A coupled 3D–1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network

Vergara, Christian; Lange, Matthias; Palamara, Simone; Lassila, Toni; Frangi, Alejandro F.; Quarteroni, Alfio

doi:10.1016/j.jcp.2015.12.016

Cited by 33 publications

(45 citation statements)

References 39 publications

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“…Currently, the feasible model for in silico studies is the eikonal model of activation time. However, our model of the PN can also be coupled with monodomain or bidomain approach for the MC …”

Section: Resultsmentioning

confidence: 99%

Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Lange

Palamara

Lassila

et al. 2016

Numer Methods Biomed Eng

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SUMMARYCardiac Purkinje fibres provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in-silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is based on operator splitting and is provided with three different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations in order to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all three implementations produce equivalent convergence rates, which shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all three implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure-GPU implementations outperform the pure-CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used.

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Section: Resultsmentioning

confidence: 99%

Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Lange

Palamara

Lassila

et al. 2016

Numer Methods Biomed Eng

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“…[213,263]). We also mention the models including fractional diffusion and other nonlinear extensions to (3.2) introduced in [205,37,124].…”

Section: Electrophysiology Of the Heartmentioning

confidence: 99%

“…As reported in several studies [39], the ratio in the conductivity coefficients is about 4:2:1 in the fiber:sheet:normal directions, respectively. Ventricular activation is initiated effectively from a series of point sources (Purkinje-muscle junctions in the sub-endocardium [263]) and will locally resemble an ellipsoidal front with axes equal to the directions of anisotropy until it reaches the other point source wavefronts to form the main propagation front (moving apex-to-base and endo-to-epi in direction of the fibers). Therefore, in physiological conditions the activation pattern can travel in all possible directions, not simply the mean fiber direction, and will experience varying velocities of propagation between the upper and lower bounds given by the longitudinal and transversal conduction velocities.…”

Section: Electrophysiology -Numerical Effects Of Front Propagation Vementioning

confidence: 99%

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

Quarteroni

Lassila

Rossi

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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211

205

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“…To model the potential propagation through the Purkinje network, we follow the approach proposed in Vigmond and Clements, which is briefly discussed in this section. For further details, see also Vergara et al and Lange et al…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…More specifically, the coupling is performed through the exchange of the currents φ j , j = 1, …, N , computed at the PMJ. From the myocardium perspective, PMJ currents φ j are prescribed as external currents with support in spheres of radius r centered at the PMJ . From the Purkinje network side, the PMJ currents φ j are imposed as Neumann boundary conditions; see Equation 15d.…”

Section: Mathematical Modelsmentioning

confidence: 99%

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

Landajuela

Vergara

Gerbi

et al. 2018

Numer Methods Biomed Eng

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In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed-point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium-Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases.

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A coupled 3D–1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network

Cited by 33 publications

References 39 publications

Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

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