterations. These transmembrane alterations are located at boundaries of the cardiac tissue, including blood vessels and the heart chamber wall, where discontinuities in electrical conductivity occur. The primary focus of this paper is the defibrillation shock and the subsequent electrical phenomena it induces. Six partially overlapping causal factors for defibrillation success are identified from the literature. We present evidence in favor of five of these and against one of them. A major conclusion is that a dynamically growing wave front starting at the heart surface appears to play a primary role during defibrillation by critically reducing the volume available to sustain the dynamic motion of scroll waves; in contrast, virtual electrodes occurring at the boundaries of small, isolated blood vessels only cause minor effects. As a consequence, we suggest that the size of the heart (specifically, the surface to volume ratio) is an important defibrillation variable.

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.

Stochastic spontaneous calcium release events and sodium channelopathies promote ventricular arrhythmias

Premature ventricular complexes (PVCs), the first initiating beats of a variety of cardiac arrhythmias, have been associated with spontaneous calcium release (SCR) events at the cell level. However, the mechanisms underlying the degeneration of such PVCs into arrhythmias are not fully understood. The objective of this study was to investigate the conditions under which SCR-mediated PVCs can lead to ventricular arrhythmias. In particular, we sought to determine whether sodium (Na⁺) current loss-of-function in the structurally normal ventricles provides a substrate for unidirectional conduction block and reentry initiated by SCR-mediated PVCs. To achieve this goal, a stochastic model of SCR was incorporated into an anatomically accurate compute model of the rabbit ventricles with the His-Purkinje system (HPS). Simulations with reduced Na⁺ current due to a negative-shift in the steady-state channel inactivation showed that SCR-mediated delayed afterdepolarizations led to PVC formation in the HPS, where the electrotonic load was lower, conduction block, and reentry in the 3D myocardium. Moreover, arrhythmia initiation was only possible when intrinsic electrophysiological heterogeneity in action potential within the ventricles was present. In conclusion, while benign in healthy individuals SCR-mediated PVCs can lead to life-threatening ventricular arrhythmias when combined with Na⁺ channelopathies.

Highly trabeculated structure of the human endocardium underlies asymmetrical response to low-energy monophasic shocks

Novel low-energy defibrillation therapies are thought to be driven by virtual-electrodes (VEs), due to the interaction of applied monophasic electric shocks with fine-scale anatomical structures within the heart. Significant inter-species differences in the cardiac (micro)-anatomy exist, however, particularly with respect to the degree of endocardial trabeculations, which may underlie important differences in response to low-energy defibrillation protocols. Understanding the interaction of monophasic electric fields with the specific human micro-anatomy is therefore imperative in facilitating the translation and optimisation of these promising experimental therapies to the clinic. In this study, we sought to investigate how electric fields from implanted devices interact with the highly trabeculated human endocardial surface to better understand shock success in order to help optimise future clinical protocols. A bi-ventricular human computational model was constructed from high resolution (350 μm) ex-vivo MR data, including anatomically accurate endocardial structures. Monophasic shocks were applied between a basal right ventricular catheter and an exterior ground. Shocks of varying strengths were applied with both anodal [positive right ventricle (RV) electrode] and cathodal (negative RV electrode) polarities at different states of tissue refractoriness and during induced arrhythmias. Anodal shocks induced isolated positive VEs at the distal side of "detached" trabeculations, which rapidly spread into hyperpolarised tissue on the surrounding endocardial surfaces following the shock. Anodal shocks thus depolarised more tissue 10 ms after the shock than cathodal shocks where the propagation of activation from VEs induced on the proximal side of "detached" trabeculations was prevented due to refractory endocardium. Anodal shocks increased arrhythmia complexity more than cathodal shocks during failed anti-arrhythmia shocks. In conclusion, multiple detached trabeculations in the human ventricle interact with anodal stimuli to induce multiple secondary sources from VEs, facilitating more rapid shock-induced ventricular excitation compared to cathodal shocks. Such a mechanism may help explain inter-species differences in response to shocks and help to develop novel defibrillation strategies.

BeatBox-HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology

The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.

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.

Parametrization of activation based cardiac electrophysiology models using bidomain model simulations

Eikonal models are useful to compute approximate solutions of cardiac excitation propagation in a computationally efficient way. In this work the underlying conduction velocities for different cell types were computed solving the classical bidomain model equations for planar wavefront propagation. It was further investigated how changes in the conductivity tensors within the bidomain model analytically correspond to changes in the conduction velocity. The error in the presence of local front curvature for the derived eikonal model parametrization were analyzed. The conduction velocity simulated based on the bidomain model was overestimated by a maximum of 10%.

Computational Representations of Myocardial Infarct Scars and Implications for Arrhythmogenesis

Image-based computational modeling is becoming an increasingly used clinical tool to provide insight into the mechanisms of reentrant arrhythmias. In the context of ischemic heart disease, faithful representation of the electrophysiological properties of the infarct region within models is essential, due to the scars known for arrhythmic properties. Here, we review the different computational representations of the infarcted region, summarizing the experimental measurements upon which they are based. We then focus on the two most common representations of the scar core (complete insulator or electrically passive tissue) and perform simulations of electrical propagation around idealized infarct geometries. Our simulations highlight significant differences in action potential duration and focal effective refractory period (ERP) around the scar, driven by differences in electrotonic loading, depending on the choice of scar representation. Finally, a novel mechanism for arrhythmia induction, following a focal ectopic beat, is demonstrated, which relies on localized gradients in ERP directly caused by the electrotonic sink effects of the neighboring passive scar.

Effect of Twisted Fiber Anisotropy in Cardiac Tissue on Ablation with Pulsed Electric Fields

BACKGROUND

Ablation of cardiac tissue with pulsed electric fields is a promising alternative to current thermal ablation methods, and it critically depends on the electric field distribution in the heart.

METHODS

We developed a model that incorporates the twisted anisotropy of cardiac tissue and computed the electric field distribution in the tissue. We also performed experiments in rabbit ventricles to validate our model. We find that the model agrees well with the experimentally determined ablation volume if we assume that all tissue that is exposed to a field greater than 3 kV/cm is ablated. In our numerical analysis, we considered how tissue thickness, degree of anisotropy, and electrode configuration affect the geometry of the ablated volume. We considered two electrode configurations: two parallel needles inserted into the myocardium ("penetrating needles" configuration) and one circular electrode each on epi- and endocardium, opposing each other ("epi-endo" configuration).

RESULTS

For thick tissues (10 mm) and moderate anisotropy ratio (a = 2), we find that the geometry of the ablated volume is almost unaffected by twisted anisotropy, i.e. it is approximately translationally symmetric from epi- to endocardium, for both electrode configurations. Higher anisotropy ratio (a = 10) leads to substantial variation in ablation width across the wall; these variations were more pronounced for the penetrating needle configuration than for the epi-endo configuration. For thinner tissues (4 mm, typical for human atria) and higher anisotropy ratio (a = 10), the epi-endo configuration yielded approximately translationally symmetric ablation volumes, while the penetrating electrodes configuration was much more sensitive to fiber twist.

CONCLUSIONS

These results suggest that the epi-endo configuration will be reliable for ablation of atrial fibrillation, independently of fiber orientation, while the penetrating electrode configuration may experience problems when the fiber orientation is not consistent across the atrial wall.

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.

Optogenetics-enabled assessment of viral gene and cell therapy for restoration of cardiac excitability

Multiple cardiac pathologies are accompanied by loss of tissue excitability, which leads to a range of heart rhythm disorders (arrhythmias). In addition to electronic device therapy (i.e. implantable pacemakers and cardioverter/defibrillators), biological approaches have recently been explored to restore pacemaking ability and to correct conduction slowing in the heart by delivering excitatory ion channels or ion channel agonists. Using optogenetics as a tool to selectively interrogate only cells transduced to produce an exogenous excitatory ion current, we experimentally and computationally quantify the efficiency of such biological approaches in rescuing cardiac excitability as a function of the mode of application (viral gene delivery or cell delivery) and the geometry of the transduced region (focal or spatially-distributed). We demonstrate that for each configuration (delivery mode and spatial pattern), the optical energy needed to excite can be used to predict therapeutic efficiency of excitability restoration. Taken directly, these results can help guide optogenetic interventions for light-based control of cardiac excitation. More generally, our findings can help optimize gene therapy for restoration of cardiac excitability.

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.

Mechanistic insights into hypothermic ventricular fibrillation: the role of temperature and tissue size

AIMS

Hypothermia is well known to be pro-arrhythmic, yet it has beneficial effects as a resuscitation therapy and valuable during intracardiac surgeries. Therefore, we aim to study the mechanisms that induce fibrillation during hypothermia. A better understanding of the complex spatiotemporal dynamics of heart tissue as a function of temperature will be useful in managing the benefits and risks of hypothermia.

METHODS AND RESULTS

We perform two-dimensional numerical simulations by using a minimal model of cardiac action potential propagation fine-tuned on experimental measurements. The model includes thermal factors acting on the ionic currents and the gating variables to correctly reproduce experimentally recorded restitution curves at different temperatures. Simulations are implemented using WebGL, which allows long simulations to be performed as they run close to real time. We describe (i) why fibrillation is easier to induce at low temperatures, (ii) that there is a minimum size required for fibrillation that depends on temperature, (iii) why the frequency of fibrillation decreases with decreasing temperature, and (iv) that regional cooling may be an anti-arrhythmic therapy for small tissue sizes however it may be pro-arrhythmic for large tissue sizes.

CONCLUSION

Using a mathematical cardiac cell model, we are able to reproduce experimental observations, quantitative experimental results, and discuss possible mechanisms and implications of electrophysiological changes during hypothermia.

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.

Tachycardia in post-infarction hearts: insights from 3D image-based ventricular models

Ventricular tachycardia, a life-threatening regular and repetitive fast heart rhythm, frequently occurs in the setting of myocardial infarction. Recently, the peri-infarct zones surrounding the necrotic scar (termed gray zones) have been shown to correlate with ventricular tachycardia inducibility. However, it remains unknown how the latter is determined by gray zone distribution and size. The goal of this study is to examine how tachycardia circuits are maintained in the infarcted heart and to explore the relationship between the tachycardia organizing centers and the infarct gray zone size and degree of heterogeneity. To achieve the goals of the study, we employ a sophisticated high-resolution electrophysiological model of the infarcted canine ventricles reconstructed from imaging data, representing both scar and gray zone. The baseline canine ventricular model was also used to generate additional ventricular models with different gray zone sizes, as well as models in which the gray zone was represented as different heterogeneous combinations of viable tissue and necrotic scar. The results of the tachycardia induction simulations with a number of high-resolution canine ventricular models (22 altogether) demonstrated that the gray zone was the critical factor resulting in arrhythmia induction and maintenance. In all models with inducible arrhythmia, the scroll-wave filaments were contained entirely within the gray zone, regardless of its size or the level of heterogeneity of its composition. The gray zone was thus found to be the arrhythmogenic substrate that promoted wavebreak and reentry formation. We found that the scroll-wave filament locations were insensitive to the structural composition of the gray zone and were determined predominantly by the gray zone morphology and size. The findings of this study have important implications for the advancement of improved criteria for stratifying arrhythmia risk in post-infarction patients and for the development of new approaches for determining the ablation targets of infarct-related tachycardia.

Subepicardial action potential characteristics are a function of depth and activation sequence in isolated rabbit hearts

BACKGROUND

Electric excitability in the ventricular wall is influenced by cellular electrophysiology and passive electric properties of the myocardium. Action potential (AP) rise time, an indicator of myocardial excitability, is influenced by conduction pattern and distance from the epicardial surface. This study examined AP rise times and conduction velocity as the depolarizing wavefront approaches the epicardial surface.

METHODS AND RESULTS

Two-photon excitation of di-4-aminonaphthenyl-pyridinum-propylsulfonate was used to measure electric activity at discrete epicardial layers of isolated Langendorff-perfused rabbit hearts to a depth of 500 μm. Endo-to-epicardial wavefronts were studied during right atrial or ventricular endocardial pacing. Similar measurements were made with epi-to-endocardial, transverse, and longitudinal pacing protocols. Results were compared with data from a bidomain model of 3-dimensional (3D) electric propagation within ventricular myocardium. During right atrial and endocardial pacing, AP rise time (10%-90% of upstroke) decreased by ≈50% between 500 and 50 μm from the epicardial surface, whereas conduction velocity increased and AP duration was only slightly shorter (≈4%). These differences were not observed with other conduction patterns. The depth-dependent changes in rise time were larger at higher pacing rates. Modeling data qualitatively reproduced the behavior seen experimentally and demonstrated a parallel reduction in peak I(Na) and electrotonic load as the wavefront approaches the epicardial surface.

CONCLUSIONS

Decreased electrotonic load at the epicardial surface results in more rapid AP upstrokes and higher conduction velocities compared with the bulk myocardium. Combined effects of tissue depth and pacing rate on AP rise time reduce conduction safety and myocardial excitability within the ventricular wall.

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.

Electroanatomical characterization of atrial microfibrosis in a histologically detailed computer model

Fibrosis is thought to play an important role in the formation and maintenance of atrial fibrillation (AF). The propensity of fibrosis to increase AF vulnerability depends not only on its amount, its texture plays a crucial role as well. While the detection of fibrotic tissue patches in the atria with extracellular recordings is feasible based on the analysis of electrogram fractionation, as used in clinical practice to identify ablation targets, the classification of fibrotic texture is a more challenging problem. This study seeks to establish a method for the electroanatomical characterization of the fibrotic textures based on the analysis of electrogram fractionation. The proposed method exploits the dependence of fractionation patterns on the incidence direction of wavefronts which differs significantly as a function of texture. A histologically detailed computer model of the right atrial isthmus was developed for testing the method. A stimulation protocol was conceived which generated various incidence directions for any given recording site where electrograms were computed. A classification method is derived then for discriminating three types of fibrosis, no fibrosis (control), diffuse, and patchy fibrosis. Simulation results showed that electrogram fractionation and amplitudes and their dependence upon incidence direction allow a robust discrimination between different classes of fibrosis. Finally, to minimize the technical effort, sensitivity analysis was performed to identify a minimum number of incidence directions required for robust classification.

Characterization and modeling of the peripheral cardiac conduction system

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

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.

Efficient simulation of cardiac electrical propagation using high order finite elements

We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

Mathematical modeling and simulation of ventricular activation sequences: implications for cardiac resynchronization therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy.

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

Cardiac tissue is always surrounded by conducting fluid, both in vivo (blood) and in experimental preparations (Tyrode's solution), which acts to increase conduction velocity (CV) close to the tissue-fluid interface, inducing transmural wavefront curvature. Despite its potential importance, computer modeling studies focused on arrhythmia mechanisms have previously not accounted for these bath-loading effects. Here, we investigate the increase in CV and concomitant change in transmural wavefront profiles upon both propagation and arrhythmia dynamics within models of differing anatomical complexity. In simplified slab models, in absence of transmural fiber rotation, bath-loading induced transmural wavefront curvature dominates, significantly increasing arrhythmia complexity compared to no bath. In the presence of fiber rotation, bath-loading effects are less striking and depend upon propagation direction: the bath accentuates natural concave curvature caused by transmurally rotating fibers, but attenuates convex curvature, which negates overall impact upon arrhythmia complexity. Finally, we demonstrate that the high degree of anatomical complexity within whole ventricular models modulates bath-loading induced transmural wavefront curvature. However, key is the increased surface CV that dramatically reduces both arrhythmia inducibility and resulting complexity by increasing wavelength and reducing the available excitable gap. Our findings highlight the importance of including bath-loading effects during arrhythmia mechanism investigations, which could have implications for interpreting and comparing simulation results with experimental data where such effects are inherently present.

The role of photon scattering in voltage-calcium fluorescent recordings of ventricular fibrillation

Recent optical mapping studies of cardiac tissue suggest that membrane voltage (V(m)) and intracellular calcium concentrations (Ca) become dissociated during ventricular fibrillation (VF), generating a proarrhythmic substrate. However, experimental methods used in these studies may accentuate measured dissociation due to differences in fluorescent emission wavelengths of optical voltage/calcium (V(opt)/Ca(opt)) signals. Here, we simulate dual voltage-calcium optical mapping experiments using a monodomain-Luo-Rudy ventricular-tissue model coupled to a photon-diffusion model. Dissociation of both electrical, V(m)/Ca, and optical, V(opt)/Ca(opt), signals is quantified by calculating mutual information (MI) for VF and rapid pacing protocols. We find that photon scattering decreases MI of V(opt)/Ca(opt) signals by 23% compared to unscattered V(m)/Ca signals during VF. Scattering effects are amplified by increasing wavelength separation between fluorescent voltage/calcium signals and respective measurement-location misalignment. In contrast, photon scattering does not affect MI during rapid pacing, but high calcium dye affinity can decrease MI by attenuating alternans in Ca(opt) but not in V(opt). We conclude that some dissociation exists between voltage and calcium at the cellular level during VF, but MI differences are amplified by current optical mapping methods.

Bidomain ECG simulations using an augmented monodomain model for the cardiac source

The electrocardiogram (ECG) is an essential clinical tool for the non-invasive assessment of cardiac function. Computational simulations of ECGs using bidomain models are considered the biophysically most detailed approach, but computational costs are significant. Alternatively, pseudo-bidomain formulations can be used, combining a monodomain model with an infrequent bidomain solve to obtain full extracellular potential (φ(e)) distributions and traces. However, previous attempts at such approaches did not see the expected significant decrease in compute time and did not include important effects of bath-loading on activation wavefront morphology (present in full bidomain models), representing a less accurate source term for φ(e) solution. ECG traces can also be derived from computationally cheaper φ(e) recovery techniques, whereby the time-course of φ(e) is approximated at a particular point using the monodomain transmembrane potential as source term. However, φ(e) recovery methods also assume tissue to be immersed in an unbounded conductive medium; not the case in most practical scenarios. We recently demonstrated how bath-loading effects in bidomain simulations could be replicated using an augmented monodomain model, faithfully reproducing bidomain wavefront shapes and activation patterns. Here, a computationally-efficient pseudobidomain formulation is suggested which combines the advantages of an augmented monodomain method with an infrequent bidomain solve, providing activation sequences, ECG traces and φ(e) distributions in a bounded medium surrounding the heart which closely match those of the full bidomain, but at ≈ 10% the computational cost. We demonstrate the important impact of both bath-loading and a finite surrounding bath on spatiotemporal φ(e) distributions, thus demonstrating the utility of our novel pseudo-bidomain model in ECG computation with respect to previous pseudo-bidomain and φ(e) recovery approaches.

Effects of boundaries and geometry on the spatial distribution of action potential duration in cardiac tissue

Increased dispersion of action potential duration across cardiac tissue has long been considered an important substrate for the development of most electrical arrhythmias. Although this dispersion has been studied previously by characterizing the static intrinsic gradients in cellular electrophysiology and dynamical gradients generated by fast pacing, few studies have concentrated on dispersions generated solely by structural effects. Here we show how boundaries and geometry can produce spatially dependent changes in action potential duration (APD) in homogeneous and isotropic tissue, where all the cells have the same APD in the absence of diffusion. Electrotonic currents due to coupling within the tissue and at the tissue boundaries can generate dispersion, and the profile of this dispersion can change dramatically depending on tissue size and shape, action potential morphology, tissue dimensionality, and stimulus frequency and location. The dispersion generated by pure geometrical effects can be on the order of tens of milliseconds, enough under certain conditions to produce conduction blocks and initiate reentrant waves.