A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth

Persistent Link:
http://hdl.handle.net/10150/614631
Title:
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth
Author:
Armstrong, Michelle Hine; Buganza Tepole, Adrián; Kuhl, Ellen; Simon, Bruce R.; Vande Geest, Jonathan P.
Affiliation:
Univ Arizona, Grad Interdisciplinary Program Appl Math; Univ Arizona, Dept Aerosp & Mech Engn; Univ Arizona, Grad Interdisciplinary Program Biomed Engn; Univ Arizona, Inst Biocollaborat Res BIO5; Univ Arizona, Dept Biomed Engn
Issue Date:
2016-04-14
Publisher:
Public Library of Science
Citation:
A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth 2016, 11 (4):e0152806 PLOS ONE
Journal:
PLOS ONE
Rights:
© 2016 Armstrong et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Collection Information:
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
Abstract:
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, concentrationdriven, 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.
ISSN:
1932-6203
DOI:
10.1371/journal.pone.0152806
Keywords:
SMOOTH-MUSCLE CONTRACTION; INTERSTITIAL GROWTH; VOLUMETRIC GROWTH; BIOLOGICAL TISSUE; RESIDUAL-STRESS; ARTERIAL GROWTH; MASS-TRANSPORT; MIXTURE MODEL; SOFT-TISSUES; MECHANICS
Version:
Final published version
Sponsors:
This work was supported by National Eye Institute 1R01EY020890 (http://www.nih.gov/, JPVG); National Heart, Lung, and Blood Institute 1R21HL111990 (http://www.nih.gov/, JPVG); Whitaker International Summer Grant (http://www.whitaker.org/, MHA); National Science Foundation 0841234 (http://www.nsf.gov/); and ARCS Foundation (https://www.arcsfoundation.org/, MHA). Support for MHA was partly provided by the National Science Foundation under award No 0841234.
Additional Links:
http://dx.plos.org/10.1371/journal.pone.0152806

Full metadata record

DC FieldValue Language
dc.contributor.authorArmstrong, Michelle Hineen
dc.contributor.authorBuganza Tepole, Adriánen
dc.contributor.authorKuhl, Ellenen
dc.contributor.authorSimon, Bruce R.en
dc.contributor.authorVande Geest, Jonathan P.en
dc.date.accessioned2016-06-24T20:56:11Z-
dc.date.available2016-06-24T20:56:11Z-
dc.date.issued2016-04-14-
dc.identifier.citationA Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth 2016, 11 (4):e0152806 PLOS ONEen
dc.identifier.issn1932-6203-
dc.identifier.doi10.1371/journal.pone.0152806-
dc.identifier.urihttp://hdl.handle.net/10150/614631-
dc.description.abstractThe 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, concentrationdriven, 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.en
dc.description.sponsorshipThis work was supported by National Eye Institute 1R01EY020890 (http://www.nih.gov/, JPVG); National Heart, Lung, and Blood Institute 1R21HL111990 (http://www.nih.gov/, JPVG); Whitaker International Summer Grant (http://www.whitaker.org/, MHA); National Science Foundation 0841234 (http://www.nsf.gov/); and ARCS Foundation (https://www.arcsfoundation.org/, MHA). Support for MHA was partly provided by the National Science Foundation under award No 0841234.en
dc.language.isoenen
dc.publisherPublic Library of Scienceen
dc.relation.urlhttp://dx.plos.org/10.1371/journal.pone.0152806en
dc.rights© 2016 Armstrong et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are crediteden
dc.subjectSMOOTH-MUSCLE CONTRACTIONen
dc.subjectINTERSTITIAL GROWTHen
dc.subjectVOLUMETRIC GROWTHen
dc.subjectBIOLOGICAL TISSUEen
dc.subjectRESIDUAL-STRESSen
dc.subjectARTERIAL GROWTHen
dc.subjectMASS-TRANSPORTen
dc.subjectMIXTURE MODELen
dc.subjectSOFT-TISSUESen
dc.subjectMECHANICSen
dc.titleA Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growthen
dc.typeArticleen
dc.contributor.departmentUniv Arizona, Grad Interdisciplinary Program Appl Mathen
dc.contributor.departmentUniv Arizona, Dept Aerosp & Mech Engnen
dc.contributor.departmentUniv Arizona, Grad Interdisciplinary Program Biomed Engnen
dc.contributor.departmentUniv Arizona, Inst Biocollaborat Res BIO5en
dc.contributor.departmentUniv Arizona, Dept Biomed Engnen
dc.identifier.journalPLOS ONEen
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en
dc.eprint.versionFinal published versionen
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