Research Papers

A Nonlinear Anisotropic Viscoelastic Model for the Tensile Behavior of the Corneal Stroma

[+] Author and Article Information
T. D. Nguyen

Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218vicky.nguyen@jhu.edu

R. E. Jones

Mechanics of Materials Department, Sandia National Laboratories, P.O. Box 0969, Livermore, CA 94551

B. L. Boyce

Microsystems Materials Department, Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87123

J Biomech Eng 130(4), 041020 (Jul 02, 2008) (10 pages) doi:10.1115/1.2947399 History: Received June 22, 2007; Revised November 30, 2007; Published July 02, 2008

Tensile strip experiments of bovine corneas have shown that the tissue exhibits a nonlinear rate-dependent stress-strain response and a highly nonlinear creep response that depends on the applied hold stress. In this paper, we present a constitutive model for the finite deformation, anisotropic, nonlinear viscoelastic behavior of the corneal stroma. The model formulates the elastic and viscous response of the stroma as the average of the elastic and viscous response of the individual lamellae weighted by a probability density function of the preferred in-plane lamellar orientations. The result is a microstructure-based model that incorporates the viscoelastic properties of the matrix and lamellae and the lamellar architecture in the response of the stroma. In addition, the model includes a fully nonlinear description of the viscoelastic response of the lamellar(fiber) level. This is in contrast to previous microstructure-based models of fibrous soft tissues, which relied on quasilinear viscoelastic formulations of the fiber viscoelasticity. Simulations of recent tensile strip experiments show that the model is able to predict, well within the bounds of experimental error and natural variations, the cyclic stress-strain behavior and nonlinear creep behavior observed in uniaxial tensile experiments of excised strips of bovine cornea.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

(a) Illustration of the lamellar microstructure of the corneal stroma. The collagen fibrils (black lines and dots) run parallel in each lamella, but subtend large angles in adjacent lamella. (b) Polar plot illustrating the spatial variation of the preferred orientations of the lamellae, based on the X-ray scattering data of Aghamohammadzadeh (6). The preferred orientation changes from the NT and IS orientations in the central cornea to a circumferential orientation in the limbus.

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Figure 2

Generalized Maxwell rheological model for the viscoelastic behavior of the stroma

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Figure 3

The stress-activation model of the lamellar viscosity. The viscosity decreases as the magnitude of the flow stress approaches the activation stress τ0k.

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Figure 4

Probability density function for the preferred in-plane orientation of collagen fibrils developed by Pinsky (24) for the human cornea based on the X-ray scattering data of Aghamohammadzadeh (6) (see Fig. 1) for (a) the central cornea region and (b) a region in the limbus. The 0deg and 90deg orientations corresponds to the NT and IS meridians.

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Figure 5

A sequence of simulations showing (a) the initial fit of the elastic parameters (α¯=αeq+∑k3αkneq,β) using the 350kPa∕s rate data and (b) fits of α1neq and α2neq to the 100kPa creep data; a prediction of the 500kPa creep data using only the α1neq, α2neq fit and fits of τ2 and (α3neq,τ3) to the 500kPa creep data

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Figure 6

Uniaxial creep strain curves obtained from experiments and simulation at three different applied engineering stresses for the central portion of corneal strips cut along the NT direction. The error bars indicate a ±1 standard deviation from the bin-averaged experimental data. The nonlinear viscoelastic model is fitted to 100kPa and 500kPa creep data and used to predict 350kPa data.

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Figure 7

Cyclic strain-time plots comparing uniaxial tension experiment and simulation results of the NT orientation for three different stress rates: (a) 350kPa∕s, (b) 35kPa∕s, and (c) 3.5kPa∕s. (d) Cyclic strain-time plot for the stress rate 35kPa∕s comparing the NT and IS orientations. The simulation results for the NT and IS orientations that are identical lie on top of each other because the fibril distribution is the same when viewed about the NT and IS meridians (see Fig. 4). Error bars indicate a ±1 standard deviation from the bin-averaged experimental data. The nonlinear viscoelastic model is fitted to the loading curve of 350kPa∕s and creep data and used to predict the response of lower stress rates.

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Figure 8

Anisotropic behavior of nonlinear viscoelastic model calculated for the fibril density function in Eq. 20: (a) stress-strain response at 500kPa∕s and (b) reduced relaxation function for λ=1.04 and reduced creep function for 500kPa. The angles θ=5π∕3 and θ=π∕3 indicate orientations with highest and lowest fibril densities.




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