Research article summary (published 11 Sep 2009):

A microsphere-based remodelling formulation for anisotropic biological tissues.

Full Abstract

Biological tissues possess the ability to adapt according to the respective local loading conditions, which results in growth and remodelling phenomena. The main goal of this work is the development of a new remodelling approach that, on the one hand, reflects the alignment of fibrous soft biological tissue with respect to representative loading directions. On the other hand, the continuum approach proposed is based on a sound micro-mechanically motivated formulation. To be specific, use of a worm-like chain model is made to describe the behaviour of long-chain molecules as present in, for instance, collageneous tissues. The extension of such a one-dimensional constitutive equation to the three-dimensional macroscopic level is performed by means of a microsphere formulation. Inherent with the algorithmic treatment of this type of modelling approach, a finite number of unit vectors is considered for the numerical integration over the domain of the unit sphere. As a key aspect of this contribution, remodelling is incorporated by setting up evolution equations for the referential orientations of these integration directions. Accordingly, the unit vectors considered now allow interpretation as internal variables, which characterize the material's anisotropic properties. Several numerical studies underline the applicability of the model that, moreover, nicely fits into iterative finite element formulations so that general boundary value problems can be solved.

Author information

Author/s: Menzel, Andreas (A); Waffenschmidt, Tobias (T);

Affiliation: Institute of Mechanics, TU Dortmund University, Leonhard-Euler-Strasse 5, 44221 Dortmund, Germany.

Journal and publication information

Publication Type: Journal Article; Research Support, Non-U.S. Gov't

Journal: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences (Philos Transact A Math Phys Eng Sci), published in England. (Language: eng)

Reference: 2009-Sep; vol 367 (issue 1902) : pp 3499-523

Dates: Created 2009/08/06; Completed 2009/10/21;

PMID: 19657009, status: MEDLINE (last retrieval date: 10/21/2009, IMS Date: )

Sourced from the National Library of Medicine. Abstract text and other information may be subject to copyright.

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MeSH headings (categories)

This article was linked to the MESH Headings shown below.

Adaptation, Physiological Algorithms Animals Anisotropy Biomechanics Elasticity

Elasticity Finite Element Analysis Humans Microspheres Models, Biological Thermodynamics

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