Theoretical study of the fibrous capsule tissue growth around a disk-shaped implant

Handle URI:
http://hdl.handle.net/10754/562278
Title:
Theoretical study of the fibrous capsule tissue growth around a disk-shaped implant
Authors:
Djellouli, Rabia; Mahserejian, Shant; Mokrane, A.; Moussaoui, Mohand; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
Abstract:
We analyze the mathematical properties of the fibrous capsule tissue concentration around a disk-shaped implant. We establish stability estimates as well as monotonicity results that illustrate the sensitivity of this growth to the biocompatibility index parameters of the implant. In addition, we prove that the growth of the tissue increases exponentially in time toward an asymptotic regime. We also study the mathematical properties of the solution of the inverse problem consisting in the determination of the values of the biocompatibility index parameters from the knowledge of some fibrous capsule tissue measurements. We prove that this model calibration problem admits a unique solution, and establish a characterization of the index parameters. Furthermore, we demonstrate analytically that such a solution is not continuous with respect to the data, and therefore the considered inverse problem is ill-posed due to the lack of the stability requirement. © 2012 Springer-Verlag.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Springer Nature
Journal:
Journal of Mathematical Biology
Issue Date:
19-Aug-2012
DOI:
10.1007/s00285-012-0566-1
PubMed ID:
22903582
Type:
Article
ISSN:
03036812
Sponsors:
The first author acknowledges the support of MiniMed/Medtronic and the office of Graduate Studies at CSUN under grant# E1515. Some of this work was conducted while the first author was visiting the Mathematical and Computer Sciences and Engineering Division at the King Abdullah University of Science and Technology. He also would like to thank KAUST for its generous hospitality. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of MiniMed/Medtronic or of the office of Graduate Studies at CSUN, or KAUST.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorDjellouli, Rabiaen
dc.contributor.authorMahserejian, Shanten
dc.contributor.authorMokrane, A.en
dc.contributor.authorMoussaoui, Mohanden
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.date.accessioned2015-08-03T09:59:09Zen
dc.date.available2015-08-03T09:59:09Zen
dc.date.issued2012-08-19en
dc.identifier.issn03036812en
dc.identifier.pmid22903582en
dc.identifier.doi10.1007/s00285-012-0566-1en
dc.identifier.urihttp://hdl.handle.net/10754/562278en
dc.description.abstractWe analyze the mathematical properties of the fibrous capsule tissue concentration around a disk-shaped implant. We establish stability estimates as well as monotonicity results that illustrate the sensitivity of this growth to the biocompatibility index parameters of the implant. In addition, we prove that the growth of the tissue increases exponentially in time toward an asymptotic regime. We also study the mathematical properties of the solution of the inverse problem consisting in the determination of the values of the biocompatibility index parameters from the knowledge of some fibrous capsule tissue measurements. We prove that this model calibration problem admits a unique solution, and establish a characterization of the index parameters. Furthermore, we demonstrate analytically that such a solution is not continuous with respect to the data, and therefore the considered inverse problem is ill-posed due to the lack of the stability requirement. © 2012 Springer-Verlag.en
dc.description.sponsorshipThe first author acknowledges the support of MiniMed/Medtronic and the office of Graduate Studies at CSUN under grant# E1515. Some of this work was conducted while the first author was visiting the Mathematical and Computer Sciences and Engineering Division at the King Abdullah University of Science and Technology. He also would like to thank KAUST for its generous hospitality. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of MiniMed/Medtronic or of the office of Graduate Studies at CSUN, or KAUST.en
dc.publisherSpringer Natureen
dc.subjectBiomaterial implantsen
dc.subjectContraction semigroupsen
dc.subjectElliptic equationsen
dc.subjectFibrous capsule formationen
dc.subjectIll-posed problemen
dc.subjectInverse identification problemen
dc.subjectMaximum principleen
dc.subjectParabolic equationsen
dc.subjectStability estimatesen
dc.titleTheoretical study of the fibrous capsule tissue growth around a disk-shaped implanten
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalJournal of Mathematical Biologyen
dc.contributor.institutionCalif State Univ Northridge, Dept Math, Northridge, CA 91330 USAen
dc.contributor.institutionCalif State Univ Northridge, IRIS, Interdisciplinary Res Inst Sci, Northridge, CA 91330 USAen
dc.contributor.institutionEcole Normale Super, Lab Equat Derivees Partielles Non Lineaires & His, Kouba, Algeriaen
dc.contributor.institutionEcole Cent Lyon, Kouba, Algeriaen
dc.contributor.institutionEcole Normale Super, Kouba, Algeriaen
kaust.authorLaleg-Kirati, Taous-Meriemen

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