Minimal model for human ventricular action potentials in tissue

Chaos control in cardiac dynamics: terminating chaotic states with local minima pacing

Current treatments of cardiac arrhythmias like ventricular fibrillation involve the application of a high-energy electric shock, that induces significant electrical currents in the myocardium and therefore involves severe side effects like possible tissue damage and post-traumatic stress. Using numerical simulations on four different models of 2D excitable media, this study demonstrates that low energy pulses applied shortly after local minima in the mean value of the transmembrane potential provide high success rates. We evaluate the performance of this approach for ten initial conditions of each model, ten spatially different stimuli, and different shock amplitudes. The investigated models of 2D excitable media cover a broad range of dominant frequencies and number of phase singularities, which demonstrates, that our findings are not limited to a specific kind of model or parameterization of it. Thus, we propose a method that incorporates the dynamics of the underlying system, even during pacing, and solely relies on a scalar observable, which is easily measurable in numerical simulations.

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.

T-wave inversion through inhomogeneous voltage diffusion within the FK3V cardiac model

The heart beats are due to the synchronized contraction of cardiomyocytes triggered by a periodic sequence of electrical signals called action potentials, which originate in the sinoatrial node and spread through the heart's electrical system. A large body of work is devoted to modeling the propagation of the action potential and to reproducing reliably its shape and duration. Connection of computational modeling of cells to macroscopic phenomenological curves such as the electrocardiogram has been also intense, due to its clinical importance in analyzing cardiovascular diseases. In this work, we simulate the dynamics of action potential propagation using the three-variable Fenton-Karma model that can account for both normal and damaged cells through a the spatially inhomogeneous voltage diffusion coefficient. We monitor the action potential propagation in the cardiac tissue and calculate the pseudo-electrocardiogram that reproduces the R and T waves. The R-wave amplitude varies according to a double exponential law as a function of the (spatially homogeneous, for an isotropic tissue) diffusion coefficient. The addition of spatial inhomogeneity in the diffusion coefficient by means of a defected region representing damaged cardiac cells may result in T-wave inversion in the calculated pseudo-electrocardiogram. The transition from positive to negative polarity of the T-wave is analyzed as a function of the length and the depth of the defected region.

Fast creation of data-driven low-order predictive cardiac tissue excitation models from recorded activation patterns

Excitable systems give rise to important phenomena such as heat waves, epidemics and cardiac arrhythmias. Understanding, forecasting and controlling such systems requires reliable mathematical representations. For cardiac tissue, computational models are commonly generated in a reaction-diffusion framework based on detailed measurements of ionic currents in dedicated single-cell experiments. Here, we show that recorded movies at the tissue-level of stochastic pacing in a single variable are sufficient to generate a mathematical model. Via exponentially weighed moving averages, we create additional state variables, and use simple polynomial regression in the augmented state space to quantify excitation wave dynamics. A spatial gradient-sensing term replaces the classical diffusion as it is more robust to noise. Our pipeline for model creation is demonstrated for an in-silico model and optical voltage mapping recordings of cultured human atrial myocytes and only takes a few minutes. Our findings have the potential for widespread generation, use and on-the-fly refinement of personalised computer models for non-linear phenomena in biology and medicine, such as predictive cardiac digital twins.

Computational Modeling of Cardiac Electrophysiology

Mathematical modeling and simulation are well-established and powerful tools to integrate experimental data of individual components of cardiac electrophysiology, excitation-contraction coupling, and regulatory signaling pathways, to gain quantitative and mechanistic insight into pathophysiological processes and guide therapeutic strategies. Here, we briefly describe the processes governing cardiac myocyte electrophysiology and Ca2+ handling and their regulation, as well as action potential propagation in tissue. We discuss the models and methods used to describe these phenomena, including procedures for model parameterization and validation, in addition to protocols for model interrogation and analysis and techniques that account for phenotypic variability and parameter uncertainty. Our objective is to provide a summary of basic concepts and approaches as a resource for scientists training in this discipline and for all researchers aiming to gain an understanding of cardiac modeling studies.

Current progress toward isogeometric modeling of the heart biophysics

In this paper, we review a powerful methodology to solve complex numerical simulations, known as isogeometric analysis, with a focus on applications to the biophysical modeling of the heart. We focus on the hemodynamics, modeling of the valves, cardiac tissue mechanics, and on the simulation of medical devices and treatments. For every topic, we provide an overview of the methods employed to solve the specific numerical issue entailed by the simulation. We try to cover the complete process, starting from the creation of the geometrical model up to the analysis and post-processing, highlighting the advantages and disadvantages of the methodology.

lifex-ep: a robust and efficient software for cardiac electrophysiology simulations

BACKGROUND

Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations, capable of accurately replicating both normal and pathological conditions, are still in the process of achieving full maturity within the scientific community.

RESULTS

This work introduces [Formula: see text]-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both normal and pathological conditions. [Formula: see text]-ep employs the monodomain equation to model the heart's electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, [Formula: see text]-ep integrates the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within [Formula: see text]-fiber. As an alternative, users can also choose to import myofibers from a file. This paper provides a concise overview of the mathematical models and numerical methods underlying [Formula: see text]-ep, along with comprehensive implementation details and instructions for users. [Formula: see text]-ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of [Formula: see text]-ep through various idealized and realistic simulations conducted in both normal and pathological scenarios. Furthermore, the software offers a user-friendly and flexible interface, simplifying the setup of simulations using self-documenting parameter files.

CONCLUSIONS

[Formula: see text]-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface. [Formula: see text]-ep represents a valuable tool for conducting in silico patient-specific simulations.

Differences in ventricular wall composition may explain inter-patient variability in the ECG response to variations in serum potassium and calcium

Objective: Chronic kidney disease patients have a decreased ability to maintain normal electrolyte concentrations in their blood, which increases the risk for ventricular arrhythmias and sudden cardiac death. Non-invasive monitoring of serum potassium and calcium concentration, [K+] and [Ca2+], can help to prevent arrhythmias in these patients. Electrocardiogram (ECG) markers that significantly correlate with [K+] and [Ca2+] have been proposed, but these relations are highly variable between patients. We hypothesized that inter-individual differences in cell type distribution across the ventricular wall can help to explain this variability. Methods: A population of human heart-torso models were built with different proportions of endocardial, midmyocardial and epicardial cells. Propagation of ventricular electrical activity was described by a reaction-diffusion model, with modified Ten Tusscher-Panfilov dynamics. [K+] and [Ca2+] were varied individually and in combination. Twelve-lead ECGs were simulated and the width, amplitude and morphological variability of T waves and QRS complexes were quantified. Results were compared to measurements from 29 end-stage renal disease (ESRD) patients undergoing hemodialysis (HD). Results: Both simulations and patients data showed that most of the analyzed T wave and QRS complex markers correlated strongly with [K+] (absolute median Pearson correlation coefficients, r, ranging from 0.68 to 0.98) and [Ca2+] (ranging from 0.70 to 0.98). The same sign and similar magnitude of median r was observed in the simulations and the patients. Different cell type distributions in the ventricular wall led to variability in ECG markers that was accentuated at high [K+] and low [Ca2+], in agreement with the larger variability between patients measured at the onset of HD. The simulated ECG variability explained part of the measured inter-patient variability. Conclusion: Changes in ECG markers were similarly related to [K+] and [Ca2+] variations in our models and in the ESRD patients. The high inter-patient ECG variability may be explained by variations in cell type distribution across the ventricular wall, with high sensitivity to variations in the proportion of epicardial cells. Significance: Differences in ventricular wall composition help to explain inter-patient variability in ECG response to [K+] and [Ca2+]. This finding can be used to improve serum electrolyte monitoring in ESRD patients.

What determines the optimal pharmacological treatment of atrial fibrillation? Insights from in silico trials in 800 virtual atria

The best pharmacological treatment for each atrial fibrillation (AF) patient is unclear. We aim to exploit AF simulations in 800 virtual atria to identify key patient characteristics that guide the optimal selection of anti-arrhythmic drugs. The virtual cohort considered variability in electrophysiology and low voltage areas (LVA) and was developed and validated against experimental and clinical data from ionic currents to ECG. AF sustained in 494 (62%) atria, with large inward rectifier K+ current (IK1 ) and Na+ /K+ pump (INaK ) densities (IK1 0.11 ± 0.03 vs. 0.07 ± 0.03 S mF-1 ; INaK 0.68 ± 0.15 vs. 0.38 ± 26 S mF-1 ; sustained vs. un-sustained AF). In severely remodelled left atrium, with LVA extensions of more than 40% in the posterior wall, higher IK1 (median density 0.12 ± 0.02 S mF-1 ) was required for AF maintenance, and rotors localized in healthy right atrium. For lower LVA extensions, rotors could also anchor to LVA, in atria presenting short refractoriness (median L-type Ca2+ current, ICaL , density 0.08 ± 0.03 S mF-1 ). This atrial refractoriness, modulated by ICaL and fast Na+ current (INa ), determined pharmacological treatment success for both small and large LVA. Vernakalant was effective in atria presenting long refractoriness (median ICaL density 0.13 ± 0.05 S mF-1 ). For short refractoriness, atria with high INa (median density 8.92 ± 2.59 S mF-1 ) responded more favourably to amiodarone than flecainide, and the opposite was found in atria with low INa (median density 5.33 ± 1.41 S mF-1 ). In silico drug trials in 800 human atria identify inward currents as critical for optimal stratification of AF patient to pharmacological treatment and, together with the left atrial LVA extension, for accurately phenotyping AF dynamics. KEY POINTS: Atrial fibrillation (AF) maintenance is facilitated by small L-type Ca2+ current (ICaL ) and large inward rectifier K+ current (IK1 ) and Na+ /K+ pump. In severely remodelled left atrium, with low voltage areas (LVA) covering more than 40% of the posterior wall, sustained AF requires higher IK1 and rotors localize in healthy right atrium. For lower LVA extensions, rotors can also anchor to LVA, if the atria present short refractoriness (low ICaL ) Vernakalant is effective in atria presenting long refractoriness (high ICaL ). For short refractoriness, atria with fast Na+ current (INa ) up-regulation respond more favourably to amiodarone than flecainide, and the opposite is found in atria with low INa . The inward currents (ICaL and INa ) are critical for optimal stratification of AF patient to pharmacological treatment and, together with the left atrial LVA extension, for accurately phenotyping AF dynamics.

Optimising low-energy defibrillation in 2D cardiac tissue with a genetic algorithm

Sequences of low-energy electrical pulses can effectively terminate ventricular fibrillation (VF) and avoid the side effects of conventional high-energy electrical defibrillation shocks, including tissue damage, traumatic pain, and worsening of prognosis. However, the systematic optimisation of sequences of low-energy pulses remains a major challenge. Using 2D simulations of homogeneous cardiac tissue and a genetic algorithm, we demonstrate the optimisation of sequences with non-uniform pulse energies and time intervals between consecutive pulses for efficient VF termination. We further identify model-dependent reductions of total pacing energy ranging from ∼4% to ∼80% compared to reference adaptive-deceleration pacing (ADP) protocols of equal success rate (100%).

A spatial threshold for astrocyte calcium surge

Astrocytes are active cells involved in brain function through the bidirectional communication with neurons, in which the astrocyte calcium signal plays a crucial role. Synaptically-evoked calcium increases can be localized to independent subcellular domains or expand to the entire cell, i.e., calcium surge. In turn, astrocytes may regulate individual synapses by calcium-dependent release of gliotransmitters. Because a single astrocyte may contact ~100,000 synapses, the control of the intracellular calcium signal propagation may have relevant consequences on brain function by regulating the spatial range of astrocyte neuromodulation of synapses. Yet, the properties governing the spatial dynamics of the astrocyte calcium signal remains poorly defined. Imaging subcellular responses of cortical astrocytes to sensory stimulation in mice, we show that sensory-evoked astrocyte calcium responses originated and remained localized in domains of the astrocytic arborization, but eventually propagated to the entire cell if a spatial threshold of >23% of the arborization being activated was surpassed. Using transgenic IP3R2-/- mice, we found that type-2 IP3 receptors were necessary for the generation of the astrocyte calcium surge. We finally show using in situ electrophysiological recordings that the spatial threshold of the astrocyte calcium signal consequently determined the gliotransmitter release. Present results reveal a fundamental property of astrocyte calcium physiology, i.e., a spatial threshold for the astrocyte intracellular calcium signal propagation, which depends on astrocyte intrinsic properties and governs the astrocyte integration of local synaptic activity and the subsequent neuromodulation.

A finite element model of the embryonic zebrafish heart electrophysiology

BACKGROUND AND OBJECTIVE

In the last 30 years, a growing interest has involved the study of zebrafish thanks to its physiological characteristics similar to those of humans. The aim of the following work is to create an electrophysiological computational model of the zebrafish heart and lay the foundation for the development of an in-silico model of the zebrafish heart that will allow to study the correlation between pathologies and drug administration with the main electrophysiological parameters as the ECG signal.

METHODS

The model considers a whole body and the two chambers of three days post fertilization (3 dpf) zebrafish. A four-variable phenomenological action potential model describes the action potential of different heart regions. Tissue conductivity was calibrated to reproduce the experimentally described activation sequence.

RESULTS

The model is able to correctly reproduce the activation sequence and times found in literature, with activation of the atrium and ventricle that correspond to 36 and 59 ms, respectively, and a delay of 14 ms caused by the presence of the atrioventricular band (AV band). Moreover, the obtained in-silico ECG reflects the main characteristics of the zebrafish ECG in good agreement with experimental records, a P-wave with a duration of approximately the total atrial activation, followed by a QRS complex of approximately 109 ms corresponding to ventricle activation.

CONCLUSIONS

The model allows the assessment of the main electrophysiological parameters in terms of activation sequence and timing, reproducing monopolar and bipolar ECG signals in line with experimental data. Coupling the proposed model with an electrophysiological detailed action potential model of zebrafish will represent a significant breakthrough toward the development of an in-silico zebrafish heart.

The role of pulse timing in cardiac defibrillation

Life-threatening cardiac arrhythmias require immediate defibrillation. For state-of-the-art shock treatments, a high field strength is required to achieve a sufficient success rate for terminating the complex spiral wave (rotor) dynamics underlying cardiac fibrillation. However, such high energy shocks have many adverse side effects due to the large electric currents applied. In this study, we show, using 2D simulations based on the Fenton-Karma model, that also pulses of relatively low energy may terminate the chaotic activity if applied at the right moment in time. In our simplified model for defibrillation, complex spiral waves are terminated by local perturbations corresponding to conductance heterogeneities acting as virtual electrodes in the presence of an external electric field. We demonstrate that time series of the success rate for low energy shocks exhibit pronounced peaks which correspond to short intervals in time during which perturbations aiming at terminating the chaotic fibrillation state are (much) more successful. Thus, the low energy shock regime, although yielding very low temporal average success rates, exhibits moments in time for which success rates are significantly higher than the average value shown in dose-response curves. This feature might be exploited in future defibrillation protocols for achieving high termination success rates with low or medium pulse energies.

Bayesian inference for fitting cardiac models to experiments: estimating parameter distributions using Hamiltonian Monte Carlo and approximate Bayesian computation

Customization of cardiac action potential models has become increasingly important with the recognition of patient-specific models and virtual patient cohorts as valuable predictive tools. Nevertheless, developing customized models by fitting parameters to data poses technical and methodological challenges: despite noise and variability associated with real-world datasets, traditional optimization methods produce a single "best-fit" set of parameter values. Bayesian estimation methods seek distributions of parameter values given the data by obtaining samples from the target distribution, but in practice widely known Bayesian algorithms like Markov chain Monte Carlo tend to be computationally inefficient and scale poorly with the dimensionality of parameter space. In this paper, we consider two computationally efficient Bayesian approaches: the Hamiltonian Monte Carlo (HMC) algorithm and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithm. We find that both methods successfully identify distributions of model parameters for two cardiac action potential models using model-derived synthetic data and an experimental dataset from a zebrafish heart. Although both methods appear to converge to the same distribution family and are computationally efficient, HMC generally finds narrower marginal distributions, while ABC-SMC is less sensitive to the algorithmic settings including the prior distribution.

Ventricular anatomical complexity and sex differences impact predictions from electrophysiological computational models

The aim of this work was to analyze the influence of sex hormones and anatomical details (trabeculations and false tendons) on the electrophysiology of healthy human hearts. Additionally, sex- and anatomy-dependent effects of ventricular tachycardia (VT) inducibility are presented. To this end, four anatomically normal, human, biventricular geometries (two male, two female), with identifiable trabeculations, were obtained from high-resolution, ex-vivo MRI and represented by detailed and smoothed geometrical models (with and without the trabeculations). Additionally one model was augmented by a scar. The electrophysiology finite element model (FEM) simulations were carried out, using O'Hara-Rudy human myocyte model with sex phenotypes of Yang and Clancy. A systematic comparison between detailed vs smooth anatomies, male vs female normal hearts was carried out. The heart with a myocardial infarction was subjected to a programmed stimulus protocol to identify the effects of sex and anatomical detail on ventricular tachycardia inducibility. All female hearts presented QT-interval prolongation however the prolongation interval in comparison to the male phenotypes was anatomy-dependent and was not correlated to the size of the heart. Detailed geometries showed QRS fractionation and increased T-wave magnitude in comparison to the corresponding smoothed geometries. A variety of sustained VTs were obtained in the detailed and smoothed male geometries at different pacing locations, which provide evidence of the geometry-dependent differences regarding the prediction of the locations of reentry channels. In the female phenotype, sustained VTs were induced in both detailed and smooth geometries with RV apex pacing, however no consistent reentry channels were identified. Anatomical and physiological cardiac features play an important role defining risk in cardiac disease. These are often excluded from cardiac electrophysiology simulations. The assumption that the cardiac endocardium is smooth may produce inaccurate predictions towards the location of reentry channels in in-silico tachycardia inducibility studies.

Taming cardiac arrhythmias: Terminating spiral wave chaos by adaptive deceleration pacing

Sequences of weak electrical pulses are considered a promising alternative for terminating ventricular and atrial fibrillations while avoiding strong defibrillation shocks with adverse side effects. In this study, using numerical simulations of four different 2D excitable media, we show that pulse trains with increasing temporal intervals between successive pulses (deceleration pacing) provide high success rates at low energies. Furthermore, we propose a simple and robust approach to calculate inter-pulse spacing directly from the frequency spectrum of the dynamics (for instance, computed based on the electrocardiogram), which can be practically used in experiments and clinical applications.

The physics of heart rhythm disorders

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

Thermal ablation effects on rotors that characterize functional re-entry cardiac arrhythmia

Thermal ablation is a well-established successful treatment for cardiac arrhythmia, but it still presents limitations that require further studies and developments. In the rotor-driven functional re-entry arrhythmia, tissue heterogeneity results on the generation of spiral/scroll waves and wave break dynamics that may cause dangerous sustainable fibrillation. The selection of the target region to perform thermal ablation to mitigate this type of arrhythmia is challenging, since it considerably affects the local electrophysiology dynamics. This work deals with the numerical simulation of the thermal ablation of a cardiac muscle tissue and its effects on the dynamics of rotor-driven functional re-entry arrhythmia. A non-homogeneous two-dimensional rectangular region is used in the present numerical analysis, where radiofrequency ablation is performed. The electrophysiology problem for the propagation of the action potential in the cardiac tissue is simulated with the Fenton-Karma model. Thermal damage caused to the tissue by the radiofrequency heating is modeled by the Arrhenius equation. The effects of size and position of a heterogeneous region in the original muscle tissue were first analyzed, in order to verify the possible existence of the functional re-entry arrhythmia during the time period considered in the simulations. For each case that exhibited re-entry arrhythmia, six different ablation procedures were analyzed, depending on the position of the radiofrequency electrode and heating time. The obtained results revealed the effects of different model parameters on the existence and possible mitigation of the functional re-entry arrhythmia.

Non-monotonous dose response function of the termination of spiral wave chaos

The conventional termination technique of life threatening cardiac arrhythmia like ventricular fibrillation is the application of a high-energy electrical defibrillation shock, coming along with severe side-effects. In order to improve the current treatment reducing these side-effects, the application of pulse sequences of lower energy instead of a single high-energy pulse are promising candidates. In this study, we show that in numerical simulations the dose-response function of pulse sequences applied to two-dimensional spiral wave chaos is not necessarily monotonously increasing, but exhibits a non-trivial frequency dependence. This insight into crucial phenomena appearing during termination attempts provides a deeper understanding of the governing termination mechanisms in general, and therefore may open up the path towards an efficient termination of cardiac arrhythmia in the future.

Numerical methods for the detection of phase defect structures in excitable media

Electrical waves that rotate in the heart organize dangerous cardiac arrhythmias. Finding the region around which such rotation occurs is one of the most important practical questions for arrhythmia management. For many years, the main method for finding such regions was so-called phase mapping, in which a continuous phase was assigned to points in the heart based on their excitation status and defining the rotation region as a point of phase singularity. Recent analysis, however, showed that in many rotation regimes there exist phase discontinuities and the region of rotation must be defined not as a point of phase singularity, but as a phase defect line. In this paper, we use this novel methodology and perform a comparative study of three different phase definitions applied to in silico data and to experimental data obtained from optical voltage mapping experiments on monolayers of human atrial myocytes. We introduce new phase defect detection algorithms and compare them with those that appeared in literature already. We find that the phase definition is more important than the algorithm to identify sudden spatial phase variations. Sharp phase defect lines can be obtained from a phase derived from local activation times observed during one cycle of arrhythmia. Alternatively, similar quality can be obtained from a reparameterization of the classical phase obtained from observation of a single timeframe of transmembrane potential. We found that the phase defect line length was (35.9 ± 6.2)mm in the Fenton-Karma model and (4.01 ± 0.55)mm in cardiac human atrial myocyte monolayers. As local activation times are obtained during standard clinical cardiac mapping, the methods are also suitable to be applied to clinical datasets. All studied methods are publicly available and can be downloaded from an institutional web-server.

A transmurally heterogeneous model of the ventricular tissue and its application for simulation of Brugada Syndrome

We present a transmurally heterogeneous phe-nomenological model of ventricular tissue that is designed to reproduce the most important features of action potential prop-agation of endocardial, midmyocardial, and epicardial tissue. Our model consists of only 3 variables and 20 parameters. Therefore, it is highly computational efficient and easy to fit to experimental data. We exploited our myocyte model to simulate action potential propagation in a 3D slab of cardiac tissue both in healthy conditions and in presence of Brugada syndrome. The results show that our model can accurately reproduce the transmural heterogeneity of the ventricular wall and the main characteristics of electrocardiographic pattern both in healthy and pathological conditions.

Low cardiac frequency associated with higher number of extrasistoles in a computational model of Brugada Syndrome

Brugada Syndrome is a form of idiopathic ventricular fibrillation, to date there is no definitive theory about how ventricular fibrillation is initiated or its substrate. Starting from the clinical observation that cardiac episodes are more frequent at rest, we developed a model in order to study the effect of cardiac frequency on reentrant activity. Our results suggest that the combination of arrhythmic substrate and cardiac frequency has a role in the insurgence of cardiac arrhythmia.

Optimal entrainment for removal of pinned spiral waves

Cardiac fibrillation is caused by self-sustaining spiral waves that occur in the myocardium, some of which can be pinned to anatomical obstacles, making them more difficult to eliminate. A small electrical stimulation is often sufficient to unpin these spirals but only if it is applied during the vulnerable unpinning window. Even if these unpinning windows can be inferred from data, when multiple pinned spirals exist, their unpinning windows will not generally overlap. Using phase-based reduction techniques, we formulate and solve an optimal control problem to yield a time-varying external voltage gradient that can synchronize a collection of spiral waves that are pinned to a collection of heterogeneous obstacles. Upon synchronization, the unpinning windows overlap so that they can be simultaneously unpinned by applying an external voltage gradient pulse at an appropriate moment. Numerical validation is presented in bidomain model simulations. Results represent a proof-of-concept illustration of the proposed unpinning strategy which explicitly incorporates heterogeneity in the problem formulation and requires no real-time feedback about the system state.

Diffuse fibrosis and repolarization disorders explain ventricular arrhythmias in Brugada syndrome: a computational study

In this work, we reported a computational study to quantitatively determine the individual contributions of three candidate arrhythmic factors associated with Brugada Syndrome. In particular, we focused our analysis on the role of structural abnormalities, dispersion of repolarization, and size of the diseased region. We developed a human phenomenological model capable of replicating the action potential characteristics both in Brugada Syndrome and in healthy conditions. Inspired by physiological observations, we employed the phenomenological model in a 2D geometry resembling the pathological RVOT coupled with healthy epicardial tissue. We assessed the insurgence of sustained reentry as a function of electrophysiological and structural abnormalities. Our computational study indicates that both structural and repolarization abnormalities are essential to induce sustained reentry. Furthermore, our results suggest that neither dispersion of repolarization nor structural abnormalities are sufficient on their own to induce sustained reentry. It should be noted how our study seems to explain an arrhythmic mechanism that unifies the classic repolarization and depolarization hypotheses of the pathophysiology of the Brugada Syndrome. Finally, we believe that this work may offer a new perspective on the computational and clinical investigation of Brugada Syndrome and its arrhythmic behaviour.

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.

Embedded Computational Heart Model for External Ventricular Assist Device Investigations

PURPOSE

External cardiac assist devices are based on a promising and simple concept for treating heart failure, but they are surprisingly difficult to design. Thus, a structured approach combining experiments with computer-based optimization is essential. The latter provides the motivation for the work presented in this paper.

METHODS

We present a computational modeling framework for realistic representation of the heart's tissue structure, electrophysiology and actuation. The passive heart tissue is described by a nonlinear anisotropic material law, considering fiber and sheetlet directions. For muscle contraction, an orthotropic active-strain model is employed, initiated by a periodically propagating electrical potential. The model allows for boundary conditions at the epicardium accounting for external assist devices, and it is coupled to a circulation network providing appropriate pressure boundary conditions inside the ventricles.

RESULTS

Simulated results from an unsupported healthy and a pathological heart model are presented and reproduce accurate deformations compared to phenomenological measurements. Moreover, cardiac output and ventricular pressure signals are in good agreement too. By investigating the impact of applying an exemplary external actuation to the pathological heart model, it shows that cardiac patches can restore a healthy blood flow.

CONCLUSION

We demonstrate that the devised computational modeling framework is capable of predicting characteristic trends (e.g. apex shortening, wall thickening and apex twisting) of a healthy heart, and that it can be used to study pathological hearts and external activation thereof.

Optical Ultrastructure of Large Mammalian Hearts Recovers Discordant Alternans by In Silico Data Assimilation

Understanding and predicting the mechanisms promoting the onset and sustainability of cardiac arrhythmias represent a primary concern in the scientific and medical communities still today. Despite the long-lasting effort in clinical and physico-mathematical research, a critical aspect to be fully characterized and unveiled is represented by spatiotemporal alternans patterns of cardiac excitation. The identification of discordant alternans and higher-order alternating rhythms by advanced data analyses as well as their prediction by reliable mathematical models represents a major avenue of research for a broad and multidisciplinary scientific community. Current limitations concern two primary aspects: 1) robust and general-purpose feature extraction techniques and 2) in silico data assimilation within reliable and predictive mathematical models. Here, we address both aspects. At first, we extend our previous works on Fourier transformation imaging (FFI), applying the technique to whole-ventricle fluorescence optical mapping. Overall, we identify complex spatial patterns of voltage alternans and characterize higher-order rhythms by a frequency-series analysis. Then, we integrate the optical ultrastructure obtained by FFI analysis within a fine-tuned electrophysiological mathematical model of the cardiac action potential. We build up a novel data assimilation procedure demonstrating its reliability in reproducing complex alternans patterns in two-dimensional computational domains. Finally, we prove that the FFI approach applied to both experimental and simulated signals recovers the same information, thus closing the loop between the experiment, data analysis, and numerical simulations.

Electrogram fractionation during sinus rhythm occurs in normal voltage atrial tissue in patients with atrial fibrillation

INTRODUCTION

Electrogram (EGM) fractionation is often associated with diseased atrial tissue; however, mechanisms for fractionation occurring above an established threshold of 0.5 mV have never been characterized. We sought to investigate during sinus rhythm (SR) the mechanisms underlying bipolar EGM fractionation with high-density mapping in patients with atrial fibrillation (AF).

METHODS

Forty-five patients undergoing AF ablation (73% paroxysmal, 27% persistent) were mapped at high density (18562 ± 2551 points) during SR (Rhythmia). Only bipolar EGMs with voltages above 0.5 mV were considered for analysis. When fractionation (>40 ms and >4 deflections) was detected, we classified the mechanisms as slow conduction, wave-front collision, or a pivot point. The relationship between EGM duration and amplitude, and tissue anisotropy and slow conduction, was then studied using a computational model.

RESULTS

Of the 45 left atria analyzed, 133 sites of EGM fragmentation were identified with voltages above 0.5 mV. The most frequent mechanism (64%) was slow conduction (velocity 0.45 m/s ± 0.2) with mean EGM voltage of 1.1 ± 0.5 mV and duration of 54.9 ± 9.4 ms. Wavefront collision was the second most frequent (19%), characterized by higher voltage (1.6 ± 0.9 mV) and shorter duration (51.3 ± 11.3 ms). Pivot points (9%) were associated with the highest degree of fractionation with 70.7 ± 6.6 ms and 1.8 ± 1 mV. In 10 sites (8%) fractionation was unexplained. The EGM duration was significantly different among the 3 mechanisms (p = 0.0351).

CONCLUSION

In patients with a history of AF, EGM fractionation can occur at amplitudes > 0.5 mV when in SR in areas often considered not to be diseased tissue. The main mechanism of EGM fractionation is slow conduction, followed by wavefront collision and pivot sites. This article is protected by copyright. All rights reserved.

A computationally efficient dynamic model of human epicardial tissue

We present a new phenomenological model of human ventricular epicardial cells and we test its reentry dynamics. The model is derived from the Rogers-McCulloch formulation of the FitzHugh-Nagumo equations and represents the total ionic current divided into three contributions corresponding to the excitatory, recovery and transient outward currents. Our model reproduces the main characteristics of human epicardial tissue, including action potential amplitude and morphology, upstroke velocity, and action potential duration and conduction velocity restitution curves. The reentry dynamics is stable, and the dominant period is about 270 ms, which is comparable to clinical values. The proposed model is the first phenomenological model able to accurately resemble human experimental data by using only 3 state variables and 17 parameters. Indeed, it is more computationally efficient than existing models (i.e., almost two times faster than the minimal ventricular model). Beyond the computational efficiency, the low number of parameters facilitates the process of fitting the model to the experimental data.

A Phase Defect Framework for the Analysis of Cardiac Arrhythmia Patterns

During cardiac arrhythmias, dynamical patterns of electrical activation form and evolve, which are of interest to understand and cure heart rhythm disorders. The analysis of these patterns is commonly performed by calculating the local activation phase and searching for phase singularities (PSs), i.e., points around which all phases are present. Here we propose an alternative framework, which focuses on phase defect lines (PDLs) and surfaces (PDSs) as more general mechanisms, which include PSs as a specific case. The proposed framework enables two conceptual unifications: between the local activation time and phase description, and between conduction block lines and the central regions of linear-core rotors. A simple PDL detection method is proposed and applied to data from simulations and optical mapping experiments. Our analysis of ventricular tachycardia in rabbit hearts (n = 6) shows that nearly all detected PSs were found on PDLs, but the PDLs had a significantly longer lifespan than the detected PSs. Since the proposed framework revisits basic building blocks of cardiac activation patterns, it can become a useful tool for further theory development and experimental analysis.

Detecting spiral wave tips using deep learning

The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves. The organizing centers of these waves are called wave tips (2D) or filaments (3D) and they play a key role in understanding and controlling the complex and chaotic electrical dynamics. Therefore, in many experimental and numerical setups it is required to detect the tips of the observed spiral waves. Most of the currently used methods significantly suffer from the influence of noise and are often adjusted to a specific situation (e.g. a specific numerical cardiac cell model). In this study, we use a specific type of deep neural networks (UNet), for detecting spiral wave tips and show that this approach is robust against the influence of intermediate noise levels. Furthermore, we demonstrate that if the UNet is trained with a pool of numerical cell models, spiral wave tips in unknown cell models can also be detected reliably, suggesting that the UNet can in some sense learn the concept of spiral wave tips in a general way, and thus could also be used in experimental situations in the future (ex-vivo, cell-culture or optogenetic experiments).

Machine Learning Identification of Pro-arrhythmic Structures in Cardiac Fibrosis

Cardiac fibrosis and other scarring of the heart, arising from conditions ranging from myocardial infarction to ageing, promotes dangerous arrhythmias by blocking the healthy propagation of cardiac excitation. Owing to the complexity of the dynamics of electrical signalling in the heart, however, the connection between different arrangements of blockage and various arrhythmic consequences remains poorly understood. Where a mechanism defies traditional understanding, machine learning can be invaluable for enabling accurate prediction of quantities of interest (measures of arrhythmic risk) in terms of predictor variables (such as the arrangement or pattern of obstructive scarring). In this study, we simulate the propagation of the action potential (AP) in tissue affected by fibrotic changes and hence detect sites that initiate re-entrant activation patterns. By separately considering multiple different stimulus regimes, we directly observe and quantify the sensitivity of re-entry formation to activation sequence in the fibrotic region. Then, by extracting the fibrotic structures around locations that both do and do not initiate re-entries, we use neural networks to determine to what extent re-entry initiation is predictable, and over what spatial scale conduction heterogeneities appear to act to produce this effect. We find that structural information within about 0.5 mm of a given point is sufficient to predict structures that initiate re-entry with more than 90% accuracy.

Interactive Simulation of the ECG: Effects of Cell Types, Distributions, Shapes and Duration

The shape of the ECG depends on the lead positions but also on the distribution and dispersion of different cell types and their action potential (AP) durations and shapes. We present an interactive JavaScript program that allows fast simulations of the ECG by solving and displaying the dynamics of cardiac cells in tissue using a web browser. We use physiologically accurate ODE models of cardiac cells of different types including SA node, right and left atria, AV node, Purkinje, and right and left ventricular cells with dispersion that accounts for apex-to-base and epi-to-endo variations. The software allows for real-time variations for each cell type and their spatial range so as to identify how the shape of the ECG varies as a function of cell type, distribution, excitation duration and AP shape. The propagation of the wave is visualized in real time through all the regions as parameters are kept fixed or varied to modify ECG morphology. The code solves thousands of simulated cells in real time and is independent of operating system, so it can run on PCs, laptops, tablets and cellphones. This program can be used to teach students, fellows and the general public how and why lead positions and the different cell physiology in the heart affect the various features of the ECG.

Characterization of the Electrophysiologic Remodeling of Patients With Ischemic Cardiomyopathy by Clinical Measurements and Computer Simulations Coupled With Machine Learning

Rationale

Patients with ischemic cardiomyopathy (ICMP) are at high risk for malignant arrhythmias, largely due to electrophysiological remodeling of the non-infarcted myocardium. The electrophysiological properties of the non-infarcted myocardium of patients with ICMP remain largely unknown.

Objectives

To assess the pro-arrhythmic behavior of non-infarcted myocardium in ICMP patients and couple computational simulations with machine learning to establish a methodology for the development of disease-specific action potential models based on clinically measured action potential duration restitution (APDR) data.

Methods and Results

We enrolled 22 patients undergoing left-sided ablation (10 ICMP) and compared APDRs between ICMP and structurally normal left ventricles (SNLVs). APDRs were clinically assessed with a decremental pacing protocol. Using genetic algorithms (GAs), we constructed populations of action potential models that incorporate the cohort-specific APDRs. The variability in the populations of ICMP and SNLV models was captured by clustering models based on their similarity using unsupervised machine learning. The pro-arrhythmic potential of ICMP and SNLV models was assessed in cell- and tissue-level simulations. Clinical measurements established that ICMP patients have a steeper APDR slope compared to SNLV (by 38%, p < 0.01). In cell-level simulations, APD alternans were induced in ICMP models at a longer cycle length compared to SNLV models (385–400 vs 355 ms). In tissue-level simulations, ICMP models were more susceptible for sustained functional re-entry compared to SNLV models.

Conclusion

Myocardial remodeling in ICMP patients is manifested as a steeper APDR compared to SNLV, which underlies the greater arrhythmogenic propensity in these patients, as demonstrated by cell- and tissue-level simulations using action potential models developed by GAs from clinical measurements. The methodology presented here captures the uncertainty inherent to GAs model development and provides a blueprint for use in future studies aimed at evaluating electrophysiological remodeling resulting from other cardiac diseases.

Reaction-diffusion informed approach to determine myocardial ischemia using stochastic in-silico ECGs and CNNs

Every year, nine million people die globally from ischemic heart disease (IHD). There are many methods of early detection of IHD which can help prevent death, but few are able to determine the configuration and severity of this disease. Our study aims to determine the severity and configuration of ischemic zones by implementing the reaction-diffusion analysis of cardiac excitation in a model of the left ventricle of the human heart. Initially, this model is applied to compute twenty thousand in-silico ECG signals with stochastic distribution of ischemic parameters. Furthermore, generated data is effectively (r²=0.85) implemented for training a one-dimensional convolutional neural network to determine the severity and configuration of ischemia using only two lead surface ECG. Our results readily demonstrate that using a minimally configured portable ECG system can be instrumental for monitoring IHD and allowing early tracking of acute ischemic events.

Multiphysics computational modelling of the cardiac ventricles

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

A 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.

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.

Blockade of sodium‑calcium exchanger via ORM-10962 attenuates cardiac alternans

Repolarization alternans, a periodic oscillation of long-short action potential duration, is an important source of arrhythmogenic substrate, although the mechanisms driving it are insufficiently understood. Despite its relevance as an arrhythmia precursor, there are no successful therapies able to target it specifically. We hypothesized that blockade of the sodium‑calcium exchanger (NCX) could inhibit alternans. The effects of the selective NCX blocker ORM-10962 were evaluated on action potentials measured with microelectrodes from canine papillary muscle preparations, and calcium transients measured using Fluo4-AM from isolated ventricular myocytes paced to evoke alternans. Computer simulations were used to obtain insight into the drug's mechanisms of action. ORM-10962 attenuated cardiac alternans, both in action potential duration and calcium transient amplitude. Three morphological types of alternans were observed, with differential response to ORM-10962 with regards to APD alternans attenuation. Analysis of APD restitution indicates that calcium oscillations underlie alternans formation. Furthermore, ORM-10962 did not markedly alter APD restitution, but increased post-repolarization refractoriness, which may be mediated by indirectly reduced L-type calcium current. Computer simulations reproduced alternans attenuation via ORM-10962, suggesting that it is acts by reducing sarcoplasmic reticulum release refractoriness. This results from the ORM-10962-induced sodium‑calcium exchanger block accompanied by an indirect reduction in L-type calcium current. Using a computer model of a heart failure cell, we furthermore demonstrate that the anti-alternans effect holds also for this disease, in which the risk of alternans is elevated. Targeting NCX may therefore be a useful anti-arrhythmic strategy to specifically prevent calcium driven alternans.

Modeling and Analysis of Cardiac Hybrid Cellular Automata via GPU-Accelerated Monte Carlo Simulation

The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and the large number of biological components involved make the modeling and the analysis of electrophysiological properties in cardiac tissue still an open challenge. We consider here a Hybrid Cellular Automata (HCA) approach modeling the cardiac cell-cell membrane resistance with a free variable. We show that the modeling approach can reproduce important and complex spatiotemporal properties paving the ground for promising future applications. We show how GPU-based technology can considerably accelerate the simulation and the analysis. Furthermore, we study the cardiac behavior within a unidimensional domain considering inhomogeneous resistance and we perform a Monte Carlo analysis to evaluate our approach.

On the Role of Ionic Modeling on the Signature of Cardiac Arrhythmias for Healthy and Diseased Hearts

Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of the optimal modeling choice for large-scale whole-heart numerical investigations. We propose an extended numerical analysis among two different electrophysiological modeling approaches: a simplified phenomenological one and a detailed biophysical one. To achieve this, we considered three-dimensional healthy and infarcted swine heart geometries. Heterogeneous electrophysiological properties, fine-tuned DT-MRI -based anisotropy features, and non-conductive ischemic regions were included in a custom-built finite element code. We provide a quantitative comparison of the electrical behaviors during steady pacing and sustained ventricular fibrillation for healthy and diseased cases analyzing cardiac arrhythmias dynamics. Action potential duration (APD) restitution distributions, vortex filament counting, and pseudo-electrocardiography (ECG) signals were numerically quantified, introducing a novel statistical description of restitution patterns and ventricular fibrillation sustainability. Computational cost and scalability associated with the two modeling choices suggests that ventricular fibrillation signatures are mainly controlled by anatomy and structural parameters, rather than by regional restitution properties. Finally, we discuss limitations and translational perspectives of the different modeling approaches in view of large-scale whole-heart in silico studies.

Mechano-Electric Coupling and Arrhythmogenic Current Generation in a Computational Model of Coupled Myocytes

A wide range of arrhythmogenic phenotypes have been associated with heterogeneous mechanical dyskinesis. Pro-arrhythmic effects are often associated with dysregulated intra-cellular calcium handling, especially via the development of intra- and inter-cellular calcium waves. Experimental evidence suggests that mechanical strain can contribute to the generation and maintenance of these calcium waves via a variety of mechano-electric coupling mechanisms. Most model studies of mechano-electric coupling mechanisms have been focused on mechano-sensitive ion channels, even though experimental studies have shown that intra- and inter-cellular calcium waves triggered by mechanical perturbations are likely to be more prevalent pro-arrhythmic mechanisms in the diseased heart. A one-dimensional strongly coupled computational model of electromechanics in rabbit ventricular cardiomyocytes showed that specific myocyte stretch sequences can modulate the susceptibility threshold for delayed after-depolarizations. In simulations of mechanically-triggered calcium waves in cardiomyocytes coupled to fibroblasts, susceptibility to calcium wave propagation was reduced as the current through the gap junction caused current drain from the myocytes. In 1D multi-cellular arrays coupled via gap junctions, mechanically-induced waves may contribute to synchronizing arrhythmogenic calcium waves and after-depolarizations.

Cardiac transmembrane ion channels and action potentials: cellular physiology and arrhythmogenic behavior

Cardiac arrhythmias are among the leading causes of mortality. They often arise from alterations in the electrophysiological properties of cardiac cells and their underlying ionic mechanisms. It is therefore critical to further unravel the pathophysiology of the ionic basis of human cardiac electrophysiology in health and disease. In the first part of this review, current knowledge on the differences in ion channel expression and properties of the ionic processes that determine the morphology and properties of cardiac action potentials and calcium dynamics from cardiomyocytes in different regions of the heart are described. Then the cellular mechanisms promoting arrhythmias in congenital or acquired conditions of ion channel function (electrical remodeling) are discussed. The focus is on human-relevant findings obtained with clinical, experimental, and computational studies, given that interspecies differences make the extrapolation from animal experiments to human clinical settings difficult. Deepening the understanding of the diverse pathophysiology of human cellular electrophysiology will help in developing novel and effective antiarrhythmic strategies for specific subpopulations and disease conditions.

A Novel Tool for the Identification and Characterization of Repetitive Patterns in High-Density Contact Mapping of Atrial Fibrillation

Introduction

Electrical contact mapping provides a detailed view of conduction patterns in the atria during atrial fibrillation (AF). Identification of repetitive wave front propagation mechanisms potentially initiating or sustaining AF might provide more insights into temporal and spatial distribution of candidate AF mechanism and identify targets for catheter ablation. We developed a novel tool based on recurrence plots to automatically identify and characterize repetitive conduction patterns in high-density contact mapping of AF.

Materials and Methods

Recurrence plots were constructed by first transforming atrial electrograms recorded by a multi-electrode array to activation-phase signals and then quantifying the degree of similarity between snapshots of the activation-phase in the electrode array. An AF cycle length dependent distance threshold was applied to discriminate between repetitive and non-repetitive snapshots. Intervals containing repetitive conduction patterns were detected in a recurrence plot as regions with a high recurrence rate. Intervals that contained similar repetitive patterns were then grouped into clusters. To demonstrate the ability to detect and quantify the incidence, duration and size of repetitive patterns, the tool was applied to left and right atrial recordings in a goat model of different duration of persistent AF [3 weeks AF (3 wkAF, n = 8) and 22 weeks AF (22 wkAF, n = 8)], using a 249-electrode mapping array (2.4 mm inter-electrode distance).

Results

Recurrence plots identified frequent recurrences of activation patterns in all recordings and indicated a strong correlation between recurrence plot threshold and AF cycle length. Prolonged AF duration was associated with shorter repetitive pattern duration [mean maximum duration 3 wkAF: 74 cycles, 95% confidence interval (54-94) vs. 22 wkAF: 41 cycles (21-62), p = 0.03], and smaller recurrent regions within repetitive patterns [3 wkAF 1.7 cm² (1.0-2.3) vs. 22 wkAF 0.5 cm² (0.0-1.2), p = 0.02]. Both breakthrough patterns and re-entry were identified as repetitive conduction patterns.

Conclusion

Recurrence plots provide a novel way to delineate high-density contact mapping of AF. Dominant repetitive conduction patterns were identified in a goat model of sustained AF. Application of the developed methodology using the new generation of multi-electrode catheters could identify additional targets for catheter ablation of AF.

Integration of activation maps of epicardial veins in computational cardiac electrophysiology

In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac electro-physiology of the left ventricle. To this aim, we consider four patients who suffered from Left Bundle Branch Block (LBBB). We use activation maps performed at the septum as input data for the model and maps at the epicardial veins for the validation. In particular, a first set (half) of the latter are used to estimate the conductivities of the patient and a second set (the remaining half) to compute the errors of the numerical simulations. We find an excellent agreement between measures and numerical results. Our validated computational tool could be used to accurately predict activation times at the epicardial veins with a short mapping, i.e. by using only a part (the most proximal) of the standard acquisition points, thus reducing the invasive procedure and exposure to radiation.

Using cardiac ionic cell models to interpret clinical data

For over 100 years cardiac electrophysiology has been measured in the clinic. The electrical signals that can be measured span from noninvasive ECG and body surface potentials measurements through to detailed invasive measurements of local tissue electrophysiology. These electrophysiological measurements form a crucial component of patient diagnosis and monitoring; however, it remains challenging to quantitatively link changes in clinical electrophysiology measurements to biophysical cellular function. Multi-scale biophysical computational models represent one solution to this problem. These models provide a formal framework for linking cellular function through to emergent whole organ function and routine clinical diagnostic signals. In this review, we describe recent work on the use of computational models to interpret clinical electrophysiology signals. We review the simulation of human cardiac myocyte electrophysiology in the atria and the ventricles and how these models are being used to link organ scale function to patient disease mechanisms and therapy response in patients receiving implanted defibrillators, \cardiac resynchronisation therapy or suffering from atrial fibrillation and ventricular tachycardia. There is a growing use of multi-scale biophysical models to interpret clinical data. This allows cardiologists to link clinical observations with cellular mechanisms to better understand cardiopathophysiology and identify novel treatment strategies. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Simulating Notch-Dome Morphology of Action Potential of Ventricular Cell: How the Speeds of Positive and Negative Feedbacks on Transmembrane Voltage Can Influence the Health of a Cell?

Ventricular action potential is well-known because of its plateau phase with a spike-notch-dome morphology. As such, the morphology of action potential is necessary for ensuring a correct heart functioning. Any distraction from normal notch-dome morphology may trigger a circus movement reentry in the form of lethal ventricular fibrillation. When the epicardial action potential dome propagates from a site where it is maintained to regions where it has been lost, it gives rise to the proposed mechanism for the Brugada syndrome. Despite the impact of notch-dome dynamics on the heart function, no independent and explicit research has been performed on the simulation of notch-dome dynamics and morphology. In this paper, using a novel mathematical approach, a three-state variable model is proposed; we show that our proposed model not only can simulate morphology of action potential of ventricular cells but also can propose a biological reasonable tool for controlling of the morphology of action potential spike-notch-dome. We show that the processes of activation and inactivation of ionic gating variables (as positive or negative feedbacks on the voltage of cell membrane) and the ratio of their speeds (time constants) can be treated as a reasonable biological tool for simulating ventricular cell notch-dome. This finding may led to a new insight to the quantification of the health of a ventricular cell and may also propose a new drug therapy strategy for cardiac diseases.

Active Force Generation in Cardiac Muscle Cells: Mathematical Modeling and Numerical Simulation of the Actin-Myosin Interaction

Cardiac in silico numerical simulations are based on mathematical models describing the physical processes involved in the heart function. In this review paper, we critically survey biophysically-detailed mathematical models describing the subcellular mechanisms behind the generation of active force, that is the process by which the chemical energy of ATP (adenosine triphosphate) is transformed into mechanical work, thus making the muscle tissue contract. While presenting these models, that feature different levels of biophysical detail, we analyze the trade-off between the accuracy in the description of the subcellular mechanisms and the number of parameters that need to be estimated from experiments. Then, we focus on a generalized version of the classic Huxley model, built on the basis of models available in the literature, that is able to reproduce the main experimental characterizations associated to the time scales typical of a heartbeat-such as the force-velocity relationship and the tissue stiffness in response to small steps-featuring only four independent parameters. Finally, we show how those parameters can be calibrated starting from macroscopic measurements available from experiments.