title: A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth.
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, 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.
authors.affiliation: Graduate Interdisciplinary Program in Applied Mathematics, The University of Arizona, Tucson, AZ, United States of America.
authors.forename: Michelle Hine
authors.initials: MH
authors.lastname: Armstrong
authors.affiliation: Department of Mechanical Engineering, Stanford University, Stanford, CA, United States of America.
authors.forename: Adrián
authors.initials: A
authors.lastname: Buganza Tepole
authors.affiliation: Department of Mechanical Engineering, Stanford University, Stanford, CA, United States of America.
authors.forename: Ellen
authors.initials: E
authors.lastname: Kuhl
authors.affiliation: Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ, United States of America.
authors.forename: Bruce R
authors.initials: BR
authors.lastname: Simon
authors.affiliation: Graduate Interdisciplinary Program in Applied Mathematics, The University of Arizona, Tucson, AZ, United States of America.|Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ, United States of America.|Graduate Interdisciplinary Program of Biomedical Engineering, The University of Arizona, Tucson, AZ, United States of America.|BIO5 Institute for Biocollaborative Research, The University of Arizona, Tucson, AZ 85721, United States of America.|Department of Biomedical Engineering, The University of Arizona, Tucson, AZ 85721, United States of America.|Department of Bioengineering, The University of Pittsburgh, Pittsburgh, PA 15219, United States of America.
authors.forename: Jonathan P
authors.initials: JP
authors.lastname: Vande Geest
mesh_terms: D000465:Algorithms; D001692:Biological Transport; D049109:Cell Proliferation; D004548:Elasticity; D020342:Finite Element Analysis; D008954:Models, Biological; D016062:Porosity; D011312:Pressure; D013314:Stress, Mechanical