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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/614631 |
| Date | 14 April 2016 |
| Creators | Armstrong, Michelle Hine, Buganza Tepole, Adrián, Kuhl, Ellen, Simon, Bruce R., Vande Geest, Jonathan P. |
| Contributors | 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 |
| Publisher | Public Library of Science |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | Article |
| 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 |
| Relation | http://dx.plos.org/10.1371/journal.pone.0152806 |
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