Models of cardiac tissue electrophysiology: progress, challenges and open questions

Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential

This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q₁₀ and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.

Incorporating inductances in tissue-scale models of cardiac electrophysiology

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and we examine the effect of intracellular and extracellular inductances on the virtual electrode phenomenon.

Suppression of turbulence by heterogeneities in a cardiac model with fiber rotation

Electrical scroll wave turbulence in human ventricles is associated with ventricular fibrillation and sudden cardiac death. We perform three-dimensional simulations on the basis of the anisotropic Fenton-Karma model and show that macroscopic, insulating heterogeneities (e.g., blood vessels) can cause the spontaneous formation of pinned scroll waves. The wave field of these vortices is periodic, and their frequencies are sufficiently high to push the free, turbulent vortices into the system boundaries where they annihilate. Our study considers cylindrical heterogeneities with radii in the range of 0.1 to 2 cm that extend either in the transmural or a perpendicular direction. Thick cylinders cause the spontaneous formation of multi-armed rotors according to a radius-dependence that is explained in terms of two-dimensional dynamics. For long cylinders, local pinning contacts spread along the heterogeneity by fast and complex self-wrapping.

Modeling hypothermia induced effects for the heterogeneous ventricular tissue from cellular level to the impact on the ECG

Hypothermia has a profound impact on the electrophysiological mechanisms of the heart. Experimental investigations provide a better understanding of electrophysiological alterations associated with cooling. However, there is a lack of computer models suitable for simulating the effects of hypothermia in cardio-electrophysiology. In this work, we propose a model that describes the cooling-induced electrophysiological alterations in ventricular tissue in a temperature range from 27°C to 37°C. To model the electrophysiological conditions in a 3D left ventricular tissue block it was essential to consider the following anatomical and physiological parameters in the model: the different cell types (endocardial, M, epicardial), the heterogeneous conductivities in longitudinal, transversal and transmural direction depending on the prevailing temperature, the distinct fiber orientations and the transmural repolarization sequences. Cooling-induced alterations on the morphology of the action potential (AP) of single myocardial cells thereby are described by an extension of the selected Bueno-Orovio model for human ventricular tissue using Q10 temperature coefficients. To evaluate alterations on tissue level, the corresponding pseudo electrocardiogram (pECG) was calculated. Simulations show that cooling-induced AP and pECG-related parameters, i.e. AP duration, morphology of the notch of epicardial AP, maximum AP upstroke velocity, AP rise time, QT interval, QRS duration and J wave formation are in good accordance with literature and our experimental data. The proposed model enables us to further enhance our knowledge of cooling-induced electrophysiological alterations from cellular to tissue level in the heart and may help to better understand electrophysiological mechanisms, e.g. in arrhythmias, during hypothermia.

In silico investigation of a KCNQ1 mutation associated with short QT syndrome

Short QT syndrome (SQTS) is a rare condition characterized by abnormally 'short' QT intervals on the ECG and increased susceptibility to cardiac arrhythmias and sudden death. This simulation study investigated arrhythmia dynamics in multi-scale human ventricle models associated with the SQT2-related V307L KCNQ1 'gain-of-function' mutation, which increases slow-delayed rectifier potassium current (I_Ks). A Markov chain (MC) model recapitulating wild type (WT) and V307L mutant I_Ks kinetics was incorporated into a model of the human ventricular action potential (AP) for investigation of QT interval changes and arrhythmia substrates. In addition, the degree of simulated I_Ks inhibition necessary to normalize the QT interval and terminate re-entry in SQT2 conditions was quantified. The developed MC model accurately reproduced AP shortening and reduced effective refractory period associated with altered I_Ks kinetics in homozygous (V307L) and heterozygous (WT-V307L) mutation conditions, which increased the lifespan and dominant frequency of re-entry in 3D human ventricle models. I_Ks reductions of 58% and 65% were sufficient to terminate re-entry in WT-V307L and V307L conditions, respectively. This study further substantiates a causal link between the V307L KCNQ1 mutation and pro-arrhythmia in human ventricles, and establishes partial inhibition of I_Ks as a potential anti-arrhythmic strategy in SQT2.

Signal Reconstruction of Pulmonary Vein Recordings Using a Phenomenological Mathematical Model: Application to Pulmonary Vein Isolation Therapy

Atrial fibrillation (AF), the most prevalent cardiac arrhythmia, is commonly initiated by ectopic beats originating from a small myocardial sleeve extending over the pulmonary veins. Pulmonary vein isolation therapy attempts to isolate the pulmonary veins from the left atrium by ablating tissue, commonly by using radiofrequency ablation. During this procedure, the cardiologist records electrical activity using a lasso catheter, and the activation pattern recorded is used as a guide toward which regions to ablate. However, poor contact between electrode and tissue can lead to important regions of electrical activity not being recorded in clinic. We reproduce these signals through the use of a phenomenological model of the cardiac action potential on a cylinder, which we fit to post-AF atrial cells, and model the bipolar electrodes of the lasso catheter by an approximation of the surface potential. The resulting activation pattern is validated by direct comparison with those of clinical recordings. A potential application of the model is to reconstruct the missing electrical activity, minimizing the impact of the information loss on the clinical procedure, and we present results to demonstrate this.

The importance of mechano-electrical feedback and inertia in cardiac electromechanics

In the past years, a number cardiac electromechanics models have been developed to better understand the excitation-contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechanoelectrical feedback and inertia in cardiac electromechanics.

Atrial arrhythmogenicity of KCNJ2 mutations in short QT syndrome: Insights from virtual human atria

Gain-of-function mutations in KCNJ2-encoded Kir2.1 channels underlie variant 3 (SQT3) of the short QT syndrome, which is associated with atrial fibrillation (AF). Using biophysically-detailed human atria computer models, this study investigated the mechanistic link between SQT3 mutations and atrial arrhythmogenesis, and potential ion channel targets for treatment of SQT3. A contemporary model of the human atrial action potential (AP) was modified to recapitulate functional changes in I_K1 due to heterozygous and homozygous forms of the D172N and E299V Kir2.1 mutations. Wild-type (WT) and mutant formulations were incorporated into multi-scale homogeneous and heterogeneous tissue models. Effects of mutations on AP duration (APD), conduction velocity (CV), effective refractory period (ERP), tissue excitation threshold and their rate-dependence, as well as the wavelength of re-entry (WL) were quantified. The D172N and E299V Kir2.1 mutations produced distinct effects on I_K1 and APD shortening. Both mutations decreased WL for re-entry through a reduction in ERP and CV. Stability of re-entrant excitation waves in 2D and 3D tissue models was mediated by changes to tissue excitability and dispersion of APD in mutation conditions. Combined block of I_K1 and I_Kr was effective in terminating re-entry associated with heterozygous D172N conditions, whereas I_Kr block alone may be a safer alternative for the E299V mutation. Combined inhibition of I_Kr and I_Kur produced a synergistic anti-arrhythmic effect in both forms of SQT3. In conclusion, this study provides mechanistic insights into atrial proarrhythmia with SQT3 Kir2.1 mutations and highlights possible pharmacological strategies for management of SQT3-linked AF.

Atrial fibrillation (AF) is the most common cardiac arrhythmia, and is characterised by complex and irregular electrical activation of the upper chambers of the heart. One rare, genetic condition associated with increased risk of AF is the short QT syndrome (SQTS), which is caused by mutations in genes involved in normal electrical function of the heart. Underlying mechanisms by which SQTS-related gene mutations facilitate development of arrhythmias in the human atria are not well understood. In this study, sophisticated computer models representing ‘virtual’ human atria, incorporating detailed electrophysiological data at the ‘ion channel’ protein level into both idealised and realistic multi-scale tissue geometries, were used to dissect mechanisms by which two mutations in the KCNJ2 gene responsible for SQTS variant 3 (SQT3) promote initiation and sustenance of arrhythmias. It was found that the D172N and E299V mutations to KCNJ2 accelerated the repolarisation process at the cellular level through distinct mechanisms. This, along with the way the mutations affected heterogeneity in electrical behaviour at the organ level, mediated stability of arrhythmias and response to simulated ion channel block. This study improves understanding of mechanisms underlying increased AF risk associated with D172N and E299V KCNJ2 mutations, and outlines potential therapeutic strategies.

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue

We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano-electrical feedback in facilitating and promoting atrial fibrillation.

Mini Electrodes on Ablation Catheters: Valuable Addition or Redundant Information?-Insights from a Computational Study

Radiofrequency ablation has become a first-line approach for curative therapy of many cardiac arrhythmias. Various existing catheter designs provide high spatial resolution to identify the best spot for performing ablation and to assess lesion formation. However, creation of transmural and nonconducting ablation lesions requires usage of catheters with larger electrodes and improved thermal conductivity, leading to reduced spatial sensitivity. As trade-off, an ablation catheter with integrated mini electrodes was introduced. The additional diagnostic benefit of this catheter is still not clear. In order to solve this issue, we implemented a computational setup with different ablation scenarios. Our in silico results show that peak-to-peak amplitudes of unipolar electrograms from mini electrodes are more suitable to differentiate ablated and nonablated tissue compared to electrograms from the distal ablation electrode. However, in orthogonal mapping position, no significant difference was observed between distal electrode and mini electrodes electrograms in the ablation scenarios. In conclusion, catheters with mini electrodes bring about additional benefit to distinguish ablated tissue from nonablated tissue in parallel position with high spatial resolution. It is feasible to detect conduction gaps in linear lesions with this catheter by evaluating electrogram data from mini electrodes.

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

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

Evaluation of a Rapid Anisotropic Model for ECG Simulation

State-of-the-art cardiac electrophysiology models that are able to deliver physiologically motivated activation maps and electrocardiograms (ECGs) can only be solved on high-performance computing architectures. This makes it nearly impossible to adopt such models in clinical practice. ECG imaging tools typically rely on simplified models, but these neglect the anisotropic electric conductivity of the tissue in the forward problem. Moreover, their results are often confined to the heart-torso interface. We propose a forward model that fully accounts for the anisotropic tissue conductivity and produces the standard 12-lead ECG in a few seconds. The activation sequence is approximated with an eikonal model in the 3d myocardium, while the ECG is computed with the lead-field approach. Both solvers were implemented on graphics processing units and massively parallelized. We studied the numerical convergence and scalability of the approach. We also compared the method to the bidomain model in terms of ECGs and activation maps, using a simplified but physiologically motivated geometry and 6 patient-specific anatomies. The proposed methods provided a good approximation of activation maps and ECGs computed with a bidomain model, in only a few seconds. Both solvers scaled very well to high-end hardware. These methods are suitable for use in ECG imaging methods, and may soon become fast enough for use in interactive simulation tools.

Micropatterned co-culture of cardiac myocytes on fibrous scaffolds for predictive screening of drug cardiotoxicities

The spatial arrangement of cardiac myocytes (CMs) and other non-myocytes scaffolds, closely resembling native tissue, is essential to control the CM morphology and function for cardiac tissue regeneration. In the current study, micropatterned fibrous scaffolds were developed to establish a CM co-culture system with cardiac fibroblasts (CFs) and endothelial cells (ECs) as a potential in vitro drug screening model. To pursue a biomimetic approach to influence CM behaviors, strip, oval and wave-patterned mats were constructed by deposition of electrospun fibers on lithographic collectors, followed by precise stacking for cell co-cultures. CMs, CFs, and ECs were located on the patterned scaffolds with controlled cellular distribution in the respective regions and no across condition was found. Compared with those after strip and oval-patterned co-culture, CMs co-cultured on wave-patterned scaffolds displayed significantly greater cell viabilities, larger cell elongation ratios, stronger expressions of cardiac-specific Troponin I, connexin 43 and sarcomeric α-actinin and higher beating rates during 15 days of incubation. The responses of co-cultured CMs to quinidine, erythromycin and sotalol show good correlations with clinical observations in the beating rate and the prolongation of the contraction and relaxation time. The in vivo safety data reflected well with the concentrations for 50% of maximal effect (EC₅₀) after drug treatment on co-cultured CMs, which was determined from the changes in the corrected field potential duration (FPDc) against the drug concentrations. During 15 days of patterned co-culture, the interbeat intervals and fluctuations of the CMs indicated quick changes in response to haloperidol treatment and sufficient restoration of the original beating profiles after drug removal. This study demonstrates the capabilities of micropatterned co-culture of CMs to establish the cardiac function as a reproducible and reliable platform for screening cardiac side effects of drugs.

Propagation of parametric uncertainty for the K+ channel model in mouse ventricular myocytes

Cardiac potassium (K+) channel plays an important role in cardiac electrical signaling. Mathematical models have been widely used to investigate the effects of K+ channels on cardiac functions. However, the model of K+ channel involves parametric uncertainties, which can be induced by fitting the model's parameters that best capture experimental data. Since the prediction of cardiac functions are highly parameter-dependent, it is critical to quantify the influence of parametric uncertainty on the model responses to provide the more reliable predictions. This paper presents a new method to efficiently propagate the uncertainty on the model's parameters of K+ channel to the gating variables as well as the current density. In this way, we can estimate the model predictions and their corresponding confidence intervals simultaneously. A generalized polynomial chaos (gPC) expansion approximating the parametric uncertainty is used in combination with the physical models to quantify and propagate the parametric uncertainties onto the modeled predictions of steady state activation and steady state inactivation of the K+ channel. Using Galerkin projection, the variation (i.e., confidence interval) of the gating variables resulting from the uncertainty of model parameters can then be estimated in a computationally efficient fashion. As compared with the Monte Carlo (MC) simulations, the proposed methodology shows it's advantageous in terms of computational efficiency and accuracy, thus demonstrating the potential for dealing with more complicated cardiac models.

Modeling an Excitable Biosynthetic Tissue with Inherent Variability for Paired Computational-Experimental Studies

To understand how excitable tissues give rise to arrhythmias, it is crucially necessary to understand the electrical dynamics of cells in the context of their environment. Multicellular monolayer cultures have proven useful for investigating arrhythmias and other conduction anomalies, and because of their relatively simple structure, these constructs lend themselves to paired computational studies that often help elucidate mechanisms of the observed behavior. However, tissue cultures of cardiomyocyte monolayers currently require the use of neonatal cells with ionic properties that change rapidly during development and have thus been poorly characterized and modeled to date. Recently, Kirkton and Bursac demonstrated the ability to create biosynthetic excitable tissues from genetically engineered and immortalized HEK293 cells with well-characterized electrical properties and the ability to propagate action potentials. In this study, we developed and validated a computational model of these excitable HEK293 cells (called “Ex293” cells) using existing electrophysiological data and a genetic search algorithm. In order to reproduce not only the mean but also the variability of experimental observations, we examined what sources of variation were required in the computational model. Random cell-to-cell and inter-monolayer variation in both ionic conductances and tissue conductivity was necessary to explain the experimentally observed variability in action potential shape and macroscopic conduction, and the spatial organization of cell-to-cell conductance variation was found to not impact macroscopic behavior; the resulting model accurately reproduces both normal and drug-modified conduction behavior. The development of a computational Ex293 cell and tissue model provides a novel framework to perform paired computational-experimental studies to study normal and abnormal conduction in multidimensional excitable tissue, and the methodology of modeling variation can be applied to models of any excitable cell.

One of the major challenges in trying to understand how arrhythmias can form in cardiac tissue is studying how the electrical activity of cardiac cells is affected by their surroundings. Current approaches have focused on studying cardiac cells in vitro and using computational models to elucidate the mechanisms behind experimental findings. However, tissue culture techniques are limited to working with neonatal, rather than adult, cells, and computational modeling of these cells has proven challenging. In this work, we have a developed a new approach for conducting paired experimental and computational studies by using a cell line engineered with the minimum machinery for excitability, and a computational model derived and validated directly from this cell line. In order to create a model that reproduces the diversity, rather than simply the average behavior, of experimental studies, we have incorporated a simple yet novel method of inherent variability, and explored what types of experimental variation must be incorporated into the model to recapitulate experimental findings. Using this new platform for paired experimental-computational studies with inherent variability, we will be able to study and better understand how changes in cardiac structure such as fibrosis and heterogeneity lead to conduction slowing, conduction failure, and arrhythmogenesis.

Model of electrical activity in cardiac tissue under electromagnetic induction

Complex electrical activities in cardiac tissue can set up time-varying electromagnetic field. Magnetic flux is introduced into the Fitzhugh-Nagumo model to describe the effect of electromagnetic induction, and then memristor is used to realize the feedback of magnetic flux on the membrane potential in cardiac tissue. It is found that a spiral wave can be triggered and developed by setting specific initials in the media, that is to say, the media still support the survival of standing spiral waves under electromagnetic induction. Furthermore, electromagnetic radiation is considered on this model as external stimuli, it is found that spiral waves encounter breakup and turbulent electrical activities are observed, and it can give guidance to understand the occurrence of sudden heart disorder subjected to heavily electromagnetic radiation.

Reentry and Ectopic Pacemakers Emerge in a Three-Dimensional Model for a Slab of Cardiac Tissue with Diffuse Microfibrosis near the Percolation Threshold

Arrhythmias in cardiac tissue are generally associated with irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. Recently, it was shown in simulations of two-dimensional (2D) discrete models of cardiac tissue that a wave crossing a fibrotic, heterogeneous region may produce reentry and transient or persistent ectopic activity provided the fraction of conducting connections is just above the percolation threshold. Here, we investigate the occurrence of these phenomena in three-dimensions by simulations of a discrete model representing a thin slab of cardiac tissue. This is motivated (i) by the necessity to study the relevance and properties of the percolation-related mechanism for the emergence of microreentries in three dimensions and (ii) by the fact that atrial tissue is quite thin in comparison with ventricular tissue. Here, we simplify the model by neglecting details of tissue anatomy, e. g. geometries of atria or ventricles and the anisotropy in the conductivity. Hence, our modeling study is confined to the investigation of the effect of the tissue thickness as well as to the comparison of the dynamics of electrical excitation in a 2D layer with the one in a 3D slab. Our results indicate a strong and non-trivial effect of the thickness even for thin tissue slabs on the probability of microreentries and ectopic beat generation. The strong correlation of the occurrence of microreentry with the percolation threshold reported earlier in 2D layers persists in 3D slabs. Finally, a qualitative agreement of 3D simulated electrograms in the fibrotic region with the experimentally observed complex fractional atrial electrograms (CFAE) as well as strong difference between simulated electrograms in 2D and 3D were found for the cases where reentry and ectopic activity were triggered by the micro-fibrotic region.

3D Finite Element Electrical Model of Larval Zebrafish ECG Signals

Assessment of heart function in zebrafish larvae using electrocardiography (ECG) is a potentially useful tool in developing cardiac treatments and the assessment of drug therapies. In order to better understand how a measured ECG waveform is related to the structure of the heart, its position within the larva and the position of the electrodes, a 3D model of a 3 days post fertilisation (dpf) larval zebrafish was developed to simulate cardiac electrical activity and investigate the voltage distribution throughout the body. The geometry consisted of two main components; the zebrafish body was modelled as a homogeneous volume, while the heart was split into five distinct regions (sinoatrial region, atrial wall, atrioventricular band, ventricular wall and heart chambers). Similarly, the electrical model consisted of two parts with the body described by Laplace's equation and the heart using a bidomain ionic model based upon the Fitzhugh-Nagumo equations. Each region of the heart was differentiated by action potential (AP) parameters and activation wave conduction velocities, which were fitted and scaled based on previously published experimental results. ECG measurements in vivo at different electrode recording positions were then compared to the model results. The model was able to simulate action potentials, wave propagation and all the major features (P wave, R wave, T wave) of the ECG, as well as polarity of the peaks observed at each position. This model was based upon our current understanding of the structure of the normal zebrafish larval heart. Further development would enable us to incorporate features associated with the diseased heart and hence assist in the interpretation of larval zebrafish ECGs in these conditions.

Slow Conduction in the Border Zones of Patchy Fibrosis Stabilizes the Drivers for Atrial Fibrillation: Insights from Multi-Scale Human Atrial Modeling

Introduction: The genesis of atrial fibrillation (AF) and success of AF ablation therapy have been strongly linked with atrial fibrosis. Increasing evidence suggests that patient-specific distributions of fibrosis may determine the locations of electrical drivers (rotors) sustaining AF, but the underlying mechanisms are incompletely understood. This study aims to elucidate a missing mechanistic link between patient-specific fibrosis distributions and AF drivers. Methods: 3D atrial models integrated human atrial geometry, rule-based fiber orientation, region-specific electrophysiology, and AF-induced ionic remodeling. A novel detailed model for an atrial fibroblast was developed, and effects of myocyte-fibroblast (M-F) coupling were explored at single-cell, 1D tissue and 3D atria levels. Left atrial LGE MRI datasets from 3 chronic AF patients were segmented to provide the patient-specific distributions of fibrosis. The data was non-linearly registered and mapped to the 3D atria model. Six distinctive fibrosis levels (0-healthy tissue, 5-dense fibrosis) were identified based on LGE MRI intensity and modeled as progressively increasing M-F coupling and decreasing atrial tissue coupling. Uniform 3D atrial model with diffuse (level 2) fibrosis was considered for comparison. Results: In single cells and tissue, the largest effect of atrial M-F coupling was on the myocyte resting membrane potential, leading to partial inactivation of sodium current and reduction of conduction velocity (CV). In the 3D atria, further to the M-F coupling, effects of fibrosis on tissue coupling greatly reduce atrial CV. AF was initiated by fast pacing in each 3D model with either uniform or patient-specific fibrosis. High variation in fibrosis distributions between the models resulted in varying complexity of AF, with several drivers emerging. In the diffuse fibrosis models, waves randomly meandered through the atria, whereas in each the patient-specific models, rotors stabilized in fibrotic regions. The rotors propagated slowly around the border zones of patchy fibrosis (levels 3-4), failing to spread into inner areas of dense fibrosis. Conclusion: Rotors stabilize in the border zones of patchy fibrosis in 3D atria, where slow conduction enable the development of circuits within relatively small regions. Our results can provide a mechanistic explanation for the clinical efficacy of ablation around fibrotic regions.

The Cardiac Electrophysiology Web Lab

Computational modeling of cardiac cellular electrophysiology has a long history, and many models are now available for different species, cell types, and experimental preparations. This success brings with it a challenge: how do we assess and compare the underlying hypotheses and emergent behaviors so that we can choose a model as a suitable basis for a new study or to characterize how a particular model behaves in different scenarios? We have created an online resource for the characterization and comparison of electrophysiological cell models in a wide range of experimental scenarios. The details of the mathematical model (quantitative assumptions and hypotheses formulated as ordinary differential equations) are separated from the experimental protocol being simulated. Each model and protocol is then encoded in computer-readable formats. A simulation tool runs virtual experiments on models encoded in CellML, and a website (https://chaste.cs.ox.ac.uk/WebLab) provides a friendly interface, allowing users to store and compare results. The system currently contains a sample of 36 models and 23 protocols, including current-voltage curve generation, action potential properties under steady pacing at different rates, restitution properties, block of particular channels, and hypo-/hyperkalemia. This resource is publicly available, open source, and free, and we invite the community to use it and become involved in future developments. Investigators interested in comparing competing hypotheses using models can make a more informed decision, and those developing new models can upload them for easy evaluation under the existing protocols, and even add their own protocols.

Space-discretization error analysis and stabilization schemes for conduction velocity in cardiac electrophysiology

In cardiac electrophysiology, the propagation of the action potential may be described by a set of reaction-diffusion equations known as the bidomain model. The shape of the solution is determined by a balance of a strong reaction and a relatively weak diffusion, which leads to steep variations in space and time. From a numerical point of view, the sharp spatial gradients may be seen as particularly problematic, because computational grid resolution on the order of 0.1 mm or less is required, yielding considerable computational efforts on human geometries. In this paper, we discuss a number of well-known numerical schemes for the bidomain equation and show how the quality of the solution is affected by the spatial discretization. In particular, we study in detail the effect of discretization on the conduction velocity (CV), which is an important quantity from a physiological point of view. We show that commonly applied finite element techniques tend to overestimate the CV on coarse grids, while it tends to be underestimated by finite difference schemes. Furthermore, the choice of interpolation and discretization scheme for the nonlinear reaction term has a strong impact on the CV. Finally, we exploit the results of the error analysis to propose improved numerical methods, including a stabilized scheme that tends to correct the CV on coarse grids but converges to the correct solution as the grid is refined. Copyright © 2016 John Wiley & Sons, Ltd.

Simulation of intracardiac electrograms around acute ablation lesions

Radiofrequency ablation (RFA) is a widely used clinical treatment for many types of cardiac arrhythmias. However, nontransmural lesions and gaps between linear lesions often lead to recurrence of the arrhythmia. Intracardiac electrograms (IEGMs) provide real-time information regarding the state of the cardiac tissue surrounding the catheter tip. Nevertheless, the formation and interpretation of IEGMs during the RFA procedure is complex and yet not fully understood. In this in-silico study, we propose a computational model for acute ablation lesions. Our model consists of a necrotic scar core and a border zone, describing irreversible and reversible temperature induced electrophysiological phenomena. These phenomena are modeled by varying the intra- and extracellular conductivity of the tissue as well as a regulating zone factor. The computational model is evaluated regarding its feasibility and validity. Therefore, this model was compared to an existing one and to clinical measurements of five patients undergoing RFA. The results show that the model can indeed be used to recreate IEGMs. We computed IEGMs arising from complex ablation scars, such as scars with gaps or two overlapping ellipsoid scars. For orthogonal catheter orientation, the presence of a second necrotic core in the near-field of a punctiform acute ablation lesion had minor impact on the resulting signal morphology. The presented model can serve as a base for further research on the formation and interpretation of IEGMs.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Light-intensity and high-intensity interval training improve cardiometabolic health in rats

Physical activity has the potential to reduce cardiometabolic risk factors but evaluation of different intensities of physical activity and the mechanisms behind their health effects still need to be fully established. This study examined the effects of sedentary behaviour, light-intensity training, and high-intensity interval training on biometric indices, glucose and lipid metabolism, inflammatory and oxidative stress markers, and vascular and cardiac function in adult rats. Rats (12 weeks old) were randomly assigned to 1 of 4 groups: control (CTL; no exercise), sedentary (SED; no exercise and housed in small cages to reduce activity), light-intensity trained (LIT; four 30-min exercise bouts/day at 8 m/min separated by 2-h rest period, 5 days/week), and high-intensity interval trained (HIIT, four 2.5-min work bouts/day at 50 m/min separated by 3-min rest periods, 5 days/week). After 12 weeks of intervention, SED had greater visceral fat accumulation (p < 0.01) and slower cardiac conduction (p = 0.04) compared with the CTL group. LIT and HIIT demonstrated beneficial changes in body weight, visceral and epididymal fat weight, glucose regulation, low-density lipoprotein cholesterol, total cholesterol, and mesenteric vessel contractile response compared with the CTL group (p < 0.05). LIT had significant improvements in insulin sensitivity and cardiac conduction compared with the CTL and SED groups whilst HIIT had significant improvements in systolic blood pressure and endothelium-independent vasodilation to aorta and mesenteric artery compared with the CTL group (p < 0.05). LIT and HIIT induce health benefits by improving traditional cardiometabolic risk factors. LIT improves cardiac health while HIIT promotes improvements in vascular health.

Cardiac Meets Skeletal: What's New in Microfluidic Models for Muscle Tissue Engineering

In the last few years microfluidics and microfabrication technique principles have been extensively exploited for biomedical applications. In this framework, organs-on-a-chip represent promising tools to reproduce key features of functional tissue units within microscale culture chambers. These systems offer the possibility to investigate the effects of biochemical, mechanical, and electrical stimulations, which are usually applied to enhance the functionality of the engineered tissues. Since the functionality of muscle tissues relies on the 3D organization and on the perfect coupling between electrochemical stimulation and mechanical contraction, great efforts have been devoted to generate biomimetic skeletal and cardiac systems to allow high-throughput pathophysiological studies and drug screening. This review critically analyzes microfluidic platforms that were designed for skeletal and cardiac muscle tissue engineering. Our aim is to highlight which specific features of the engineered systems promoted a typical reorganization of the engineered construct and to discuss how promising design solutions exploited for skeletal muscle models could be applied to improve cardiac tissue models and vice versa.

Spatial reproducibility of complex fractionated atrial electrogram depending on the direction and configuration of bipolar electrodes: an in-silico modeling study

Although 3D-complex fractionated atrial electrogram (CFAE) mapping is useful in radiofrequency catheter ablation for persistent atrial fibrillation (AF), the directions and configuration of the bipolar electrodes may affect the electrogram. This study aimed to compare the spatial reproducibility of CFAE by changing the catheter orientations and electrode distance in an in-silico left atrium (LA). We conducted this study by importing the heart CT image of a patient with AF into a 3D-homogeneous human LA model. Electrogram morphology, CFAE-cycle lengths (CLs) were compared for 16 different orientations of a virtual bipolar conventional catheter (conv-cath: size 3.5 mm, inter-electrode distance 4.75 mm). Additionally, the spatial correlations of CFAE-CLs and the percentage of consistent sites with CFAE-CL<120 ms were analyzed. The results from the conv-cath were compared with that obtained using a mini catheter (mini-cath: size 1 mm, inter-electrode distance 2.5 mm). Depending on the catheter orientation, the electrogram morphology and CFAE-CLs varied (conv-cath: 11.5±0.7% variation, mini-cath: 7.1±1.2% variation), however the mini-cath produced less variation of CFAE-CL than conv-cath (p<0.001). There were moderate spatial correlations among CFAE-CL measured at 16 orientations (conv-cath: r=0.3055±0.2194 vs. mini-cath: 0.6074±0.0733, p<0.001). Additionally, the ratio of consistent CFAE sites was higher for mini catheter than conventional one (38.3±4.6% vs. 22.3±1.4%, p<0.05). Electrograms and CFAE distribution are affected by catheter orientation and electrode configuration in the in-silico LA model. However, there was moderate spatial consistency of CFAE areas, and narrowly spaced bipolar catheters were less influenced by catheter direction than conventional catheters.

Coupled electro-mechanical models of fiber-distributed active tissues

We discuss a constitutive model for stochastically distributed fiber reinforced tissues, where the active behavior of the fibers depends on the relative orientation of the electric field. Unlike other popular approaches, based on numerical integration over the unit sphere, or on the use of second order structure tensors, for the passive behavior we adopt a second order approximation of the strain energy density of the distribution. The purely mechanical quantities result to be dependent on two (second and fourth order, respectively) averaged structure tensors. In line with the approximation used for the passive behavior, we model the active behavior accounting for the statistical fiber distribution. We extend the Helmholtz free energy density by introducing a directional active potential, dependent on a stochastic permittivity tensor associated to a particular direction, and approximate the total active potential through a second order Taylor expansion of the permittivity tensor. The approximation allows us to derive explicitly the active stress and the active constitutive tensors, which result to be dependent on the same two averaged structure tensors that characterize the passive response. Active anisotropy follows from the distribution of the fibers and inherits its stochastic parameters. Examples of passive and active behaviors predicted by the model in terms of response to biaxial testing are presented, and comparisons with passive experimental data are provided.

Personalized Computer Simulation of Diastolic Function in Heart Failure

The search for a parameter representing left ventricular relaxation from non-invasive and invasive diagnostic tools has been extensive, since heart failure (HF) with preserved ejection fraction (HF-pEF) is a global health problem. We explore here the feasibility using patient-specific cardiac computer modeling to capture diastolic parameters in patients suffering from different degrees of systolic HF. Fifty eight patients with idiopathic dilated cardiomyopathy have undergone thorough clinical evaluation, including cardiac magnetic resonance imaging (MRI), heart catheterization, echocardiography, and cardiac biomarker assessment. A previously-introduced framework for creating multi-scale patient-specific cardiac models has been applied on all these patients. Novel parameters, such as global stiffness factor and maximum left ventricular active stress, representing cardiac active and passive tissue properties have been computed for all patients. Invasive pressure measurements from heart catheterization were then used to evaluate ventricular relaxation using the time constant of isovolumic relaxation Tau (τ). Parameters from heart catheterization and the multi-scale model have been evaluated and compared to patient clinical presentation. The model parameter global stiffness factor, representing diastolic passive tissue properties, is correlated significantly across the patient population with τ. This study shows that multi-modal cardiac models can successfully capture diastolic (dys) function, a prerequisite for future clinical trials on HF-pEF.

The Spatiotemporal Stability of Dominant Frequency Sites in In-Silico Modeling of 3-Dimensional Left Atrial Mapping of Atrial Fibrillation

BACKGROUND

We previously reported that stable rotors were observed in in-silico human atrial fibrillation (AF) models, and were well represented by dominant frequency (DF). We explored the spatiotemporal stability of DF sites in 3D-AF models imported from patient CT images of the left atrium (LA).

METHODS

We integrated 3-D CT images of the LA obtained from ten patients with persistent AF (male 80%, 61.8 ± 13.5 years old) into an in-silico AF model. After induction, we obtained 6 seconds of AF simulation data for DF analyses in 30 second intervals (T1-T9). The LA was divided into ten sections. Spatiotemporal changes and variations in the temporal consistency of DF were evaluated at each section of the LA. The high DF area was defined as the area with the highest 10% DF.

RESULTS

1. There was no spatial consistency in the high DF distribution at each LA section during T1-T9 except in one patient (p = 0.027). 2. Coefficients of variation for the high DF area were highly different among the ten LA sections (p < 0.001), and they were significantly higher in the four pulmonary vein (PV) areas, the LA appendage, and the peri-mitral area than in the other LA sections (p < 0.001). 3. When we conducted virtual ablation of 10%, 15%, and 20% of the highest DF areas (n = 270 cases), AF was changed to atrial tachycardia (AT) or terminated at a rate of 40%, 57%, and 76%, respectively.

CONCLUSIONS

Spatiotemporal consistency of the DF area was observed in 10% of AF patients, and high DF areas were temporally variable. Virtual ablation of DF is moderately effective in AF termination and AF changing into AT.

Modeling Current Density Maps Using Aliev-Panfilov Electrophysiological Heart Model

Most existing studies of cardiac arrhythmia rely on surface measurements through optical or electrical mapping techniques. Current density imaging (CDI) is a method which enables us to study current pathways inside the tissue. However, this method entails implementation complexities for beating ex vivo hearts. Hence, this work presents an approach to simulate and study the current distributions in different cardiac electrophysiological states. The results are corroborated by experimental data, and they indicate that different states were distinguishable. The CDI simulations can be used for studying cardiac arrhythmias under simulation conditions which are otherwise impossible or difficult to be implemented experimentally.

A self-taught artificial agent for multi-physics computational model personalization

Personalization is the process of fitting a model to patient data, a critical step towards application of multi-physics computational models in clinical practice. Designing robust personalization algorithms is often a tedious, time-consuming, model- and data-specific process. We propose to use artificial intelligence concepts to learn this task, inspired by how human experts manually perform it. The problem is reformulated in terms of reinforcement learning. In an off-line phase, Vito, our self-taught artificial agent, learns a representative decision process model through exploration of the computational model: it learns how the model behaves under change of parameters. The agent then automatically learns an optimal strategy for on-line personalization. The algorithm is model-independent; applying it to a new model requires only adjusting few hyper-parameters of the agent and defining the observations to match. The full knowledge of the model itself is not required. Vito was tested in a synthetic scenario, showing that it could learn how to optimize cost functions generically. Then Vito was applied to the inverse problem of cardiac electrophysiology and the personalization of a whole-body circulation model. The obtained results suggested that Vito could achieve equivalent, if not better goodness of fit than standard methods, while being more robust (up to 11% higher success rates) and with faster (up to seven times) convergence rate. Our artificial intelligence approach could thus make personalization algorithms generalizable and self-adaptable to any patient and any model.

Improving cardiomyocyte model fidelity and utility via dynamic electrophysiology protocols and optimization algorithms

Mathematical models of cardiac electrophysiology are instrumental in determining mechanisms of cardiac arrhythmias. However, the foundation of a realistic multiscale heart model is only as strong as the underlying cell model. While there have been myriad advances in the improvement of cellular-level models, the identification of model parameters, such as ion channel conductances and rate constants, remains a challenging problem. The primary limitations to this process include: (1) such parameters are usually estimated from data recorded using standard electrophysiology voltage-clamp protocols that have not been developed with model building in mind, and (2) model parameters are typically tuned manually to subjectively match a desired output. Over the last decade, methods aimed at overcoming these disadvantages have emerged. These approaches include the use of optimization or fitting tools for parameter estimation and incorporating more extensive data for output matching. Here, we review recent advances in parameter estimation for cardiomyocyte models, focusing on the use of more complex electrophysiology protocols and global search heuristics. We also discuss future applications of such parameter identification, including development of cell-specific and patient-specific mathematical models to investigate arrhythmia mechanisms and predict therapy strategies.

Protective Role of False Tendon in Subjects with Left Bundle Branch Block: A Virtual Population Study

False tendons (FTs) are fibrous or fibromuscular bands that can be found in both the normal and abnormal human heart in various anatomical forms depending on their attachment points, tissue types, and geometrical properties. While FTs are widely considered to affect the function of the heart, their specific roles remain largely unclear and unexplored. In this paper, we present an in silico study of the ventricular activation time of the human heart in the presence of FTs. This study presents the first computational model of the human heart that includes a FT, Purkinje network, and papillary muscles. Based on this model, we perform simulations to investigate the effect of different types of FTs on hearts with the electrical conduction abnormality of a left bundle branch block (LBBB). We employ a virtual population of 70 human hearts derived from a statistical atlas, and run a total of 560 simulations to assess ventricular activation time with different FT configurations. The obtained results indicate that, in the presence of a LBBB, the FT reduces the total activation time that is abnormally augmented due to a branch block, to such an extent that surgical implant of cardiac resynchronisation devices might not be recommended by international guidelines. Specifically, the simulation results show that FTs reduce the QRS duration at least 10 ms in 80% of hearts, and up to 45 ms for FTs connecting to the ventricular free wall, suggesting a significant reduction of cardiovascular mortality risk. In further simulation studies we show the reduction in the QRS duration is more sensitive to the shape of the heart then the size of the heart or the exact location of the FT. Finally, the model suggests that FTs may contribute to reducing the activation time difference between the left and right ventricles from 12 ms to 4 ms. We conclude that FTs may provide an alternative conduction pathway that compensates for the propagation delay caused by the LBBB. Further investigation is needed to quantify the clinical impact of FTs on cardiovascular mortality risk.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

A model model: a commentary on DiFrancesco and Noble (1985) 'A model of cardiac electrical activity incorporating ionic pumps and concentration changes'

This paper summarizes the advances made by the DiFrancesco and Noble (DFN) model of cardiac cellular electrophysiology, which was published in Philosophical Transactions B in 1985. This model was developed at a time when the introduction of new techniques and provision of experimental data had resulted in an explosion of knowledge about the cellular and biophysical properties of the heart. It advanced the cardiac modelling field from a period when computer models considered only the voltage-dependent channels in the surface membrane. In particular, it included a consideration of changes of both intra- and extracellular ionic concentrations. In this paper, we summarize the most important contributions of the DiFrancesco and Noble paper. We also describe how computer modelling has developed subsequently with the extension from the single cell to the whole heart as well as its use in understanding disease and predicting the effects of pharmaceutical interventions. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

On the Order of the Fractional Laplacian in Determining the Spatio-Temporal Evolution of a Space-Fractional Model of Cardiac Electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

An electromechanical left ventricular wedge model to study the effects of deformation on repolarization during heart failure

Heart failure is a major and costly problem in public health, which, in certain cases, may lead to death. The failing heart undergo a series of electrical and structural changes that provide the underlying basis for disturbances like arrhythmias. Computer models of coupled electrical and mechanical activities of the heart can be used to advance our understanding of the complex feedback mechanisms involved. In this context, there is a lack of studies that consider heart failure remodeling using strongly coupled electromechanics. We present a strongly coupled electromechanical model to study the effects of deformation on a human left ventricle wedge considering normal and hypertrophic heart failure conditions. We demonstrate through a series of simulations that when a strongly coupled electromechanical model is used, deformation results in the thickening of the ventricular wall that in turn increases transmural dispersion of repolarization. These effects were analyzed in both normal and failing heart conditions. We also present transmural electrograms obtained from these simulations. Our results suggest that the waveform of electrograms, particularly the T-wave, is influenced by cardiac contraction on both normal and pathological conditions.

Conditions for Waveblock Due to Anisotropy in a Model of Human Ventricular Tissue

Waveblock formation is the main cause of reentry. We have performed a comprehensive numerical modeling study of block formation due to anisotropy in Ten Tusscher and Panfilov (2006) ionic model for human ventricular tissue. We have examined the border between different areas of myocardial fiber alignment and have shown that blockage can occur for a wave traveling from a transverse fiber area to a longitudinal one. Such blockage occurs for reasonable values of the anisotropy ratio (AR): from 2.4 to 6.2 with respect to propagation velocities. This critical AR decreases by the suppression of INa and ICa, slightly decreases by the suppression of IKr and IKs, and substantially increases by the suppression of IK1. Hyperkalemia affects the block formation in a complex, biphasic way. We provide examples of reentry formation due to the studied effects and have concluded that the suppression of IK1 should be the most effective way to prevent waveblock at the areas of abrupt change in anisotropy.

A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method

Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca²⁺ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

Clinical Diagnostic Biomarkers from the Personalization of Computational Models of Cardiac Physiology

Computational modelling of the heart is rapidly advancing to the point of clinical utility. However, the difficulty of parameterizing and validating models from clinical data indicates that the routine application of truly predictive models remains a significant challenge. We argue there is significant value in an intermediate step towards prediction. This step is the use of biophysically based models to extract clinically useful information from existing patient data. Specifically in this paper we review methodologies for applying modelling frameworks for this goal in the areas of quantifying cardiac anatomy, estimating myocardial stiffness and optimizing measurements of coronary perfusion. Using these indicative examples of the general overarching approach, we finally discuss the value, ongoing challenges and future potential for applying biophysically based modelling in the clinical context.

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology.

Accelerating mono-domain cardiac electrophysiology simulations using OpenCL

Using OpenCL, we developed a cross-platform software to compute electrical excitation conduction in cardiac tissue. OpenCL allowed the software to run parallelized and on different computing devices (e.g., CPUs and GPUs). We used the macroscopic mono-domain model for excitation conduction and an atrial myocyte model by Courtemanche et al. for ionic currents. On a CPU with 12 HyperThreading-enabled Intel Xeon 2.7 GHz cores, we achieved a speed-up of simulations by a factor of 1.6 against existing software that uses OpenMPI. On two high-end AMD FirePro D700 GPUs the OpenCL software ran 2.4 times faster than the OpenMPI implementation. The more nodes the discretized simulation domain contained, the higher speed-ups were achieved.

Models of ventricular arrhythmia mechanisms

The mechanisms that initiate and sustain ventricular arrhythmias in the human heart are clinically important, but hard to study experimentally. In this study, a monodomain model of electrical activation was used to examine how dynamics of electrophysiology at the cell scale influence the surface activation patterns of VF at the tissue scale. Cellular electrophysiology was described with two variants of a phenomenological model of the human ventricular epicardial action potential. The tissue geometry was an 8.0 × 8.0 × 1.2 cm 3D tissue slab with axially symmetric anisotropy. In both cases an initial re-entrant wave fragmented into multiple wavelets of activation. The model variant with steep action potential duration restitution produced much more complex activation, with a greater average number of filaments (13.79) than the variant with less steep restitution (3.08). More complex activation was associated with proportionally fewer transmural filaments, and so the average number of epicardial wavefronts and phase singularities per filament was lower. The average number of epicardial phase singularities and wavefronts for the model variant with less steep restitution were consistent with experimental observations in the human heart. This study shows that small changes in cell scale dynamics can have a large influence on the complexity of re-entrant activation in simulated 3D tissue, as well as on the features observed on the epicardial surface.