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TECHNICAL PAPERS: Soft Tissue

Regional Multiaxial Mechanical Properties of the Porcine Anterior Lens Capsule

[+] Author and Article Information
G. David, R. M. Pedrigi, M. R. Heistand

Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843

J. D. Humphrey1

Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843jhumphrey@tamu.edu

1

Corresponding author.

J Biomech Eng 129(1), 97-104 (Jun 26, 2006) (8 pages) doi:10.1115/1.2401188 History: Received January 16, 2006; Revised June 26, 2006

The lens capsule of the eye plays fundamental biomechanical roles in both normal physiological processes and clinical interventions. There has been modest attention given to the mechanical properties of this important membrane, however, and prior studies have focused on 1-D analyses of the data. We present results that suggest that the porcine anterior lens capsule has a complex, regionally dependent, nonlinear, anisotropic behavior. Specifically, using a subdomain inverse finite element method to analyze data collected via a new biplane video-based test system, we found that the lens capsule is nearly isotropic (in-plane) near the pole but progressively stiffer in the circumferential compared to the meridional direction as one approaches the equator. Because the porcine capsule is a good model of the young human capsule, there is strong motivation to determine if similar regional variations exist in the human lens capsule for knowledge of such complexities may allow us to improve the design of surgical procedures and implants.

FIGURES IN THIS ARTICLE
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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 5

(a) Subdomain inverse finite element results for material parameter c, based on the Choi-Vito model. ANOVA tests reveal no significant differences between groups of marker sets (p<0.01), as in for the Fung model. (b) Associated subdomain inverse finite element results for the ratio of material parameters c1∕c2 (ratio of circumferential to meridional “stiffness”) based on the Choi-Vito model.

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Figure 6

Stress-strain simulations for the Fung model based on best-fit values of the material parameters for set F (Table 2). Left panels show stresses due to uniaxial stretch tests in circumferential and meridional directions; right panels show stresses due to equibiaxial stretch test. Note that the undeformed thickness was assumed to be 60μm in this region for purposes of calculation; this thickness changed due to deformation and the assumption of incompressibility.

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Figure 7

Stress-strain simulations for the Choi-Vito model based on material parameters for set F from Table 4. Left panels show stresses due to uniaxial stretch tests in circumferential and meridional directions; right panels show stresses due to equibiaxial stretch test.

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Figure 3

(a) Subdomain inverse finite element results for material parameter c, based on the Fung exponential model. ANOVA tests revealed no significant difference between groups of marker sets (p<0.01). Note that parameters were difficult to estimate at set D, presumably because of the near equibiaxial strain near the pole (cf. (1)). Moreover, because some markers from individual sets of five were lost during the excision required to obtain the stress-free configuration, complete results were obtained for 27 of the 36 “experiments.” (b) Associated subdomain inverse finite element results for the ratio of material parameters c1∕c2 (ratio of circumferential to meridional “stiffness”) based on the Fung exponential model.

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Figure 2

Simulation of a best-fit parameter estimation based on equibiaxial stretch data for the isotropic Fung model. The associated error (vertical axis) is plotted versus values of the two material parameters α and β. The error structure takes the form of a parabolic cylinder, hence there is no unique solution (indeed, the family of solutions lie along a line). That is, results obtained by the inverse finite element method depend on the initial guess in this special case.

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Figure 1

Arrangement of seven overlapping sets of five 40μm diameter microspheres on the anterior lens capsule for use as video tracking markers. The center marker of set D is placed at the pole (Y-suture). Sets A to D lie along the minor equatorial axis and sets D to G lie along the major equatorial axis, with the anterior lens capsule imagined as a hemi-ellipsoid. Note that each set of five markers defines a four-element “subdomain” (see exploded view for set A) for inverse finite element estimation of regional properties, independent of the overall geometry of the lens capsule and boundary conditions at the equator. Each inverse finite element estimation is performed by specifying the four outer nodes as displacement boundary conditions and using the (x,y,z) coordinates of the center node to minimize the difference between predicted and experimentally measured positions.

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Figure 4

Mean values of the material parameters, by region, for the Fung model (+ symbols) as well as for a proposed regional variation (solid line). Note that the parameter c has units of N/mm whereas the other three parameters are dimensionless.

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