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research-article

Finite Element Formulation of Multiphasic Shell Elements for Cell Mechanics Analyses in FEBio

[+] Author and Article Information
Jay C. Hou

Department of Mechanical Engineering, Columbia University, New York, NY 10027
chiehhou@gmail.com

Steve A. Maas

Department of Bioengineering, University of Utah, Salt Lake City, UT 84112
steve.maas@utah.edu

Jeffrey A. Weiss

Department of Bioengineering, University of Utah, Salt Lake City, UT 84112
jeff.weiss@utah.edu

Gerard A. Ateshian

Department of Mechanical Engineering, Columbia University, New York, NY 10027
ateshian@columbia.edu

1Corresponding author.

ASME doi:10.1115/1.4041043 History: Received April 09, 2018; Revised July 17, 2018

Abstract

With the recent implementation of multiphasic materials in the open-source finite element (FE) software FEBio (febio.org), 3D models of cells embedded within the tissue may now be analyzed, accounting for porous solid matrix deformation, transport of interstitial fluid and solutes, membrane potential, and reactions. The cell membrane is a critical component in cell models, which selectively regulates the transport of fluid and solutes in the presence of large concentration and electric potential gradients, while also facilitating the transport of various proteins. The cell membrane is much thinner than the cell; therefore, in an FE environment, shell elements formulated as 2D surfaces in 3D space would be preferred for modeling the cell membrane, for the convenience of mesh generation from image-based data, especially for convoluted membranes. However, multiphasic shell elements are yet to be developed in the FE literature and commercial FE software. This study presents a novel formulation of multiphasic shell elements and its implementation in FEBio. The shell model includes front- and back-face nodal degrees of freedom for the solid displacement, effective fluid pressure and effective solute concentrations, and a linear interpolation of these variables across the shell thickness. This formulation was verified against classical models of cell physiology and validated against reported experimental measurements in chondrocytes. This implementation of passive transport of fluid and solutes across multiphasic membranes makes it possible to model the biomechanics of isolated cells or cells embedded in their extracellular matrix, accounting for solvent and solute transport.

Copyright (c) 2018 by ASME
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