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Numerical analysis of a porous–elastic model for convection enhanced drug delivery

2022Journal article Restricted access
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dc.contributor.authorFerreira, J. A.
dc.contributor.authorPinto, L.
dc.contributor.authorSantos, R. F.
dc.date.accessioned2021-09-27T15:37:38Z
dc.date.available2021-09-27T15:37:38Z
dc.date.issued2022
dc.description.abstractConvection enhanced drug delivery (CED) is a technique used to make therapeutic agents reach, through a catheter, sites of difficult access. The name of this technique comes from the convective flow originated by a pressure gradient induced at the tip of the catheter. This flow enhances passive diffusion and allows a more efficient spread of the agents by the target site. CED is particularly useful in the treatment of diseases that affect the central nervous system, where the blood-brain barrier prevents the diffusion of most therapeutic agents from the cerebral blood vessels to the brain interstitial space. In this work we deal with the numerical analysis of a coupled system of partial differential equations that can be used to simulate CED in an elastic medium like brain tissue. The model variables are the fluid velocity, the pressure, the tissue deformation, and the agents concentration. We prove the stability of the coupled problem and from the numerical point of view we propose a fully discrete piecewise linear finite element method (FEM). The convergence analysis shows that the method has second order convergence for the pressure, displacement, and concentration. Numerical experiments illustrating the theoretical convergence rates and the behavior of the system are also given.pt_PT
dc.description.sponsorshipUIDB/00324/2020; UIDB/04621/2020pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1016/j.cam.2021.113719pt_PT
dc.identifier.issn0377-0427
dc.identifier.urihttp://hdl.handle.net/10400.1/17162
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.relationCenter for Mathematics, University of Coimbra
dc.relationCenter for Computational and Stochastic Mathematics
dc.relationCenter for Computational and Stochastic Mathematics
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectConvection enhanced drug deliverypt_PT
dc.subjectFinite difference methodpt_PT
dc.subjectFinite element methodpt_PT
dc.subjectConvergence analysispt_PT
dc.titleNumerical analysis of a porous–elastic model for convection enhanced drug deliverypt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter for Mathematics, University of Coimbra
oaire.awardTitleCenter for Computational and Stochastic Mathematics
oaire.awardTitleCenter for Computational and Stochastic Mathematics
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00324%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04621%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04621%2F2020/PT
oaire.citation.startPage113719pt_PT
oaire.citation.titleJournal of Computational and Applied Mathematicspt_PT
oaire.citation.volume399pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsrestrictedAccesspt_PT
rcaap.typearticlept_PT
relation.isProjectOfPublicationcc5c6f18-6c18-4a92-a774-29a0be2997f8
relation.isProjectOfPublication876a2628-7096-425d-9332-1393c0407c8e
relation.isProjectOfPublication8d4cc19d-12bd-471a-b0bb-dbc7c3e2e81f
relation.isProjectOfPublication.latestForDiscoverycc5c6f18-6c18-4a92-a774-29a0be2997f8

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