A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth.
The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transpor...
Main Authors: | , , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Public Library of Science (PLoS)
2016-01-01
|
Series: | PLoS ONE |
Online Access: | http://europepmc.org/articles/PMC4831841?pdf=render |
id |
doaj-fe2c71f7db7941a6b93d592587a0147e |
---|---|
record_format |
Article |
spelling |
doaj-fe2c71f7db7941a6b93d592587a0147e2020-11-25T02:39:59ZengPublic Library of Science (PLoS)PLoS ONE1932-62032016-01-01114e015280610.1371/journal.pone.0152806A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth.Michelle Hine ArmstrongAdrián Buganza TepoleEllen KuhlBruce R SimonJonathan P Vande GeestThe purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.http://europepmc.org/articles/PMC4831841?pdf=render |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Michelle Hine Armstrong Adrián Buganza Tepole Ellen Kuhl Bruce R Simon Jonathan P Vande Geest |
spellingShingle |
Michelle Hine Armstrong Adrián Buganza Tepole Ellen Kuhl Bruce R Simon Jonathan P Vande Geest A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth. PLoS ONE |
author_facet |
Michelle Hine Armstrong Adrián Buganza Tepole Ellen Kuhl Bruce R Simon Jonathan P Vande Geest |
author_sort |
Michelle Hine Armstrong |
title |
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth. |
title_short |
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth. |
title_full |
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth. |
title_fullStr |
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth. |
title_full_unstemmed |
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth. |
title_sort |
finite element model for mixed porohyperelasticity with transport, swelling, and growth. |
publisher |
Public Library of Science (PLoS) |
series |
PLoS ONE |
issn |
1932-6203 |
publishDate |
2016-01-01 |
description |
The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues. |
url |
http://europepmc.org/articles/PMC4831841?pdf=render |
work_keys_str_mv |
AT michellehinearmstrong afiniteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT adrianbuganzatepole afiniteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT ellenkuhl afiniteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT brucersimon afiniteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT jonathanpvandegeest afiniteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT michellehinearmstrong finiteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT adrianbuganzatepole finiteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT ellenkuhl finiteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT brucersimon finiteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth AT jonathanpvandegeest finiteelementmodelformixedporohyperelasticitywithtransportswellingandgrowth |
_version_ |
1724783743798870016 |