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An unfitted radial basis function generated finite difference method applied to thoracic diaphragm simulations

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Métodos Numéricos y Aplicacioneses
dc.contributor.authorTominec, Igor
dc.contributor.authorVillard, Pierre-Frédéric
dc.contributor.authorLarsson, Elisabeth
dc.contributor.authorBayona Revilla, Víctor
dc.contributor.authorCacciani, Nicola
dc.date.accessioned2023-02-10T14:32:04Z
dc.date.available2023-02-10T14:32:04Z
dc.date.issued2022-11-15
dc.description.abstractThe thoracic diaphragm is the muscle that drives the respiratory cycle of a human being. Using a system of partial differential equations (PDEs) that models linear elasticity we compute displacements and stresses in a two-dimensional cross section of the diaphragm in its contracted state. The boundary data consists of a mix of displacement and traction conditions. If these are imposed as they are, and the conditions are not compatible, this leads to reduced smoothness of the solution. Therefore, the boundary data is first smoothed using the least-squares radial basis function generated finite difference (RBF-FD) framework. Then the boundary conditions are reformulated as a Robin boundary condition with smooth coefficients. The same framework is also used to approximate the boundary curve of the diaphragm cross section based on data obtained from a slice of a computed tomography (CT) scan. To solve the PDE we employ the unfitted least-squares RBF-FD method. This makes it easier to handle the geometry of the diaphragm, which is thin and non-convex. We show numerically that our solution converges with high-order towards a finite element solution evaluated on a fine grid. Through this simplified numerical model we also gain an insight into the challenges associated with the diaphragm geometry and the boundary conditions before approaching a more complex three-dimensional model.en
dc.description.sponsorshipThe INVIVE project is funded by the Swedish Research Council, grant number 2016-04849.en
dc.format.extent17
dc.identifier.bibliographicCitationTominec, I., Villard, P. F., Larsson, E., Bayona, V. & Cacciani, N. (2022). An unfitted radial basis function generated finite difference method applied to thoracic diaphragm simulations. Journal of Computational Physics, 469, 111496.en
dc.identifier.doihttps://doi.org/10.1016/j.jcp.2022.111496
dc.identifier.issn0021-9991
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue111496
dc.identifier.publicationlastpage17
dc.identifier.publicationtitleJournal of Computational Physicsen
dc.identifier.publicationvolume469
dc.identifier.urihttps://hdl.handle.net/10016/36538
dc.identifier.uxxiAR/0000031147
dc.language.isoeng
dc.publisherElsevieren
dc.rights© 2022 The Author(s).en
dc.rightsAtribución 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subject.ecienciaBiología y Biomedicinaes
dc.subject.ecienciaMatemáticases
dc.subject.otherUnfitteden
dc.subject.otherRBF-FDen
dc.subject.otherLeast-squaresen
dc.subject.otherElasticityen
dc.subject.otherDiaphragmen
dc.subject.otherMixed boundary conditionen
dc.titleAn unfitted radial basis function generated finite difference method applied to thoracic diaphragm simulationsen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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