Simulation Of Cardiac Electrophysiology Research Articles

ForCEPSS—A framework for cardiac electrophysiology simulations standardization

Background and Objective:Simulation of cardiac electrophysiology (CEP) is an important research tool that is increasingly being adopted in industrial and clinical applications. Typical workflows for CEP simulation consist of a sequence of processing stages starting with building an anatomical model and then calibrating its electrophysiological properties to match observable data. While the calibration stages are common and generalizable, most CEP studies re-implement these steps in complex and highly variable workflows. This lack of standardization renders the execution of computational CEP studies in an efficient, robust, and reproducible manner a significant challenge. Here, we propose ForCEPSS as an efficient and robust, yet flexible, software framework for standardizing CEP simulation studies. Methods and Results:Key processing stages of CEP simulation studies are identified and implemented in a standardized workflow that builds on openCARP11https://opencarp.org/. Plank et al. (2021) and the Python-based carputils22https://git.opencarp.org/openCARP/carputils. framework. Stages include (i) the definition and initialization of action potential phenotypes, (ii) the tissue scale calibration of conduction properties, (iii) the functional initialization to approximate a limit cycle corresponding to the dynamic reference state according to an experimental protocol, and, (iv) the execution of the CEP study where the electrophysiological response to a perturbation of the limit cycle is probed. As an exemplar application, we employ ForCEPSS to prepare a CEP study according to the Virtual Arrhythmia Risk Prediction protocol used for investigating the arrhythmogenic risk of developing infarct-related ventricular tachycardia (VT) in ischemic cardiomyopathy patients. We demonstrate that ForCEPSS enables a fully automated execution of all stages of this complex protocol. Conclusion:ForCEPSS offers a novel comprehensive, standardized, and automated CEP simulation workflow. The high degree of automation accelerates the execution of CEP simulation studies, reduces errors, improves robustness, and makes CEP studies reproducible. Verification of simulation studies within the CEP modeling community is thus possible. As such, ForCEPSS makes an important contribution towards increasing transparency, standardization, and reproducibility of in silico CEP experiments.

A comparison of Algebraic Multigrid Bidomain solvers on hybrid CPU–GPU architectures

The numerical simulation of cardiac electrophysiology is a highly challenging problem in scientific computing. The Bidomain system is the most complete mathematical model of cardiac bioelectrical activity. It consists of an elliptic and a parabolic partial differential equation (PDE), of reaction–diffusion type, describing the spread of electrical excitation in the cardiac tissue. The two PDEs are coupled with a stiff system of ordinary differential equations (ODEs), representing ionic currents through the cardiac membrane. Developing efficient and scalable preconditioners for the linear systems arising from the discretization of such computationally challenging model is crucial in order to reduce the computational costs required by the numerical simulations of cardiac electrophysiology. In this work, focusing on the Bidomain system as a model problem, we have benchmarked two popular implementations of the Algebraic Multigrid (AMG) preconditioner embedded in the PETSc library and we have studied the performance on the calibration of specific parameters. We have conducted our analysis on modern HPC architectures, performing scalability tests on multi-core and multi-GPUs settings. The results have shown that, for our problem, although scalability is verified on CPUs, GPUs are the optimal choice, since they yield the best performance in terms of solution time.

Computational Modeling and Simulation of the Fibrotic Human Atria.

Patient-specific modeling of atrial electrical activity enables the execution of simulations that can provide mechanistic insights and provide novel solutions to vexing clinical problems. The geometry and fibrotic remodeling of the heart can be reconstructed from clinical-grade medical scans and used to inform personalized models with detail incorporated at the cell- and tissue-scale to represent changes in image-identified diseased regions. Here, we provide a rubric for the reconstruction of realistic atrial models from pre-segmented 3D renderings of the left atrium with fibrotic tissue regions delineated, which are the output from clinical-grade systems for quantifying fibrosis. We then provide a roadmap for using those models to carry out patient-specific characterization of the fibrotic substrate in terms of its potential to harbor reentrant drivers via cardiac electrophysiology simulations.

Cardiac Electrophysiology Meshfree Modeling through the Mixed Collocation Method

We present the meshfree mixed collocation method (MCM) for cardiac electrophysiology simulation. Capitalizing on the meshfree property of MCM, we introduce an immersed grid approach for automated generation of meshfree node grids from medical image data. This approach allows us to avoid the time-consuming mesh generation and processing that mesh-based methods like the finite element method (FEM) require. We employ the MCM to solve the cardiac monodomain model considering electrical propagation in 2D tissue sheets, 3D tissue slabs, and a realistic biventricular anatomy. We demonstrate that the solutions obtained by the MCM are in good agreement with the FEM, particularly when immersed grid is used. These findings confirm the suitability of the MCM for cardiac electrophysiology simulation and make the MCM a promising alternative to the FEM for cardiac electrical investigations.

Lifex-ep: a robust and efficient software for cardiac electrophysiology simulations

BackgroundSimulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations, capable of accurately replicating both normal and pathological conditions, are still in the process of achieving full maturity within the scientific community.ResultsThis work introduces texttt {life}^{text{x}}-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both normal and pathological conditions. texttt {life}^{text{x}}-ep employs the monodomain equation to model the heart’s electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, texttt {life}^{text{x}}-ep integrates the generation of myocardial fibers based on Laplace–Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within texttt {life}^{text{x}}-fiber. As an alternative, users can also choose to import myofibers from a file. This paper provides a concise overview of the mathematical models and numerical methods underlying texttt {life}^{text{x}}-ep, along with comprehensive implementation details and instructions for users. texttt {life}^{text{x}}-ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of texttt {life}^{text{x}}-ep through various idealized and realistic simulations conducted in both normal and pathological scenarios. Furthermore, the software offers a user-friendly and flexible interface, simplifying the setup of simulations using self-documenting parameter files.Conclusionstexttt {life}^{text{x}}-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface. texttt {life}^{text{x}}-ep represents a valuable tool for conducting in silico patient-specific simulations.

Branched Latent Neural Maps

We introduce Branched Latent Neural Maps (BLNMs) to learn finite dimensional input–output maps encoding complex physical processes. A BLNM is defined by a simple and compact feedforward partially-connected neural network that structurally disentangles inputs with different intrinsic roles, such as the time variable from model parameters of a differential equation, while transferring them into a generic field of interest. BLNMs leverage latent outputs to enhance the learned dynamics and break the curse of dimensionality by showing excellent in-distribution generalization properties with small training datasets and short training times on a single processor. Indeed, their in-distribution generalization error remains comparable regardless of the adopted discretization during the testing phase. Moreover, the partial connections, in place of a fully-connected structure, significantly reduce the number of tunable parameters. We show the capabilities of BLNMs in a challenging test case involving biophysically detailed electrophysiology simulations in a biventricular cardiac model of a pediatric patient with hypoplastic left heart syndrome. The model includes a 1D Purkinje network for fast conduction and a 3D heart-torso geometry. Specifically, we trained BLNMs on 150 in silico generated 12-lead electrocardiograms (ECGs) while spanning 7 model parameters, covering cell-scale, organ-level and electrical dyssynchrony. Although the 12-lead ECGs manifest very fast dynamics with sharp gradients, after automatic hyperparameter tuning the optimal BLNM, trained in less than 3 h on a single CPU, retains just 7 hidden layers and 19 neurons per layer. The resulting mean square error is on the order of 10−4 on an independent test dataset comprised of 50 additional electrophysiology simulations. In the online phase, the BLNM allows for 5000x faster real-time simulations of cardiac electrophysiology on a single core standard computer and can be employed to solve inverse problems via global optimization in a few seconds of computational time. This paper provides a novel computational tool to build reliable and efficient reduced-order models for digital twinning in engineering applications. The Julia implementation is publicly available under MIT License at https://github.com/StanfordCBCL/BLNM.jl.

Efficient, cell-based simulations of cardiac electrophysiology; The Kirchhoff Network Model (KNM)

Mathematical models based on homogenized representation of cardiac tissue have greatly improved our understanding of cardiac electrophysiology. However, these models are too coarse to investigate the dynamics at the level of the myocytes since the cells are not present in homogenized models. Recently, fine scale models have been proposed to allow for cell-level resolution of the dynamics, but these models are too computationally expensive to be used in applications like whole heart simulations of large animals. To address this issue, we propose a model that balances computational demands and physiological accuracy. The model is founded on Kirchhoff’s current law, and represents every myocyte in the tissue. This allows specific properties to be assigned to individual cardiomyocytes, and other cell types like fibroblasts can be added to the model in an accurate manner while keeping the computing efforts reasonable.

Ventricular anatomical complexity and sex differences impact predictions from electrophysiological computational models.

The aim of this work was to analyze the influence of sex hormones and anatomical details (trabeculations and false tendons) on the electrophysiology of healthy human hearts. Additionally, sex- and anatomy-dependent effects of ventricular tachycardia (VT) inducibility are presented. To this end, four anatomically normal, human, biventricular geometries (two male, two female), with identifiable trabeculations, were obtained from high-resolution, ex-vivo MRI and represented by detailed and smoothed geometrical models (with and without the trabeculations). Additionally one model was augmented by a scar. The electrophysiology finite element model (FEM) simulations were carried out, using O'Hara-Rudy human myocyte model with sex phenotypes of Yang and Clancy. A systematic comparison between detailed vs smooth anatomies, male vs female normal hearts was carried out. The heart with a myocardial infarction was subjected to a programmed stimulus protocol to identify the effects of sex and anatomical detail on ventricular tachycardia inducibility. All female hearts presented QT-interval prolongation however the prolongation interval in comparison to the male phenotypes was anatomy-dependent and was not correlated to the size of the heart. Detailed geometries showed QRS fractionation and increased T-wave magnitude in comparison to the corresponding smoothed geometries. A variety of sustained VTs were obtained in the detailed and smoothed male geometries at different pacing locations, which provide evidence of the geometry-dependent differences regarding the prediction of the locations of reentry channels. In the female phenotype, sustained VTs were induced in both detailed and smooth geometries with RV apex pacing, however no consistent reentry channels were identified. Anatomical and physiological cardiac features play an important role defining risk in cardiac disease. These are often excluded from cardiac electrophysiology simulations. The assumption that the cardiac endocardium is smooth may produce inaccurate predictions towards the location of reentry channels in in-silico tachycardia inducibility studies.

An inner-outer subcycling algorithm for parallel cardiac electrophysiology simulations.

This paper explores cardiac electrophysiological simulations of the monodomain equations and introduces a novel subcycling time integration algorithm to exploit the structure of the ionic model. The aim of this work is to improve upon the efficiency of parallel cardiac monodomain simulations by using our subcycling algorithm in the computation of the ionic model to handle the local sharp changes of the solution. This will reduce the turnaround time for the simulation of basic cardiac electrical function on both idealized and patient-specific geometry. Numerical experiments show that the proposed approach is accurate and also has close to linear parallel scalability on a computer with more than 1000 processor cores. Ultimately, the reduction in simulation time can be beneficial in clinical applications, where multiple simulations are often required to tune a model to match clinical measurements.

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

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

Personalization of biomechanical simulations of the left ventricle by in-vivo cardiac DTI data: Impact of fiber interpolation methods.

Simulations of cardiac electrophysiology and mechanics have been reported to be sensitive to the microstructural anisotropy of the myocardium. Consequently, a personalized representation of cardiac microstructure is a crucial component of accurate, personalized cardiac biomechanical models. In-vivo cardiac Diffusion Tensor Imaging (cDTI) is a non-invasive magnetic resonance imaging technique capable of probing the heart's microstructure. Being a rather novel technique, issues such as low resolution, signal-to noise ratio, and spatial coverage are currently limiting factors. We outline four interpolation techniques with varying degrees of data fidelity, different amounts of smoothing strength, and varying representation error to bridge the gap between the sparse in-vivo data and the model, requiring a 3D representation of microstructure across the myocardium. We provide a workflow to incorporate in-vivo myofiber orientation into a left ventricular model and demonstrate that personalized modelling based on fiber orientations from in-vivo cDTI data is feasible. The interpolation error is correlated with a trend in personalized parameters and simulated physiological parameters, strains, and ventricular twist. This trend in simulation results is consistent across material parameter settings and therefore corresponds to a bias introduced by the interpolation method. This study suggests that using a tensor interpolation approach to personalize microstructure with in-vivo cDTI data, reduces the fiber uncertainty and thereby the bias in the simulation results.

A meshless fragile points method for the solution of the monodomain model for cardiac electrophysiology simulation

Meshless methods for in silico modeling and simulation of cardiac electrophysiology are gaining more and more popularity. These methods do not require a mesh and are more suitable than the Finite Element Method (FEM) to simulate the activity of complex geometrical structures like the human heart. However, challenges such as numerical integration accuracy and time efficiency remain, which limit their applicability. Recently, the Fragile Points Method (FPM) has been introduced in the meshless methods family. It uses local, simple, polynomial, discontinuous functions to construct trial and test functions in the Galerkin weak form. This allows for accurate integration and improved efficiency while enabling the imposition of essential and natural boundary conditions as in FEM. In this work, we consider the application of FPM for cardiac electrophysiology simulation. We derive the cardiac monodomain model using the FPM formulation and we solve several benchmark problems in 2D and 3D. We show that FPM leads to solutions of accuracy and efficiency similar to FEM while alleviating the need for a mesh. Additionally, FPM demonstrates comparable convergence to FEM in the considered benchmarks.

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.

Refining the Eikonal Model to Reproduce the Influence of Atrial Tissue Geometry on Conduction Velocity

Abstract Atrial fibrillation is responsible for a significant and steadily rising burden. Simultaneously, the treatment options for atrial fibrillation are far from optimal. Personalized simulations of cardiac electrophysiology could assist clinicians in the risk stratification and therapy planning for atrial fibrillation. However, the use of personalized simulations in clinics is currently not possible due to either too high computational costs or non-sufficient accuracy. Eikonal simulations come with low computational costs but cannot replicate the influence of cardiac tissue geometry on the conduction velocity of the wave propagation. Consequently, they currently lack the required accuracy to be applied in clinics. Biophysically detailed simulations on the other hand are accurate but associated with too high computational costs. To tackle this issue, a regression model is created based on biophysically detailed bidomain simulation data. This regression formula calculates the conduction velocity dependent on the thickness and curvature of the heart wall. Afterwards the formula was implemented into the eikonal model with the goal to increase the accuracy of the eikonal model without losing its advantage of computational efficiency. The results of the modified eikonal simulations demonstrate that (i) the local activation times become significantly closer to those of the biophysically detailed bidomain simulations, (ii) the advantage of the eikonal model of a low sensitivity to the resolution of the mesh was reduced further, and (iii) the unrealistic occurrence of endo-epicardial dissociation in simulations was remedied. The results suggest that the accuracy of the eikonal model was significantly increased. At the same time, the additional computational costs caused by the implementation of the regression formula are neglectable. In conclusion, a successful step towards a more accurate and fast computational model of cardiac electrophysiology was achieved.

OpenEP-Py and OpenEP-GUI: An interactive platform for the visualisation and analysis of clinical and simulated cardiac electrophysiology data

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): 1) King’s Health Partnership Research & Development Challenge Fund Award (funded through Medical Research Council, UK) 2) British Heart Foundation, UK Background Electroanatomic mapping data is typically stored in proprietary formats and is difficult to access and analyse. This presents a barrier to electrophysiology research. OpenEP has been developed over the past decade to address this issue, with the first public release of the software in late 2020. OpenEP provides a standard format for storing electrophysiology data as well as an extensive suite of analysis tools. However, the current implementation of OpenEP has several limitations. Firstly, it is written in Matlab and thus not accessible to researchers without a Matlab license. Secondly, it lacks a graphical interface mandating a level of programming expertise to use. Finally, it lacks interfaces for computational modelling data, limiting its use to clinical rather than simulated data. Purpose In this work we address these limitations by developing (1) a Python-based implementation of OpenEP; (2) a graphical interface for interacting with OpenEP data and (3) interfaces for computational modelling environments. Methods Following review of the OpenEP source code, we developed use-case documentation for each OpenEP function and the proposed graphical user interface. By inspection of simulation outputs from an open-source simulation environment (openCARP) we designed new interfaces for modelling data. The implementation of OpenEP-py and OpenEP-GUI is based on the standard scientific Python stack with a PyQt front-end. Results OpenEP-Py is an open-source Python implementation for manipulation of electrophysiology data. The feature set is under active development and aims to match that of the Matlab implementation of OpenEP. In addition, OpenEP-Py can read data from cardiac electrophysiology simulations. The simulated data is stored in the standard OpenEP data structure, meaning analysis tools for clinical data can be used on the simulated data. Further, clinical data can be exported into the openCARP format, streamlining the creation of patient-specific models for simulations. Finally, because the software is open-source, OpenEP provides a transparent process for analysing data and thereby improves the reproducibility of studies. OpenEP-GUI (Figure 1) is a cross-platform desktop application for the visualisation and analysis of clinical and simulated cardiac electrophysiology data. It uses OpenEP-Py for loading, visualising, analysis and exporting electroanatomic mapping data. Multiple cases can be loaded via the System Manager, facilitating qualitative and quantitative comparison between cases. OpenEP-Py and OpenEP-GUI are licensed under the GNU-GPL v3 [WS1] and available online. Conclusions OpenEP-Py and OpenEP-GUI provide a simple yet effective way to perform cardiac electrophysiology research. The software is both open-source and under active development. We welcome feedback, feature requests, and contributions from the wider electrophysiology research community.

A Review of Healthy and Fibrotic Myocardium Microstructure Modeling and Corresponding Intracardiac Electrograms.

Computational simulations of cardiac electrophysiology provide detailed information on the depolarization phenomena at different spatial and temporal scales. With the development of new hardware and software, in silico experiments have gained more importance in cardiac electrophysiology research. For plane waves in healthy tissue, in vivo and in silico electrograms at the surface of the tissue demonstrate symmetric morphology and high peak-to-peak amplitude. Simulations provided insight into the factors that alter the morphology and amplitude of the electrograms. The situation is more complex in remodeled tissue with fibrotic infiltrations. Clinically, different changes including fractionation of the signal, extended duration and reduced amplitude have been described. In silico, numerous approaches have been proposed to represent the pathological changes on different spatial and functional scales. Different modeling approaches can reproduce distinct subsets of the clinically observed electrogram phenomena. This review provides an overview of how different modeling approaches to incorporate fibrotic and structural remodeling affect the electrogram and highlights open challenges to be addressed in future research.

Confocal microscopy-based estimation of intracellular conductivities in myocardium for modeling of the normal and infarcted heart

Ventricular arrhythmias are the leading cause of mortality in patients with ischemic heart diseases, such as myocardial infarction (MI). Computational simulation of cardiac electrophysiology provides insights into these arrhythmias and their treatment. However, only sparse information is available on crucial model parameters, for instance, the anisotropic intracellular electrical conductivities. Here, we introduced an approach to estimate these conductivities in normal and MI hearts. We processed and analyzed images from confocal microscopy of left ventricular tissue of a rabbit MI model to generate 3D reconstructions. We derived tissue features including the volume fraction of myocytes (Vmyo), gap junctions-containing voxels (Vgj), and fibrosis (Vfibrosis). We generated models of the intracellular space and intercellular coupling. Applying numerical methods for solving Poisson's equation for stationary electrical currents, we calculated normal (σmyo,n), longitudinal (σmyo,l), and transverse (σmyo,t) intracellular conductivities. Using linear regression analysis, we assessed relationships of conductivities to tissue features. Vgj and Vmyo were reduced in MI vs. control, but Vfibrosis was increased. Both σmyo,l and σmyo,n were lower in MI than in control. Differences of σmyo,t between control and MI were not significant. We found strong positive relationships of σmyo,l with Vmyo and Vgj, and a strong negative relationship with Vfibrosis. The relationships of σmyo,n with these tissue features were similar but less pronounced. Our study provides quantitative insights into the intracellular conductivities in the normal and MI heart. We suggest that our study establishes a framework for the estimation of intracellular electrical conductivities of myocardium with various pathologies.

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

In Memory of Dr. Mitsuharu Okajima, A Pioneer in Digital Simulation of Cardiac Electrophysiology

In Memory of Dr. Mitsuharu Okajima, A Pioneer in Digital Simulation of Cardiac Electrophysiology

POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.