Stability analysis for a peri-implant osseointegration model
type: Item
instance of: scholarly article
title: Stability analysis for a peri-implant osseointegration model
zbMATH Open document ID: 1264.35036
published in: Journal of Mathematical Biology
publication date: 2013-02-01T00:00:00Z
review text: This paper concerns the stability of the solution for a peri-implant osseointegration process. ``For certain parameter values, the solution has a `wave-like' profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This `wave-like' profile contradicts experimental observations.'' The authors investigate conditions, under which such profile appears in the solution and express them ``in terms of model parameters, by means of linear stability analysis, carried out at one of the constant solutions of the simplified system.'' The stability analysis is done for the reduced system of PDE's which is equivalent to the original system, with respect to the stability properties of constant solutions. The case of large perturbations is investigated as well. It has been shown that if the constant solution is unstable, then the solution of the system does not converge to it. Numerical tests are presented. They ``show, that stability of the constant solution could determine the behavior of the solution of the whole system, if certain initial conditions are considered.''
reviewed by: Sebastian Aniţa
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 92C15
Mathematics Subject Classification ID: 35B36
zbMATH DE Number: 6133587
zbMATH Keywords: bone-implant ingrowth
zbMATH Keywords: finite element method
zbMATH Keywords: linear stability analysis
Wikidata QID: Q51425076
author: Pavel A. Prokharau
author: Fred J. Vermolen
MaRDI profile type: Publication
full work available at URL: s00285-012-0513-1
OpenAlex ID: W1497295363
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DOI: 10.1007/S00285-012-0513-1
description: scientific article; zbMATH DE number 6133587