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Research Papers

# Elasticity of the Porcine Lens Capsule as Measured by Osmotic Swelling

[+] Author and Article Information
Tracy A. Powell, Rouzbeh Amini, Alina Oltean

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455

Vincent A. Barnett

Department of Integrative Biology and Physiology, University of Minnesota, Minneapolis, MN 55455

Kevin D. Dorfman

Department of Chemical Engineering and Material Science, University of Minnesota, Minneapolis, MN 55455

Yoav Segal

Department of Medicine, University of Minnesota, Minneapolis, MN; Minneapolis VA Medical Center, Minneapolis, MN 55417

Victor H. Barocas1

Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455baroc001@umn.edu

1

Corresponding author.

J Biomech Eng 132(9), 091008 (Aug 26, 2010) (9 pages) doi:10.1115/1.4002024 History: Received October 05, 2009; Revised June 10, 2010; Posted June 22, 2010; Published August 26, 2010; Online August 26, 2010

## Abstract

As an alternative to purely mechanical methods, optical tracking of passive osmotic swelling was used to assess mechanical properties of the porcine lens capsule. A simple model was developed accounting for the permeability of the lens fiber cells and capsule to water, the concentration of fixed charges in the fiber cells, and the capsule’s resistance to the swelling of fiber cells. Fitting the model solution to experimental data provided an estimate of the elastic modulus of the lens capsule under the assumption of linear isotropic elasticity. The calculated elastic modulus at a fixed charge density of $20 mol m−3$ was $2.0±0.5 MPa$ ($mean±95%$ confidence interval; $n=15$) for 0.1% saline solution, $0.64±0.3 MPa$$(n=10)$ for 0.2% saline solution, and $0.28±0.5 MPa$$(n=6)$ for 0.5% saline solution. These values are comparable to previously reported moduli of elasticity for the porcine lens capsule at small strains $(<10%)$, and the slight increase with hypotonicity is consistent with the nonlinear mechanical behavior of the lens capsule. Although limited by being a single measurement on a heterogeneous tissue, osmotic swelling provides a quantitative assessment of the stiffness of the lens capsule without requiring dissection or manipulation of the lens. Thus, the new method could be useful for small animal models.

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## Figures

Figure 1

Experimental images of lens: Image of a lens (a) captured from camera during experiment and (b) after binomial conversion in MATLAB . The arrow indicates points from which the radius was calculated, depicted as small circles. The radius is 4.66 mm.

Figure 4

Sum of squared error versus elasticity and Darcy conductivity of the mushy zone: SSE (a) plotted versus modulus of elasticity of the lens capsule, E, and (b) plotted versus E and Darcy conductivity of the mushy zone, Km. A shallow trough lies along the line E=Km+0.02, with units of MPa and 10−16 m2 Pa−1 s−1 for E and Km, respectively. Results are from a 0.1% NaCl bath and based on zc=20 mol m−3.

Figure 5

Experimental and literature values of the elastic modulus of the porcine ocular lens capsule: Modulus of elasticity of the porcine lens capsule calculated in the current work and reported in the literature. Error bars are 95% confidence intervals.

Figure 6

Charge distribution within bath and lens

Figure 7

Model volume definitions

Figure 2

Anatomical and model schematic of ocular lens: (a) Anatomy of ocular lens. (b) Model schematic of ocular lens before placement in hypotonic solution and (c) after some time in hypotonic solution. The subscripts c and o refer to the core of the lens and the outside bath, respectively. Initially the lens is not swollen and a mushy zone does not exist. After placement in hypotonic solution, water penetrates the lens capsule and the lens fibers swell in layers. The swollen fibers constitute the mushy zone, and the interface between the mushy zone and the core marks the water front. The difference in osmolarity between the core and outside bath is the driving force for lens expansion, which is opposed by mechanical pressure from the stretched lens capsule.

Figure 3

Mathematical model with experimental data. Mathematical model (solid lines) fitted to the experimental data (symbols) for lens expansion in (a) 0.1%, (b) 0.2%, and (c) 0.5% NaCl with the fixed charge density, zc, set at 20 mol m−3. Discrete steps in the experimental data were caused by the limit of measurement resolution.

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