Performance evaluation of GPU parallelization, space-time adaptive algorithms, and their combination for simulating cardiac electrophysiology

Digital twinning of the human ventricular activation sequence to Clinical 12-lead ECGs and magnetic resonance imaging using realistic Purkinje networks for in silico clinical trials

Cardiac in silico clinical trials can virtually assess the safety and efficacy of therapies using human-based modelling and simulation. These technologies can provide mechanistic explanations for clinically observed pathological behaviour. Designing virtual cohorts for in silico trials requires exploiting clinical data to capture the physiological variability in the human population. The clinical characterisation of ventricular activation and the Purkinje network is challenging, especially non-invasively. Our study aims to present a novel digital twinning pipeline that can efficiently generate and integrate Purkinje networks into human multiscale biventricular models based on subject-specific clinical 12-lead electrocardiogram and magnetic resonance recordings. Essential novel features of the pipeline are the human-based Purkinje network generation method, personalisation considering ECG R wave progression as well as QRS morphology, and translation from reduced-order Eikonal models to equivalent biophysically-detailed monodomain ones. We demonstrate ECG simulations in line with clinical data with clinical image-based multiscale models with Purkinje in four control subjects and two hypertrophic cardiomyopathy patients (simulated and clinical QRS complexes with Pearson's correlation coefficients > 0.7). Our methods also considered possible differences in the density of Purkinje myocardial junctions in the Eikonal-based inference as regional conduction velocities. These differences translated into regional coupling effects between Purkinje and myocardial models in the monodomain formulation. In summary, we demonstrate a digital twin pipeline enabling simulations yielding clinically consistent ECGs with clinical CMR image-based biventricular multiscale models, including personalised Purkinje in healthy and cardiac disease conditions.

Effects of ranolazine on the arrhythmic substrate in hypertrophic cardiomyopathy

Introduction: Hypertrophic cardiomyopathy (HCM) is a leading cause of lethal arrhythmias in the young. Although the arrhythmic substrate has been hypothesised to be amenable to late Na+ block with ranolazine, the specific mechanisms are not fully understood. Therefore, this study aimed to investigate the substrate mechanisms of safety and antiarrhythmic efficacy of ranolazine in HCM. Methods: Computational models of human tissue and ventricles were used to simulate the electrophysiological behaviour of diseased HCM myocardium for variable degrees of repolarisation impairment, validated against in vitro and clinical recordings. S1-S2 pacing protocols were used to quantify arrhythmic risk in scenarios of (i) untreated HCM-remodelled myocardium and (ii) myocardium treated with 3µM, 6µM and 10µM ranolazine, for variable repolarisation heterogeneity sizes and pacing rates. ECGs were derived from biventricular simulations to identify ECG biomarkers linked to antiarrhythmic effects. Results: 10µM ranolazine given to models manifesting ventricular tachycardia (VT) at baseline led to a 40% reduction in number of VT episodes on pooled analysis of >40,000 re-entry inducibility simulations. Antiarrhythmic efficacy and safety were dependent on the degree of repolarisation impairment, with optimal benefit in models with maximum JTc interval <370 ms. Ranolazine increased risk of VT only in models with severe-extreme repolarisation impairment. Conclusion: Ranolazine efficacy and safety may be critically dependent upon the degree of repolarisation impairment in HCM. For moderate repolarisation impairment, reductions in refractoriness heterogeneity by ranolazine may prevent conduction blocks and re-entry. With severe-extreme disease substrates, reductions of the refractory period can increase re-entry sustainability.

Electrophysiological mechanisms underlying T wave pseudonormalisation on stress ECGs in hypertrophic cardiomyopathy

BACKGROUND

Pseudonormal T waves may be detected on stress electrocardiograms (ECGs) in hypertrophic cardiomyopathy (HCM). Either myocardial ischaemia or purely exercise-induced changes have been hypothesised to contribute to this phenomenon, but the precise electrophysiological mechanisms remain unknown.

METHODS

Computational models of human HCM ventricles (n = 20) with apical and asymmetric septal hypertrophy phenotypes with variable severities of repolarisation impairment were used to investigate the effects of acute myocardial ischaemia on ECGs with T wave inversions at baseline. Virtual 12-lead ECGs were derived from a total of 520 biventricular simulations, for cases with regionally ischaemic K+ accumulation in hypertrophied segments, global exercise-induced serum K+ increases, and/or increased pacing frequency, to analyse effects on ECG biomarkers including ST segments, T wave amplitudes, and QT intervals.

RESULTS

Regional ischaemic K+ accumulation had a greater impact on T wave pseudonormalisation than exercise-induced serum K+ increases, due to larger reductions in repolarisation gradients. Increases in serum K+ and pacing rate partially corrected T waves in some anatomical and electrophysiological phenotypes. T wave morphology was more sensitive than ST segment elevation to regional K+ increases, suggesting that T wave pseudonormalisation may sometimes be an early, or the only, ECG feature of myocardial ischaemia in HCM.

CONCLUSIONS

Ischaemia-induced T wave pseudonormalisation can occur on stress ECG testing in HCM before significant ST segment changes. Some anatomical and electrophysiological phenotypes may enable T wave pseudonormalisation due to exercise-induced increased serum K+ and pacing rate. Consideration of dynamic T wave abnormalities could improve the detection of myocardial ischaemia in HCM.

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.

Enhanced optimization-based method for the generation of patient-specific models of Purkinje networks

Cardiac Purkinje networks are a fundamental part of the conduction system and are known to initiate a variety of cardiac arrhythmias. However, patient-specific modeling of Purkinje networks remains a challenge due to their high morphological complexity. This work presents a novel method based on optimization principles for the generation of Purkinje networks that combines geometric and activation accuracy in branch size, bifurcation angles, and Purkinje-ventricular-junction activation times. Three biventricular meshes with increasing levels of complexity are used to evaluate the performance of our approach. Purkinje-tissue coupled monodomain simulations are executed to evaluate the generated networks in a realistic scenario using the most recent Purkinje/ventricular human cellular models and physiological values for the Purkinje-ventricular-junction characteristic delay. The results demonstrate that the new method can generate patient-specific Purkinje networks with controlled morphological metrics and specified local activation times at the Purkinje-ventricular junctions.

A simple and efficient adaptive time stepping technique for low-order operator splitting schemes applied to cardiac electrophysiology

We present a simple, yet efficient adaptive time stepping scheme for cardiac electrophysiology (EP) simulations based on standard operator splitting techniques. The general idea is to exploit the relation between the splitting error and the reaction's magnitude-found in a previous one-dimensional analytical study by Spiteri and Ziaratgahi-to construct the new time step controller for three-dimensional problems. Accordingly, we propose to control the time step length of the operator splitting scheme as a function of the reaction magnitude, in addition to the common approach of adapting the reaction time step. This conforms with observations in numerical experiments supporting the need for a significantly smaller time step length during depolarization than during repolarization. The proposed scheme is compared with classical proportional-integral-differential controllers using state-of-the-art error estimators, which are also presented in details as they have not been previously applied in the context of cardiac EP with operator splitting techniques. Benchmarks show that choosing the time step as a sigmoidal function of the reaction magnitude is highly efficient and full cardiac cycles can be computed with precision even in a realistic biventricular setup. The proposed scheme outperforms common adaptive time stepping techniques, while depending on fewer tuning parameters.

Homogenisation for the monodomain model in the presence of microscopic fibrotic structures

Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to incorporate structural heterogeneities on small spatial scales, preventing a full understanding of the critical arrhythmogenic effects of conditions such as cardiac fibrosis. In this work, we explore the technique of homogenisation by volume averaging for the inclusion of non-conductive micro-structures into larger-scale cardiac meshes with minor computational overhead. Importantly, our approach is not restricted to periodic patterns, enabling homogenised models to represent, for example, the intricate patterns of collagen deposition present in different types of fibrosis. We first highlight the importance of appropriate boundary condition choice for the closure problems that define the parameters of homogenised models. Then, we demonstrate the technique's ability to correctly upscale the effects of fibrotic patterns with a spatial resolution of 10 µm into much larger numerical mesh sizes of 100- 250 µm . The homogenised models using these coarser meshes correctly predict critical pro-arrhythmic effects of fibrosis, including slowed conduction, source/sink mismatch, and stabilisation of re-entrant activation patterns. As such, this approach to homogenisation represents a significant step towards whole organ simulations that unravel the effects of microscopic cardiac tissue heterogeneities.

In-silico drug trials for precision medicine in atrial fibrillation: From ionic mechanisms to electrocardiogram-based predictions in structurally-healthy human atria

Atrial fibrillation (AF) inducibility, sustainability and response to pharmacological treatment of individual patients are expected to be determined by their ionic current properties, especially in structurally-healthy atria. Mechanisms underlying AF and optimal cardioversion are however still unclear. In this study, in-silico drug trials were conducted using a population of human structurally-healthy atria models to 1) identify key ionic current properties determining AF inducibility, maintenance and pharmacological cardioversion, and 2) compare the prognostic value for predicting individual AF cardioversion of ionic current properties and electrocardiogram (ECG) metrics. In the population of structurally-healthy atria, 477 AF episodes were induced in ionic current profiles with both steep action potential duration (APD) restitution (eliciting APD alternans), and high excitability (enabling propagation at fast rates that transformed alternans into discordant). High excitability also favored 211 sustained AF episodes, so its decrease, through prolonged refractoriness, explained pharmacological cardioversion. In-silico trials over 200 AF episodes, 100 ionic profiles and 10 antiarrhythmic compounds were consistent with previous clinical trials, and identified optimal treatments for individual electrophysiological properties of the atria. Algorithms trained on 211 simulated AF episodes exhibited >70% accuracy in predictions of cardioversion for individual treatments using either ionic current profiles or ECG metrics. In structurally-healthy atria, AF inducibility and sustainability are enabled by discordant alternans, under high excitability and steep restitution conditions. Successful pharmacological cardioversion is predicted with 70% accuracy from either ionic or ECG properties, and it is optimal for treatments maximizing refractoriness (thus reducing excitability) for the given ionic current profile of the atria.

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

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

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.

Basic Research Approaches to Evaluate Cardiac Arrhythmia in Heart Failure and Beyond

Patients with heart failure often develop cardiac arrhythmias. The mechanisms and interrelations linking heart failure and arrhythmias are not fully understood. Historically, research into arrhythmias has been performed on affected individuals or in vivo (animal) models. The latter however is constrained by interspecies variation, demands to reduce animal experiments and cost. Recent developments in in vitro induced pluripotent stem cell technology and in silico modelling have expanded the number of models available for the evaluation of heart failure and arrhythmia. An agnostic approach, combining the modalities discussed here, has the potential to improve our understanding for appraising the pathology and interactions between heart failure and arrhythmia and can provide robust and validated outcomes in a variety of research settings. This review discusses the state of the art models, methodologies and techniques used in the evaluation of heart failure and arrhythmia and will highlight the benefits of using them in combination. Special consideration is paid to assessing the pivotal role calcium handling has in the development of heart failure and arrhythmia.

Interactive 3D Human Heart Simulations on Segmented Human MRI Hearts

Understanding cardiac arrhythmic mechanisms and developing new strategies to control and terminate them using computer simulations requires realistic physiological cell models with anatomically accurate heart structures. Furthermore, numerical simulations must be fast enough to study and validate model and structure parameters. Here, we present an interactive parallel approach for solving detailed cell dynamics in high-resolution human heart structures with a local PC's GPU. In vitro human heart MRI scans were manually segmented to produce 3D structures with anatomically realistic electrophysiology. The Abubu.js library was used to create an interactive code to solve the OVVR human ventricular cell model and the FDA extension of the model in the human MRI heart structures, allowing the simulation of reentrant waves and investigation of their dynamics in real time. Interactive simulations of a physiological cell model in a detailed anatomical human heart reveals propagation of waves through the fine structures of the trabeculae and pectinate muscle that can perpetuate arrhythmias, thereby giving new insights into effects that may need to be considered when planning ablation and other defibrillation methods.

Personalized Evaluation of Atrial Complexity of Patients Undergoing Atrial Fibrillation Ablation: A Clinical Computational Study

Simple Summary

Atrial fibrillation is a type of arrhythmia that occurs when the electrical activity of the heart in the atrium is not coordinated, and its consequences can be lethal. The driving source that initiates this chaotic activity can be located anywhere in the atrium, but most frequently appears in certain areas such as the pulmonary veins. In this study, we developed a new estimation method to evaluate possible source location and complexity of the arrhythmia using computer simulations. This method represents mathematical descriptions of natural processes that can be used to mimic a real scenario, including specific information such as the atrial anatomy. Here, we identified a specific biomarker the enabled obtaining a foci distribution map and found that elimination of pulmonary vein drivers was associated with a successful long-term ablation outcome. This study could, therefore, help to identify and characterize patients in order to better plan the ablation procedure.

Abstract

Current clinical guidelines establish Pulmonary Vein (PV) isolation as the indicated treatment for Atrial Fibrillation (AF). However, AF can also be triggered or sustained due to atrial drivers located elsewhere in the atria. We designed a new simulation workflow based on personalized computer simulations to characterize AF complexity of patients undergoing PV ablation, validated with non-invasive electrocardiographic imaging and evaluated at one year after ablation. We included 30 patients using atrial anatomies segmented from MRI and simulated an automata model for the electrical modelling, consisting of three states (resting, excited and refractory). In total, 100 different scenarios were simulated per anatomy varying rotor number and location. The 3 states were calibrated with Koivumaki action potential, entropy maps were obtained from the electrograms and compared with ECGi for each patient to analyze PV isolation outcome. The completion of the workflow indicated that successful AF ablation occurred in patients with rotors mainly located at the PV antrum, while unsuccessful procedures presented greater number of driving sites outside the PV area. The number of rotors attached to the PV was significantly higher in patients with favorable long-term ablation outcome (1-year freedom from AF: 1.61 ± 0.21 vs. AF recurrence: 1.40 ± 0.20; p-value = 0.018). The presented workflow could improve patient stratification for PV ablation by screening the complexity of the atria.

Improved Accuracy of Cardiac Tissue-Level Simulations by Considering Membrane Resistance as a Cellular-Level Optimization Objective

Cardiac cellular models are utilized as the building blocks for tissue simulation. One of the imprecisions of conventional cellular modeling, especially when the models are used in tissue-level modeling, stems from the mere consideration of cellular properties (e.g., action potential shape) in parameter tuning of the model. In our previous work, we put forward an accurate framework in which membrane resistance (R_m) reflecting inter-cellular characteristics, i.e., electrotonic effects, was considered alongside cellular features in cellular model fitting. This paper, for the first time, examines the hypothesis that considering R_m as an additional optimization objective improves the accuracy of tissue-level modeling. To study this hypothesis, after cellular-level optimization of a well-known model, source-sink mismatch configurations in a 2-dimensional model are investigated. The results demonstrate that including R_m in the optimization protocol yields a substantial improvement in the relative error of the critical transition border which is defined as the minimum window size between source and sink that wave propagates. Model developers can utilize the proposed concept during parameter tuning to increase the accuracy of models.

Deep learning-based reduced order models in cardiac electrophysiology

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters), as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach relying on deep learning (DL) algorithms—such as deep feedforward neural networks and convolutional autoencoders—to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate four challenging test cases in cardiac electrophysiology, thus demonstrating that DL-ROM outperforms classical projection-based ROMs.

A memory optimization method combined with adaptive time-step method for cardiac cell simulation based on multi-GPU

Cardiac electrophysiological simulation is a very complex computational process, which can be run on graphics processing unit (GPU) to save computational cost greatly. The use of adaptive time-step can further effectively speed up the simulation of heart cells. However, if the adaptive time-step method applies to GPU, it suffers synchronization problem on GPU, weakening the acceleration of adaptive time-step method. The previous work ran on a single GPU with the adaptive time-step to get only 1.5 times (× 1.5) faster than the fixed time-step. This study proposes a memory allocation method, which can effectively implement the adaptive time-step method on GPU. The proposed method mainly focuses on the stimulus point and potential memory arrangement in order to achieve optimal memory storage efficiency. All calculation is implemented on GPU. Large matrices such as potential are arranged in column order, and the cells on the left are stimulated. The Luo-Rudy passive (LR1) and dynamic (LRd) ventricular action potential models are used with adaptive time-step methods, such as the traditional hybrid method (THM) and Chen-Chen-Luo's (CCL) "quadratic adaptive algorithm" method. As LR1 is solved by the THM or CCL on a single GPU, the acceleration is × 34 and × 75 respectively compared with the fixed time-step. With 2 or 4 GPUs, the acceleration of the THM and CCL is × 34 or × 35 and × 73 or × 75, but it would decrease to × 5 or × 3 and × 20 or × 15 without optimization. In an LRd model, the acceleration reaches × 27 or × 85 as solved by the THM or CCL compared with the fixed time-step on multi-GPU with linear speed up increase versus the number of GPU. However, with the increase of GPUs number, the acceleration of the THM and CCL is continuously weakened before optimization. The mixed root mean square error (MRMSE) lower than 5% is applied to ensure the accuracy of simulation. The result shows that the proposed memory arrangement method can save computational cost a lot to speed up the heart simulation greatly. Graphical abstract Acceleration ratio compared with CPU with fixed time-step (dt = 0.001 ms).

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

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

Variability in electrophysiological properties and conducting obstacles controls re-entry risk in heterogeneous ischaemic tissue

Ischaemia, in which inadequate blood supply compromises and eventually kills regions of cardiac tissue, can cause many types of arrhythmia, some life-threatening. A significant component of this is the effects of the resulting hypoxia, and concomitant hyperklaemia and acidosis, on the electrophysiological properties of myocytes. Clinical and experimental data have also shown that regions of structural heterogeneity (fibrosis, necrosis, fibro-fatty infiltration) can act as triggers for arrhythmias under acute ischaemic conditions. Mechanistic models have successfully captured these effects in silico. However, the relative significance of these separate facets of the condition, and how sensitive arrhythmic risk is to the extents of each, is far less explored. In this work, we use partitioned Gaussian process emulation and new metrics for source-sink mismatch that rely on simulations of bifurcating cardiac fibres to interrogate a model of heterogeneous ischaemic tissue. Re-entries were most sensitive to the level of hypoxia and the fraction of non-excitable tissue. In addition, our results reveal both protective and pro-arrhythmic effects of hyperklaemia, and present the levels of hyperklaemia, hypoxia and percentage of non-excitable tissue that pose the highest arrhythmic risks. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Ectopic beats arise from micro-reentries near infarct regions in simulations of a patient-specific heart model

Ectopic beats are known to be involved in the initiation of a variety of cardiac arrhythmias. Although their location may vary, ectopic excitations have been found to originate from infarct areas, regions of micro-fibrosis and other heterogeneous tissues. However, the underlying mechanisms that link ectopic foci to heterogeneous tissues have yet to be fully understood. In this work, we investigate the mechanism of micro-reentry that leads to the generation of ectopic beats near infarct areas using a patient-specific heart model. The patient-specific geometrical model of the heart, including scar and peri-infarct zones, is obtained through magnetic resonance imaging (MRI). The infarct region is composed of ischemic myocytes and non-conducting cells (fibrosis, for instance). Electrophysiology is captured using an established cardiac myocyte model of the human ventricle modified to describe ischemia. The simulation results clearly reveal that ectopic beats emerge from micro-reentries that are sustained by the heterogeneous structure of the infarct regions. Because microscopic information about the heterogeneous structure of the infarct regions is not available, Monte-Carlo simulations are used to identify the probabilities of an infarct region to behave as an ectopic focus for different levels of ischemia and different percentages of non-conducting cells. From the proposed model, it is observed that ectopic beats are generated when a percentage of non-conducting cells is near a topological metric known as the percolation threshold. Although the mechanism for micro-reentries was proposed half a century ago to be a source of ectopic beats or premature ventricular contractions during myocardial infarction, the present study is the first to reproduce this mechanism in-silico using patient-specific data.

Killing Many Birds With Two Stones: Hypoxia and Fibrosis Can Generate Ectopic Beats in a Human Ventricular Model

During cardiac diseases many types of anatomical and functional remodeling of cardiac tissue can occur. In this work, we focus on two conditions: hypoxia and fibrosis, which are part of complex pathological modifications that take place in many cardiac diseases (hypertrophic cardiomyopathy, hypertensive heart disease, and recurrent myocardial infarction) and respiratory diseases (obstructive pulmonary disease, obstructive sleep apnea, and cystic fibrosis). Using computational models of cardiac electrophysiology, we evaluate if the interplay between hypoxia and fibrosis is sufficient to trigger cardiac arrhythmia. We study the mechanisms behind the generation of ectopic beats, an arrhythmic trigger also known as premature ventricular contractions (PVCs), in regions with high hypoxia and fibrosis. First, we modify an electrophysiological model of myocytes of the human left ventricle to include the effects of hypoxia. Second, diffuse fibrosis is modeled by randomly replacing cardiac myocytes by non-excitable and non-conducting cells. The Monte Carlo method is used to evaluate the probability of a region to generate ectopic beats with respect to different levels of hypoxia and fibrosis. In addition, we evaluate the minimum size of three-dimensional slabs needed to sustain reentries for different stimulation protocols. The observed mechanism behind the initiation of ectopic beats is unidirectional block, giving rise to sustained micro-reentries inside the region with diffuse fibrosis and hypoxia. In summary, our results suggest that hypoxia and fibrosis are sufficient for the creation of a focal region in the heart that generates PVCs.