A computer model of human atria with reasonable computation load and realistic anatomical properties

Cycle length statistics during human atrial fibrillation reveal refractory properties of the underlying substrate: a combined in silico and clinical test of concept study

AIMS

The treatment of atrial fibrillation beyond pulmonary vein isolation has remained an unsolved challenge. Targeting regions identified by different substrate mapping approaches for ablation resulted in ambiguous outcomes. With the effective refractory period being a fundamental prerequisite for the maintenance of fibrillatory conduction, this study aims at estimating the effective refractory period with clinically available measurements.

METHODS AND RESULTS

A set of 240 simulations in a spherical model of the left atrium with varying model initialization, combination of cellular refractory properties, and size of a region of lowered effective refractory period was implemented to analyse the capabilities and limitations of cycle length mapping. The minimum observed cycle length and the 25% quantile were compared to the underlying effective refractory period. The density of phase singularities was used as a measure for the complexity of the excitation pattern. Finally, we employed the method in a clinical test of concept including five patients. Areas of lowered effective refractory period could be distinguished from their surroundings in simulated scenarios with successfully induced multi-wavelet re-entry. Larger areas and higher gradients in effective refractory period as well as complex activation patterns favour the method. The 25% quantile of cycle lengths in patients with persistent atrial fibrillation was found to range from 85 to 190 ms.

CONCLUSION

Cycle length mapping is capable of highlighting regions of pathologic refractory properties. In combination with complementary substrate mapping approaches, the method fosters confidence to enhance the treatment of atrial fibrillation beyond pulmonary vein isolation particularly in patients with complex activation patterns.

Computational Modeling of Electrophysiology and Pharmacotherapy of Atrial Fibrillation: Recent Advances and Future Challenges

The pathophysiology of atrial fibrillation (AF) is broad, with components related to the unique and diverse cellular electrophysiology of atrial myocytes, structural complexity, and heterogeneity of atrial tissue, and pronounced disease-associated remodeling of both cells and tissue. A major challenge for rational design of AF therapy, particularly pharmacotherapy, is integrating these multiscale characteristics to identify approaches that are both efficacious and independent of ventricular contraindications. Computational modeling has long been touted as a basis for achieving such integration in a rapid, economical, and scalable manner. However, computational pipelines for AF-specific drug screening are in their infancy, and while the field is progressing quite rapidly, major challenges remain before computational approaches can fill the role of workhorse in rational design of AF pharmacotherapies. In this review, we briefly detail the unique aspects of AF pathophysiology that determine requirements for compounds targeting AF rhythm control, with emphasis on delimiting mechanisms that promote AF triggers from those providing substrate or supporting reentry. We then describe modeling approaches that have been used to assess the outcomes of drugs acting on established AF targets, as well as on novel promising targets including the ultra-rapidly activating delayed rectifier potassium current, the acetylcholine-activated potassium current and the small conductance calcium-activated potassium channel. Finally, we describe how heterogeneity and variability are being incorporated into AF-specific models, and how these approaches are yielding novel insights into the basic physiology of disease, as well as aiding identification of the important molecular players in the complex AF etiology.

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

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

Cytoplasm resistivity of mammalian atrial myocardium determined by dielectrophoresis and impedance methods

Many cardiac arrhythmias are caused by slowed conduction of action potentials, which in turn can be due to an abnormal increase of intracellular myocardial resistance. Intracellular resistivity is a linear sum of that offered by gap junctions between contiguous cells and the cytoplasm of the myocytes themselves. However, the relative contribution of the two components is unclear, especially in atrial myocardium, as there are no precise measurements of cytoplasmic resistivity, R(c). In this study, R(c) was measured in atrial tissue using several methods: a dielectrophoresis technique with isolated cells and impedance measurements with both isolated cells and multicellular preparations. All methods yielded similar values for R(c), with a mean of 138 ± 5 Ω·cm at 23°C, and a Q(10) value of 1.20. This value is about half that of total intracellular resistivity and thus will be a significant determinant of the actual value of action potential conduction velocity. The dielectrophoresis experiments demonstrated the importance of including divalent cations (Ca(2+) and Mg(2+)) in the suspension medium, as their omission reduced cell integrity by lowering membrane resistivity and increasing cytoplasm resistivity. Accurate measurement of R(c) is essential to develop quantitative computational models that determine the key factors contributing to the development of cardiac arrhythmias.

Drift laws for spiral waves on curved anisotropic surfaces

Rotating spiral waves organize spatial patterns in chemical, physical, and biological excitable systems. Factors affecting their dynamics, such as spatiotemporal drift, are of great interest for particular applications. Here, we propose a quantitative description for spiral wave dynamics on curved surfaces which shows that for a wide class of systems, including the Belousov-Zhabotinsky reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the surface is the main determinant of spiral wave drift. The theory provides explicit equations for spiral wave drift direction, drift velocity, and the period of rotation. Depending on the parameters, the drift can be directed to the regions of either maximal or minimal Ricci scalar curvature, which was verified by direct numerical simulations.

Simulation of biatrial conduction via different pathways during sinus rhythm with a detailed human atrial model

In order to better understand biatrial conduction, investigate various conduction pathways, and compare the differences between isotropic and anisotropic conductions in human atria, we present a simulation study of biatrial conduction with known/assumed conduction pathways using a recently developed human atrial model. In addition to known pathways: (1) Bachmann's bundle (BB), (2) limbus of fossa ovalis (LFO), and (3) coronary sinus (CS), we also hypothesize that there exist two fast conduction bundles that connect the crista terminalis (CT), LFO, and CS. Our simulation demonstrates that use of these fast conduction bundles results in a conduction pattern consistent with experimental data. The comparison of isotropic and anisotropoic conductions in the BB case showed that the atrial working muscles had small effect on conduction time and conduction speed, although the conductivities assigned in anisotropic conduction were two to four times higher than the isotropic conduction. In conclusion, we suggest that the hypothesized intercaval bundles play a significant role in the biatrial conduction and that myofiber orientation has larger effects on the conduction system than the atrial working muscles. This study presents readers with new insights into human atrial conduction.

Modeling atrial arrhythmias: impact on clinical diagnosis and therapies

Atrial arrhythmias are the most frequent sustained rhythm disorders in humans and often lead to severe complications such as heart failure and stroke. Despite the important insights provided by animal models into the mechanisms of atrial arrhythmias, direct translation of experimental findings to new therapies in patients has not been straightforward. With the advances in computer technology, large-scale electroanatomical computer models of the atria that integrate information from the molecular to organ scale have reached a level of sophistication that they can be used to interpret the outcome of experimental and clinical studies and aid in the rational design of therapies. This paper reviews the state-of-the-art of computer models of the electrical dynamics of the atria and discusses the evolving role of simulation in assisting the clinical diagnosis and treatment of atrial arrhythmias.

Computational modeling of the human atrial anatomy and electrophysiology

This review article gives a comprehensive survey of the progress made in computational modeling of the human atria during the last 10 years. Modeling the anatomy has emerged from simple "peanut"-like structures to very detailed models including atrial wall and fiber direction. Electrophysiological models started with just two cellular models in 1998. Today, five models exist considering e.g. details of intracellular compartments and atrial heterogeneity. On the pathological side, modeling atrial remodeling and fibrotic tissue are the other important aspects. The bridge to data that are measured in the catheter laboratory and on the body surface (ECG) is under construction. Every measurement can be used either for model personalization or for validation. Potential clinical applications are briefly outlined and future research perspectives are suggested.

GK BASED FUZZY CLUSTERING FOR THE DIAGNOSIS OF CARDIAC ARRHYTHMIA

Abstract-Cardiac arrhythmia is one of the major causes of human death, and most of the time it cannot be predicted well in advance at the right time. Computational intelligence algorithms can help in extracting the hidden patterns of biological datasets. This paper explores the use of advanced and intelligent computational algorithms for automated detection, classification and clustering of cardiac arrhythmia (CA). Application of Fuzzy C-Mean and Extended Fuzzy C-Mean method to the arrhythmia dataset (165 normal healthy and 138 with CA) demonstrated their good CA classification capabilities. Fuzzy C Mean algorithm was able to classify the two group of data set with an overall accuracy of 97.2% [sensitivity 96.4%, specificity 98.12% and area under the receiver operating curve (AUC-ROC = 0.963)]. The classification accuracy improved significantly when GK-based extended Fuzzy was employed, and an overall accuracy of 99.14% was achieved (sensitivity 97.11%, specificity 99.18% and AUC-ROC = 0.995). These accuracy results were respectively, 19.02%, 7%, 9.14% and 11.06% higher when compared to multi-input single layer perceptron (SLP), feed forward back propagation (FFBP), self organizing maps (SOM) and support vector machine (SVM). The performance measures of fuzzy techniques were found to be better if a Principal Component Analysis (PCA) technique was used to preprocess the arrhythmia datasets.

Simulating the effects of atrial fibrillation induced electrical remodeling: a comprehensive simulation study

Mechanisms underlying atrial fibrillation (AF) are poorly understood. In this study, we computationally evaluated the functional roles of AF induced electrical remodeling (AFER) on atrial electrical excitations. Experimental data of AFER on human atrial myocytes were incorporated into a biophysically detailed model of human atrial cells to simulate the effects of AFER at cellular and tissue levels. Our results show that AFER dramatically abbreviated atrial action potential duration (APD90) and effective refractory period that were quantitatively consistent with experimental data. A typical feature of loss in rate dependent accommodation of APD90 was observed. AFER slowed down atrial conduction velocity, but facilitated atrial conduction at high excitation rates. AFER increased tissue's spatial vulnerability for initiation and maintenance of AF remarkably. The overall susceptibility of human atrium to arrhythmia was increased. Most importantly AFER increased the stability of reentrant waves in 2D and 3D models prolonging their lifespan. While reentrant excitation waves self-terminated under Control conditions, the same became persistent or degenerated into multiple wavelets leading to spatio-temporal chaos under AFER conditions with accelerated re-entrant excitation rates. There was an increase in dominant frequency. In conclusion, our simulations substantiated a link between AFER and persistence of AF, providing mechanistic insights towards better understanding of "AF begets AF".

A tissue-specific model of reentry in the right atrial appendage

INTRODUCTION

Atrial fibrillation is prevalent in the elderly and contributes to mortality in congestive heart failure. Development of computer models of atrial electrical activation that incorporate realistic structures provides a means of investigating the mechanisms that initiate and maintain reentrant atrial arrhythmia. As a step toward this, we have developed a model of the right atrial appendage (RAA) including detailed geometry of the pectinate muscles (PM) and crista terminalis (CT) with high spatial resolution, as well as complete fiber architecture.

METHODS AND RESULTS

Detailed structural images of a pig RAA were acquired using a semiautomated extended-volume imaging system. The generally accepted anisotropic ratio of 10:1 was adopted in the computer model. To deal with the regional action potential duration heterogeneity in the RAA, a Courtemanche cell model and a Luo-Rudy cell model were used for the CT and PM, respectively. Activation through the CT and PM network was adequately reproduced with acceptable accuracy using reduced-order computer models. Using a train of reducing cycle length stimuli applied to a CT/PM junction, we observed functional block both parallel with and perpendicular to the axis of the CT.

CONCLUSION

With stimulation from the CT at the junction of a PM, we conclude: (a) that conduction block within the CT is due to a reduced safety factor; and (b) that unidirectional block and reentry within the CT is due to its high anisotropy. Regional differences in effective refractive period do not explain the observed conduction block.

A morphologically realistic shell model of atrial propagation and ablation

A three dimensional morphologically realistic model of atrial propagation is developed, based on the male Visible Human dataset and the Fitzhugh-Nagumo equations for cardiac excitation. The atrial shell geometry incorporates eleven different anatomical structures, including the pulmonary veins, and the septum, Bachmann's bundle and coronary sinus as interatrial conduction pathways. Although the model utilizes a simplified cellular model of cardiac excitation it is able to reproduce a variety of electrophysiological phenomena including: autorhythmicity of the sinoatrial node and its ability to excite surrounding atrial tissue, spiral re-entrant wavefronts, ectopic beats originating in the PV and their termination by circumferential ablation of the PV. The model is an important tool to quantitatively study atrial excitation under normal conditions and during atrial fibrillation.

Spatial-temporal filter effect in a computer model study of ventricular fibrillation

Prediction of countershock success from ventricular fibrillation (VF) ECG is a major challenge in critical care medicine. Recent findings indicate that stable, high frequency mother rotors are one possible mechanism maintaining VF. A computer model study was performed to investigate how epicardiac sources are reflected in the ECG. In the cardiac tissues of two computer models - a model with cubic geometry and a simplified torso model with a left ventricle - a mother rotor was induced by increasing the potassium rectifier current. On the epicardium, the dominant frequency (DF) map revealed a constant DF of 23 Hz (cubic model) and 24.4 Hz (torso model) in the region of the mother rotor, respectively. A sharp drop of frequency (3-18 Hz in the cubic model and 12.4-18 Hz in the torso model) occurred in the surrounding epicardial tissue of chaotic fibrillatory conduction. While no organized pattern was observable on the body surface of the cubic model, the mother rotor frequency can be identified in the anterior surface of the torso model because of the chosen position of the mother rotor in the ventricle (shortest distance to the body surface). Nevertheless, the DFs were damped on the body surfaces of both models (4.6-8.5 Hz in the cubic model and 14.4-16.4 Hz in the torso model). Thus, it was shown in this computer model study that wave propagation transforms the spatial low pass filtering of the thorax into a temporal low pass. In contrast to the resistive-capacitive low pass filter formed by the tissue, this spatial-temporal low pass filter becomes effective at low frequencies (tens of Hertz). This effect damps the high frequency components arising from the heart and it hampers a direct observation of rapid, organized sources of VF in the ECGs, when in an emergency case an artifact-free recording is not possible.

Computational model of atrial electrical activation and propagation

We have developed a finite-element surface model of human atria, in order to study normal and abnormal patterns of atrial activation. To characterize electrical activity in both atrial muscle and cardiac pacemaker regions, Fitzhugh-Nagumo-type equations were employed. Model equations were tested using a simplified geometry containing major topological features of both atria. The model is able to generate spontaneous activation of electrical impulses within the sinoatrial node which propagate across the atria. The model can be used as a basis for investigating mechanisms underlying normal and abnormal atrial rhythms, including re-entrant activation by an ectopic focus.

The missing link between cardiovascular rhythm control and myocardial cell modeling

Cardiac arrhythmia is currently investigated from two different points of view. One considers ECG bio-signal analysis and investigates heart rate variability, baroreflex control, heart rate turbulence, alternans phenomena, etc. The other involves building computer models of the heart based on ion channels, bio-domain models and forward calculations to finally reach ECG and body surface potential maps. Both approaches aim to support the cardiologist in better understanding of arrhythmia, improving diagnosis and reliable risk stratification, and optimizing therapy. This article summarizes recent results and aims to trigger new research to bridge the different views.

Spiral wave dynamics in excitable media with spherical geometries

We describe the spatial and temporal organization of spiral and scroll waves in spherical shells of different sizes and solid spheres. We present simulation results for the evolution of the dynamics and clustering of spiral waves as a function of the excitability of the medium. The excitability, topology, and size of the domain places restrictions on how single and multiarmed spiral waves are organized in space. The results in spherical geometries are compared with those in planar two-dimensional media. These studies are relevant to the dynamics of spiral waves in a variety of media including the heart, and chemical reactions on spherical surfaces.

Heterogeneous three-dimensional anatomical and electrophysiological model of human atria

Investigating the mechanisms underlying the genesis and conduction of electrical excitation in the atria at physiological and pathological states is of great importance. To provide knowledge concerning the mechanisms of excitation, we constructed a biophysical detailed and anatomically accurate computer model of human atria that incorporates both structural and electrophysiological heterogeneities. The three-dimensional geometry was extracted from the visible female dataset. The sinoatrial node (SAN) and atrium, including crista terminalis (CT), pectinate muscles (PM), appendages (APG) and Bachmann's bundle (BB) were segmented in this work. Fibre orientation in CT, PM and BB was set to local longitudinal direction. Descriptions for all used cell types were based on modifications of the Courtemanche et al. model of a human atrial cell. Maximum conductances of Ito, IKr and ICa,L were modified for PM, CT, APG and atrioventricular ring to reproduce measured action potentials (AP). Pacemaker activity in the human SAN was reproduced by removing IK1, but including If, ICa,T, and gradients of channel conductances as described in previous studies for heterogeneous rabbit SAN. Anisotropic conduction was computed with a monodomain model using the finite element method. The transversal to longitudinal ratio of conductivity for PM, CT and BB was 1:9. Atrial working myocardium (AWM) was set to be isotropic. Simulation of atrial electrophysiology showed initiation of APs in the SAN centre. The excitation spread afterwards to the periphery near to the region of the CT and preferentially towards the atrioventricular region. The excitation extends over the right atrium along PM. Both CT and PM activated the right AWM. Earliest activation of the left atrium was through BB and excitation spread over to the APG. The conduction velocities were 0.6ms-1 for AWM, 1.2ms-1 for CT, 1.6ms-1 for PM and 1.1ms-1 for BB at a rate of 63bpm. The simulations revealed that bundles form dominant pathways for atrial conduction. The preferential conduction towards CT and along PM is comparable with clinical mapping. Repolarization is more homogeneous than excitation due to the heterogeneous distribution of electrophysiological properties and hence the action potential duration.

A membrane model of electrically remodelled atrial myocardium derived from in vivo measurements*

Aims

Contemporary ionic-based membrane models are computationally expensive and are not intended to match the properties of a given experimental preparation. The aim of this work was to use measured restitution properties of electrically remodelled atrial tissue to develop a simplified membrane model based on the Fenton–Karma (FK) equations amenable to large-scale simulation of chronic atrial fibrillation (CAF).

Methods

Two membrane models, the FK-CAF and FK-CNTRL parameter sets, were developed to match action potential duration (APD) and conduction velocity (CV) restitution properties of rapid-pacing-induced electrically remodelled sheep atria and healthy atria, respectively. The models were tested by inducing reentry in a two-dimensional anisotropic monodomain and comparing the resulting cycle lengths (CL) with measured CLs.

Results

Parameters for the FK models were obtained that reproduced APD and CV restitution properties measured in the CAF and healthy sheep atria. Using the FK-CAF parameters, reentry was sustained in a 2.5 by 2.5 cm sheet with a CL = 91.0 ± 3.0 ms. Reentry (CL = 113.2 ± 5.2 ms) could only be sustained in the FK-CNTRL model after the tissue was first activated at a fast rate (136.5 ms).

Conclusions

The FK-CAF model is shown to approximate the restitution properties of remodelled sheep atria and can be used to simulate reentry with short CLs similar to those measured during AF episodes.

One‐Dimensional Rabbit Sinoatrial Node Models:

INTRODUCTION

Cardiac multicellular modeling has traditionally focused on ventricular electromechanics. More recently, models of the atria have started to emerge, and there is much interest in addressing sinoatrial node structure and function.

METHODS AND RESULTS

We implemented a variety of one-dimensional sinoatrial models consisting of descriptions of central, transitional, and peripheral sinoatrial node cells, as well as rabbit or human atrial cells. These one-dimensional models were implemented using CMISS on an SGI Origin 2000 supercomputer. Intercellular coupling parameters recorded in experimental studies on sinoatrial node and atrial cell-pairs under-represent the electrotonic interactions that any cardiomyocyte would have in a multidimensional setting. Unsurprisingly, cell-to-cell coupling had to be scaled-up (by a factor of 5) in order to obtain a stable leading pacemaker site in the sinoatrial node center. Further critical parameters include the gradual increase in intercellular coupling from sinoatrial node center to periphery, and the presence of electrotonic interaction with atrial cells. Interestingly, the electrotonic effect of the atrium on sinoatrial node periphery is best described as opposing depolarization, rather than necessarily hyperpolarizing, as often assumed.

CONCLUSION

Multicellular one-dimensional models of sinoatrial node and atrium can provide useful insight into the origin and spread of normal cardiac excitation. They require larger than "physiologic" intercellular conductivities in order to make up for a lack of "anatomical" spatial scaling. Multicellular models for more in-depth quantitative studies will require more realistic anatomico-physiologic properties.

A numerical scheme for modeling wavefront propagation on a monolayer of arbitrary geometry

The majority of models of wavefront propagation in cardiac tissue have assumed relatively simple geometries. Extensions to complicated three-dimensional (3-D) representations are computationally challenging due to issues related both to problem size and to the correct implementation of flux conservation. In this paper, we present a generalized finite difference scheme (GDFS) to simulate the reaction-diffusion system on a 3-D monolayer of arbitrary shape. GDFS is a vertex-centered variant of the finite-volume method that ensures local flux conservation. Owing to an effectively lower dimensionality, the overall computation time is reduced compared to full 3-D models at the same spatial resolution. We present the theoretical background to compute both the wavefront conduction and local electrograms using a matrix formulation. The same matrix is used for both these quantities. We then give some results of simulation for simple monolayers and complex monolayers resembling a human atria.

Study of atrial arrhythmias in a computer model based on magnetic resonance images of human atria

The maintenance of multiple wavelets appears to be a consistent feature of atrial fibrillation (AF). In this paper, we investigate possible mechanisms of initiation and perpetuation of multiple wavelets in a computer model of AF. We developed a simplified model of human atria that uses an ionic-based membrane model and whose geometry is derived from a segmented magnetic resonance imaging data set. The three-dimensional surface has a realistic size and includes obstacles corresponding to the location of major vessels and valves, but it does not take into account anisotropy. The main advantage of this approach is its ability to simulate long duration arrhythmias (up to 40 s). Clinically relevant initiation protocols, such as single-site burst pacing, were used. The dynamics of simulated AF were investigated in models with different action potential durations and restitution properties, controlled by the conductance of the slow inward current in a modified Luo-Rudy model. The simulation studies show that (1) single-site burst pacing protocol can be used to induce wave breaks even in tissue with uniform membrane properties, (2) the restitution-based wave breaks in an atrial model with realistic size and conduction velocities are transient, and (3) a significant reduction in action potential duration (even with apparently flat restitution) increases the duration of AF. (c) 2002 American Institute of Physics.