A microsphere-based remodelling formulation for anisotropic biological tissues
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1478134
- author
- Menzel, Andreas LU and Waffenschmidt, Tobias
- organization
- publishing date
- 2009
- 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
- 2022-03-29 21:08:21
@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}}, keywords = {{anisotropic biological tissues; remodelling; adaptation; finite element; method}}, 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}}, }