Multipatch Isogeometric Analysis for electrophysiology: Simulation in a human heart

Bucelli, Michele; Salvador, Matteo; Dedè, Luca; Quarteroni, Alfio

doi:10.1016/j.cma.2021.113666

Cited by 34 publications

(16 citation statements)

References 59 publications

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“…We use either Q 1 or Q 2 Finite Elements for electrophysiology, and Q 1 for both activation and mechanics. We show one simulation with Q 2 Finite Elements for electrophysiology to underline that our mathematical discretization can be extended to high order methods, which are known to be more suitable than standard FEM for wave propagation problems [10,40]. We observe that the activation map resulting from Q 2 elements has slightly more pronounced anisotropy of the isochrones.…”

Section: Mesh Convergencementioning

confidence: 86%

“…This can be considered as a first step towards possible investigation of high-order methods in our cardiac electromechanics computational framework. Indeed, wave propagation problems, such as the one arising in cardiac electrophysiology, can be more suitably represented using high-order basis functions than classical FEM [10,40].…”

Section: Discussionmentioning

confidence: 99%

“…Indeed, we see that Mesh2 with h mean ≈ 0.75 mm for electrophysiology and h mean ≈ 3 mm for activation and mechanics already provides a good convergence of both mechanical and fluid dynamics relevant properties for the left ventricle. Under the assumption of properly distributed mesh elements, the number of DOFs itself can potentially be an indicator to evaluate the accuracy of the discretization for cardiac simulations, unifying approximations coming from different mesh elements (e.g., tetrahedra, hexaedra and prisms) and different techniques, such as Finite Element Method, Spectral Element Method or Isogeometric Analysis [10,40,42].…”

Section: Mesh Convergencementioning

confidence: 99%

See 2 more Smart Citations

A cardiac electromechanical model coupled with a lumped-parameter model for closed-loop blood circulation

Regazzoni

Salvador

Africa

et al. 2022

Journal of Computational Physics

135

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Section: Mesh Convergencementioning

confidence: 86%

Section: Discussionmentioning

confidence: 99%

Section: Mesh Convergencementioning

confidence: 99%

See 1 more Smart Citation

A cardiac electromechanical model coupled with a lumped-parameter model for closed-loop blood circulation

Regazzoni

Salvador

Africa

et al. 2022

Journal of Computational Physics

135

View full text Add to dashboard Cite

“…This choice is motivated by the suitability of high order polynomials, with high order global continuity, to control and limit numerical dispersions and, thus, to accurately capture wavefronts (Dedè et al, 2015 ; Pegolotti et al, 2019 ) and the smoothness in the representation of the computational domain (Cottrell et al, 2009 ). These relevant features have been exploited to address cardiac EP problems in Patelli et al ( 2017 ), Pegolotti et al ( 2019 ), and Bucelli et al ( 2021 ). It is also worthy to highlight that, so far, only few works provide a combination of IGA-based FOMs and reduced order modeling techniques.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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“…In ABAQUS [19][20][21], an application of IGA was implemented for linear elasticity problems. IGA has been employed in a variety of engineering fields, including the mechanics of vibration [22,23], fluid mechanics [24], electromagnetic problems [25], the medical field [26], and digital image correlation [27]. The issues addressed are diverse, including nonlinear mechanics [28], shell analysis [29][30][31][32][33][34], contact problems [35,36], fluidstructure interactions [24], the optimization of structural design [37], buckling failure [38], and crack problem analysis [39].…”

Section: Introductionmentioning

confidence: 99%

Fracture Modelling of a Cracked Pressurized Cylindrical Structure by Using Extended Iso-Geometric Analysis (X-IGA)

et al. 2021

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In this study, a NURBS basis function-based extended iso-geometric analysis (X-IGA) has been implemented to simulate a two-dimensional crack in a pipe under uniform pressure using MATLAB code. Heaviside jump and asymptotic crack-tip enrichment functions are used to model the crack’s behaviour. The accuracy of this investigation was ensured with the stress intensity factors (SIFs) and the J-integral. The X-IGA—based SIFs of a 2-D pipe are compared using MATLAB code with the conventional finite element method available in ABAQUS FEA, and the extended finite element method is compared with a user-defined element. Therefore, the results demonstrate the possibility of using this technique as an alternative to other existing approaches to modeling cracked pipelines.

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Multipatch Isogeometric Analysis for electrophysiology: Simulation in a human heart

Cited by 34 publications

References 59 publications

A cardiac electromechanical model coupled with a lumped-parameter model for closed-loop blood circulation

A cardiac electromechanical model coupled with a lumped-parameter model for closed-loop blood circulation

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

Fracture Modelling of a Cracked Pressurized Cylindrical Structure by Using Extended Iso-Geometric Analysis (X-IGA)

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