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Research Papers

A Phenomenological Model for Mechanically Mediated Growth, Remodeling, Damage, and Plasticity of Gel-Derived Tissue Engineered Blood Vessels

[+] Author and Article Information
Julia Raykin

Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Alexander I. Rachev

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Rudolph L. Gleason1

Department of Biomedical Engineering, School of Mechanical Engineering, and Petite Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, GA 30332rudy.gleason@me.gatech.edu

1

Corresponding author.

J Biomech Eng 131(10), 101016 (Oct 13, 2009) (12 pages) doi:10.1115/1.4000124 History: Received January 15, 2009; Revised August 19, 2009; Posted September 01, 2009; Published October 13, 2009

Mechanical stimulation has been shown to dramatically improve mechanical and functional properties of gel-derived tissue engineered blood vessels (TEBVs). Adjusting factors such as cell source, type of extracellular matrix, cross-linking, magnitude, frequency, and time course of mechanical stimuli (among many other factors) make interpretation of experimental results challenging. Interpretation of data from such multifactor experiments requires modeling. We present a modeling framework and simulations for mechanically mediated growth, remodeling, plasticity, and damage of gel-derived TEBVs that merge ideas from classical plasticity, volumetric growth, and continuum damage mechanics. Our results are compared with published data and suggest that this model framework can predict the evolution of geometry and material behavior under common experimental loading scenarios.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

General schema for the kinematics of combined plasticity and volumetric growth

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Figure 2

Kinematics of growth and plasticity of a thick-walled axisymmetric tube. Note that the configurations βp(t) and βo(t) consist of infinitesimally thin rings (each with thickness dRp(t)) that pass through radial location R(0) in βo(0); since each ring is infinitesimally thin and cannot support a residual stress.

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Figure 3

Model predicted evolution of loaded and unloaded radii (a), axial length (b), and opening angle (c) for static culture on a mandrel. Data from Seliktar (5) from constrained (open circles) and unconstrained (solid triangles) static cultures are included for comparison to modeling results.

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Figure 4

Model predicted nominal stress-engineering strain curves that would result from fixed length pressure-diameter testing (a), evolution of modulus (b), and yield stress (c) for static culture on a mandrel. Data from Seliktar (5) from constrained (open circles) static culture are included for comparison to modeling results.

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Figure 6

Model predicted evolution of loaded and unloaded radii (a) and opening angle (b) for culture on a distensible tube with 10% cyclic strain. Data from Seliktar (5) from constrained (open circles) and unconstrained (solid triangles) static cultures are included for comparison to modeling results.

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Figure 7

Evolution of the yield stress (a), local circumferential stress (b), amplitude of cyclic Green strain (c), distribution of the circumferential plastic-growth stretch versus radius (d), distribution of the elastic stretch (e), and the circumferential damage and remodeling parameter Γθ (f)

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Figure 5

Evolution of the local circumferential stress ((a) and (b)), circumferential damage and remodeling parameter Γθ (c), distribution of the elastic stretch (d), plastic-growth stretches in the radial, circumferential, and axial directions (e), and distribution of the circumferential plastic-growth stretch versus radius at different time points (f) for static culture on a mandrel

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