Modelling of the ventricular conduction system

Effects of cardiac growth on electrical dyssynchrony in the single ventricle patient

Single ventricle patients, including those with hypoplastic left heart syndrome (HLHS), typically undergo three palliative heart surgeries culminating in the Fontan procedure. HLHS is associated with high rates of morbidity and mortality, and many patients develop arrhythmias, electrical dyssynchrony, and eventually ventricular failure. However, the correlation between ventricular enlargement and electrical dysfunction in HLHS physiology remains poorly understood. Here we characterize the relationship between growth and electrophysiology in HLHS using computational modeling. We integrate a personalized finite element model, a volumetric growth model, and a personalized electrophysiology model to perform controlled in silico experiments. We show that right ventricle enlargement negatively affects QRS duration and interventricular dyssynchrony. Conversely, left ventricle enlargement can partially compensate for this dyssynchrony. These findings have potential implications on our understanding of the origins of electrical dyssynchrony and, ultimately, the treatment of HLHS patients.

hESC derived cardiomyocyte biosensor to detect the different types of arrhythmogenic properties of drugs

In the present work, we introduce a new cell-based biosensor for detecting arrhythmias based on a novel utilization of the combination of the Atomic Force Microscope (AFM) lateral force measurement as a nanosensor with a dual 3D cardiomyocyte syncytium. Two spontaneously coupled clusters of cardiomyocytes form this. The syncytium's functional contraction behavior was assessed using video sequences analyzed with Musclemotion ImageJ/Fiji software, and immunocytochemistry evaluated phenotype composition. The application of caffeine solution induced arrhythmia as a model drug, and its spontaneous resolution was monitored by AFM lateral force recording and interpretation and calcium fluorescence imaging as a reference method describing non-synchronized contractions of cardiomyocytes. The phenotypic analysis revealed the syncytium as a functional contractile and conduction cardiac behavior model. Calcium fluorescence imaging was used to validate that AFM fully enabled to discriminate cardiac arrhythmias in this in vitro cellular model. The described novel 3D hESCs-based cellular biosensor is suitable to detect arrhythmic events on the level of cardiac contractile and conduction tissue cellular model. The resulting biosensor allows for screening of arrhythmogenic properties of tailored drugs enabling its use in precision medicine.

Automated Framework for the Inclusion of a His-Purkinje System in Cardiac Digital Twins of Ventricular Electrophysiology

Personalized models of cardiac electrophysiology (EP) that match clinical observation with high fidelity, referred to as cardiac digital twins (CDTs), show promise as a tool for tailoring cardiac precision therapies. Building CDTs of cardiac EP relies on the ability of models to replicate the ventricular activation sequence under a broad range of conditions. Of pivotal importance is the His-Purkinje system (HPS) within the ventricles. Workflows for the generation and incorporation of HPS models are needed for use in cardiac digital twinning pipelines that aim to minimize the misfit between model predictions and clinical data such as the 12 lead electrocardiogram (ECG). We thus develop an automated two stage approach for HPS personalization. A fascicular-based model is first introduced that modulates the endocardial Purkinje network. Only emergent features of sites of earliest activation within the ventricular myocardium and a fast-conducting sub-endocardial layer are accounted for. It is then replaced by a topologically realistic Purkinje-based representation of the HPS. Feasibility of the approach is demonstrated. Equivalence between both HPS model representations is investigated by comparing activation patterns and 12 lead ECGs under both sinus rhythm and right-ventricular apical pacing. Predominant ECG morphology is preserved by both HPS models under sinus conditions, but elucidates differences during pacing.

A Multi-Scale Computational Model for the Rat Ventricle: Construction, Parallelization, and Applications

BACKGROUND

Cardiovascular diseases are the top killer of human beings. The ventricular arrhythmia, as a type of malignant cardiac arrhythmias, typically leads to death if not treated within minutes. The multi-scale virtual heart provides an idealized tool for exploring the underlying mechanisms, by means of incorporating abundant experimental data at the level of ion channels and analyzing the subsequent pathological changes at organ levels. However, there are few studies on building a virtual heart model for rats-a species most widely used in experiments.

OBJECTIVE

To build a multi-scale computational model for rats, with detailed methodology for the model construction, computational optimization, and its applications.

METHODS

First, approaches for building multi-scale models ranging from cellular to 3-D organ levels are introduced, with detailed descriptions of handling the ventricular myocardium heterogeneity, geometry processing, and boundary conditions, etc. Next, for dealing with the expensive computational costs of 3-D models, optimization approaches including an optimized representation and a GPU-based parallelization method are introduced. Finally, methods for reproducing of some key phenomenon (e.g., electrocardiograph, spiral/scroll waves) are demonstrated.

RESULTS

Three types of heterogeneity, including the transmural heterogeneity, the interventricular heterogeneity, and the base-apex heterogeneity are incorporated into the model. The normal and reentrant excitation waves, as well as the corresponding pseudo-ECGs are reproduced by the constructed ventricle model. In addition, the temporal and spatial vulnerability to reentry arrhythmias are quantified based on the evaluation experiments of vulnerable window and the critical length.

CONCLUSIONS

The constructed multi-scale rat ventricle model is able to reproduce both the physiological and the pathological phenomenon in different scales. Evaluation experiments suggest that the apex is the most susceptible area to arrhythmias. The model can be a promising tool for the investigation of arrhythmogenesis and the screening of anti-arrhythmic drugs.

New Insights into the Development and Morphogenesis of the Cardiac Purkinje Fiber Network: Linking Architecture and Function

The rapid propagation of electrical activity through the ventricular conduction system (VCS) controls spatiotemporal contraction of the ventricles. Cardiac conduction defects or arrhythmias in humans are often associated with mutations in key cardiac transcription factors that have been shown to play important roles in VCS morphogenesis in mice. Understanding of the mechanisms of VCS development is thus crucial to decipher the etiology of conduction disturbances in adults. During embryogenesis, the VCS, consisting of the His bundle, bundle branches, and the distal Purkinje network, originates from two independent progenitor populations in the primary ring and the ventricular trabeculae. Differentiation into fast-conducting cardiomyocytes occurs progressively as ventricles develop to form a unique electrical pathway at late fetal stages. The objectives of this review are to highlight the structure–function relationship between VCS morphogenesis and conduction defects and to discuss recent data on the origin and development of the VCS with a focus on the distal Purkinje fiber network.

Model Systems for Addressing Mechanism of Arrhythmogenesis in Cardiac Repair

PURPOSE OF REVIEW

Cardiac cell-based therapy represents a promising approach for cardiac repair. However, one of the main challenges is cardiac arrhythmias associated with stem cell transplantation. The current review summarizes the recent progress in model systems for addressing mechanisms of arrhythmogenesis in cardiac repair.

RECENT FINDINGS

Animal models have been extensively developed for mechanistic studies of cardiac arrhythmogenesis. Advances in human induced pluripotent stem cells (hiPSCs), patient-specific disease models, tissue engineering, and gene editing have greatly enhanced our ability to probe the mechanistic bases of cardiac arrhythmias. Additionally, recent development in multiscale computational studies and machine learning provides yet another powerful tool to quantitatively decipher the mechanisms of cardiac arrhythmias. Advancing efforts towards the integrations of experimental and computational studies are critical to gain insights into novel mitigation strategies for cardiac arrhythmias in cell-based therapy.

A Framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs

Cardiac digital twins (Cardiac Digital Twin (CDT)s) of human electrophysiology (Electrophysiology (EP)) are digital replicas of patient hearts derived from clinical data that match like-for-like all available clinical observations. Due to their inherent predictive potential, CDTs show high promise as a complementary modality aiding in clinical decision making and also in the cost-effective, safe and ethical testing of novel EP device therapies. However, current workflows for both the anatomical and functional twinning phases within CDT generation, referring to the inference of model anatomy and parameters from clinical data, are not sufficiently efficient, robust and accurate for advanced clinical and industrial applications. Our study addresses three primary limitations impeding the routine generation of high-fidelity CDTs by introducing; a comprehensive parameter vector encapsulating all factors relating to the ventricular EP; an abstract reference frame within the model allowing the unattended manipulation of model parameter fields; a novel fast-forward electrocardiogram (Electrocardiogram (ECG)) model for efficient and bio-physically-detailed simulation required for parameter inference. A novel workflow for the generation of CDTs is then introduced as an initial proof of concept. Anatomical twinning was performed within a reasonable time compatible with clinical workflows (<4h) for 12 subjects from clinically-attained magnetic resonance images. After assessment of the underlying fast forward ECG model against a gold standard bidomain ECG model, functional twinning of optimal parameters according to a clinically-attained 12 lead ECG was then performed using a forward Saltelli sampling approach for a single subject. The achieved results in terms of efficiency and fidelity demonstrate that our workflow is well-suited and viable for generating biophysically-detailed CDTs at scale.

An effective heterogeneous whole-heart mathematical model of cardiac induction system with heart rate variability

The main objective of this research work is to develop an effective mathematical model of cardiac conduction system using a heterogeneous whole-heart model. The model is in the form of a system of modified Van der Pol and FitzHugh-Nagumo differential equations capable of describing the heart dynamics. The proposed model extends the range of normal and pathological electrocardiogram (ECG) waveforms that can be generated by the model. The effects of the respiratory sinus arrhythmia (RSA) and the Mayer waves (MW) are both incorporated to modulate the intrinsic frequency of the main oscillator that represents the sinoatrial node. Also, three pathological conditions are incorporated into the model. The heart rate variability (HRV) phenomenon is incorporated into the synthetic ECGs produced which yields valuable information about the cardiovascular health and the performance of the autonomic nervous system. The spectral analysis of the generated RR tachogram delivers power spectrums that resemble those obtained from real recordings. Also, the proposed model generates synthetic ECGs that characteristic the three considered pathological conditions, namely, the tall T wave, the ECG with U wave, and the Wolff-Parkinson-White syndrome. In general, the significance of this research work is in developing a mathematical model that represents the interactions between different pacemakers and allows analysis of cardiac rhythms. To show the effectiveness and the accuracy of the presented model, the results are compared to published results. The proposed model can be a useful tool to study the influences of different physiological conditions on the profile of the ECG. The synthetic ECG signals produced can be used as signal sources for the assessment of diagnostic ECG signal processing devices.

Delayed afterdepolarization-induced triggered activity in cardiac purkinje cells mediated through cytosolic calcium diffusion waves

Cardiac Purkinje cells (PCs) are more susceptible to action potential abnormalities as compared to ventricular myocytes (VMs), which could be associated with their distinct intracellular calcium handling. We developed a detailed biophysical model of a mouse cardiac PC, which importantly reproduces the experimentally observed biphasic cytosolic calcium waves. The model includes a stochastic gating formulation for the opening and closing of ryanodine receptor (RyR) channels, simulated with a Monte Carlo method, to accurately reproduce cytosolic calcium wave propagation and the effects of spontaneous calcium release events. Simulations predict that during an action potential, smaller cytosolic calcium wavelets propagated from the sarcolemma towards the center of the cell and initiated larger magnitude cell‐wide calcium waves via a calcium‐induced‐calcium release mechanism. In the presence of RyR mutations, frequent spontaneous calcium leaks from sarcoplasmic reticulum (SR) initiated calcium waves, which upon reaching the cell periphery produced delayed afterdepolarizations (DADs) via sodium‐calcium exchanger (NCX) and T‐type calcium (I_CaT) channel activation. In the presence of isoproterenol‐mediated effects, DADs induced triggered activity by reactivation of fast sodium channels. Based on our model, we found that the activation of either L‐type calcium channels (I_CaL), I_CaT, sodium‐potassium exchanger (I_NaK) or NCX is sufficient for occurrence of triggered activity; however, a partial blockade of I_CaT or I_NaK is essential for its successful termination. Our modeling study highlights valuable insights into the mechanisms of DAD‐induced triggered activity mediated via cytosolic calcium waves in cardiac PCs and may elucidate the increased arrhythmogeneity in PCs.

Myocardial Fibrosis in a 3D Model: Effect of Texture on Wave Propagation

Non-linear electrical waves propagate through the heart and control cardiac contraction. Abnormal wave propagation causes various forms of the heart disease and can be lethal. One of the main causes of abnormality is a condition of cardiac fibrosis, which, from mathematical point of view, is the presence of multiple non-conducting obstacles for wave propagation. The fibrosis can have different texture which varies from diffuse (e.g., small randomly distributed obstacles), patchy (e.g., elongated interstitional stria), and focal (e.g., post-infarct scars) forms. Recently, Nezlobinsky et al. (2020) used 2D biophysical models to quantify the effects of elongation of obstacles (fibrosis texture) and showed that longitudinal and transversal propagation differently depends on the obstacle length resulting in anisotropy for wave propagation. In this paper, we extend these studies to 3D tissue models. We show that 3D consideration brings essential new effects; for the same obstacle length in 3D systems, anisotropy is about two times smaller compared to 2D, however, wave propagation is more stable with percolation threshold of about 60% (compared to 35% in 2D). The percolation threshold increases with the obstacle length for the longitudinal propagation, while it decreases for the transversal propagation. Further, in 3D, the dependency of velocity on the obstacle length for the transversal propagation disappears.

Human Purkinje in silico model enables mechanistic investigations into automaticity and pro-arrhythmic abnormalities

Cardiac Purkinje cells (PCs) are implicated in lethal arrhythmias caused by cardiac diseases, mutations, and drug action. However, the pro-arrhythmic mechanisms in PCs are not entirely understood, particularly in humans, as most investigations are conducted in animals. The aims of this study are to present a novel human PCs electrophysiology biophysically-detailed computational model, and to disentangle ionic mechanisms of human Purkinje-related electrophysiology, pacemaker activity and arrhythmogenicity. The new Trovato2020 model incorporates detailed Purkinje-specific ionic currents and Ca²⁺ handling, and was developed, calibrated and validated using human experimental data acquired at multiple frequencies, both in control conditions and following drug application. Multiscale investigations were performed in a Purkinje cell, in fibre and using an experimentally-calibrated population of PCs to evaluate biological variability. Simulations demonstrate the human Purkinje Trovato2020 model is the first one to yield: (i) all key AP features consistent with human Purkinje recordings; (ii) Automaticity with funny current up-regulation (iii) EADs at slow pacing and with 85% hERG block; (iv) DADs following fast pacing; (v) conduction velocity of 160 cm/s in a Purkinje fibre, as reported in human. The human in silico PCs population highlights that: (1) EADs are caused by I_CaL reactivation in PCs with large inward currents; (2) DADs and triggered APs occur in PCs experiencing Ca²⁺ accumulation, at fast pacing, caused by large L-type calcium current and small Na⁺/Ca²⁺ exchanger. The novel human Purkinje model unlocks further investigations into the role of cardiac Purkinje in ventricular arrhythmias through computer modeling and multiscale simulations.

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A human in silico AP model was developed to investigate arrhythmia in cardiac Purkinje.

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The new Purkinje model enables multiscale investigations from single cell to tissue.

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Populations of human Purkinje models reproduce and explain experimental variability.

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Ca²⁺-current reactivation triggers EADs in virtual Purkinje cells with weak repolarisation reserve.

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Ca²⁺ accumulation caused by increased Ca²⁺ and NCX currents triggers DADs.

Embedding high-dimensional Bayesian optimization via generative modeling: Parameter personalization of cardiac electrophysiological models

The estimation of patient-specific tissue properties in the form of model parameters is important for personalized physiological models. Because tissue properties are spatially varying across the underlying geometrical model, it presents a significant challenge of high-dimensional (HD) optimization at the presence of limited measurement data. A common solution to reduce the dimension of the parameter space is to explicitly partition the geometrical mesh. In this paper, we present a novel concept that uses a generative variational auto-encoder (VAE) to embed HD Bayesian optimization into a low-dimensional (LD) latent space that represents the generative code of HD parameters. We further utilize VAE-encoded knowledge about the generative code to guide the exploration of the search space. The presented method is applied to estimating tissue excitability in a cardiac electrophysiological model in a range of synthetic and real-data experiments, through which we demonstrate its improved accuracy and substantially reduced computational cost in comparison to existing methods that rely on geometry-based reduction of the HD parameter space.

Generation of ECG signals from a reaction-diffusion model spatially discretized

We propose a model to generate electrocardiogram signals based on a discretized reaction-diffusion system to produce a set of three nonlinear oscillators that simulate the main pacemakers in the heart. The model reproduces electrocardiograms from healthy hearts and from patients suffering various well-known rhythm disorders. In particular, it is shown that under ventricular fibrillation, the electrocardiogram signal is chaotic and the transition from sinus rhythm to chaos is consistent with the Ruelle-Takens-Newhouse route to chaos, as experimental studies indicate. The proposed model constitutes a useful tool for research, medical education, and clinical testing purposes. An electronic device based on the model was built for these purposes

Percutaneous Intramyocardial Septal Radiofrequency Ablation for Interventricular Septal Reduction: An Ovine Model with 1-Year Outcomes

BACKGROUND

Percutaneous intramyocardial (PIM) septal radiofrequency ablation (SRA) is a novel treatment approach for hypertrophic obstructive cardiomyopathy patients, but there has been lack of a large animal model to study PIM-SRA. We aimed to validate the long-term safety and efficacy of PIM-SRA and to observe pathological changes of the ablated interventricular septum (IVS) in a healthy sheep model.

METHODS AND RESULTS

Twelve sheep were randomized to the PIM-SRA group (n = 6) and the sham group (n = 6). In the PIM-SRA group, a radiofrequency (RF) electrode was inserted into the IVS with a maximum power of 80 W for 5 min. In the sham group, the RF electrode tip was positioned in the IVS segment but without RF power delivery. Septal hypokinesis was seen in all PIM-SRA group animals immediately after the procedure; the systolic wall thickening rate and motion amplitude of the ablated region decreased (p < 0.01), and the diastolic IVS thickness also decreased significantly over time (p < 0.01). ECG showed that all the sheep had normal sinus rhythm during the follow-up. Pathological examinations revealed scar tissue in the ablated region as expected.

CONCLUSIONS

PIM-SRA produced precisely ablated myocardial tissue, reduced the IVS thickness significantly, preserved the global LV function, and avoided the incidence of conduction system damage in the long term. PIM-SRA was found to be a safe and effective minimally invasive septal reduction therapy.

Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks

In this paper, we propose an improvement of the cardiac conduction system based on three modified Van der Pol oscillators. Each oscillator represents one of the components of the heart conduction system: Sino-Atrial node (SA), Atrio-Ventricular node (AV) and His–Purkinje system (HP). However, while SA and AV nodes can be modelled through a single oscillator, the modelling of HP by using a single oscillator is a rough simplification of the cardiac behaviour. In fact, the HP bundle is composed of Right (RB) and Left Bundle (LB) branches that serve, respectively, the right and left ventricles. In order to describe the behaviour of each bundle branch, we build a phenomenological model based on four oscillators: SA, AV, RB and LB. For the characterization of the atrial and ventricular muscles, we used the modified FitzHugh–Nagumo (FHN) equations. The numerical simulation of the model has been implemented in Simulink. The simulation results show that the new model is able to reproduce the heart dynamics generating, besides the physiological signal, also the pathological rhythm in case of Right Bundle Branch Block (RBBB) and Left Bundle Branch Block (LBBB). In particular, our model is able to describe the communication interruption of the conduction system, when one of the HP bundle branches is damaged.

Cardiac Electrical Modeling for Closed-Loop Validation of Implantable Devices

OBJECTIVE

Evaluating and testing cardiac electrical devices in a closed-physiologic-loop can help design safety, but this is rarely practical or comprehensive. Furthermore, in silico closed-loop testing with biophysical computer models cannot meet the requirements of time-critical cardiac device systems, while simplified models meeting time-critical requirements may not have the necessary dynamic features. We propose a new high-level (abstracted) physiologically-based computational heart model that is time-critical and dynamic.

METHODS

The model comprises cardiac regional cellular-electrophysiology types connected by a path model along a conduction network. The regional electrophysiology and paths are modeled with hybrid automata that capture non-linear dynamics, such as action potential and conduction velocity restitution and overdrive suppression. The hierarchy of pacemaker functions is incorporated to generate sinus rhythms, while abnormal automaticity can be introduced to form a variety of arrhythmias such as escape ectopic rhythms. Model parameters are calibrated using experimental data and prior model simulations.

CONCLUSION

Regional electrophysiology and paths in the model match human action potentials, dynamic behavior, and cardiac activation sequences. Connected in closed loop with a pacing device in DDD mode, the model generates complex arrhythmia such as atrioventricular nodal reentry tachycardia. Such device-induced outcomes have been observed clinically and we can establish the key physiological features of the heart model that influence the device operation.

SIGNIFICANCE

These findings demonstrate how an abstract heart model can be used for device validation and to design personalized treatment.

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed-point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium-Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases.

Conduction in the Heart Wall: Helicoidal Fibers Minimize Diffusion Bias

The mammalian heart must function as an efficient pump while simultaneously conducting electrical signals to drive the contraction process. In the ventricles, electrical activation begins at the insertion points of the Purkinje network in the endocardium. How does the diffusion component of the subsequent excitation wave propagate from the endocardium in a healthy heart wall without creating directional biases? We show that this is a consequence of the particular geometric organization of myocytes in the heart wall. Using a generalized helicoid to model fiber orientation, we treat the myocardium as a curved space via Riemannian geometry, and then use stochastic calculus to model local signal diffusion. Our analysis shows that the helicoidal arrangement of myocytes minimizes the directional biases that could lead to aberrant propagation, thereby explaining how electrophysiological principles are consistent with local measurements of cardiac fiber geometry. We discuss our results in the context of the need to balance electrical and mechanical requirements for heart function.

Efficient Computational Modeling of Human Ventricular Activation and Its Electrocardiographic Representation: A Sensitivity Study

Patient-specific models of the ventricular myocardium, combined with the computational power to run rapid simulations, are approaching the level where they could be used for personalized cardiovascular medicine. A major remaining challenge is determining model parameters from available patient data, especially for models of the Purkinje-myocardial junctions (PMJs): the sites of initial ventricular electrical activation. There are no non-invasive methods for localizing PMJs in patients, and the relationship between the standard clinical ECG and PMJ model parameters is underexplored. Thus, this study aimed to determine the sensitivity of the QRS complex of the ECG to the anatomical location and regional number of PMJs. The QRS complex was simulated using an image-based human torso and biventricular model, and cardiac electrophysiology was simulated using Cardioid. The PMJs were modeled as discrete current injection stimuli, and the location and number of stimuli were varied within initial activation regions based on published experiments. Results indicate that the QRS complex features were most sensitive to the presence or absence of four “seed” stimuli, and adjusting locations of nearby “regional” stimuli provided finer tuning. Decreasing number of regional stimuli by an order of magnitude resulted in virtually no change in the QRS complex. Thus, a minimal 12-stimuli configuration was identified that resulted in physiological excitation, defined by QRS complex feature metrics and ventricular excitation pattern. Overall, the sensitivity results suggest that parameterizing PMJ location, rather than number, be given significantly higher priority in future studies creating personalized ventricular models from patient-derived ECGs.

Effects of early afterdepolarizations on excitation patterns in an accurate model of the human ventricles

Early Afterdepolarizations, EADs, are defined as the reversal of the action potential before completion of the repolarization phase, which can result in ectopic beats. However, the series of mechanisms of EADs leading to these ectopic beats and related cardiac arrhythmias are not well understood. Therefore, we aimed to investigate the influence of this single cell behavior on the whole heart level. For this study we used a modified version of the Ten Tusscher-Panfilov model of human ventricular cells (TP06) which we implemented in a 3D ventricle model including realistic fiber orientations. To increase the likelihood of EAD formation at the single cell level, we reduced the repolarization reserve (RR) by reducing the rapid delayed rectifier Potassium current and raising the L-type Calcium current. Varying these parameters defined a 2D parametric space where different excitation patterns could be classified. Depending on the initial conditions, by either exciting the ventricles with a spiral formation or burst pacing protocol, we found multiple different spatio-temporal excitation patterns. The spiral formation protocol resulted in the categorization of a stable spiral (S), a meandering spiral (MS), a spiral break-up regime (SB), spiral fibrillation type B (B), spiral fibrillation type A (A) and an oscillatory excitation type (O). The last three patterns are a 3D generalization of previously found patterns in 2D. First, the spiral fibrillation type B showed waves determined by a chaotic bi-excitable regime, i.e. mediated by both Sodium and Calcium waves at the same time and in same tissue settings. In the parameter region governed by the B pattern, single cells were able to repolarize completely and different (spiral) waves chaotically burst into each other without finishing a 360 degree rotation. Second, spiral fibrillation type A patterns consisted of multiple small rotating spirals. Single cells failed to repolarize to the resting membrane potential hence prohibiting the Sodium channel gates to recover. Accordingly, we found that Calcium waves mediated these patterns. Third, a further reduction of the RR resulted in a more exotic parameter regime whereby the individual cells behaved independently as oscillators. The patterns arose due to a phase-shift of different oscillators as disconnection of the cells resulted in continuation of the patterns. For all patterns, we computed realistic 9 lead ECGs by including a torso model. The B and A type pattern exposed the behavior of Ventricular Tachycardia (VT). We conclude that EADs at the single cell level can result in different types of cardiac fibrillation at the tissue and 3D ventricle level.

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

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

Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Cardiac Purkinje fibers provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is on the basis of operator splitting and is provided with 3 different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all 3 implementations produce equivalent convergence rates, and shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all 3 implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure GPU implementations outperform the pure CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.

Analysis of Microstructure of the Cardiac Conduction System Based on Three-Dimensional Confocal Microscopy

The specialised conducting tissues present in the ventricles are responsible for the fast distribution of the electrical impulse from the atrio-ventricular node to regions in the subendocardial myocardium. Characterisation of anatomical features of the specialised conducting tissues in the ventricles is highly challenging, in particular its most distal section, which is connected to the working myocardium via Purkinje-myocardial junctions. The goal of this work is to characterise the architecture of the distal section of the Purkinje network by differentiating Purkinje cells from surrounding tissue, performing a segmentation of Purkinje fibres at cellular scale, and mathematically describing its morphology and interconnections. Purkinje cells from rabbit hearts were visualised by confocal microscopy using wheat germ agglutinin labelling. A total of 16 3D stacks including labeled Purkinje cells were collected, and semi-automatically segmented. State-of-the-art graph metrics were applied to estimate regional and global features of the Purkinje network complexity. Two types of cell types, tubular and star-like, were characterised from 3D segmentations. The analysis of 3D imaging data confirms the previously suggested presence of two types of Purkinje-myocardium connections, a 2D interconnection sheet and a funnel one, in which the narrow side of a Purkinje fibre connect progressively to muscle fibres. The complex network analysis of interconnected Purkinje cells showed no small-world connectivity or assortativity properties. These results might help building more realistic computational PK systems at high resolution levels including different cell configurations and shapes. Better knowledge on the organisation of the network might help in understanding the effects that several treatments such as radio-frequency ablation might have when the PK system is disrupted locally.

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.

A Computer Simulation Study of Anatomy Induced Drift of Spiral Waves in the Human Atrium

The interaction of spiral waves of excitation with atrial anatomy remains unclear. This simulation study isolates the role of atrial anatomical structures on spiral wave spontaneous drift in the human atrium. We implemented realistic and idealised 3D human atria models to investigate the functional impact of anatomical structures on the long-term (∼40 s) behaviour of spiral waves. The drift of a spiral wave was quantified by tracing its tip trajectory, which was correlated to atrial anatomical features. The interaction of spiral waves with the following idealised geometries was investigated: (a) a wedge-like structure with a continuously varying atrial wall thickness; (b) a ridge-like structure with a sudden change in atrial wall thickness; (c) multiple bridge-like structures consisting of a bridge connected to the atrial wall. Spiral waves drifted from thicker to thinner regions and along ridge-like structures. Breakthrough patterns caused by pectinate muscles (PM) bridges were also observed, albeit infrequently. Apparent anchoring close to PM-atrial wall junctions was observed. These observations were similar in both the realistic and the idealised models. We conclude that spatially altering atrial wall thickness is a significant cause of drift of spiral waves. PM bridges cause breakthrough patterns and induce transient anchoring of spiral waves.

Image-Based Structural Modeling of the Cardiac Purkinje Network

The Purkinje network is a specialized conduction system within the heart that ensures the proper activation of the ventricles to produce effective contraction. Its role during ventricular arrhythmias is less clear, but some experimental studies have suggested that the Purkinje network may significantly affect the genesis and maintenance of ventricular arrhythmias. Despite its importance, few structural models of the Purkinje network have been developed, primarily because current physical limitations prevent examination of the intact Purkinje network. In previous modeling efforts Purkinje-like structures have been developed through either automated or hand-drawn procedures, but these networks have been created according to general principles rather than based on real networks. To allow for greater realism in Purkinje structural models, we present a method for creating three-dimensional Purkinje networks based directly on imaging data. Our approach uses Purkinje network structures extracted from photographs of dissected ventricles and projects these flat networks onto realistic endocardial surfaces. Using this method, we create models for the combined ventricle-Purkinje system that can fully activate the ventricles through a stimulus delivered to the Purkinje network and can produce simulated activation sequences that match experimental observations. The combined models have the potential to help elucidate Purkinje network contributions during ventricular arrhythmias.

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

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

Optogenetic determination of the myocardial requirements for extrasystoles by cell type-specific targeting of ChannelRhodopsin-2

Extrasystoles lead to several consequences, ranging from uneventful palpitations to lethal ventricular arrhythmias, in the presence of pathologies, such as myocardial ischemia. The role of working versus conducting cardiomyocytes, as well as the tissue requirements (minimal cell number) for the generation of extrasystoles, and the properties leading ectopies to become arrhythmia triggers (topology), in the normal and diseased heart, have not been determined directly in vivo. Here, we used optogenetics in transgenic mice expressing ChannelRhodopsin-2 selectively in either cardiomyocytes or the conduction system to achieve cell type-specific, noninvasive control of heart activity with high spatial and temporal resolution. By combining measurement of optogenetic tissue activation in vivo and epicardial voltage mapping in Langendorff-perfused hearts, we demonstrated that focal ectopies require, in the normal mouse heart, the simultaneous depolarization of at least 1,300-1,800 working cardiomyocytes or 90-160 Purkinje fibers. The optogenetic assay identified specific areas in the heart that were highly susceptible to forming extrasystolic foci, and such properties were correlated to the local organization of the Purkinje fiber network, which was imaged in three dimensions using optical projection tomography. Interestingly, during the acute phase of myocardial ischemia, focal ectopies arising from this location, and including both Purkinje fibers and the surrounding working cardiomyocytes, have the highest propensity to trigger sustained arrhythmias. In conclusion, we used cell-specific optogenetics to determine with high spatial resolution and cell type specificity the requirements for the generation of extrasystoles and the factors causing ectopies to be arrhythmia triggers during myocardial ischemia.

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

The Generalized Hill Model: A Kinematic Approach Towards Active Muscle Contraction

Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion.

Computational generation of the Purkinje network driven by clinical measurements: the case of pathological propagations

To properly describe the electrical activity of the left ventricle, it is necessary to model the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times related to pathological propagations. In this case, one needs to consider a strongly coupled problem between the network and the muscle, where the feedback from the latter to the former cannot be neglected as in a normal propagation. We apply the proposed strategy to data acquired on three subjects, one of them suffering from muscular conduction problems owing to a scar and the other two with a muscular pre-excitation syndrome (Wolff-Parkinson-White). To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network generated by our strategy with the ones obtained by using a non-patient-specific network. The results show that the mean absolute errors in the activation time is reduced for all the cases, highlighting the importance of including a patient-specific Purkinje network in computational models.

Effect of global cardiac ischemia on human ventricular fibrillation: insights from a multi-scale mechanistic model of the human heart

Acute regional ischemia in the heart can lead to cardiac arrhythmias such as ventricular fibrillation (VF), which in turn compromise cardiac output and result in secondary global cardiac ischemia. The secondary ischemia may influence the underlying arrhythmia mechanism. A recent clinical study documents the effect of global cardiac ischaemia on the mechanisms of VF. During 150 seconds of global ischemia the dominant frequency of activation decreased, while after reperfusion it increased rapidly. At the same time the complexity of epicardial excitation, measured as the number of epicardical phase singularity points, remained approximately constant during ischemia. Here we perform numerical studies based on these clinical data and propose explanations for the observed dynamics of the period and complexity of activation patterns. In particular, we study the effects on ischemia in pseudo-1D and 2D cardiac tissue models as well as in an anatomically accurate model of human heart ventricles. We demonstrate that the fall of dominant frequency in VF during secondary ischemia can be explained by an increase in extracellular potassium, while the increase during reperfusion is consistent with washout of potassium and continued activation of the ATP-dependent potassium channels. We also suggest that memory effects are responsible for the observed complexity dynamics. In addition, we present unpublished clinical results of individual patient recordings and propose a way of estimating extracellular potassium and activation of ATP-dependent potassium channels from these measurements.

A heterogeneous coupled oscillator model for simulation of ECG signals

We present a novel model of cardiac conduction system including main pacemakers and heart muscles. Sinoatrial node, atrioventricular node and His-Purkinje system are represented by modified van der Pol-type oscillators connected with time-delay velocity coupling. For description of atrial and ventricular muscles, where depolarization and repolarization processes are considered as separate waves, we use modified FitzHugh-Nagumo model. In this work, we obtained synthetic ECG as a combined signal of atrial and ventricular muscles and reproduced several normal and pathological rhythms. Inclusion of cardiac muscle response allows to investigate interactions between pacemakers and resulting global heartbeat dynamics by means of clinically comparable realistic ECG signals. This feature distinguishes our model from existing cardiac oscillator models. To solve the system of differential equations describing the proposed heterogeneous coupled oscillator model we developed a software in MATLAB environment utilizing special DDE23 function.

Patient-specific generation of the Purkinje network driven by clinical measurements of a normal propagation

The propagation of the electrical signal in the Purkinje network is the starting point for the activation of the ventricular muscular cells leading to the contraction of the ventricle. In the computational models, describing the electrical activity of the ventricle is therefore important to account for the Purkinje fibers. Until now, the inclusion of such fibers has been obtained either by using surrogates such as space-dependent conduction properties or by generating a network based on an a priori anatomical knowledge. The aim of this work was to propose a new method for the generation of the Purkinje network using clinical measures of the activation times on the endocardium related to a normal electrical propagation, allowing to generate a patient-specific network. The measures were acquired by means of the EnSite NavX system. This system allows to measure for each point of the ventricular endocardium the time at which the activation front, that spreads through the ventricle, has reached the subjacent muscle. We compared the accuracy of the proposed method with the one of other strategies proposed so far in the literature for three subjects with a normal electrical propagation. The results showed that with our method we were able to reduce the absolute errors, intended as the difference between the measured and the computed data, by a factor in the range 9-25 %, with respect to the best of the other strategies. This highlighted the reliability of the proposed method and the importance of including a patient-specific Purkinje network in computational models.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

Selection of multiarmed spiral waves in a regular network of neurons

Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.

Three-dimensional impulse propagation in myocardium: arrhythmogenic mechanisms at the tissue level

Impulse propagation in the heart depends on the excitability of individual cardiomyocytes, impulse transmission between adjacent myocytes, and the 3-dimensional arrangement of those cells. Here, we review the role of each of these factors in normal and aberrant cardiac electric activation, with particular emphasis on the effects of 3-dimensional myocyte architecture at the tissue scale. The analysis draws on findings from in vivo and in vitro experiments, as well as biophysically based computer models that have been used to integrate and interpret these experimental data. It indicates that discontinuous arrangement of myocytes and extracellular connective tissue at the tissue scale can give rise to current source-to-sink mismatch, spatiotemporal distribution of refractoriness, and rate-sensitive electric instability, which contribute to the initiation and maintenance of reentrant cardiac arrhythmia. This exacerbates the risk of rhythm disturbance associated with heart disease. We conclude that structure-based, multiscale computer models that incorporate accurate information about local cellular electric activity provide a powerful platform for investigating the basis of reentrant cardiac arrhythmia. However, it is important that these models capture key features of structure and related electric function at the tissue scale.

Characterization and modeling of the peripheral cardiac conduction system

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

An image-based model of the whole human heart with detailed anatomical structure and fiber orientation

Many heart anatomy models have been developed to study the electrophysiological properties of the human heart. However, none of them includes the geometry of the whole human heart. In this study, an anatomically detailed mathematical model of the human heart was firstly reconstructed from the computed tomography images. In the reconstructed model, the atria consisted of atrial muscles, sinoatrial node, crista terminalis, pectinate muscles, Bachmann's bundle, intercaval bundles, and limbus of the fossa ovalis. The atrioventricular junction included the atrioventricular node and atrioventricular ring, and the ventricles had ventricular muscles, His bundle, bundle branches, and Purkinje network. The epicardial and endocardial myofiber orientations of the ventricles and one layer of atrial myofiber orientation were then measured. They were calculated using linear interpolation technique and minimum distance algorithm, respectively. To the best of our knowledge, this is the first anatomically-detailed human heart model with corresponding experimentally measured fibers orientation. In addition, the whole heart excitation propagation was simulated using a monodomain model. The simulated normal activation sequence agreed well with the published experimental findings.

Construction of 3D Realistic Purkinje System: A Locally Linear Embedding-Based Method

The geometry of canine ventricle with purkinje system provides the data basis for the simulation and analysis of the mechanisms of ventricular pathophysiology. The acquisition of the geometry of the purkinje system, however, is very challenging, and traditional construction approaches are mainly based on modeling using fractal geometry. In this paper, we propose a novel locally linear embedding (LLE)-based method to construct 3D anatomical purkinje system of the canine left ventricle (LV). First, we collect the 2D purkinje system data in a canine ventricle and extract the endocardial surface of the canine left ventricle from 3D canine ventricle. Then, LLE is used to map the 3D geometry of the endocardial surface to a 2D subspace, and the 2D purkinje system data is further embedded into this 2D subspace. Finally, LLE is adopted to map both the 3D geometry of the endocardial surface and the 2D purkinje system data back to the 3D space. An experiment is designed to verify the effectiveness of the LLE-based construction method. The proposed method approaches is promising in restoring realistic purkinje system of the left canine ventricle.

Construction of a computational anatomical model of the peripheral cardiac conduction system

A methodology is presented here for automatic construction of a ventricular model of the cardiac conduction system (CCS), which is currently a missing block in many multiscale cardiac electromechanic models. It includes the His bundle, left bundle branches, and the peripheral CCS. The algorithm is fundamentally an enhancement of a rule-based method known as the Lindenmayer systems (L-systems). The generative procedure has been divided into three consecutive independent stages, which subsequently build the CCS from proximal to distal sections. Each stage is governed by a set of user parameters together with anatomical and physiological constrains to direct the generation process and adhere to the structural observations derived from histology studies. Several parameters are defined using statistical distributions to introduce stochastic variability in the models. The CCS built with this approach can generate electrical activation sequences with physiological characteristics.

Rabbit-specific ventricular model of cardiac electrophysiological function including specialized conduction system

The function of the ventricular specialized conduction system in the heart is to ensure the coordinated electrical activation of the ventricles. It is therefore critical to the overall function of the heart, and has also been implicated as an important player in various diseases, including lethal ventricular arrhythmias such as ventricular fibrillation and drug-induced torsades de pointes. However, current ventricular models of electrophysiology usually ignore, or include highly simplified representations of the specialized conduction system. Here, we describe the development of an image-based, species-consistent, anatomically-detailed model of rabbit ventricular electrophysiology that incorporates a detailed description of the free-running part of the specialized conduction system. Techniques used for the construction of the geometrical model of the specialized conduction system from a magnetic resonance dataset and integration of the system model into a ventricular anatomical model, developed from the same dataset, are described. Computer simulations of rabbit ventricular electrophysiology are conducted using the novel anatomical model and rabbit-specific membrane kinetics to investigate the importance of the components and properties of the conduction system in determining ventricular function under physiological conditions. Simulation results are compared to panoramic optical mapping experiments for model validation and results interpretation. Full access is provided to the anatomical models developed in this study.

Flexible modeling for anatomically-based cardiac conduction system construction

We present a method to automatically deploy the peripheral section of the cardiac conduction system in ventricles. The method encodes anatomical information thorough rules that ensure that Purkinje network structures generated are realistic and comparable to those observed in ex-vivo studies. The core methodology is based in non-deterministic production rules that are parameterized by means of statistical functions. Input parameters allow the construction of a great diversity of Purkinje structures that could be incorporated in fine element ventricular models to perform electrophysiology simulations. Resulting Purkinje trees show good geometrical approximations of Purkinje core network and bundles when compared to histological diagrams and do not require user interaction. Simulations carried out with these models result in activation sequences remarkably similar to micro-electrode electrical mapping studies.

Integrated approach for the study of anatomical variability in the cardiac Purkinje system: from high resolution MRI to electrophysiology simulation

The ordered electrical stimulation of the ventricles is achieved by a specialized network of fibres known as the Purkinje system. The gross anatomy and basic functional role of the Purkinje system is well understood. However, very little is known about the detailed anatomy of the Purkinje system, its inter-individual variability and the implications of the variability in ventricular function, in part due to limitations in experimental techniques. In this study, we aim to provide new insight into the inter-individual variability of the free running Purkinje system anatomy and its impact on ventricular electrophysiological function. As a first step towards achieving this aim, high resolution magnetic resonance imaging (MRI) datasets of rat and the rabbit ventricles are obtained and analysed using a novel semi-automatic image processing algorithm for segmentation of the free-running Purkinje system. Segmented geometry from the MRI datasets is used to construct a computational model of the Purkinje system, which is incorporated in to an anatomically-based ventricular geometry to simulate ventricular electrophysiological activity.