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A microsphere-based remodelling formulation for anisotropic biological tissues

Menzel, Andreas LU and Waffenschmidt, Tobias (2009) In Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Science 367(1902). p.3499-3523
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... (More)
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. (Less)
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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
anisotropic biological tissues, remodelling, adaptation, finite element, method
in
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Science
volume
367
issue
1902
pages
3499 - 3523
publisher
Royal Society Publishing
external identifiers
  • wos:000268735700008
  • scopus:69749121423
  • pmid:19657009
ISSN
1364-503X
DOI
10.1098/rsta.2009.0103
language
English
LU publication?
yes
id
f9c25780-5b59-428f-b128-636f2e13dc1b (old id 1478134)
date added to LUP
2016-04-01 14:28:43
date last changed
2021-09-01 03:00:05
@article{f9c25780-5b59-428f-b128-636f2e13dc1b,
  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       = {Menzel, Andreas and Waffenschmidt, Tobias},
  issn         = {1364-503X},
  language     = {eng},
  number       = {1902},
  pages        = {3499--3523},
  publisher    = {Royal Society Publishing},
  series       = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Science},
  title        = {A microsphere-based remodelling formulation for anisotropic biological tissues},
  url          = {http://dx.doi.org/10.1098/rsta.2009.0103},
  doi          = {10.1098/rsta.2009.0103},
  volume       = {367},
  year         = {2009},
}