A Finite Element Method for an Eikonal Equation Model of Myocardial Excitation Wavefront Propagation

Pullan, Andrew J.; Tomlinson, Karl A.; Hunter, Peter

doi:10.1137/s0036139901389513

Cited by 73 publications

(25 citation statements)

References 15 publications

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“…The utility of such simulations is therefore limited to applications such as the one described above where only the activation pattern is required. Other computational approaches to determine activation patterns, such as eikonal methods (Pullan et al, 2002 ), could be considered for this application. However, the monodomain solutions may be preferred especially if they are part of a coarse grain parameter optimization for subsequent fine grain simulations.…”

Section: Discussionmentioning

confidence: 99%

“…For reaction-diffusion problems, the Thiele modulus, used in chemical engineering, describes the ratio of the rate of reaction to the rate of diffusion (Thiele, 1939 ; Hill and Root, 2014 ). Analogous to the local or cell Péclet number for advection diffusion problems (Brooks and Hughes, 1982 ; Pullan et al, 2002 ; Quarteroni, 2009 ), we define the dimensionless cell Thiele modulus (ϕ c ) as the ratio of the discretization length to the characteristic length of the monodomain equation with the form:

where k is the reaction rate (normalized dV/dt max , defined as dV/dt max of the single cell ionic model divided the action potential amplitude), h is the mean element edge length, and D is the diffusivity along an eigenaxes of the conductivity tensor. A derivation of the cell Thiele modulus from the non-dimensionalization of the monodomain equation is provided in Supplementary Material.…”

Section: Methods and Modelsmentioning

confidence: 99%

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High-order finite element methods for cardiac monodomain simulations

et al. 2015

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Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.

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Section: Discussionmentioning

confidence: 99%

Section: Methods and Modelsmentioning

confidence: 99%

High-order finite element methods for cardiac monodomain simulations

et al. 2015

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“…The right-hand side of this equation represents an eigenvalue decomposition of the conductivity tensor. The principal eigenvalue n describes the conductivity in the main direction of the cell while n defines the anisotropic ratio (for human atrial cells, n is of the order of 0.4 [13]). The columns of the orthonormal matrix A n are the eigenvectors of the conductivity tensor and define the orientation of the cell in the global coordinate system.…”

Section: Compact Matrix Model For Electrograms Based On Conductivitymentioning

confidence: 99%

“…In Refs. [13,14], a quite different approach was used based on Eikonal equations to approximately model the cells' activation times, based on the apparent conductivity while ignoring all the microscopic details of the process, including per cell potentials and electrograms.…”

Section: Introductionmentioning

confidence: 99%

A compact matrix model for atrial electrograms for tissue conductivity estimation

Abdi

Hendriks

Veen

et al. 2019

Computers in Biology and Medicine

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A B S T R A C TFinding the hidden parameters of the cardiac electrophysiological model would help to gain more insight on the mechanisms underlying atrial fibrillation, and subsequently, facilitate the diagnosis and treatment of the disease in later stages. In this work, we aim to estimate tissue conductivity from recorded electrograms as an indication of tissue (mal)functioning. To do so, we first develop a simple but effective forward model to replace the computationally intensive reaction-diffusion equations governing the electrical propagation in tissue. Using the simplified model, we present a compact matrix model for electrograms based on conductivity. Subsequently, we exploit the simplicity of the compact model to solve the ill-posed inverse problem of estimating tissue conductivity. The algorithm is demonstrated on simulated data as well as on clinically recorded data. The results show that the model allows to efficiently estimate the conductivity map. In addition, based on the estimated conductivity, realistic electrograms can be regenerated demonstrating the validity of the model.

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“…The EK model is governed by the EK diffusion equation [15,36] and is solved using the fast marching method (FMM). It can be written as .…”

Section: Eikonal Modelmentioning

confidence: 99%

Coupled personalization of cardiac electrophysiology models for prediction of ischaemic ventricular tachycardia

et al. 2011

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In order to translate the important progress in cardiac electrophysiology modelling of the last decades into clinical applications, there is a requirement to make macroscopic models that can be used for the planning and performance of the clinical procedures. This requires model personalization, i.e. estimation of patient-specific model parameters and computations compatible with clinical constraints. Simplified macroscopic models can allow a rapid estimation of the tissue conductivity, but are often unreliable to predict arrhythmias. Conversely, complex biophysical models are more complete and have mechanisms of arrhythmogenesis and arrhythmia sustainibility, but are computationally expensive and their predictions at the organ scale still have to be validated. We present a coupled personalization framework that combines the power of the two kinds of models while keeping the computational complexity tractable. A simple eikonal model is used to estimate the conductivity parameters, which are then used to set the parameters of a biophysical model, the Mitchell -Schaeffer (MS) model. Additional parameters related to action potential duration restitution curves for the tissue are further estimated for the MS model. This framework is applied to a clinical dataset derived from a hybrid X-ray/magnetic resonance imaging and non-contact mapping procedure on a patient with heart failure. This personalized MS model is then used to perform an in silico simulation of a ventricular tachycardia (VT) stimulation protocol to predict the induction of VT. This proof of concept opens up possibilities of using VT induction modelling in order to both assess the risk of VT for a given patient and also to plan a potential subsequent radio-frequency ablation strategy to treat VT.

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A Finite Element Method for an Eikonal Equation Model of Myocardial Excitation Wavefront Propagation

Cited by 73 publications

References 15 publications

High-order finite element methods for cardiac monodomain simulations

High-order finite element methods for cardiac monodomain simulations

A compact matrix model for atrial electrograms for tissue conductivity estimation

Coupled personalization of cardiac electrophysiology models for prediction of ischaemic ventricular tachycardia

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