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

Rabia Djellouli, Shant Mahserejian, A. Mokrane, Mohand Moussaoui, Taous-Meriem Laleg-Kirati

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)833-867
Number of pages35
JournalJournal of Mathematical Biology
Volume67
Issue number4
DOIs
StatePublished - Aug 19 2012

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics
  • Agricultural and Biological Sciences (miscellaneous)

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