Patelli, A.S., Dedè, L., Lassila, T. orcid.org/0000-0001-8947-1447 et al. (2 more authors) (2017) Isogeometric approximation of cardiac electrophysiology models on surfaces: An accuracy study with application to the human left atrium. Computer Methods in Applied Mechanics and Engineering, 317. pp. 248-273. ISSN 0045-7825
Abstract
We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison between basis functions of degree p ≥ 1 and globally C k -continuous, with k = 0 or p − 1, to find the most accurate approximation of a propagating front with the minimal number of degrees of freedom. We show that B-spline basis functions of degree p ≥ 1, which are C p−1 -continuous capture accurately the front velocity of the transmembrane potential even with moderately refined meshes; similarly, we show that, for accurate tracking of curved fronts, high-order continuous B-spline basis functions should be used. Finally, we apply Isogeometric Analysis to an idealized human left atrial geometry described by NURBS with physiologically sound fiber directions and anisotropic conductivity tensor to demonstrate that the numerical scheme retains its favorable approximation properties also in a more realistic setting.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Elsevier. This is an author produced version of a paper subsequently published in Computer Methods in Applied Mechanics and Engineering. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Isogeometric Analysis; cardiac electrophysiology; surface PDEs; high-order approximation |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Electronic and Electrical Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 Dec 2016 12:09 |
Last Modified: | 30 Jun 2023 16:24 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.cma.2016.12.022 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109488 |