Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

Hurtado, Daniel E.; Rojas, Guillermo

doi:10.1007/s00466-017-1473-5

Cited by 19 publications

(19 citation statements)

References 27 publications

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“…From the computational point of view, a deeper investigation of the CV in the circumferential direction using a more realistic gastric geometry should be accomplished, considering also the presence of the fundus, which is electrically quiescent but responsible for other, specific mechanical effects, namely the storage function of the stomach. Also, more efficient numerical schemes and GPU‐based codes are foreseen to speed‐up the wide numerical analyses necessary to fully characterize a complex organ like the stomach.…”

Section: Resultsmentioning

confidence: 99%

Computational model of gastric motility with active‐strain electromechanics

et al. 2018

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We present an electro-mechanical constitutive framework for the modeling of gastric motility, including pacemaker electrophysiology and smooth muscle contractility. In this framework, we adopt a phenomenological description of the gastric tissue. Tissue electrophysiology is represented by a set of two minimal two-variable models and tissue electromechanics by an active-strain finite elasticity approach. We numerically investigate the implication of the spatial distribution of pacemaker cells on the entrainment and synchronization of the slow waves characterizing gastric motility in health and disease. On simple schematic model geometries, we demonstrate that the proposed computational framework is amenable to large scale in-silico analyses of the complex gastric motility including the underlying electro-mechanical coupling. K E Y W O R D Sactive-strain electro-mechanics, electrophysiology, finite elasticity, gastric motility Abbreviations: ICC, interstitial cell of Cajal; ICC-MY, myenteric interstitial cell of Cajal; SMC, smooth muscle cell; VDCC, voltage-dependent calcium channel; cpm, cycles per minute This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Resultsmentioning

confidence: 99%

Computational model of gastric motility with active‐strain electromechanics

et al. 2018

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“…An interesting finding of this work is that the mesh dependence found in continuum models is accentuated for cellular models and that the consideration of voltage sensitivity in the conduction model does not strongly affect the relation between CV and mesh size (Fig 8). Future developments of numerical methods for the NOHM may include the consideration of enhanced spatial interpolation and temporal integration schemes [40,41] which have shown to attenuate the mesh dependence of continuum model of cardiac propagation, allowing for the efficient simulation of larger domains.…”

Section: Discussionmentioning

confidence: 99%

Non-ohmic tissue conduction in cardiac electrophysiology: Upscaling the non-linear voltage-dependent conductance of gap junctions

2020

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Gap junctions are key mediators of intercellular communication in cardiac tissue, and their function is vital to sustaining normal cardiac electrical activity. Conduction through gap junctions strongly depends on the hemichannel arrangement and transjunctional voltage, rendering the intercellular conductance highly non-Ohmic, particularly under steady-state regimes of conduction. Despite this marked non-linear behavior, current tissue-level models of cardiac conduction are rooted in the assumption that gap-junctions conductance is constant (Ohmic), which results in inaccurate predictions of electrical propagation, particularly in the low junctional-coupling regime observed under pathological conditions. In this work, we present a novel non-Ohmic homogenization model (NOHM) of cardiac conduction that is suitable to tissue-scale simulations. Using non-linear homogenization theory, we develop a conductivity model that seamlessly upscales the voltage-dependent conductance of gap junctions, without the need of explicitly modeling gap junctions. The NOHM model allows for the simulation of electrical propagation in tissue-level cardiac domains that accurately resemble that of cell-based microscopic models for a wide range of junctional coupling scenarios, recovering key conduction features at a fraction of the computational complexity. A unique feature of the NOHM model is the possibility of upscaling the response of non-symmetric gap-junction conductance distributions, which result in conduction velocities that strongly depend on the direction of propagation, thus allowing to model the normal and retrograde conduction observed in certain regions of the heart. We envision that the NOHM model will enable organ-level simulations that are informed by sub-and inter-cellular mechanisms, delivering an accurate and predictive in-silico tool for understanding the heart function. Codes are available for download at https://github.com/dehurtado/ NonOhmicConduction.

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“…In this work, we consider a non-conforming spatial-discretization scheme for the monodomain equations (Hurtado and Rojas, 2018 ). To this end, we rewrite the residuals as…”

Section: Methodsmentioning

confidence: 99%

“…It should be noted, however, that higher-order FE schemes based on Lagrange basis functions necessarily increase the total number of DOFs in simulations when compared to linear-element formulations, as well as they require an additional computational effort for quadrature procedures, as higher-order basis functions demand the use of more quadrature-point evaluations (Cantwell et al, 2014 ). Recently, Hurtado and Rojas ( 2018 ) introduced a non-conforming finite-element scheme (NCFES) for the spatial discretization of the monodomain equation of cardiac electrophysiology that allows for the use of coarse meshes without significant loss of accuracy measured in terms of CV and wavefront shape. More specifically, hexahedral trilinear elements (Q1) were enhanced with non-conforming basis functions of degree 2 to create a non-conforming element (Q1NC) that is capable of representing a second-order polynomial within the element domain, a concept widely employed in the context of solid mechanics FE simulations (Wilson et al, 1973 ; Taylor et al, 1976 ).…”

Section: Introductionmentioning

confidence: 99%

“…During the development of the NCFES for cardiac electrophysiology, a fully-implicit (FI) backward-Euler time-stepping method was considered (Hurtado and Rojas, 2018 ). While FI schemes have important advantages in delivering a larger time-step stability region in cardiac simulations (Ying et al, 2008 ; Hurtado and Henao, 2014 ), they require the solution of a large system of non-linear equations at each time step that can be very costly in computational terms, and may not be well-suited to parallel-computing platforms when compared to other numerical schemes.…”

Section: Introductionmentioning

confidence: 99%

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Semi-implicit Non-conforming Finite-Element Schemes for Cardiac Electrophysiology: A Framework for Mesh-Coarsening Heart Simulations

Jilberto

Hurtado

2018

Front. Physiol.

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The field of computational cardiology has steadily progressed toward reliable and accurate simulations of the heart, showing great potential in clinical applications such as the optimization of cardiac interventions and the study of pro-arrhythmic effects of drugs in humans, among others. However, the computational effort demanded by in-silico studies of the heart remains challenging, highlighting the need of novel numerical methods that can improve the efficiency of simulations while targeting an acceptable accuracy. In this work, we propose a semi-implicit non-conforming finite-element scheme (SINCFES) suitable for cardiac electrophysiology simulations. The accuracy and efficiency of the proposed scheme are assessed by means of numerical simulations of the electrical excitation and propagation in regular and biventricular geometries. We show that the SINCFES allows for coarse-mesh simulations that reduce the computation time when compared to fine-mesh models while delivering wavefront shapes and conduction velocities that are more accurate than those predicted by traditional finite-element formulations based on the same coarse mesh, thus improving the accuracy-efficiency trade-off of cardiac simulations.

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Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

Cited by 19 publications

References 27 publications

Computational model of gastric motility with active‐strain electromechanics

Computational model of gastric motility with active‐strain electromechanics

Non-ohmic tissue conduction in cardiac electrophysiology: Upscaling the non-linear voltage-dependent conductance of gap junctions

Semi-implicit Non-conforming Finite-Element Schemes for Cardiac Electrophysiology: A Framework for Mesh-Coarsening Heart Simulations

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