Computational modeling of the human atrial anatomy and electrophysiology

Influence of genetic mutations to atria vulnerability to atrial fibrillation: An in-silico 3D human atria study

BACKGROUND AND OBJECTIVE

Personalized 3D computer models of atria have been extensively implemented in the last yearsas a tool to facilitate the understanding of the mechanisms underlying different forms of arrhythmia, such as atrial fibrillation (AF). Meanwhile, genetic mutations acting on potassium channel dynamics were demonstrated to induce fibrillatory episodes in asymptomatic patients. This research study aims at assessing the effects and the atrial susceptibility to AF of three gain-of-function mutations - namely, KCNH2 T895M, KCNH2 T436M, and KCNE3-V17M - associated with AF outbreaks, using highly detailed 3D atrial models with realistic wall thickness and heterogenous histological properties.

METHODS

The 3D atrial model was generated by reconstructing segmented anatomical structures from CT scans of an AF patient. Modified versions of the Courtemanche human atrial myocyte model were used to reproduce the electrophysiological activity of the WT and of the three mutant cells. Ectopic foci (EF) were simulated in sixteen locations across the atrial mesh using an S1-S2 protocol with two S2 basic cycle lengths (BCL) and eleven coupling intervals in order to induce arrhythmias.

RESULTS

The three genetic mutations at 3D level reduced the APD90. The KCNE3-V17M mutation provoked the highest shortening (55 % in RA and LA with respect to WT), followed by KCNH2 T895M (14 % in RA and 18 % LA with respect to WT)and KCNH2 T436M (7 % in RA and 9 % LA with respect to WT). The KCNE3-V17M mutation led to arrhythmia in 67 % of the cases simulated and in 94 % of ectopic foci considered, at S2 BCL equal to 100 ms. The KCNH2 T436M and KCNH2 T895M mutations increased the vulnerability to AF in a similar way, leading to arrhythmic episodes in 7 % of the simulated conditions, at S2 BCL set to 160 ms. Overall, 60 % of the arrhythmic events generated arise in the left atrium. Spiral waves, multiple rotors and disordered electrical pattern were elicited in the presence of the KCNE3-V17M mutation, exhibiting an instantaneous mean frequency of 7.6 Hz with a mean standard deviation of 1.12 Hz. The scroll waves induced in the presence of the KCNH2 T436M and KCNH2 T895M mutations showed steadiness and regularity with an instantaneous mean frequencies in the range of 4.9 - 5.1 Hz and a mean standard deviation within 0.19 - 0.53 Hz.

CONCLUSIONS

The pro-arrhythmogenicity of the KCNE3-V17M, KCNH2 T895M and KCNH2 T436M mutations was studied and proved on personalized 3D cardiac models. The three genetic mutations were demonstrated to increase the predisposition of atrial tissue to the formation of AF-susceptible substrate in different ways based on their effects on electrophysiological properties of the atria.

Non-invasive estimation of atrial fibrillation driver position using long-short term memory neural networks and body surface potentials

BACKGROUND AND OBJECTIVE

Atrial Fibrillation (AF) is a supraventricular tachyarrhythmia that can lead to thromboembolism, hearlt failure, ischemic stroke, and a decreased quality of life. Characterizing the locations where the mechanisms of AF are initialized and maintained is key to accomplishing an effective ablation of the targets, hence restoring sinus rhythm. Many methods have been investigated to locate such targets in a non-invasive way, such as Electrocardiographic Imaging, which enables an on-invasive and panoramic characterization of cardiac electrical activity using recording Body Surface Potentials (BSP) and a torso model of the patient. Nonetheless, this technique entails some major issues stemming from solving the inverse problem, which is known to be severely ill-posed. In this context, many machine learning and deep learning approaches aim to tackle the characterization and classification of AF targets to improve AF diagnosis and treatment.

METHODS

In this work, we propose a method to locate AF drivers as a supervised classification problem. We employed a hybrid form of the convolutional-recurrent network which enables feature extraction and sequential data modeling utilizing labeled realistic computerized AF models. Thus, we used 16 AF electrograms, 1 atrium, and 10 torso geometries to compute the forward problem. Previously, the AF models were labeled by assigning each sample of the signals a region from the atria from 0 (no driver) to 7, according to the spatial location of the AF driver. The resulting 160 BSP signals, which resemble a 64-lead vest recording, are preprocessed and then introduced into the network following a 4-fold cross-validation in batches of 50 samples.

RESULTS

The results show a mean accuracy of 74.75% among the 4 folds, with a better performance in detecting sinus rhythm, and drivers near the left superior pulmonary vein (R1), and right superior pulmonary vein (R3) whose mean sensitivity bounds around 84%-87%. Significantly good results are obtained in mean sensitivity (87%) and specificity (83%) in R1.

CONCLUSIONS

Good results in R1 are highly convenient since AF drivers are commonly found in this area: the left atrial appendage, as suggested in some previous studies. These promising results indicate that using CNN-LSTM networks could lead to new strategies exploiting temporal correlations to address this challenge effectively.

Interactions between calcium-induced arrhythmia triggers and the electrophysiological-anatomical substrate underlying the induction of atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia and is sustained by spontaneous focal excitations and re-entry. Spontaneous electrical firing in the pulmonary vein (PV) sleeves is implicated in AF generation. The aim of this simulation study was to identify the mechanisms determining the localisation of AF triggers in the PVs and their contribution to the genesis of AF. A novel biophysical model of the canine atria was used that integrates stochastic, spontaneous subcellular Ca2+ release events (SCRE) with regional electrophysiological heterogeneity in ionic properties and a detailed three-dimensional model of atrial anatomy, microarchitecture and patchy fibrosis. Simulations highlighted the importance of the smaller inward rectifier potassium current (IK1 ) in PV cells compared to the surrounding atria, which enabled SCRE more readily to result in delayed-afterdepolarisations that induced triggered activity. There was a leftward shift in the dependence of the probability of triggered activity on sarcoplasmic reticulum Ca2+ load. This feature was accentuated in 3D tissue compared to single cells (Δ half-maximal [Ca2+ ]SR  = 58 μM vs. 22 μM). In 3D atria incorporating electrical heterogeneity, excitations preferentially emerged from the PV region. These triggered focal excitations resulted in transient re-entry in the left atrium. Addition of fibrotic patches promoted localised emergence of focal excitations and wavebreaks that had a more substantial impact on generating AF-like patterns than the PVs. Thus, a reduced IK1 , less negative resting membrane potential, and fibrosis-induced changes of the electrotonic load all contribute to the emergence of complex excitation patterns from spontaneous focal triggers. KEY POINTS: Focal excitations in the atria are most commonly associated with the pulmonary veins, but the mechanisms for this localisation are yet to be elucidated. We applied a multi-scale computational modelling approach to elucidate the mechanisms underlying such localisations. Myocytes in the pulmonary vein region of the atria have a less negative resting membrane potential and reduced time-independent potassium current; we demonstrate that both of these factors promote triggered activity in single cells and tissues. The less negative resting membrane potential also contributes to heterogeneous inactivation of the fast sodium current, which can enable re-entrant-like excitation patterns to emerge without traditional conduction block.

Transition mechanisms from atrial flutter to atrial fibrillation during anti-tachycardia pacing therapy

BACKGROUND

Atrial anti-tachycardia pacing (aATP) has been shown to be effective for the termination of atrial tachyarrhythmias, but its success rate is still not high enough.

OBJECTIVE

The main objective of this study was to investigate the mechanisms of atrial flutter (AFL) termination by aATP and the transition from AFL to atrial fibrillation (AF) during aATP.

METHODS

We developed a multi-scale model of the human atrium based on magnetic resonance images and examined the atrial electrophysiology of AFL during aATP with a ramp protocol.

RESULTS

In successful cases of aATP, paced excitation entered the excitable gap and collided with the leading edge of the reentrant wave front. Furthermore, the excitation propagating in the opposite direction collided with the trailing edge of the reentrant wave to terminate AFL. The second collision was made possible by the distribution of the wave propagation velocity in the atria. The detailed analysis revealed that the slowing of propagation velocity occurred at the exit of the sub-Eustachian isthmus, probably due to source-sink mismatch. During the transition from AFL to AF, the excitation collided with the refractory zone of the preceding wave and broke into multiple wave fronts to induce AF. A similar observation was made for the transition from AF to sinus rhythm. In both cases, the complex anatomy of the atria played an essential role.

CONCLUSION

The complex anatomy of atria plays an essential role in the maintenance of stable AFL and its termination by aATP, which were revealed by the realistic three-dimensional simulation model.

An expert review of the inverse problem in electrocardiographic imaging for the non-invasive identification of atrial fibrillation drivers

BACKGROUND AND OBJECTIVE

Electrocardiographic imaging (ECGI) has emerged as a non-invasive approach to identify atrial fibrillation (AF) driver sources. This paper aims to collect and review the current research literature on the ECGI inverse problem, summarize the research progress, and propose potential research directions for the future.

METHODS AND RESULTS

The effectiveness and feasibility of using ECGI to map AF driver sources may be influenced by several factors, such as inaccuracies in the atrial model due to heart movement or deformation, noise interference in high-density body surface potential (BSP), inconvenient and time-consuming BSP acquisition, errors in solving the inverse problem, and incomplete interpretation of the AF driving source information derived from the reconstructed epicardial potential. We review the current research progress on these factors and discuss possible improvement directions. Additionally, we highlight the limitations of ECGI itself, including the lack of a gold standard to validate the accuracy of ECGI technology in locating AF drivers and the challenges associated with guiding AF ablation based on post-processed epicardial potentials due to the intrinsic difference between epicardial and endocardial potentials.

CONCLUSIONS

Before performing ablation, ECGI can provide operators with predictive information about the underlying locations of AF driver by non-invasively and globally mapping the biatrial electrical activity. In the future, endocardial catheter mapping technology may benefit from the use of ECGI to enhance the diagnosis and ablation of AF.

A detailed mathematical model of the human atrial cardiomyocyte: integration of electrophysiology and cardiomechanics

Mechano-electric regulations (MER) play an important role in the maintenance of cardiac performance. Mechano-calcium and mechano-electric feedback (MCF and MEF) pathways adjust the cardiomyocyte contractile force according to mechanical perturbations and affects electro-mechanical coupling. MER integrates all these regulations in one unit resulting in a complex phenomenon. Computational modelling is a useful tool to accelerate the mechanistic understanding of complex experimental phenomena. We have developed a novel model that integrates the MER loop for human atrial cardiomyocytes with proper consideration of feedforward and feedback pathways. The model couples a modified version of the action potential (AP) Koivumäki model with the contraction model by Quarteroni group. The model simulates iso-sarcometric and isometric twitches and the feedback effects on AP and Ca2+ -handling. The model showed a biphasic response of Ca2+ transient (CaT) peak to increasing pacing rates and highlights the possible mechanisms involved. The model has shown a shift of the threshold for AP and CaT alternans from 4.6 to 4 Hz under post-operative atrial fibrillation, induced by depressed SERCA activity. The alternans incidence was dependent on a chain of mechanisms including RyRs availability time, MCF coupling, CaMKII phosphorylation, and the stretch levels. As a result, the model predicted a 10% slowdown of conduction velocity for a 20% stretch, suggesting a role of stretch in creation of substrate formation for atrial fibrillation. Overall, we conclude that the developed model provides a physiological CaT followed by a physiological twitch. This model can open pathways for the future studies of human atrial electromechanics. KEY POINTS: With the availability of human atrial cellular data, interest in atrial-specific model integration has been enhanced. We have developed a detailed mathematical model of human atrial cardiomyocytes including the mechano-electric regulatory loop. The model has gone through calibration and evaluation phases against a wide collection of available human in-vitro data. The usefulness of the model for analysing clinical problems has been preliminaryly tested by simulating the increased incidence of Ca2+ transient and action potential alternans at high rates in post-operative atrial fibrillation condition. The model determines the possible role of mechano-electric feedback in alternans incidence, which can increase vulnerability to atrial arrhythmias by varying stretch levels. We found that our physiologically accurate description of Ca2+ handling can reproduce many experimental phenomena and can help to gain insights into the underlying pathophysiological mechanisms.

The Impact of Standard Ablation Strategies for Atrial Fibrillation on Cardiovascular Performance in a Four-Chamber Heart Model

PURPOSE

Atrial fibrillation is one of the most frequent cardiac arrhythmias in the industrialized world and ablation therapy is the method of choice for many patients. However, ablation scars alter the electrophysiological activation and the mechanical behavior of the affected atria. Different ablation strategies with the aim to terminate atrial fibrillation and prevent its recurrence exist but their impact on the performance of the heart is often neglected.

METHODS

In this work, we present a simulation study analyzing five commonly used ablation scar patterns and their combinations in the left atrium regarding their impact on the pumping function of the heart using an electromechanical whole-heart model. We analyzed how the altered atrial activation and increased stiffness due to the ablation scars affect atrial as well as ventricular contraction and relaxation.

RESULTS

We found that systolic and diastolic function of the left atrium is impaired by ablation scars and that the reduction of atrial stroke volume of up to 11.43% depends linearly on the amount of inactivated tissue. Consequently, the end-diastolic volume of the left ventricle, and thus stroke volume, was reduced by up to 1.4 and 1.8%, respectively. During ventricular systole, left atrial pressure was increased by up to 20% due to changes in the atrial activation sequence and the stiffening of scar tissue.

CONCLUSION

This study provides biomechanical evidence that atrial ablation has acute effects not only on atrial contraction but also on ventricular performance. Therefore, the position and extent of ablation scars is not only important for the termination of arrhythmias but is also determining long-term pumping efficiency. If confirmed in larger cohorts, these results have the potential to help tailoring ablation strategies towards minimal global cardiovascular impairment.

A meshless fragile points method for rule-based definition of myocardial fiber orientation

BACKGROUND AND OBJECTIVE

Rule-based methods are commonly used to estimate the arrangement of myocardial fibers by solving the Laplace problem with appropriate Dirichlet boundary conditions. Existing algorithms are using the Finite Element Method (FEM) to solve the Laplace-Dirichlet problem. However, meshless methods are under development for cardiac electrophysiology simulation. The objective of this work is to propose a meshless rule based method for the determination of myocardial fiber arrangement without requiring a mesh discretization as it is required by FEM.

METHODS

The proposed method employs the Fragile Points Method (FPM) for the solution of the Laplace-Dirichlet problem. FPM uses simple discontinuous trial functions and single-point exact integration for linear trial functions that set it as a promising alternative to the Finite Element Method. We derive the FPM formulation of the Laplace-Dirichlet and we estimate ventricular and atrial fiber arrangements according to rules based on histology findings for four different geometries. The obtained fiber arrangements from FPM are compared with the ones obtained from FEM by calculating the angle between the fiber vector fields of the two methods for three different directions (i.e., longitudinal, sheet, transverse).

RESULTS

The fiber arrangements that were generated with FPM were in close agreement with the generated arrangements from FEM for all three directions. The mean angle difference between the FPM and FEM vector fields were lower than 0.030^∘ for the ventricular fiber arrangements and lower than 0.036^∘ for the atrial fiber arrangements.

DISCUSSION

The proposed meshless rule-based method was proven to generate myocardial fiber arrangements with very close agreement with FEM while alleviates the requirement for a mesh of the latter. This is of great value for cardiac electrophysiology solvers that are based on meshless methods since they require a well defined myocardial fiber arrangement to simulate accurately the propagation of electrical signals in the heart. Combining a meshless solution for both the determination of the fibers and the electrical signal propagation can allow for solution that do not require the definition of a mesh. To our knowledge, this work is the first one to propose a meshless rule-based method for myocardial fiber arrangement determination.

Rule-based definition of muscle bundles in patient-specific models of the left atrium

Atrial fibrillation (AF) is the most common arrhythmia encountered clinically, and as the population ages, its prevalence is increasing. Although the CHA2DS2- VASc score is the most used risk-stratification system for stroke risk in AF, it lacks personalization. Patient-specific computer models of the atria can facilitate personalized risk assessment and treatment planning. However, a challenge faced in creating such models is the complexity of the atrial muscle arrangement and its influence on the atrial fiber architecture. This work proposes a semi-automated rule-based algorithm to generate the local fiber orientation in the left atrium (LA). We use the solutions of several harmonic equations to decompose the LA anatomy into subregions. Solution gradients define a two-layer fiber field in each subregion. The robustness of our approach is demonstrated by recreating the fiber orientation on nine models of the LA obtained from AF patients who underwent WATCHMAN device implantation. This cohort of patients encompasses a variety of morphology variants of the left atrium, both in terms of the left atrial appendages (LAAs) and the number of pulmonary veins (PVs). We test the fiber construction algorithm by performing electrophysiology (EP) simulations. Furthermore, this study is the first to compare its results with other rule-based algorithms for the LA fiber architecture definition available in the literature. This analysis suggests that a multi-layer fiber architecture is important to capture complex electrical activation patterns. A notable advantage of our approach is the ability to reconstruct the main LA fiber bundles in a variety of morphologies while solving for a small number of harmonic fields, leading to a comparatively straightforward and reproducible approach.

Arrhythmogenic influence of mutations in a myocyte-based computational model of the pulmonary vein sleeve

In the heart, electrophysiological dysregulation arises from defects at many biological levels (from point mutations in ion channel proteins to gross structural abnormalities). These defects disrupt the normal pattern of electrical activation, producing ectopic activity and reentrant arrhythmia. To interrogate mechanisms that link these primary biological defects to macroscopic electrophysiologic dysregulation most prior computational studies have utilized either (i) detailed models of myocyte ion channel dynamics at limited spatial scales, or (ii) homogenized models of action potential conduction that reproduce arrhythmic activity at tissue and organ levels. Here we apply our recent model (EMI), which integrates electrical activation and propagation across these scales, to study human atrial arrhythmias originating in the pulmonary vein (PV) sleeves. These small structures initiate most supraventricular arrhythmias and include pronounced myocyte-to-myocyte heterogeneities in ion channel expression and intercellular coupling. To test EMI's cell-based architecture in this physiological context we asked whether ion channel mutations known to underlie atrial fibrillation are capable of initiating arrhythmogenic behavior via increased excitability or reentry in a schematic PV sleeve geometry. Our results illustrate that EMI's improved spatial resolution can directly interrogate how electrophysiological changes at the individual myocyte level manifest in tissue and as arrhythmia in the PV sleeve.

Non-invasive Estimation of Atrial Fibrillation Driver Position With Convolutional Neural Networks and Body Surface Potentials

Atrial fibrillation (AF) is characterized by complex and irregular propagation patterns, and AF onset locations and drivers responsible for its perpetuation are the main targets for ablation procedures. ECG imaging (ECGI) has been demonstrated as a promising tool to identify AF drivers and guide ablation procedures, being able to reconstruct the electrophysiological activity on the heart surface by using a non-invasive recording of body surface potentials (BSP). However, the inverse problem of ECGI is ill-posed, and it requires accurate mathematical modeling of both atria and torso, mainly from CT or MR images. Several deep learning-based methods have been proposed to detect AF, but most of the AF-based studies do not include the estimation of ablation targets. In this study, we propose to model the location of AF drivers from BSP as a supervised classification problem using convolutional neural networks (CNN). Accuracy in the test set ranged between 0.75 (SNR = 5 dB) and 0.93 (SNR = 20 dB upward) when assuming time independence, but it worsened to 0.52 or lower when dividing AF models into blocks. Therefore, CNN could be a robust method that could help to non-invasively identify target regions for ablation in AF by using body surface potential mapping, avoiding the use of ECGI.

Computer Modeling of the Heart for ECG Interpretation—A Review

Computer modeling of the electrophysiology of the heart has undergone significant progress. A healthy heart can be modeled starting from the ion channels via the spread of a depolarization wave on a realistic geometry of the human heart up to the potentials on the body surface and the ECG. Research is advancing regarding modeling diseases of the heart. This article reviews progress in calculating and analyzing the corresponding electrocardiogram (ECG) from simulated depolarization and repolarization waves. First, we describe modeling of the P-wave, the QRS complex and the T-wave of a healthy heart. Then, both the modeling and the corresponding ECGs of several important diseases and arrhythmias are delineated: ischemia and infarction, ectopic beats and extrasystoles, ventricular tachycardia, bundle branch blocks, atrial tachycardia, flutter and fibrillation, genetic diseases and channelopathies, imbalance of electrolytes and drug-induced changes. Finally, we outline the potential impact of computer modeling on ECG interpretation. Computer modeling can contribute to a better comprehension of the relation between features in the ECG and the underlying cardiac condition and disease. It can pave the way for a quantitative analysis of the ECG and can support the cardiologist in identifying events or non-invasively localizing diseased areas. Finally, it can deliver very large databases of reliably labeled ECGs as training data for machine learning.

Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning

We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.

Arrhythmogenic Effects of Genetic Mutations Affecting Potassium Channels in Human Atrial Fibrillation: A Simulation Study

Genetic mutations in genes encoding for potassium channel protein structures have been recently associated with episodes of atrial fibrillation in asymptomatic patients. The aim of this study is to investigate the potential arrhythmogenicity of three gain-of-function mutations related to atrial fibrillation-namely, KCNH2 T895M, KCNH2 T436M, and KCNE3-V17M-using modeling and simulation of the electrophysiological activity of the heart. A genetic algorithm was used to tune the parameters' value of the original ionic currents to reproduce the alterations experimentally observed caused by the mutations. The effects on action potentials, ionic currents, and restitution properties were analyzed using versions of the Courtemanche human atrial myocyte model in different tissues: pulmonary vein, right, and left atrium. Atrial susceptibility of the tissues to spiral wave generation was also investigated studying the temporal vulnerability. The presence of the three mutations resulted in an overall more arrhythmogenic substrate. Higher current density, action potential duration shortening, and flattening of the restitution curves were the major effects of the three mutations at the single-cell level. The genetic mutations at the tissue level induced a higher temporal vulnerability to the rotor's initiation and progression, by sustaining spiral waves that perpetuate until the end of the simulation. The mutation with the highest pro-arrhythmic effects, exhibiting the widest sustained VW and the smallest meandering rotor's tip areas, was KCNE3-V17M. Moreover, the increased susceptibility to arrhythmias and rotor's stability was tissue-dependent. Pulmonary vein tissues were more prone to rotor's initiation, while in left atrium tissues rotors were more easily sustained. Re-entries were also progressively more stable in pulmonary vein tissue, followed by the left atrium, and finally the right atrium. The presence of the genetic mutations increased the susceptibility to arrhythmias by promoting the rotor's initiation and maintenance. The study provides useful insights into the mechanisms underlying fibrillatory events caused by KCNH2 T895M, KCNH2 T436M, and KCNE3-V17M and might aid the planning of patient-specific targeted therapies.

Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function

In order to simulate the cardiac function for a patient-specific geometry, the generation of the computational mesh is crucially important. In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images. These surfaces need ad-hoc processing to be suitable for a volumetric mesh generation. In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process. In particular, we focus on different aspects of a cardiac mesh generation pipeline: (1) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs; (2) generation of accurate boundary tags; (3) definition of mesh-size functions dependent on relevant geometric quantities; (4) processing and connecting together several volumetric meshes. The new algorithms-implemented in the open-source software vmtk-can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled. Thanks to these features, the proposed tools can significantly speed-up the mesh generation process for a large range of cardiac applications, from single-chamber single-physics simulations to multi-chambers multi-physics simulations. We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.

Fluid-structure interaction in a fully coupled three-dimensional mitral-atrium-pulmonary model

This paper aims to investigate detailed mechanical interactions between the pulmonary haemodynamics and left heart function in pathophysiological situations (e.g. atrial fibrillation and acute mitral regurgitation). This is achieved by developing a complex computational framework for a coupled pulmonary circulation, left atrium and mitral valve model. The left atrium and mitral valve are modelled with physiologically realistic three-dimensional geometries, fibre-reinforced hyperelastic materials and fluid–structure interaction, and the pulmonary vessels are modelled as one-dimensional network ended with structured trees, with specified vessel geometries and wall material properties. This new coupled model reveals some interesting results which could be of diagnostic values. For example, the wave propagation through the pulmonary vasculature can lead to different arrival times for the second systolic flow wave (S2 wave) among the pulmonary veins, forming vortex rings inside the left atrium. In the case of acute mitral regurgitation, the left atrium experiences an increased energy dissipation and pressure elevation. The pulmonary veins can experience increased wave intensities, reversal flow during systole and increased early-diastolic flow wave (D wave), which in turn causes an additional flow wave across the mitral valve (L wave), as well as a reversal flow at the left atrial appendage orifice. In the case of atrial fibrillation, we show that the loss of active contraction is associated with a slower flow inside the left atrial appendage and disappearances of the late-diastole atrial reversal wave (AR wave) and the first systolic wave (S1 wave) in pulmonary veins. The haemodynamic changes along the pulmonary vessel trees on different scales from microscopic vessels to the main pulmonary artery can all be captured in this model. The work promises a potential in quantifying disease progression and medical treatments of various pulmonary diseases such as the pulmonary hypertension due to a left heart dysfunction.

Integration of activation maps of epicardial veins in computational cardiac electrophysiology

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

Atrial location optimization by electrical measures for Electrocardiographic Imaging

BACKGROUND

The Electrocardiographic Imaging (ECGI) technique, used to non-invasively reconstruct the epicardial electrical activity, requires an accurate model of the atria and torso anatomy. Here we evaluate a new automatic methodology able to locate the atrial anatomy within the torso based on an intrinsic electrical parameter of the ECGI solution.

METHODS

In 28 realistic simulations of the atrial electrical activity, we randomly displaced the atrial anatomy for ±2.5 cm and ±30° on each axis. An automatic optimization method based on the L-curve curvature was used to estimate the original position using exclusively non-invasive data.

RESULTS

The automatic optimization algorithm located the atrial anatomy with a deviation of 0.5 ± 0.5 cm in position and 16.0 ± 10.7° in orientation. With these approximate locations, the obtained electrophysiological maps reduced the average error in atrial rate measures from 1.1 ± 1.1 Hz to 0.5 ± 1.0 Hz and in the phase singularity position from 7.2 ± 4.0 cm to 1.6 ± 1.7 cm (p < 0.01).

CONCLUSIONS

This proposed automatic optimization may help to solve spatial inaccuracies provoked by cardiac motion or respiration, as well as to use ECGI on torso and atrial anatomies from different medical image systems.

Investigating cardiac stimulation limits of MRI gradient coils using electromagnetic and electrophysiological simulations in human and canine body models

Purpose:

Cardiac stimulation (CS) limits to gradient coil switching speed are difficult to measure in humans; instead, current regulatory guidelines (IEC 60601–2-33) are based on animal experiments and electric field–to-dB/dt conversion factors computed for a simple, homogeneous body model. We propose improvement to this methodology by using more detailed CS modeling based on realistic body models and electrophysiological models of excitable cardiac fibers.

Methods:

We compute electric fields induced by a solenoid, coplanar loops, and a commercial gradient coil in two human body models and a canine model. The canine simulations mimic previously published experiments. We generate realistic fiber topologies for the cardiac Purkinje and ventricular muscle fiber networks using rule-based algorithms, and evaluate CS thresholds using validated electrodynamic models of these fibers.

Results:

We were able to reproduce the average measured canine CS thresholds within 5%. In all simulations, the Purkinje fibers were stimulated before the ventricular fibers, and therefore set the effective CS threshold. For the investigated gradient coil, simulated CS thresholds for the x-, y-, and z-axis were at least one order of magnitude greater than the International Electrotechnical Commission limit.

Conclusion:

We demonstrate an approach to simulate gradient-induced CS using a combination of electromagnetic and electrophysiological modeling. Pending additional validation, these simulations could guide the assessment of CS limits to MRI gradient coil switching speed. Such an approach may lead to less conservative, but still safe, operation limits, enabling the use of the maximum gradient amplitude versus slew rate parameter space of recent, powerful gradient systems.

Characterization of atrial arrhythmias in body surface potential mapping: A computational study

PURPOSE

Atrial tachycardia (AT), flutter (AFL) and fibrillation (AF) are very common cardiac arrhythmias and are driven by localized sources that can be ablation targets. Non-invasive body surface potential mapping (BSPM) can be useful for early diagnosis and ablation planning. We aimed to characterize and differentiate the arrhythmic mechanisms behind AT, AFL and AF from the BSPM perspective using basic features reflecting their electrophysiology.

METHODS

19 simulations of 567-lead BSPMs were used to obtain dominant frequency (DF) maps and estimate the atrial driving frequencies using the highest DF (HDF). Regions with |DF-HDF|≤1Hz were segmented and characterized (size, area); the spatial distribution of the differences |DF-atrialHDFestimate| was qualitatively analyzed. Phase singularity points (SPs) were detected on maps generated with Hilbert transform after band-pass filtering around the HDF (±1Hz). Connected SPs along time (filaments) and their histogram (heatmaps) were used for rotational activity characterization (duration, spatiotemporal stability). Results were reproduced in clinical layouts (252 to 12 leads) and with different rotations and translations of the atria within the torso, and compared with the original 567-lead outcomes using structural similarity index (SSIM) between maps, sensitivity and precision in SP detection and direct feature comparison. Random forest and least-square based algorithms were used to classify the arrhythmias and their mechanisms' location, respectively, based on the obtained features.

RESULTS

Frequency and phase analyses revealed distinct behavior between arrhythmias. AT and AFL presented uniform DF maps with low variance, while AF maps were more heterogeneous. Lower differences from the atrial HDF regions correlated with the driver location. Rotational activity was most stable in AFL, followed by AT and AF. Features were robust to lower spatial resolution layouts and modifications in the atrial geometry; DF and heatmaps presented decreasing SSIM along the layouts. The classification of the arrhythmias and their mechanisms' location achieved balanced accuracy of 72.0% and 73.9%, respectively.

CONCLUSION

Non-invasive characterization of AT, AFL and AF based on realistic models highlights intrinsic differences between the arrhythmias, enhancing the BSPM utility as an auxiliary clinical tool.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

A robust computational framework for estimating 3D Bi-Atrial chamber wall thickness

Atrial fibrillation (AF) is the most prevalent form of cardiac arrhythmia. The atrial wall thickness (AWT) can potentially improve our understanding of the mechanism underlying atrial structure that drives AF and provides important clinical information. However, most existing studies for estimating AWT rely on ruler-based measurements performed on only a few selected locations in 2D or 3D using digital calipers. Only a few studies have developed automatic approaches to estimate the AWT in the left atrium, and there are currently no methods to robustly estimate the AWT of both atrial chambers. Therefore, we have developed a computational pipeline to automatically calculate the 3D AWT across bi-atrial chambers and extensively validated our pipeline on both ex vivo and in vivo human atria data. The atrial geometry was first obtained by segmenting the atrial wall from the MRIs using a novel machine learning approach. The epicardial and endocardial surfaces were then separated using a multi-planar convex hull approach to define boundary conditions, from which, a Laplace equation was solved numerically to automatically separate bi-atrial chambers. To robustly estimate the AWT in each atrial chamber, coupled partial differential equations by coupling the Laplace solution with two surface trajectory functions were formulated and solved. Our pipeline enabled the reconstruction and visualization of the 3D AWT for bi-atrial chambers with a relative error of 8% and outperformed existing algorithms by >7%. Our approach can potentially lead to improved clinical diagnosis, patient stratification, and clinical guidance during ablation treatment for patients with AF.

Understanding AF Mechanisms Through Computational Modelling and Simulations

AF is a progressive disease of the atria, involving complex mechanisms related to its initiation, maintenance and progression. Computational modelling provides a framework for integration of experimental and clinical findings, and has emerged as an essential part of mechanistic research in AF. The authors summarise recent advancements in development of multi-scale AF models and focus on the mechanistic links between alternations in atrial structure and electrophysiology with AF. Key AF mechanisms that have been explored using atrial modelling are pulmonary vein ectopy; atrial fibrosis and fibrosis distribution; atrial wall thickness heterogeneity; atrial adipose tissue infiltration; development of repolarisation alternans; cardiac ion channel mutations; and atrial stretch with mechano-electrical feedback. They review modelling approaches that capture variability at the cohort level and provide cohort-specific mechanistic insights. The authors conclude with a summary of future perspectives, as envisioned for the contributions of atrial modelling in the mechanistic understanding of AF.

The role of personalized atrial modeling in understanding atrial fibrillation mechanisms and improving treatment

Atrial fibrillation is the most common arrhythmia in humans and is associated with high morbidity, mortality and health-related expenses. Computational approaches have been increasingly utilized in atrial electrophysiology. In this review we summarize the recent advancements in atrial fibrillation modeling at the organ scale. Multi-scale atrial models now incorporate high level detail of atrial anatomy, tissue ultrastructure and fibrosis distribution. We provide the state-of-the art methodologies in developing personalized atrial fibrillation models with realistic geometry and tissue properties. We then focus on the use of multi-scale atrial models to gain mechanistic insights in AF. Simulations using atrial models have provided important insight in the mechanisms underlying AF, showing the importance of the atrial fibrotic substrate and altered atrial electrophysiology in initiation and maintenance of AF. Last, we summarize the translational evidence that supports incorporation of computational modeling in clinical practice for development of personalized treatment strategies for patients with AF. In early-stages clinical studies, AF models successfully identify patients where pulmonary vein isolation alone is not adequate for treatment of AF and suggest novel targets for ablation. We conclude with a summary of the future developments envisioned for the field of atrial computational electrophysiology.

Extinction dynamics of spiral defect chaos

Spatially extended excitable systems can exhibit spiral defect chaos (SDC) during which spiral waves continuously form and disappear. To address how this dynamical state terminates using simulations can be computationally challenging, especially for large systems. To circumvent this limitation, we treat the number of spiral waves as a stochastic population with a corresponding birth-death equation and use techniques from statistical physics to determine the mean episode duration of SDC. Motivated by cardiac fibrillation, during which the heart's electrical activity becomes disorganized and shows fragmenting spiral waves, we use generic models of cardiac electrophysiology. We show that the duration can be computed in minimal computational time and that it depends exponentially on domain size. Therefore, the approach can result in efficient and accurate predictions of mean episode duration which may be extended to more complex geometries and models.

Clinical Usefulness of Computational Modeling-Guided Persistent Atrial Fibrillation Ablation: Updated Outcome of Multicenter Randomized Study

OBJECTIVE

Catheter ablation of persistent atrial fibrillation (AF) is still challenging, no optimal extra-pulmonary vein lesion set is known. We previously reported the clinical feasibility of computational modeling-guided AF catheter ablation.

METHODS

We randomly assigned 118 patients with persistent AF (77.8% men, age 60.8 ± 9.9 years) to the computational modeling-guided ablation group (53 patients) and the empirical ablation group (55 patients) based on the operators' experience. For virtual ablation, four virtual linear and one electrogram-guided lesion sets were tested on patient heart computed tomogram-based models, and the lesion set with the fastest termination time was reported to the operator in the modeling-guided ablation group. The primary outcome was freedom from atrial tachyarrhythmias lasting longer than 30 s after a single procedure.

RESULTS

During 31.5 ± 9.4 months, virtual ablation procedures were available in 95.2% of the patients (108/118). Clinical recurrence rate was significantly lower after a modeling-guided ablation than after an empirical ablation (20.8 vs. 40.0%, log-rank p = 0.042). Modeling-guided ablation was independently associated with a better long-term rhythm outcome of persistent AF ablation (HR = 0.29 [0.12-0.69], p = 0.005). The rhythm outcome of the modeling-guided ablation showed better trends in males, non-obese patients with a less remodeled atrium (left atrial dimension < 50 mm), ejection fraction ≥ 50%, and those without hypertension or diabetes (p < 0.01). There were no significant differences between the groups for the total procedure time (p = 0.403), ablation time (p = 0.510), and major complication rate (p = 0.900).

CONCLUSION

Among patients with persistent AF, the computational modeling-guided ablation was superior to the empirical catheter ablation regarding the rhythm outcome.

CLINICAL TRIAL REGISTRATION

This study was registered with the ClinicalTrials.gov, number NCT02171364.

Spatio-temporal Analysis of Multichannel Atrial Electrograms Based on a Concept of Active Areas

Atrial tachycardia and atrial flutter are frequent arrhythmia that occur spontaneously and after ablation of atrial fibrillation. Depolarization waves that differ significantly from sinus rhythm propagate across the atria with high frequency (typically 140 to 220 beats per minute). A detailed and personalized analysis of the spread of depolarization is imperative for a successful ablation therapy. Thus, catheters with several electrodes are employed to measure multichannel electrograms inside the atria. Here we propose a new concept for spatio-temporal analysis of multichannel electrograms during atrial tachycardia and atrial flutter. It is based on the calculation of simultaneously active areas. The method allows to identify atrial tachycardia and to automatically distinguish between subtypes of focal activity, micro-reentry and macro-reentry.

Myocyte Remodeling Due to Fibro-Fatty Infiltrations Influences Arrhythmogenicity

The onset of cardiac arrhythmias depends on the electrophysiological and structural properties of cardiac tissue. Electrophysiological remodeling of myocytes due to the presence of adipocytes constitutes a possibly important pathway in the pathogenesis of atrial fibrillation. In this paper we perform an in-silico study of the effect of such myocyte remodeling on the onset of atrial arrhythmias and study the dynamics of arrhythmia sources—spiral waves. We use the Courtemanche model for atrial myocytes and modify their electrophysiological properties based on published cellular electrophysiological measurements in myocytes co-cultered with adipocytes (a 69–87 % increase in APD₉₀ and an increase of the RMP by 2.5–5.5 mV). In a generic 2D setup we show that adipose tissue remodeling substantially affects the spiral wave dynamics resulting in complex arrhythmia and such arrhythmia can be initiated under high frequency pacing if the size of the remodeled tissue is sufficiently large. These results are confirmed in simulations with an anatomically accurate model of the human atria.

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.

A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

Atrial Fibrosis Hampers Non-invasive Localization of Atrial Ectopic Foci From Multi-Electrode Signals: A 3D Simulation Study

Introduction: Focal atrial tachycardia is commonly treated by radio frequency ablation with an acceptable long-term success. Although the location of ectopic foci tends to appear in specific hot-spots, they can be located virtually in any atrial region. Multi-electrode surface ECG systems allow acquiring dense body surface potential maps (BSPM) for non-invasive therapy planning of cardiac arrhythmia. However, the activation of the atria could be affected by fibrosis and therefore biomarkers based on BSPM need to take these effects into account. We aim to analyze the effect of fibrosis on a BSPM derived index, and its potential application to predict the location of ectopic foci in the atria.

Methodology: We have developed a 3D atrial model that includes 5 distributions of patchy fibrosis in the left atrium at 5 different stages. Each stage corresponds to a different amount of fibrosis that ranges from 2 to 40%. The 25 resulting 3D models were used for simulation of Focal Atrial Tachycardia (FAT), triggered from 19 different locations described in clinical studies. BSPM were obtained for all simulations, and the body surface potential integral maps (BSPiM) were calculated to describe atrial activations. A machine learning (ML) pipeline using a supervised learning model and support vector machine was developed to learn the BSPM patterns of each of the 475 activation sequences and relate them to the origin of the FAT source.

Results: Activation maps for stages with more than 15% of fibrosis were greatly affected, producing conduction blocks and delays in propagation. BSPiMs did not always cluster into non-overlapped groups since BSPiMs were highly altered by the conduction blocks. From stage 3 (15% fibrosis) the BSPiMs showed differences for ectopic beats placed around the area of the pulmonary veins. Classification results were mostly above 84% for all the configurations studied when a large enough number of electrodes were used to map the torso. However, the presence of fibrosis increases the area of the ectopic focus location and therefore decreases the utility for the electrophysiologist.

Conclusions: The results indicate that the proposed ML pipeline is a promising methodology for non-invasive ectopic foci localization from BSPM signal even when fibrosis is present.

Personalized computational modeling of left atrial geometry and transmural myofiber architecture

Atrial fibrillation (AF) is a supraventricular tachyarrhythmia characterized by complete absence of coordinated atrial contraction and is associated with an increased morbidity and mortality. Personalized computational modeling provides a novel framework for integrating and interpreting the role of atrial electrophysiology (EP) including the underlying anatomy and microstructure in the development and sustenance of AF. Coronary computed tomography angiography data were segmented using a statistics-based approach and the smoothed voxel representations were discretized into high-resolution tetrahedral finite element (FE) meshes. To estimate the complex left atrial myofiber architecture, individual fiber fields were generated according to morphological data on the endo- and epicardial surfaces based on local solutions of Laplace’s equation and transmurally interpolated to tetrahedral elements. The influence of variable transmural microstructures was quantified through EP simulations on 3 patients using 5 different fiber interpolation functions. Personalized geometrical models included the heterogeneous thickness distribution of the left atrial myocardium and subsequent discretization led to high-fidelity tetrahedral FE meshes. The novel algorithm for automated incorporation of the left atrial fiber architecture provided a realistic estimate of the atrial microstructure and was able to qualitatively capture all important fiber bundles. Consistent maximum local activation times were predicted in EP simulations using individual transmural fiber interpolation functions for each patient suggesting a negligible effect of the transmural myofiber architecture on EP. The established modeling pipeline provides a robust framework for the rapid development of personalized model cohorts accounting for detailed anatomy and microstructure and facilitates simulations of atrial EP.

Factors affecting basket catheter detection of real and phantom rotors in the atria: A computational study

Anatomically based procedures to ablate atrial fibrillation (AF) are often successful in terminating paroxysmal AF. However, the ability to terminate persistent AF remains disappointing. New mechanistic approaches use multiple-electrode basket catheter mapping to localize and target AF drivers in the form of rotors but significant concerns remain about their accuracy. We aimed to evaluate how electrode-endocardium distance, far-field sources and inter-electrode distance affect the accuracy of localizing rotors. Sustained rotor activation of the atria was simulated numerically and mapped using a virtual basket catheter with varying electrode densities placed at different positions within the atrial cavity. Unipolar electrograms were calculated on the entire endocardial surface and at each of the electrodes. Rotors were tracked on the interpolated basket phase maps and compared with the respective atrial voltage and endocardial phase maps, which served as references. Rotor detection by the basket maps varied between 35-94% of the simulation time, depending on the basket's position and the electrode-to-endocardial wall distance. However, two different types of phantom rotors appeared also on the basket maps. The first type was due to the far-field sources and the second type was due to interpolation between the electrodes; increasing electrode density decreased the incidence of the second but not the first type of phantom rotors. In the simulations study, basket catheter-based phase mapping detected rotors even when the basket was not in full contact with the endocardial wall, but always generated a number of phantom rotors in the presence of only a single real rotor, which would be the desired ablation target. Phantom rotors may mislead and contribute to failure in AF ablation procedures.

Solving Inaccuracies in Anatomical Models for Electrocardiographic Inverse Problem Resolution by Maximizing Reconstruction Quality

Electrocardiographic Imaging has become an increasingly used technique for non-invasive diagnosis of cardiac arrhythmias, although the need for medical imaging technology to determine the anatomy hinders its introduction in the clinical practice. This paper explores the ability of a new metric based on the inverse reconstruction quality for the location and orientation of the atrial surface inside the torso. Body surface electrical signals from 31 realistic mathematical models and four AF patients were used to estimate the optimal position of the atria inside the torso. The curvature of the L-curve from the Tikhonov method, which was found to be related to the inverse reconstruction quality, was measured after application of deviations in atrial position and orientation. Independent deviations in the atrial position were solved by finding the maximal L-curve curvature with an error of 1.7 ± 2.4 mm in mathematical models and 9.1 ± 11.5 mm in patients. For the case of independent angular deviations, the error in location by using the L-curve was 5.8±7.1° in mathematical models and 12.4° ± 13.2° in patients. The ability of the L-curve curvature was tested also under superimposed uncertainties in the three axis of translation and in the three axis of rotation, and the error in location was of 2.3 ± 3.2 mm and 6.4° ± 7.1° in mathematical models, and 7.9±10.7 mm and 12.1°±15.5° in patients. The curvature of L-curve is a useful marker for the atrial position and would allow emending the inaccuracies in its location.

Technical Considerations on Phase Mapping for Identification of Atrial Reentrant Activity in Direct- and Inverse-Computed Electrograms

BACKGROUND

Phase mapping has become a broadly used technique to identify atrial reentrant circuits for ablative therapy guidance. This work studies the phase mapping process and how the signal nature and its filtering affect the reentrant pattern characterization in electrogram (EGM), body surface potential mapping, and electrocardiographic imaging signals.

METHODS AND RESULTS

EGM, body surface potential mapping, and electrocardiographic imaging phase maps were obtained from 17 simulations of atrial fibrillation, atrial flutter, and focal atrial tachycardia. Reentrant activity was identified by singularity point recognition in raw signals and in signals after narrow band-pass filtering at the highest dominant frequency (HDF). Reentrant activity was dominantly present in the EGM recordings only for atrial fibrillation and some atrial flutter propagations patterns, and HDF filtering allowed increasing the reentrant activity detection from 60% to 70% of time in atrial fibrillation in unipolar recordings and from 0% to 62% in bipolar. In body surface potential mapping maps, HDF filtering increased from 10% to 90% the sensitivity, although provoked a residual false reentrant activity ≈30% of time. In electrocardiographic imaging, HDF filtering allowed to increase ≤100% the time with detected rotors, although provoked the apparition of false rotors during 100% of time. Nevertheless, raw electrocardiographic imaging phase maps presented reentrant activity just in atrial fibrillation recordings accounting for ≈80% of time.

CONCLUSIONS

Rotor identification is accurate and sensitive and does not require additional signal processing in measured or noninvasively computed unipolar EGMs. Bipolar EGMs and body surface potential mapping do require HDF filtering to detect rotors at the expense of a decreased specificity.

Three-dimensional Integrated Functional, Structural, and Computational Mapping to Define the Structural "Fingerprints" of Heart-Specific Atrial Fibrillation Drivers in Human Heart Ex Vivo

BACKGROUND

Structural remodeling of human atria plays a key role in sustaining atrial fibrillation (AF), but insufficient quantitative analysis of human atrial structure impedes the treatment of AF. We aimed to develop a novel 3-dimensional (3D) structural and computational simulation analysis tool that could reveal the structural contributors to human reentrant AF drivers.

METHODS AND RESULTS

High-resolution panoramic epicardial optical mapping of the coronary-perfused explanted intact human atria (63-year-old woman, chronic hypertension, heart weight 608 g) was conducted during sinus rhythm and sustained AF maintained by spatially stable reentrant AF drivers in the left and right atrium. The whole atria (107×61×85 mm³) were then imaged with contrast-enhancement MRI (9.4 T, 180×180×360-μm³ resolution). The entire 3D human atria were analyzed for wall thickness (0.4-11.7 mm), myofiber orientations, and transmural fibrosis (36.9% subendocardium; 14.2% midwall; 3.4% subepicardium). The 3D computational analysis revealed that a specific combination of wall thickness and fibrosis ranges were primarily present in the optically defined AF driver regions versus nondriver tissue. Finally, a 3D human heart-specific atrial computer model was developed by integrating 3D structural and functional mapping data to test AF induction, maintenance, and ablation strategies. This 3D model reproduced the optically defined reentrant AF drivers, which were uninducible when fibrosis and myofiber anisotropy were removed from the model.

CONCLUSIONS

Our novel 3D computational high-resolution framework may be used to quantitatively analyze structural substrates, such as wall thickness, myofiber orientation, and fibrosis, underlying localized AF drivers, and aid the development of new patient-specific treatments.

Non-invasive localization of atrial ectopic beats by using simulated body surface P-wave integral maps

Non-invasive localization of continuous atrial ectopic beats remains a cornerstone for the treatment of atrial arrhythmias. The lack of accurate tools to guide electrophysiologists leads to an increase in the recurrence rate of ablation procedures. Existing approaches are based on the analysis of the P-waves main characteristics and the forward body surface potential maps (BSPMs) or on the inverse estimation of the electric activity of the heart from those BSPMs. These methods have not provided an efficient and systematic tool to localize ectopic triggers. In this work, we propose the use of machine learning techniques to spatially cluster and classify ectopic atrial foci into clearly differentiated atrial regions by using the body surface P-wave integral map (BSPiM) as a biomarker. Our simulated results show that ectopic foci with similar BSPiM naturally cluster into differentiated non-intersected atrial regions and that new patterns could be correctly classified with an accuracy of 97% when considering 2 clusters and 96% for 4 clusters. Our results also suggest that an increase in the number of clusters is feasible at the cost of decreasing accuracy.

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

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

Myocyte-fibroblast communication in cardiac fibrosis and arrhythmias: Mechanisms and model systems

Development of cardiac fibrosis and arrhythmias is controlled by the activity of and communication between cardiomyocytes and fibroblasts in the heart. Myocyte-fibroblast interactions occur via both direct and indirect means including paracrine mediators, extracellular matrix interactions, electrical modulators, mechanical junctions, and membrane nanotubes. In the diseased heart, cardiomyocyte and fibroblast ratios and activity, and thus myocyte-fibroblast interactions, change and are thought to contribute to the course of disease including development of fibrosis and arrhythmogenic activity. Fibroblasts have a developing role in modulating cardiomyocyte electrical and hypertrophic activity, however gaps in knowledge regarding these interactions still exist. Research in this field has necessitated the development of unique approaches to isolate and control myocyte-fibroblast interactions. Numerous methods for 2D and 3D co-culture systems have been developed, while a growing part of this field is in the use of better tools for in vivo systems including cardiomyocyte and fibroblast specific Cre mouse lines for cell type specific genetic ablation. This review will focus on (i) mechanisms of myocyte-fibroblast communication and their effects on disease features such as cardiac fibrosis and arrhythmias as well as (ii) methods being used and currently developed in this field.

ASSESSMENT OF PARAMETER UNCERTAINTY IN RIGID MUSCULOSKELETAL SIMULATION USING A PROBABILISTIC APPROACH

Experimental investigation coupled with numerical simulations is commonly used for solving multi-physical problems. In the field of biomechanics, in which the aim is to understand the mechanics of living system, the main difficulties are to provide experimental data reflecting the multi-physical behavior of the system of interest. These experimental data are used as input data for numerical simulations to quantify output responses through physical and/or biological laws expressed by constitutive mathematical equations. However, uncertainties on the experimentally available data exist from factors such as human variability and differences in protocols parameters and techniques. Thus, the true values of these data could never be experimentally measured. The objective of this study was to develop a modeling workflow to assess and account for the parameter uncertainty in rigid musculoskeletal simulation. A generic musculoskeletal model was used. Data uncertainties of the right thigh mass, physiological cross-sectional area (pCSA) and muscle tension coefficient of the rectus femoris were accounted to estimate their effect on the joint moment and muscle force computing, respectively. A guideline was developed to fuse data from multiple sources into a sample variation space leading to establish input data distribution. Uncertainty propagation was performed using Monte Carlo and most probable point methods. A high degree of sensitivity of 0.98 was noted for the effect of thigh mass uncertainty on the hip joint moment using inverse dynamics method. A strong deviation of rectus femoris muscle force (around 260 N) was found under effect of pCSA and muscle tension coefficient on the force estimation using static optimization method. Accounting parameter uncertainty into rigid musculoskeletal simulation plays an essential role in the evaluation of the confidence in the model outputs. Thus, simulation outcome may be computed and represented in a more reliable manner with a global range of plausible values.

Lessons from computer simulations of ablation of atrial fibrillation

This paper reviews the simulations of catheter ablation in computer models of the atria, from the first attempts to the most recent anatomical models. It describes how postulated substrates of atrial fibrillation can be incorporated into mathematical models, how modelling studies can be designed to test ablation strategies, what their current trade-offs and limitations are, and what clinically relevant lessons can be learnt from these simulations. Drawing a parallel between clinical and modelling studies, six ablation targets are considered: pulmonary vein isolation, linear ablation, ectopic foci, complex fractionated atrial electrogram, rotors and ganglionated plexi. The examples presented for each ablation target illustrate a major advantage of computer models, the ability to identify why a therapy is successful or not in a given atrial fibrillation substrate. The integration of pathophysiological data to create detailed models of arrhythmogenic substrates is expected to solidify the understanding of ablation mechanisms and to provide theoretical arguments supporting substrate-specific ablation strategies.

Identification of Dominant Excitation Patterns and Sources of Atrial Fibrillation by Causality Analysis

Burden of atrial fibrillation (AF) can be reduced by ablation of sources of electrical impulses driving AF but driver identification is still challenging. This study presents a new methodology based on causality analysis that allows identifying the hierarchically dominant areas driving AF. Identification of dominant propagation patterns was achieved by computing causal relations between intracardiac multi-electrode catheter recordings of four paroxysmal AF patients during sinus rhythm, pacing and AF. In addition, realistic mathematical models of the atria during AF were used to validate the methodology both in the presence and absence of dominant frequency (DF) gradients. During electrical pacing, sources of propagation patterns detected by causality analysis were consistent with the location of the stimulating catheter. During AF, propagation patterns presented temporal variability, but a dominant direction accounted for significantly more propagations than other directions (49 ± 15% vs. 14 ± 13% or less, p < 0.01). Both in patients with a DF gradient and in mathematical models, causal maps allowed the identification of sites responsible for maintenance of AF. Causal maps allowed the identification of atrial dominant sites. In particular, causality analysis resulted in stable dominant cause-effect propagation directions during AF and could serve as a guide for performing ablation procedures in AF patients.

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

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

How computer simulations of the human heart can improve anti-arrhythmia therapy

Over the last decade, the state-of-the-art in cardiac computational modelling has progressed rapidly. The electrophysiological function of the heart can now be simulated with a high degree of detail and accuracy, opening the doors for simulation-guided approaches to anti-arrhythmic drug development and patient-specific therapeutic interventions. In this review, we outline the basic methodology for cardiac modelling, which has been developed and validated over decades of research. In addition, we present several recent examples of how computational models of the human heart have been used to address current clinical problems in cardiac electrophysiology. We will explore the use of simulations to improve anti-arrhythmic pacing and defibrillation interventions; to predict optimal sites for clinical ablation procedures; and to aid in the understanding and selection of arrhythmia risk markers. Together, these studies illustrate how the tremendous advances in cardiac modelling are poised to revolutionize medical treatment and prevention of arrhythmia.

Parameter Estimation of Ion Current Formulations Requires Hybrid Optimization Approach to Be Both Accurate and Reliable

Computational models of cardiac electrophysiology provided insights into arrhythmogenesis and paved the way toward tailored therapies in the last years. To fully leverage in silico models in future research, these models need to be adapted to reflect pathologies, genetic alterations, or pharmacological effects, however. A common approach is to leave the structure of established models unaltered and estimate the values of a set of parameters. Today's high-throughput patch clamp data acquisition methods require robust, unsupervised algorithms that estimate parameters both accurately and reliably. In this work, two classes of optimization approaches are evaluated: gradient-based trust-region-reflective and derivative-free particle swarm algorithms. Using synthetic input data and different ion current formulations from the Courtemanche et al. electrophysiological model of human atrial myocytes, we show that neither of the two schemes alone succeeds to meet all requirements. Sequential combination of the two algorithms did improve the performance to some extent but not satisfactorily. Thus, we propose a novel hybrid approach coupling the two algorithms in each iteration. This hybrid approach yielded very accurate estimates with minimal dependency on the initial guess using synthetic input data for which a ground truth parameter set exists. When applied to measured data, the hybrid approach yielded the best fit, again with minimal variation. Using the proposed algorithm, a single run is sufficient to estimate the parameters. The degree of superiority over the other investigated algorithms in terms of accuracy and robustness depended on the type of current. In contrast to the non-hybrid approaches, the proposed method proved to be optimal for data of arbitrary signal to noise ratio. The hybrid algorithm proposed in this work provides an important tool to integrate experimental data into computational models both accurately and robustly allowing to assess the often non-intuitive consequences of ion channel-level changes on higher levels of integration.

Computational models of atrial cellular electrophysiology and calcium handling, and their role in atrial fibrillation

The complexity of the heart makes an intuitive understanding of the relative contribution of ion channels, transporters and signalling pathways to cardiac electrophysiology challenging. Computational modelling of cardiac cellular electrophysiology has proven useful to integrate experimental findings, extrapolate results obtained in expression systems or animal models to other systems, test quantitatively ideas based on experimental data and provide novel hypotheses that are experimentally testable. While the bulk of computational modelling has traditionally been directed towards ventricular bioelectricity, increasing recognition of the clinical importance of atrial arrhythmias, particularly atrial fibrillation, has led to widespread efforts to apply computational approaches to understanding atrial electrical function. The increasing availability of detailed, atrial-specific experimental data has stimulated the development of novel computational models of atrial-cellular electrophysiology and Ca(2+) handling. To date, more than 300 studies have employed mathematical simulations to enhance our understanding of atrial electrophysiology, arrhythmogenesis and therapeutic responses. Future modelling studies are likely to move beyond current whole-cell models by incorporating new data on subcellular architecture, macromolecular protein complexes, and localized ion-channel regulation by signalling pathways. At the same time, more integrative multicellular models that take into account regional electrophysiological and Ca(2+) handling properties, mechano-electrical feedback and/or autonomic regulation will be needed to investigate the mechanisms governing atrial arrhythmias. A combined experimental and computational approach is expected to provide the more comprehensive understanding of atrial arrhythmogenesis that is required to develop improved diagnostic and therapeutic options. Here, we review this rapidly expanding area, with a particular focus on Ca(2+) handling, and provide ideas about potential future directions.

Detailed Anatomical and Electrophysiological Models of Human Atria and Torso for the Simulation of Atrial Activation

Atrial arrhythmias, and specifically atrial fibrillation (AF), induce rapid and irregular activation patterns that appear on the torso surface as abnormal P-waves in electrocardiograms and body surface potential maps (BSPM). In recent years both P-waves and the BSPM have been used to identify the mechanisms underlying AF, such as localizing ectopic foci or high-frequency rotors. However, the relationship between the activation of the different areas of the atria and the characteristics of the BSPM and P-wave signals are still far from being completely understood. In this work we developed a multi-scale framework, which combines a highly-detailed 3D atrial model and a torso model to study the relationship between atrial activation and surface signals in sinus rhythm. Using this multi scale model, it was revealed that the best places for recording P-waves are the frontal upper right and the frontal and rear left quadrants of the torso. Our results also suggest that only nine regions (of the twenty-one structures in which the atrial surface was divided) make a significant contribution to the BSPM and determine the main P-wave characteristics.