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dc.contributor.authorDjellouli, Rabia
dc.contributor.authorMahserejian, Shant
dc.contributor.authorMokrane, A.
dc.contributor.authorMoussaoui, Mohand
dc.contributor.authorLaleg-Kirati, Taous-Meriem
dc.date.accessioned2015-08-03T09:59:09Z
dc.date.available2015-08-03T09:59:09Z
dc.date.issued2012-08-19
dc.identifier.issn03036812
dc.identifier.pmid22903582
dc.identifier.doi10.1007/s00285-012-0566-1
dc.identifier.urihttp://hdl.handle.net/10754/562278
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.
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.
dc.publisherSpringer Nature
dc.subjectBiomaterial implants
dc.subjectContraction semigroups
dc.subjectElliptic equations
dc.subjectFibrous capsule formation
dc.subjectIll-posed problem
dc.subjectInverse identification problem
dc.subjectMaximum principle
dc.subjectParabolic equations
dc.subjectStability estimates
dc.titleTheoretical study of the fibrous capsule tissue growth around a disk-shaped implant
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputational Bioscience Research Center (CBRC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.identifier.journalJournal of Mathematical Biology
dc.contributor.institutionCalif State Univ Northridge, Dept Math, Northridge, CA 91330 USA
dc.contributor.institutionCalif State Univ Northridge, IRIS, Interdisciplinary Res Inst Sci, Northridge, CA 91330 USA
dc.contributor.institutionEcole Normale Super, Lab Equat Derivees Partielles Non Lineaires & His, Kouba, Algeria
dc.contributor.institutionEcole Cent Lyon, Kouba, Algeria
dc.contributor.institutionEcole Normale Super, Kouba, Algeria
kaust.personLaleg-Kirati, Taous-Meriem
dc.date.published-online2012-08-19
dc.date.published-print2013-10


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