Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology

The frequency of atrial fibrillatory waves is modulated by the spatiotemporal pattern of acetylcholine release: a 3D computational study

In atrial fibrillation (AF), the ECG P-wave, which represents atrial depolarization, is replaced with chaotic and irregular fibrillation waves (f waves). The f-wave frequency, F f, shows significant variations over time. Cardiorespiratory interactions regulated by the autonomic nervous system have been suggested to play a role in such variations. We conducted a simulation study to test whether the spatiotemporal release pattern of the parasympathetic neurotransmitter acetylcholine (ACh) modulates the frequency of atrial reentrant circuits. Understanding parasympathetic involvement in AF may guide more effective treatment approaches and could help to design autonomic markers alternative to heart rate variability (HRV), which is not available in AF patients. 2D tissue and 3D whole-atria models of human atrial electrophysiology in persistent AF were built. Different ACh release percentages (8% and 30%) and spatial ACh release patterns, including spatially random release and release from ganglionated plexi (GPs) and associated nerves, were considered. The temporal pattern of ACh release, ACh(t), was simulated following a sinusoidal waveform of frequency 0.125 Hz to represent the respiratory frequency. Different mean concentrations ( A C h ¯ ) and peak-to-peak ranges of ACh (ΔACh) were tested. We found that temporal variations in F f, F f(t), followed the simulated temporal ACh(t) pattern in all cases. The temporal mean of F f(t), F ¯ f , depended on the fibrillatory pattern (number and location of rotors), the percentage of ACh release nodes and A C h ¯ . The magnitude of F f(t) modulation, ΔF f, depended on the percentage of ACh release nodes and ΔACh. The spatial pattern of ACh release did not have an impact on F ¯ f and only a mild impact on ΔF f. The f-wave frequency, being indicative of vagal activity, has the potential to drive autonomic-based therapeutic actions and could replace HRV markers not quantifiable from AF patients.

Combining pharmacokinetic and electrophysiological models for early prediction of drug-induced arrhythmogenicity

BACKGROUND AND OBJECTIVE

In silico methods are gaining attention for predicting drug-induced Torsade de Pointes (TdP) in different stages of drug development. However, many computational models tended not to account for inter-individual response variability due to demographic covariates, such as sex, or physiologic covariates, such as renal function, which may be crucial when predicting TdP. This study aims to compare the effects of drugs in male and female populations with normal and impaired renal function using in silico methods.

METHODS

Pharmacokinetic models considering sex and renal function as covariates were implemented from data published in pharmacokinetic studies. Drug effects were simulated using an electrophysiologically calibrated population of cellular models of 300 males and 300 females. The population of models was built by modifying the endocardial action potential model published by O'Hara et al. (2011) according to the experimentally measured gene expression levels of 12 ion channels.

RESULTS

Fifteen pharmacokinetic models for CiPA drugs were implemented and validated in this study. Eight pharmacokinetic models included the effect of renal function and four the effect of sex. The mean difference in action potential duration (APD) between male and female populations was 24.9 ms (p<0.05). Our simulations indicated that women with impaired renal function were particularly susceptible to drug-induced arrhythmias, whereas healthy men were less prone to TdP. Differences between patient groups were more pronounced for high TdP-risk drugs. The proposed in silico tool also revealed that individuals with impaired renal function, electrophysiologically simulated with hyperkalemia (extracellular potassium concentration [K+]o = 7 mM) exhibited less pronounced APD prolongation than individuals with normal potassium levels. The pharmacokinetic/electrophysiological framework was used to determine the maximum safe dose of dofetilide in different patient groups. As a proof of concept, 3D simulations were also run for dofetilide obtaining QT prolongation in accordance with previously reported clinical values.

CONCLUSIONS

This study presents a novel methodology that combines pharmacokinetic and electrophysiological models to incorporate the effects of sex and renal function into in silico drug simulations and highlights their impact on TdP-risk assessment. Furthermore, it may also help inform maximum dose regimens that ensure TdP-related safety in a specific sub-population of patients.

Characterization of airborne particulate matter and its toxic and proarrhythmic effects: A case study in Aburrá Valley, Colombia

Particle matter (PM) is a complex mixture of particles suspended in the air, mainly caused by fuel combustion from vehicles and industry, and has been related to pulmonary and cardiovascular diseases. The Metropolitan Area of Aburrá Valley in Colombia is the second most populous urban agglomeration in the country and the third densest in the world, composed of ten municipalities. Examining the physicochemical properties of PM is crucial in comprehending its composition and its effects on human health, as it varies based on the socioeconomic dynamics specific to each city. This study characterized the PM collected from the north, south, and central zones to evaluate its chemical composition and morphology. Different elements such as silicon, carbon, aluminum, potassium, calcium, sodium, iron, magnesium, and copper and the presence of unburned fuel, motor oil, and silicon fibers were identified. In vitro and in silico studies were conducted to evaluate the toxicity of the PM, and it was found that the PM collected from the central zone had the greatest impact on cell viability and caused DNA damage. The in silico study demonstrated that PM has concentration-dependent proarrhythmic effects, reflected in an action potential duration shortening and an increased number of reentries, which may contribute to the development of cardiac arrhythmias. Overall, the results suggest that the size and chemical composition of ambient PM can induce toxicity and play an important role in the generation of arrhythmias.

An inner-outer subcycling algorithm for parallel cardiac electrophysiology simulations

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

Manifold analysis of the P-wave changes induced by pulmonary vein isolation during cryoballoon procedure

BACKGROUND/AIM

In atrial fibrillation (AF) ablation procedures, it is desirable to know whether a proper disconnection of the pulmonary veins (PVs) was achieved. We hypothesize that information about their isolation could be provided by analyzing changes in P-wave after ablation. Thus, we present a method to detect PV disconnection using P-wave signal analysis.

METHODS

Conventional P-wave feature extraction was compared to an automatic feature extraction procedure based on creating low-dimensional latent spaces for cardiac signals with the Uniform Manifold Approximation and Projection (UMAP) method. A database of patients (19 controls and 16 AF individuals who underwent a PV ablation procedure) was collected. Standard 12-lead ECG was recorded, and P-waves were segmented and averaged to extract conventional features (duration, amplitude, and area) and their manifold representations provided by UMAP on a 3-dimensional latent space. A virtual patient was used to validate these results further and study the spatial distribution of the extracted characteristics over the whole torso surface.

RESULTS

Both methods showed differences between P-wave before and after ablation. Conventional methods were more prone to noise, P-wave delineation errors, and inter-patient variability. P-wave differences were observed in the standard leads recordings. However, higher differences appeared in the torso region over the precordial leads. Recordings near the left scapula also yielded noticeable differences.

CONCLUSIONS

P-wave analysis based on UMAP parameters detects PV disconnection after ablation in AF patients and is more robust than heuristic parameterization. Moreover, additional leads different from the standard 12-lead ECG should be used to detect PV isolation and possible future reconnections better.

Efficient time splitting schemes for the monodomain equation in cardiac electrophysiology

Approximating the fast dynamics of depolarization waves in the human heart described by the monodomain model is numerically challenging. Splitting methods for the PDE-ODE coupling enable the computation with very fine space and time discretizations. Here, we compare different splitting approaches regarding convergence, accuracy, and efficiency. Simulations were performed for a benchmark problem with the Beeler-Reuter cell model on a truncated ellipsoid approximating the left ventricle including a localized stimulation. For this configuration, we provide a reference solution for the transmembrane potential. We found a semi-implicit approach with state variable interpolation to be the most efficient scheme. The results are transferred to a more physiological setup using a bi-ventricular domain with a complex external stimulation pattern to evaluate the accuracy of the activation time for different resolutions in space and time.

Cardiac cells stimulated with an axial current-like waveform reproduce electrophysiological properties of tissue fibers

BACKGROUND AND OBJECTIVE

In silico electrophysiological models are generally validated by comparing simulated results with experimental data. When dealing with single-cell and tissue scales simultaneously, as occurs frequently during model development and calibration, the effects of inter-cellular coupling should be considered to ensure the trustworthiness of model predictions. The hypothesis of this paper is that the cell-tissue mismatch can be reduced by incorporating the effects of conduction into the single-cell stimulation current.

METHODS

Five different stimulation waveforms were applied to the human ventricular O'Hara-Rudy cell model. The waveforms included the commonly used monophasic and biphasic (symmetric and asymmetric) pulses, a triangular waveform and a newly proposed asymmetric waveform (stimulation A) that resembles the transmembrane current associated with AP conduction in tissue. A comparison between single-cell and fiber simulated results was established by computing the relative difference between the values of AP-derived properties at different scales, and by evaluating the differences in the contributions of ionic conductances to each evaluated property. As a proof of the benefit, we investigated multi-scale differences in the simulation of the effects induced by dofetilide, a selective I_Kr blocker with high torsadogenic risk, on ventricular repolarization at different pacing rates.

RESULTS

Out of the five tested stimulation waveforms, stimulation A produced the closest correspondence between cell and tissue simulations in terms of AP properties at steady-state and under dynamic pacing and of ionic contributors to those AP properties. Also, stimulation A reproduced the effects of dofetilide better than the other alternative waveforms, mirroring the 'beat-skipping' behavior observed at fast pacing rates in experiments with human tissue.

CONCLUSIONS

The proposed stimulation current waveform accounts for inter-cellular coupling effects by mimicking cell excitation during AP conduction. The proposed waveform improves the correspondence between simulation scales, which could improve the trustworthiness of single-cell simulations without adding computational cost.

Cellular heterogeneity and repolarisation across the atria: an in silico study

Mechanisms of atrial fibrillation and the susceptibility to reentries can be impacted by the repolarization across the atria. Studies into atrial fibrillation ignore cell-to-cell heterogeneity due to electrotonic coupling. Recent studies show that cellular variability may have a larger impact on electrophysiological behaviour than assumed. This paper aims to determine the impact of cellular heterogeneity on the repolarization phase across the AF remodelled atria. Using a population of models approach, 10 anatomically identical atrial models were created to include cellular heterogeneity. Atrial models were compared with an equivalent homogenous model. Activation, APD90, and repolarization maps were used to compare models. The impact of electrotonic coupling in the tissue was determined through a comparison of RMP, APD20, APD50, APD90, and triangulation between regional atrial tissue and the single cell populations. After calibration, cellular heterogeneity does not impact atrial depolarization. Repolarization patterns were significantly impacted by cellular heterogeneity, with the APD90 across the LA increasing due to heterogeneity and the reverse occurring in the RA. Electrotonic coupling caused a reduction in variability across all biomarkers but did not fully remove variability. Electrotonic coupling resulted in an increase in APD20 and APD50, and reduced triangulation compared to isolated cell populations. Heterogeneity also caused a reduction in triangulation compared with regionally homogeneous atria.

Atrial fibrosis identification with unipolar electrogram eigenvalue distribution analysis in multi-electrode arrays

Abstract

Atrial fibrosis plays a key role in the initiation and progression of atrial fibrillation (AF). Atrial fibrosis is typically identified by a peak-to-peak amplitude of bipolar electrograms (b-EGMs) lower than 0.5 mV, which may be considered as ablation targets. Nevertheless, this approach disregards signal spatiotemporal information and b-EGM sensitivity to catheter orientation. To overcome these limitations, we propose the dominant-to-remaining eigenvalue dominance ratio (EIGDR) of unipolar electrograms (u-EGMs) within neighbor electrode cliques as a waveform dispersion measure, hypothesizing that it is correlated with the presence of fibrosis. A simulated 2D tissue with a fibrosis patch was used for validation. We computed EIGDR maps from both original and time-aligned u-EGMs, denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}$$\end{document}R and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R}^{\mathcal{A}}$$\end{document}RA, respectively, also mapping the gain in eigenvalue concentration obtained by the alignment, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \mathcal{R}^{\mathcal{A}}$$\end{document}ΔRA. The performance of each map in detecting fibrosis was evaluated in scenarios including noise and variable electrode-tissue distance. Best results were achieved by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R}^{\mathcal{A}}$$\end{document}RA, reaching 94% detection accuracy, versus the 86% of b-EGMs voltage maps. The proposed strategy was also tested in real u-EGMs from fibrotic and non-fibrotic areas over 3D electroanatomical maps, supporting the ability of the EIGDRs as fibrosis markers, encouraging further studies to confirm their translation to clinical settings.

Graphical Abstract

Upper panels: map of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}^{\mathcal {A}}$$\end{document}RA from 3×3 cliques for Ψ= 0^∘ and bipolar voltage map V^b-m, performed assuming a variable electrode-to-tissue distance and noisy u-EGMs (noise level σ_v = 46.4 μV ). Lower panels: detected fibrotic areas (brown), using the thresholds that maximize detection accuracy of each map

Training machine learning models with synthetic data improves the prediction of ventricular origin in outflow tract ventricular arrhythmias

In order to determine the site of origin (SOO) in outflow tract ventricular arrhythmias (OTVAs) before an ablation procedure, several algorithms based on manual identification of electrocardiogram (ECG) features, have been developed. However, the reported accuracy decreases when tested with different datasets. Machine learning algorithms can automatize the process and improve generalization, but their performance is hampered by the lack of large enough OTVA databases. We propose the use of detailed electrophysiological simulations of OTVAs to train a machine learning classification model to predict the ventricular origin of the SOO of ectopic beats. We generated a synthetic database of 12-lead ECGs (2,496 signals) by running multiple simulations from the most typical OTVA SOO in 16 patient-specific geometries. Two types of input data were considered in the classification, raw and feature ECG signals. From the simulated raw 12-lead ECG, we analyzed the contribution of each lead in the predictions, keeping the best ones for the training process. For feature-based analysis, we used entropy-based methods to rank the obtained features. A cross-validation process was included to evaluate the machine learning model. Following, two clinical OTVA databases from different hospitals, including ECGs from 365 patients, were used as test-sets to assess the generalization of the proposed approach. The results show that V2 was the best lead for classification. Prediction of the SOO in OTVA, using both raw signals or features for classification, presented high accuracy values (>0.96). Generalization of the network trained on simulated data was good for both patient datasets (accuracy of 0.86 and 0.84, respectively) and presented better values than using exclusively real ECGs for classification (accuracy of 0.84 and 0.76 for each dataset). The use of simulated ECG data for training machine learning-based classification algorithms is critical to obtain good SOO predictions in OTVA compared to real data alone. The fast implementation and generalization of the proposed methodology may contribute towards its application to a clinical routine.

Balancing conduction velocity error in cardiac electrophysiology using a modified quadrature approach

Conduction velocity error is often the main culprit behind the need for very fine spatial discretizations and high computational effort in cardiac electrophysiology problems. In light of this, a novel approach for simulating an accurate conduction velocity in coarse meshes with linear elements is suggested based on a modified quadrature approach. In this approach, the quadrature points are placed at arbitrary offsets of the isoparametric coordinates. A numerical study illustrates the dependence of the conduction velocity on the spatial discretization and the conductivity when using different quadrature rules and calculation approaches. Additionally, examples using the modified quadrature in coarse meshes for wave propagation demonstrate the improved accuracy of the conduction velocity with this method. This novel approach possesses great potential in reducing the computational effort required but remains limited to specific linear elements and experiences a reduction in accuracy for irregular meshes and heterogeneous conductivities. Further research can focus on developing an adaptive quadrature and extending the approach to other element formulations in order to make the approach more generally applicable.

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

Analysis of vulnerability to reentry in acute myocardial ischemia using a realistic human heart model

Electrophysiological alterations of the myocardium caused by acute ischemia constitute a pro-arrhythmic substrate for the generation of potentially lethal arrhythmias. Experimental evidence has shown that the main components of acute ischemia that induce these electrophysiological alterations are hyperkalemia, hypoxia (or anoxia in complete artery occlusion), and acidosis. However, the influence of each ischemic component on the likelihood of reentry is not completely established. Moreover, the role of the His-Purkinje system (HPS) in the initiation and maintenance of arrhythmias is not completely understood. In the present work, we investigate how the three components of ischemia affect the vulnerable window (VW) for reentry using computational simulations. In addition, we analyze the role of the HPS on arrhythmogenesis. A 3D biventricular/torso human model that includes a realistic geometry of the central and border ischemic zones with one of the most electrophysiologically detailed model of ischemia to date, as well as a realistic cardiac conduction system, were used to assess the VW for reentry. Four scenarios of ischemic severity corresponding to different minutes after coronary artery occlusion were simulated. Our results suggest that ischemic severity plays an important role in the generation of reentries. Indeed, this is the first 3D simulation study to show that ventricular arrhythmias could be generated under moderate ischemic conditions, but not in mild and severe ischemia. Moreover, our results show that anoxia is the ischemic component with the most significant effect on the width of the VW. Thus, a change in the level of anoxia from moderate to severe leads to a greater increment in the VW (40 ms), in comparison with the increment of 20 ms and 35 ms produced by the individual change in the level of hyperkalemia and acidosis, respectively. Finally, the HPS was a necessary element for the generation of approximately 17% of reentries obtained. The retrograde conduction from the myocardium to HPS in the ischemic region, conduction blocks in discrete sections of the HPS, and the degree of ischemia affecting Purkinje cells, are suggested as mechanisms that favor the generation of ventricular arrhythmias.

Directed Network Mapping Approach to Rotor Localization in Atrial Fibrillation Simulation

Catheter ablation for atrial fibrillation (AF) is one of the most commonly performed electrophysiology procedures. Despite significant advances in our understanding of AF mechanisms in the last years, ablation outcomes remain suboptimal for many patients, particularly those with persistent or long-standing AF. A possible reason is that ablation techniques mainly focus on anatomic, rather than patient-specific functional targets for ablation. The identification of such ablation targets remains challenging. The purpose of this study is to investigate a novel approach based on directed networks, which allow the automatic detection of important arrhythmia mechanisms, that can be convenient for guiding the ablation strategy. The networks are generated by processing unipolar electrograms (EGMs) collected by the catheters positioned at the different regions of the atria. Network vertices represent the locations of the recordings and edges are determined using cross-covariance time-delay estimation method. The algorithm identifies rotational activity, spreading from vertex to vertex creating a cycle. This work is a simulation study and it uses a highly detailed computational 3D model of human atria in which sustained rotor activation of the atria was achieved. Virtual electrodes were placed on the endocardial surface, and EGMs were calculated at each of these electrodes. The propagation of the electric wave fronts in the atrial myocardium during AF is very complex, so in order to properly capture wave propagation patterns, we split EGMs into multiple short time frames. Then, a specific network for each of these time frames was generated, and the cycles repeating in consecutive networks point us to the stable rotor's location. The respective atrial voltage map served as reference. By detecting a cycle between the same 3 nodes in 19 out of 58 networks, where 10 of these networks were in consecutive time frames, a stable rotor was successfully located.

Macrophage-Dependent Interleukin-6-Production and Inhibition of IK Contributes to Acquired QT Prolongation in Lipotoxic Guinea Pig Heart

In the heart, the delayed rectifier K current, I_K, composed of the rapid (I_Kr) and slow (I_Ks) components contributes prominently to normal cardiac repolarization. In lipotoxicity, chronic elevation of pro-inflammatory cytokines may remodel I_K, elevating the risk for ventricular arrythmias and sudden cardiac death. We investigated whether and how the pro-inflammatory interleukin-6 altered I_K in the heart, using electrophysiology to evaluate changes in I_K in adult guinea pig ventricular myocytes. We found that palmitic acid (a potent inducer of lipotoxicity), induced a rapid (~24 h) and significant increase in IL-6 in RAW264.7 cells. PA-diet fed guinea pigs displayed a severely prolonged QT interval when compared to low-fat diet fed controls. Exposure to isoproterenol induced torsade de pointes, and ventricular fibrillation in lipotoxic guinea pigs. Pre-exposure to IL-6 with the soluble IL-6 receptor produced a profound depression of I_Kr and I_Ks densities, prolonged action potential duration, and impaired mitochondrial ATP production. Only with the inhibition of I_Kr did a proarrhythmic phenotype of I_Ks depression emerge, manifested as a further prolongation of action potential duration and QT interval. Our data offer unique mechanistic insights with implications for pathological QT interval in patients and vulnerability to fatal arrhythmias.

The Effects of Fibrotic Cell Type and Its Density on Atrial Fibrillation Dynamics: An In Silico Study

Remodeling in atrial fibrillation (AF) underlines the electrical and structural changes in the atria, where fibrosis is a hallmark of arrhythmogenic structural alterations. Fibrosis is an important feature of the AF substrate and can lead to abnormal conduction and, consequently, mechanical dysfunction. The fibrotic process comprises the presence of fibrotic cells, including fibroblasts, myofibroblasts and fibrocytes, which play an important role during fibrillatory dynamics. This work assesses the effect of the diffuse fibrosis density and the intermingled presence of the three types of fibrotic cells on the dynamics of persistent AF. For this purpose, the three fibrotic cells were electrically coupled to cardiomyocytes in a 3D realistic model of human atria. Low (6.25%) and high (25%) fibrosis densities were implemented in the left atrium according to a diffuse fibrosis representation. We analyze the action potential duration, conduction velocity and fibrillatory conduction patterns. Additionally, frequency analysis was performed in 50 virtual electrograms. The tested fibrosis configurations generated a significant conduction velocity reduction, where the larger effect was observed at high fibrosis density (up to 82% reduction in the fibrocytes configuration). Increasing the fibrosis density intensifies the vulnerability to multiple re-entries, zigzag propagation, and chaotic activity in the fibrillatory conduction. The most complex propagation patterns were observed at high fibrosis densities and the fibrocytes are the cells with the largest proarrhythmic effect. Left-to-right dominant frequency gradients can be observed for all fibrosis configurations, where the fibrocytes configuration at high density generates the most significant gradients (up to 4.5 Hz). These results suggest the important role of different fibrotic cell types and their density in diffuse fibrosis on the chaotic propagation patterns during persistent AF.

Atrial proarrhythmic effect of lead as one of the PM10 metal components of air pollution. An in-silico study

Particulate matter (PM) is considered the most severe environmental pollution problem due to its serious effects on human health associated with an increased risk of cardiovascular morbidity and mortality. In this work, a physicochemical characterization of PM10 from the city of Medellin was developed. The results evince that lead (Pb) is one of the most abundant elements since it is present in all analyzed samples. Therefore, Pb was chosen to perform an in-silico study to assess its effects on atrial arrhythmias generation. For this purpose, we developed a model representing the Pb2+ blocking effect on the L-type calcium channel. This formulation was incorporated in a human atrial cell mathematical model and in 2D and 3D models of human atria. The simulations showed a proarrhythmic effect at high Pb2+ concentrations, through shortening of action potential duration inducing the generation of reentrant activity and atrial flutter. The results contribute to the knowledge about the cardiac physiopathological processes, triggered by lead as one of the main PM10 metal components of air pollution, that yields the generation of arrhythmias.

Characterization of Atrial Propagation Patterns and Fibrotic Substrate With a Modified Omnipolar Electrogram Strategy in Multi-Electrode Arrays

Introduction: The omnipolar electrogram method was recently proposed to try to generate orientation-independent electrograms. It estimates the electric field from the bipolar electrograms of a clique, under the assumption of locally plane and homogeneous propagation. The local electric field evolution over time describes a loop trajectory from which omnipolar signals in the propagation direction, substrate and propagation features, are derived. In this work, we propose substrate and conduction velocity mapping modalities based on a modified version of the omnipolar electrogram method, which aims to reduce orientation-dependent residual components in the standard approach.

Methods: A simulated electrical propagation in 2D, with a tissue including a circular patch of diffuse fibrosis, was used for validation. Unipolar electrograms were calculated in a multi-electrode array, also deriving bipolar electrograms along the two main directions of the grid. Simulated bipolar electrograms were also contaminated with real noise, to assess the robustness of the mapping strategies against noise. The performance of the maps in identifying fibrosis and in reproducing unipolar reference voltage maps was evaluated. Bipolar voltage maps were also considered for performance comparison.

Results: Results show that the modified omnipolar mapping strategies are more accurate and robust against noise than bipolar and standard omnipolar maps in fibrosis detection (accuracies higher than 85 vs. 80% and 70%, respectively). They present better correlation with unipolar reference voltage maps than bipolar and original omnipolar maps (Pearson's correlations higher than 0.75 vs. 0.60 and 0.70, respectively).

Conclusion: The modified omnipolar method improves fibrosis detection, characterization of substrate and propagation, also reducing the residual sensitivity to directionality over the standard approach and improving robustness against noise. Nevertheless, studies with real electrograms will elucidate its impact in catheter ablation interventions.

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.

Analysis of the response of human iPSC-derived cardiomyocyte tissue to ICaL block. A combined in vitro and in silico approach

The high incidence of cardiac arrythmias underlines the need for the assessment of pharmacological therapies. In this field of drug efficacy, as in the field of drug safety highlighted by the Comprehensive in Vitro Proarrhythmia Assay initiative, new pillars for research have become crucial: firstly, the integration of in-silico experiments, and secondly the evaluation of fully integrated biological systems, such as human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). In this study, we therefore aimed to combine in-vitro experiments and in-silico simulations to evaluate the antiarrhythmic effect of L-type calcium current (I_CaL) block in hiPSC-CMs. For this, hiPSC-CM preparations were cultured and an equivalent virtual tissue was modeled. Re-entry patterns of electrical activation were induced and several biomarkers were obtained before and after I_CaL block. The virtual hiPSC-CM simulations were also reproduced using a tissue composed of adult ventricular cardiomyocytes (hAdultV-CMs). The analysis of phases, currents and safety factor for propagation showed an increased size of the re-entry core when I_CaL was blocked as a result of depressed cellular excitability. The bigger wavefront curvature yielded reductions of 12.2%, 6.9%, and 4.2% in the frequency of the re-entry for hiPSC-CM cultures, virtual hiPSC-CM, and hAdultV-CM tissues, respectively. Furthermore, I_CaL block led to a 47.8% shortening of the vulnerable window for re-entry in the virtual hiPSC-CM tissue and to re-entry vanishment in hAdultV-CM tissue. The consistent behavior between in-vitro and in-silico hiPSC-CMs and between in-silico hiPSC-CMs and hAdultV-CMs evidences that virtual hiPSC-CM tissues are suitable for assessing cardiac efficacy, as done in the present study through the analysis of I_CaL block.

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

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

Arrhythmogenic Effects of Genetic Mutations Affecting Potassium Channels in Human Atrial Fibrillation: A Simulation Study

Genetic mutations in genes encoding for potassium channel protein structures have been recently associated with episodes of atrial fibrillation in asymptomatic patients. The aim of this study is to investigate the potential arrhythmogenicity of three gain-of-function mutations related to atrial fibrillation—namely, KCNH2 T895M, KCNH2 T436M, and KCNE3-V17M—using modeling and simulation of the electrophysiological activity of the heart. A genetic algorithm was used to tune the parameters’ value of the original ionic currents to reproduce the alterations experimentally observed caused by the mutations. The effects on action potentials, ionic currents, and restitution properties were analyzed using versions of the Courtemanche human atrial myocyte model in different tissues: pulmonary vein, right, and left atrium. Atrial susceptibility of the tissues to spiral wave generation was also investigated studying the temporal vulnerability. The presence of the three mutations resulted in an overall more arrhythmogenic substrate. Higher current density, action potential duration shortening, and flattening of the restitution curves were the major effects of the three mutations at the single-cell level. The genetic mutations at the tissue level induced a higher temporal vulnerability to the rotor’s initiation and progression, by sustaining spiral waves that perpetuate until the end of the simulation. The mutation with the highest pro-arrhythmic effects, exhibiting the widest sustained VW and the smallest meandering rotor’s tip areas, was KCNE3-V17M. Moreover, the increased susceptibility to arrhythmias and rotor’s stability was tissue-dependent. Pulmonary vein tissues were more prone to rotor’s initiation, while in left atrium tissues rotors were more easily sustained. Re-entries were also progressively more stable in pulmonary vein tissue, followed by the left atrium, and finally the right atrium. The presence of the genetic mutations increased the susceptibility to arrhythmias by promoting the rotor’s initiation and maintenance. The study provides useful insights into the mechanisms underlying fibrillatory events caused by KCNH2 T895M, KCNH2 T436M, and KCNE3-V17M and might aid the planning of patient-specific targeted therapies.

A numerical study on the effects of spatial and temporal discretization in cardiac electrophysiology

Millions of degrees of freedom are often required to accurately represent the electrophysiology of the myocardium due to the presence of discretization effects. This study seeks to explore the influence of temporal and spatial discretization on the simulation of cardiac electrophysiology in conjunction with changes in modeling choices. Several finite element analyses are performed to examine how discretization affects solution time, conduction velocity and electrical excitation. Discretization effects are considered along with changes in the electrophysiology model and solution approach. Two action potential models are considered: the Aliev-Panfilov model and the ten Tusscher-Noble-Noble-Panfilov model. The solution approaches consist of two time integration schemes and different treatments for solving the local system of ordinary differential equations. The efficiency and stability of the calculation approaches are demonstrated to be dependent on the action potential model. The dependency of the conduction velocity on the element size and time step is shown to be different for changes in material parameters. Finally, the discrepancies between the wave propagation in coarse and fine meshes are analyzed based on the temporal evolution of the transmembrane potential at a node and its neighboring Gauss points. Insight obtained from this study can be used to suggest new methods to improve the efficiency of simulations in cardiac electrophysiology.

Immuno-Electrophysiological Mechanisms of Functional Electrical Connections Between Recipient and Donor Heart in Patients With Orthotopic Heart Transplantation Presenting With Atrial Arrhythmias

[Figure: see text].

The role of β-adrenergic system remodeling in human heart failure: A mechanistic investigation

β-adrenergic receptor antagonists (β-blockers) are extensively used to improve cardiac performance in heart failure (HF), but the electrical improvements with these clinical treatments are not fully understood. The aim of this study was to analyze the electrophysiological effects of β-adrenergic system remodeling in heart failure with reduced ejection fraction and the underlying mechanisms. We used a combined mathematical model that integrated β-adrenergic signaling with electrophysiology and calcium cycling in human ventricular myocytes. HF remodeling, both in the electrophysiological and signaling systems, was introduced to quantitatively analyze changes in electrophysiological properties due to the stimulation of β-adrenergic receptors in failing myocytes. We found that the inotropic effect of β-adrenergic stimulation was reduced in HF due to the altered Ca²⁺ dynamics resulting from the combination of structural, electrophysiological and signaling remodeling. Isolated cells showed proarrhythmic risk after sympathetic stimulation because early afterdepolarizations appeared, and the vulnerability was greater in failing myocytes. When analyzing coupled cells, β-adrenergic stimulation reduced transmural repolarization gradients between endocardium and epicardium in normal tissue, but was less effective at reducing these gradients after HF remodeling. The comparison of the selective activation of β-adrenergic isoforms revealed that the response to β₂-adrenergic receptors stimulation was blunted in HF while β₁-adrenergic receptors downstream effectors regulated most of the changes observed after sympathetic stimulation. In conclusion, this study was able to reproduce an altered β-adrenergic activity on failing myocytes and to explain the mechanisms involved. The derived predictions could help in the treatment of HF and guide in the design of future experiments.

Characterization of T Wave Amplitude, Duration and Morphology Changes During Hemodialysis: Relationship With Serum Electrolyte Levels and Heart Rate

OBJECTIVE

Chronic kidney disease affects more than 10% of the world population. Changes in serum ion concentrations increase the risk for ventricular arrhythmias and sudden cardiac death, particularly in end-stage renal disease (ESRD) patients. We characterized how T wave amplitude, duration and morphology descriptors change with variations in serum levels of potassium and calcium and in heart rate, both in ESRD patients and in simulated ventricular fibers.

METHODS

Electrocardiogram (ECG) recordings from twenty ESRD patients undergoing hemodialysis (HD) and pseudo-ECGs (pECGs) calculated from twenty-two simulated ventricular fibers at varying transmural heterogeneity levels were processed to quantify T wave width ( T_w), T wave slope-to-amplitude ratio ([Formula: see text]) and four indices of T wave morphological variability based on time warping ( d_w, [Formula: see text], d_a and [Formula: see text]). Serum potassium and calcium levels and heart rate were measured along HD.

RESULTS

[Formula: see text] was the marker most strongly correlated with serum potassium, dw with calcium and da with heart rate, after correction for covariates. Median values of partial correlation coefficients were 0.75, -0.74 and -0.90, respectively. For all analyzed T wave descriptors, high inter-patient variability was observed in the pattern of such relationships. This variability, accentuated during the first HD time points, was reproduced in the simulations and shown to be influenced by differences in transmural heterogeneity.

CONCLUSION

Changes in serum potassium and calcium levels and in heart rate strongly affect T wave descriptors, particularly those quantifying morphological variability.

SIGNIFICANCE

ECG markers have the potential to be used for monitoring serum ion concentrations in ESRD patients.

The Antimalarial Chloroquine Reduces the Burden of Persistent Atrial Fibrillation

In clinical practice, reducing the burden of persistent atrial fibrillation by pharmacological means is challenging. We explored if blocking the background and the acetylcholine-activated inward rectifier potassium currents (I_K1 and I_KACh) could be antiarrhythmic in persistent atrial fibrillation. We thus tested the hypothesis that blocking I_K1 and I_KACh with chloroquine decreases the burden of persistent atrial fibrillation. We used patch clamp to determine the IC₅₀ of I_K1 and I_KACh block by chloroquine and molecular modeling to simulate the interaction between chloroquine and Kir2.1 and Kir3.1, the molecular correlates of I_K1 and I_KACh. We then tested, as a proof of concept, if oral chloroquine administration to a patient with persistent atrial fibrillation can decrease the arrhythmia burden. We also simulated the effects of chloroquine in a 3D model of human atria with persistent atrial fibrillation. In patch clamp the IC₅₀ of I_K1 block by chloroquine was similar to that of I_KACh. A 14-day regimen of oral chloroquine significantly decreased the burden of persistent atrial fibrillation in a patient. Mathematical simulations of persistent atrial fibrillation in a 3D model of human atria suggested that chloroquine prolonged the action potential duration, leading to failure of reentrant excitation, and the subsequent termination of the arrhythmia. The combined block of I_K1 and I_KACh can be a targeted therapeutic strategy for persistent atrial fibrillation.

Mechanistic investigation of Ca2+ alternans in human heart failure and its modulation by fibroblasts

Background

Heart failure (HF) is characterized, among other factors, by a progressive loss of contractile function and by the formation of an arrhythmogenic substrate, both aspects partially related to intracellular Ca²⁺ cycling disorders. In failing hearts both electrophysiological and structural remodeling, including fibroblast proliferation, contribute to changes in Ca²⁺ handling which promote the appearance of Ca²⁺ alternans (Ca-alt). Ca-alt in turn give rise to repolarization alternans, which promote dispersion of repolarization and contribute to reentrant activity. The computational analysis of the incidence of Ca²⁺ and/or repolarization alternans under HF conditions in the presence of fibroblasts could provide a better understanding of the mechanisms leading to HF arrhythmias and contractile function disorders.

Methods and findings

The goal of the present study was to investigate in silico the mechanisms leading to the formation of Ca-alt in failing human ventricular myocytes and tissues with disperse fibroblast distributions. The contribution of ionic currents variability to alternans formation at the cellular level was analyzed and the results show that in normal ventricular tissue, altered Ca²⁺ dynamics lead to Ca-alt, which precede APD alternans and can be aggravated by the presence of fibroblasts. Electrophysiological remodeling of failing tissue alone is sufficient to develop alternans. The incidence of alternans is reduced when fibroblasts are present in failing tissue due to significantly depressed Ca²⁺ transients. The analysis of the underlying ionic mechanisms suggests that Ca-alt are driven by Ca²⁺-handling protein and Ca²⁺ cycling dysfunctions in the junctional sarcoplasmic reticulum and that their contribution to alternans occurrence depends on the cardiac remodeling conditions and on myocyte-fibroblast interactions.

Conclusion

It can thus be concluded that fibroblasts modulate the formation of Ca-alt in human ventricular tissue subjected to heart failure-related electrophysiological remodeling. Pharmacological therapies should thus consider the extent of both the electrophysiological and structural remodeling present in the failing heart.

Personalized Cardiac Computational Models: From Clinical Data to Simulation of Infarct-Related Ventricular Tachycardia

In the chronic stage of myocardial infarction, a significant number of patients develop life-threatening ventricular tachycardias (VT) due to the arrhythmogenic nature of the remodeled myocardium. Radiofrequency ablation (RFA) is a common procedure to isolate reentry pathways across the infarct scar that are responsible for VT. Unfortunately, this strategy show relatively low success rates; up to 50% of patients experience recurrent VT after the procedure. In the last decade, intensive research in the field of computational cardiac electrophysiology (EP) has demonstrated the ability of three-dimensional (3D) cardiac computational models to perform in-silico EP studies. However, the personalization and modeling of certain key components remain challenging, particularly in the case of the infarct border zone (BZ). In this study, we used a clinical dataset from a patient with a history of infarct-related VT to build an image-based 3D ventricular model aimed at computational simulation of cardiac EP, including detailed patient-specific cardiac anatomy and infarct scar geometry. We modeled the BZ in eight different ways by combining the presence or absence of electrical remodeling with four different levels of image-based patchy fibrosis (0, 10, 20, and 30%). A 3D torso model was also constructed to compute the ECG. Patient-specific sinus activation patterns were simulated and validated against the patient's ECG. Subsequently, the pacing protocol used to induce reentrant VTs in the EP laboratory was reproduced in-silico. The clinical VT was induced with different versions of the model and from different pacing points, thus identifying the slow conducting channel responsible for such VT. Finally, the real patient's ECG recorded during VT episodes was used to validate our simulation results and to assess different strategies to model the BZ. Our study showed that reduced conduction velocities and heterogeneity in action potential duration in the BZ are the main factors in promoting reentrant activity. Either electrical remodeling or fibrosis in a degree of at least 30% in the BZ were required to initiate VT. Moreover, this proof-of-concept study confirms the feasibility of developing 3D computational models for cardiac EP able to reproduce cardiac activation in sinus rhythm and during VT, using exclusively non-invasive clinical data.

Far-field contributions in multi-electrodes atrial recordings blur distinction between anatomical and functional reentries and may cause imaginary phase singularities - A computational study

BACKGROUND

Atrial fibrillation (AF) is the most common cardiac arrhythmia and the most important cause of embolic stroke, requiring new technologies for its better understanding and therapies. Recent approaches to map the electrical activity during AF with multi-electrode systems aim at localizing patient-specific ablation targets of reentrant patterns. However, there is a critical need to determine the accuracy of those mapping systems. We performed computer simulations as a numerical approach of systematically evaluating the influence of far-field sources on the electrical recordings and detection of rotors.

METHODS

We constructed 2 computer models of atrial tissue: (i) a 2D sheet model with varying non-active cells area in its center, and (ii) a whole realistic 3D atrial model. Phase maps were built based on the Hilbert transform of the unipolar electrograms recorded by virtual 2D and 3D multi-electrode systems and rotors were tracked through phase singularities detections.

RESULTS

Analysis of electrograms recorded away from the 2D atrial model shows that the larger the distance between an electrode and the tissue model, the stronger the far-field sources contribution to the electrogram is. Importantly, even if an electrode is positioned in contact with the tissue, the electrogram contains significant contributions from distal sources that blur the distinction between anatomical and functional reentries. Moreover, when mapping the 3D atrial model, remote activity generated false phase singularities at locations without local reentrant excitation patterns.

CONCLUSIONS

Far-field contributions to electrograms during AF reduce the accuracy of detecting and interpreting reentrant activity.

Optimization of Lead Placement in the Right Ventricle During Cardiac Resynchronization Therapy. A Simulation Study

Patients suffering from heart failure and left bundle branch block show electrical ventricular dyssynchrony causing an abnormal blood pumping. Cardiac resynchronization therapy (CRT) is recommended for these patients. Patients with positive therapy response normally present QRS shortening and an increased left ventricle (LV) ejection fraction. However, around one third do not respond favorably. Therefore, optimal location of pacing leads, timing delays between leads and/or choosing related biomarkers is crucial to achieve the best possible degree of ventricular synchrony during CRT application. In this study, computational modeling is used to predict the optimal location and delay of pacing leads to improve CRT response. We use a 3D electrophysiological computational model of the heart and torso to get insight into the changes in the activation patterns obtained when the heart is paced from different regions and for different atrioventricular and interventricular delays. The model represents a heart with left bundle branch block and heart failure, and allows a detailed and accurate analysis of the electrical changes observed simultaneously in the myocardium and in the QRS complex computed in the precordial leads. Computational simulations were performed using a modified version of the O'Hara et al. action potential model, the most recent mathematical model developed for human ventricular electrophysiology. The optimal location for the pacing leads was determined by QRS maximal reduction. Additionally, the influence of Purkinje system on CRT response was assessed and correlation analysis between several parameters of the QRS was made. Simulation results showed that the right ventricle (RV) upper septum near the outflow tract is an alternative location to the RV apical lead. Furthermore, LV endocardial pacing provided better results as compared to epicardial stimulation. Finally, the time to reach the 90% of the QRS area was a good predictor of the instant at which 90% of the ventricular tissue was activated. Thus, the time to reach the 90% of the QRS area is suggested as an additional index to assess CRT effectiveness to improve biventricular synchrony.

Computational Multiscale Solvers for Continuum Approaches

Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper.

DENIS: Solving cardiac electrophysiological simulations with volunteer computing

Cardiac electrophysiological simulations are computationally intensive tasks. The growing complexity of cardiac models, together with the increasing use of large ensembles of models (known as populations of models), make extensive simulation studies unfeasible for regular stand-alone computers. To address this problem, we developed DENIS, a cardiac electrophysiology simulator based on the volunteer computing paradigm. We evaluated the performance of DENIS by testing the effect of simulation length, task deadline, and batch size, on the time to complete a batch of simulations. In the experiments, the time to complete a batch of simulations did not increase with simulation length, and had little dependence on batch size. In a test case involving the generation of a population of models, DENIS was able to reduce the simulation time from years to a few days when compared to a stand-alone computer. Such capacity makes it possible to undertake large cardiac simulation projects without the need for high performance computing infrastructure.

A response surface optimization approach to adjust ionic current conductances of cardiac electrophysiological models. Application to the study of potassium level changes

Cardiac electrophysiological computational models are often developed from previously published models. The new models may incorporate additional features to adapt the model to a different species or may upgrade a specific ionic formulation based on newly available experimental data. A relevant challenge in the development of a new model is the estimation of certain ionic current conductances that cannot be reliably identified from experiments. A common strategy to estimate those conductances is by means of constrained non-linear least-squares optimization. In this work, a novel methodology is proposed for estimation of ionic current conductances of cardiac electrophysiological models by using a response surface approximation-based constrained optimization with trust region management. Polynomial response surfaces of a number of electrophysiological markers were built using statistical sampling methods. These markers included action potential duration (APD), triangulation, diastolic and systolic intracellular calcium concentration, and time constants of APD rate adaptation. The proposed methodology was applied to update the Carro et al. human ventricular action potential model after incorporation of intracellular potassium ([K⁺]_i) dynamics. While the Carro et al. model was well suited for investigation of arrhythmogenesis, it did not allow simulation of [K⁺]_i changes. With the methodology proposed in this study, the updated Carro et al. human ventricular model could be used to simulate [K⁺]_i changes in response to varying extracellular potassium ([K⁺]_o) levels. Additionally, it rendered values of evaluated electrophysiological markers within physiologically plausible ranges. The optimal values of ionic current conductances in the updated model were found in a notably shorter time than with previously proposed methodologies. As a conclusion, the response surface optimization-based approach proposed in this study allows estimating ionic current conductances of cardiac electrophysiological computational models while guaranteeing replication of key electrophysiological features and with an important reduction in computational cost with respect to previously published approaches. The updated Carro et al. model developed in this study is thus suitable for the investigation of arrhythmic risk-related conditions, including those involving large changes in potassium concentration.

Hierarchical Algorithms for Causality Retrieval in Atrial Fibrillation Intracavitary Electrograms

Multichannel intracavitary electrograms (EGMs) are acquired at the electrophysiology laboratory to guide radio frequency catheter ablation of patients suffering from atrial fibrillation. These EGMs are used by cardiologists to determine candidate areas for ablation (e.g., areas corresponding to high dominant frequencies or complex fractionated electrograms). In this paper, we introduce two hierarchical algorithms to retrieve the causal interactions among these multiple EGMs. Both algorithms are based on Granger causality, but other causality measures can be easily incorporated. In both cases, they start by selecting a root node, but they differ on the way in which they explore the set of signals to determine their cause-effect relationships: either testing the full set of unexplored signals (GS-CaRe) or performing a local search only among the set of neighbor EGMs (LS-CaRe). The ensuing causal model provides important information about the propagation of the electrical signals inside the atria, uncovering wavefronts and activation patterns that can guide cardiologists towards candidate areas for catheter ablation. Numerical experiments, on both synthetic signals and annotated real-world signals, show the good performance of the two proposed approaches.

Atrial Fibrosis Hampers Non-invasive Localization of Atrial Ectopic Foci From Multi-Electrode Signals: A 3D Simulation Study

Introduction: Focal atrial tachycardia is commonly treated by radio frequency ablation with an acceptable long-term success. Although the location of ectopic foci tends to appear in specific hot-spots, they can be located virtually in any atrial region. Multi-electrode surface ECG systems allow acquiring dense body surface potential maps (BSPM) for non-invasive therapy planning of cardiac arrhythmia. However, the activation of the atria could be affected by fibrosis and therefore biomarkers based on BSPM need to take these effects into account. We aim to analyze the effect of fibrosis on a BSPM derived index, and its potential application to predict the location of ectopic foci in the atria.

Methodology: We have developed a 3D atrial model that includes 5 distributions of patchy fibrosis in the left atrium at 5 different stages. Each stage corresponds to a different amount of fibrosis that ranges from 2 to 40%. The 25 resulting 3D models were used for simulation of Focal Atrial Tachycardia (FAT), triggered from 19 different locations described in clinical studies. BSPM were obtained for all simulations, and the body surface potential integral maps (BSPiM) were calculated to describe atrial activations. A machine learning (ML) pipeline using a supervised learning model and support vector machine was developed to learn the BSPM patterns of each of the 475 activation sequences and relate them to the origin of the FAT source.

Results: Activation maps for stages with more than 15% of fibrosis were greatly affected, producing conduction blocks and delays in propagation. BSPiMs did not always cluster into non-overlapped groups since BSPiMs were highly altered by the conduction blocks. From stage 3 (15% fibrosis) the BSPiMs showed differences for ectopic beats placed around the area of the pulmonary veins. Classification results were mostly above 84% for all the configurations studied when a large enough number of electrodes were used to map the torso. However, the presence of fibrosis increases the area of the ectopic focus location and therefore decreases the utility for the electrophysiologist.

Conclusions: The results indicate that the proposed ML pipeline is a promising methodology for non-invasive ectopic foci localization from BSPM signal even when fibrosis is present.

Real-Time Rotational Activity Detection in Atrial Fibrillation

Rotational activations, or spiral waves, are one of the proposed mechanisms for atrial fibrillation (AF) maintenance. We present a system for assessing the presence of rotational activity from intracardiac electrograms (EGMs). Our system is able to operate in real-time with multi-electrode catheters of different topologies in contact with the atrial wall, and it is based on new local activation time (LAT) estimation and rotational activity detection methods. The EGM LAT estimation method is based on the identification of the highest sustained negative slope of unipolar signals. The method is implemented as a linear filter whose output is interpolated on a regular grid to match any catheter topology. Its operation is illustrated on selected signals and compared to the classical Hilbert-Transform-based phase analysis. After the estimation of the LAT on the regular grid, the detection of rotational activity in the atrium is done by a novel method based on the optical flow of the wavefront dynamics, and a rotation pattern match. The methods have been validated using in silico and real AF signals.

Factors affecting basket catheter detection of real and phantom rotors in the atria: A computational study

Anatomically based procedures to ablate atrial fibrillation (AF) are often successful in terminating paroxysmal AF. However, the ability to terminate persistent AF remains disappointing. New mechanistic approaches use multiple-electrode basket catheter mapping to localize and target AF drivers in the form of rotors but significant concerns remain about their accuracy. We aimed to evaluate how electrode-endocardium distance, far-field sources and inter-electrode distance affect the accuracy of localizing rotors. Sustained rotor activation of the atria was simulated numerically and mapped using a virtual basket catheter with varying electrode densities placed at different positions within the atrial cavity. Unipolar electrograms were calculated on the entire endocardial surface and at each of the electrodes. Rotors were tracked on the interpolated basket phase maps and compared with the respective atrial voltage and endocardial phase maps, which served as references. Rotor detection by the basket maps varied between 35-94% of the simulation time, depending on the basket's position and the electrode-to-endocardial wall distance. However, two different types of phantom rotors appeared also on the basket maps. The first type was due to the far-field sources and the second type was due to interpolation between the electrodes; increasing electrode density decreased the incidence of the second but not the first type of phantom rotors. In the simulations study, basket catheter-based phase mapping detected rotors even when the basket was not in full contact with the endocardial wall, but always generated a number of phantom rotors in the presence of only a single real rotor, which would be the desired ablation target. Phantom rotors may mislead and contribute to failure in AF ablation procedures.

An atlas- and data-driven approach to initializing reaction-diffusion systems in computer cardiac electrophysiology

The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the initialization of reaction-diffusion systems for numerical simulations of cardiac EP from steady-state conditions. We exploit surface point correspondence to establish volumetric point correspondence. Upon introduction of a new 3D anatomy with surface point correspondence, a prediction of the cell model steady states is derived from the set of earlier biophysical simulations. We show that the prediction error is typically less than 10% for all model variables, with most variables showing even greater accuracy. When initializing simulations with the predicted model states, it is demonstrated that simulation times can be cut by at least two-thirds and potentially more, which saves hours or days of high-performance computing. Overall, these results increase the clinical applicability of detailed computational EP studies on personalized anatomies.

Non-invasive localization of atrial ectopic beats by using simulated body surface P-wave integral maps

Non-invasive localization of continuous atrial ectopic beats remains a cornerstone for the treatment of atrial arrhythmias. The lack of accurate tools to guide electrophysiologists leads to an increase in the recurrence rate of ablation procedures. Existing approaches are based on the analysis of the P-waves main characteristics and the forward body surface potential maps (BSPMs) or on the inverse estimation of the electric activity of the heart from those BSPMs. These methods have not provided an efficient and systematic tool to localize ectopic triggers. In this work, we propose the use of machine learning techniques to spatially cluster and classify ectopic atrial foci into clearly differentiated atrial regions by using the body surface P-wave integral map (BSPiM) as a biomarker. Our simulated results show that ectopic foci with similar BSPiM naturally cluster into differentiated non-intersected atrial regions and that new patterns could be correctly classified with an accuracy of 97% when considering 2 clusters and 96% for 4 clusters. Our results also suggest that an increase in the number of clusters is feasible at the cost of decreasing accuracy.

Atrial Fibrillation Dynamics and Ionic Block Effects in Six Heterogeneous Human 3D Virtual Atria with Distinct Repolarization Dynamics

Atrial fibrillation (AF) usually manifests as reentrant circuits propagating through the whole atria creating chaotic activation patterns. Little is yet known about how differences in electrophysiological and ionic properties between patients modulate reentrant patterns in AF. The goal of this study is to quantify how variability in action potential duration (APD) at different stages of repolarization determines AF dynamics and their modulation by ionic block using a set of virtual whole-atria human models. Six human whole-atria models are constructed based on the same anatomical structure and fiber orientation, but with different electrophysiological phenotypes. Membrane kinetics for each whole-atria model are selected with distinct APD characteristics at 20, 50, and 90% repolarization, from an experimentally calibrated population of human atrial action potential models, including AF remodeling and acetylcholine parasympathetic effects. Our simulations show that in all whole-atria models, reentrant circuits tend to organize around the pulmonary veins and the right atrial appendage, thus leading to higher dominant frequency (DF) and more organized activation in the left atrium than in the right atrium. Differences in APD in all phases of repolarization (not only APD₉₀) yielded quantitative differences in fibrillation patterns with long APD associated with slower and more regular dynamics. Long APD₅₀ and APD₂₀ were associated with increased interatrial conduction block and interatrial differences in DF and organization index, creating reentry instability and self-termination in some cases. Specific inhibitions of I_K1, I_NaK, or I_Na reduce DF and organization of the arrhythmia by enlarging wave meandering, reducing the number of secondary wavelets, and promoting interatrial block in all six virtual patients, especially for the phenotypes with short APD at 20, 50, and/or 90% repolarization. This suggests that therapies aiming at prolonging the early phase of repolarization might constitute effective antiarrhythmic strategies for the pharmacological management of AF. In summary, simulations report significant differences in atrial fibrillatory dynamics resulting from differences in APD at all phases of repolarization.

Limitations in electrophysiological model development and validation caused by differences between simulations and experimental protocols

Models of ion channel dynamics are usually built by fitting isolated cell experimental values of individual parameters while neglecting the interaction between them. Another shortcoming regards the estimation of ionic current conductances, which is often based on quantification of Action Potential (AP)-derived markers. Although this procedure reduces the uncertainty in the calculation of conductances, many studies evaluate electrophysiological AP-derived markers from single cell simulations, whereas experimental measurements are obtained from tissue preparations. In this work, we explore the limitations of these approaches to estimate ion channel dynamics and maximum current conductances and how they could be overcome by using multiscale simulations of experimental protocols. Four human ventricular cell models, namely ten Tusscher and Panfilov (2006), Grandi et al. (2010), O'Hara et al. (2011), and Carro et al. (2011), were used. Two problems involving scales from ion channels to tissue were investigated: 1) characterization of L-type calcium voltage-dependent inactivation I_Ca,L; 2) identification of major ionic conductance contributors to steady-state AP markers, including APD₉₀, APD₇₅, APD₅₀, APD₂₅, Triangulation and maximal and minimal values of V and dV/dt during the AP (V_max, V_min, dV/dt_max, dV/dt_min). Our results show that: 1) I_Ca,L inactivation characteristics differed significantly when calculated from model equations and from simulations reproducing the experimental protocols. 2) Large differences were found in the ionic currents contributors to APD₂₅, Triangulation, V_max, dV/dt_max and dV/dt_min between single cells and 1D-tissue. When proposing any new model formulation, or evaluating an existing model, consistency between simulated and experimental data should be verified considering all involved effects and scales.

Effect of the electrograms density in detecting and ablating the tip of the rotor during chronic atrial fibrillation: an in silico study

AIMS

Identification in situ of arrhythmogenic mechanisms could improve the rate of ablation success in atrial fibrillation (AF). Our research group reported that rotors could be located through dynamic approximate entropy (DApEn) maps. However, it is unknown how much the spatial resolution of catheter electrodes could affect substrates localization. The present work looked for assessing the electrograms (EGMs) spatial resolution needed to locate the rotor tip using DApEn maps.

METHODS AND RESULTS

A stable rotor in a two-dimensional computational model of human atrial tissue was simulated using the Courtemanche electrophysiological model and implementing chronic AF features. The spatial resolution is 0.4 mm (150 × 150 EGM). Six different lower resolution arrays were obtained from the initial mesh. For each array, DApEn maps were constructed using the inverse distance weighting (IDW) algorithm. Three simple ablation patterns were applied. The full DApEn map detected the rotor tip and was able to follow the small meander of the tip through the shape of the area containing the tip. Inverse distance weighting was able to reconstruct DApEn maps after applying different spatial resolutions. These results show that spatial resolutions from 0.4 to 4 mm accurately detect the rotor tip position. An ablation line terminates the rotor only if it crosses the tip and ends at a tissue boundary.

CONCLUSION

A previous work has shown that DApEn maps successfully detected simulated rotor tips using a high spatial resolution. In this work, it was evinced that DApEn maps could be applied using a spatial resolution similar to that available in commercial catheters, by adding an interpolation stage. This is the first step to translate this tool into medical practice with a view to the detection of ablation targets.

Detailed Anatomical and Electrophysiological Models of Human Atria and Torso for the Simulation of Atrial Activation

Atrial arrhythmias, and specifically atrial fibrillation (AF), induce rapid and irregular activation patterns that appear on the torso surface as abnormal P-waves in electrocardiograms and body surface potential maps (BSPM). In recent years both P-waves and the BSPM have been used to identify the mechanisms underlying AF, such as localizing ectopic foci or high-frequency rotors. However, the relationship between the activation of the different areas of the atria and the characteristics of the BSPM and P-wave signals are still far from being completely understood. In this work we developed a multi-scale framework, which combines a highly-detailed 3D atrial model and a torso model to study the relationship between atrial activation and surface signals in sinus rhythm. Using this multi scale model, it was revealed that the best places for recording P-waves are the frontal upper right and the frontal and rear left quadrants of the torso. Our results also suggest that only nine regions (of the twenty-one structures in which the atrial surface was divided) make a significant contribution to the BSPM and determine the main P-wave characteristics.

Modeling the different sections of the cardiac conduction system to obtain realistic electrocardiograms

The cardiac conduction system is divided in different sections that play an important role in the cardiac depolarization sequence and define the morphology of the electrocardiogram. In this study we have built several configurations for each section based on anatomical descriptions. The effect of the morphology of the bundle branches, and the density of both Purkinje branches and Purkinje-myocardial junctions (PMJ) has been studied by comparing the pseudo-ECGs obtained with the standard precordial leads of the electrocardiogram. A functional model for the PMJs based on the existence of a conduction adaptation layer is also presented. Simulation results showed a large influence of the His bundle and bundle branches in the pseudo-ECG and helped to elucidate the most appropriate morphology. The functional PMJ model allowed bidirectional communication between the conduction system and the myocardium with realistic transmission delays between both mediums. These results can help to improve current conduction system models and improve depolarization sequences of activation in the ventricles.

Three-dimensional cardiac computational modelling: methods, features and applications

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

Dynamic approximate entropy electroanatomic maps detect rotors in a simulated atrial fibrillation model

There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.

Electrophysiological and structural remodeling in heart failure modulate arrhythmogenesis. 1D simulation study

Background

Heart failure is a final common pathway or descriptor for various cardiac pathologies. It is associated with sudden cardiac death, which is frequently caused by ventricular arrhythmias. Electrophysiological remodeling, intercellular uncoupling, fibrosis and autonomic imbalance have been identified as major arrhythmogenic factors in heart failure etiology and progression.

Objective

In this study we investigate in silico the role of electrophysiological and structural heart failure remodeling on the modulation of key elements of the arrhythmogenic substrate, i.e., electrophysiological gradients and abnormal impulse propagation.

Methods

Two different mathematical models of the human ventricular action potential were used to formulate models of the failing ventricular myocyte. This provided the basis for simulations of the electrical activity within a transmural ventricular strand. Our main goal was to elucidate the roles of electrophysiological and structural remodeling in setting the stage for malignant life-threatening arrhythmias.

Results

Simulation results illustrate how the presence of M cells and heterogeneous electrophysiological remodeling in the human failing ventricle modulate the dispersion of action potential duration and repolarization time. Specifically, selective heterogeneous remodeling of expression levels for the Na⁺/Ca²⁺ exchanger and SERCA pump decrease these heterogeneities. In contrast, fibroblast proliferation and cellular uncoupling both strongly increase repolarization heterogeneities. Conduction velocity and the safety factor for conduction are also reduced by the progressive structural remodeling during heart failure.

Conclusion

An extensive literature now establishes that in human ventricle, as heart failure progresses, gradients for repolarization are changed significantly by protein specific electrophysiological remodeling (either homogeneous or heterogeneous). Our simulations illustrate and provide new insights into this. Furthermore, enhanced fibrosis in failing hearts, as well as reduced intercellular coupling, combine to increase electrophysiological gradients and reduce electrical propagation. In combination these changes set the stage for arrhythmias.

Electrophysiological and structural remodeling in heart failure modulate arrhythmogenesis. 2D simulation study

BACKGROUND

Heart failure is operationally defined as the inability of the heart to maintain blood flow to meet the needs of the body and it is the final common pathway of various cardiac pathologies. Electrophysiological remodeling, intercellular uncoupling and a pro-fibrotic response have been identified as major arrhythmogenic factors in heart failure.

OBJECTIVE

In this study we investigate vulnerability to reentry under heart failure conditions by incorporating established electrophysiological and anatomical remodeling using computer simulations.

METHODS

The electrical activity of human transmural ventricular tissue (5 cm × 5 cm) was simulated using the human ventricular action potential model Grandi et al. under control and heart failure conditions. The MacCannell et al. model was used to model fibroblast electrical activity, and their electrotonic interactions with myocytes. Selected degrees of diffuse fibrosis and variations in intercellular coupling were considered and the vulnerable window (VW) for reentry was evaluated following cross-field stimulation.

RESULTS

No reentry was observed in normal conditions or in the presence of HF ionic remodeling. However, defined amount of fibrosis and/or cellular uncoupling were sufficient to elicit reentrant activity. Under conditions where reentry was generated, HF electrophysiological remodeling did not alter the width of the VW. However, intermediate fibrosis and cellular uncoupling significantly widened the VW. In addition, biphasic behavior was observed, as very high fibrotic content or very low tissue conductivity hampered the development of reentry. Detailed phase analysis of reentry dynamics revealed an increase of phase singularities with progressive fibrotic components.

CONCLUSION

Structural remodeling is a key factor in the genesis of vulnerability to reentry. A range of intermediate levels of fibrosis and intercellular uncoupling can combine to favor reentrant activity.