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TECHNICAL PAPERS: Cell

# A Biphasic Model for Micro-Indentation of a Hydrogel-Based Contact Lens

[+] Author and Article Information
Xiaoming Chen, Alison C. Dunn, W. Gregory Sawyer

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611

Malisa Sarntinoranont

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611msarnt@ufl.edu

J Biomech Eng 129(2), 156-163 (Sep 13, 2006) (8 pages) doi:10.1115/1.2472373 History: Received December 09, 2005; Revised September 13, 2006

## Abstract

The stiffness and hydraulic permeability of soft contact lenses may influence its clinical performance, e.g., on-eye movement, fitting, and wettability, and may be related to the occurrence of complications; e.g., lesions. It is therefore important to determine these properties in the design of comfortable contact lenses. Micro-indentation provides a nondestructive means of measuring mechanical properties of soft, hydrated contact lenses. However, certain geometrical and material considerations must be taken into account when analyzing output force-displacement $(F-D)$ data. Rather than solely having a solid response, mechanical behavior of hydrogel contact lenses can be described as the coupled interaction between fluid transport through pores and solid matrix deformation. In addition, indentation of thin membranes $(∼100μm)$ requires special consideration of boundary conditions at lens surfaces and at the indenter contact region. In this study, a biphasic finite element model was developed to simulate the micro-indentation of a hydrogel contact lens. The model accounts for a curved, thin hydrogel membrane supported on an impermeable mold. A time-varying boundary condition was implemented to model the contact interface between the impermeable spherical indenter and the lens. Parametric studies varying the indentation velocities and hydraulic permeability show $F-D$ curves have a sensitive region outside of which the force response reaches asymptotic limits governed by either the solid matrix (slow indentation velocity, large permeability) or the fluid transport (high indentation velocity, low permeability). Using these results, biphasic properties (Young’s modulus and hydraulic permeability) were estimated by fitting model results to $F-D$ curves obtained at multiple indentation velocities (1.2 and $20μm∕s$). Fitting to micro-indentation tests of Etafilcon A resulted in an estimated permeability range of $1.0×10−15$ to $5.0×10−15m4∕Ns$ and Young’s modulus range of $130to170kPa$.

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## Figures

Figure 1

Schematic representation of the micro-indentation experiment. The indenter, located at the end of the stage-controlled cantilever, was lowered onto the center of the submerged contact lens. Reaction force was calculated from cantilever flexure which was measured using an optical sensor.

Figure 2

Cantilever force response during micro-indentation (unsubmerged).

Figure 3

Axisymmetric FEM mesh of the contact lens and imposed boundary conditions on the top and bottom surfaces. The impermeable spherical indenter (r=1mm) which contacts with the hydrogel surface is represented by the pink arc. Lenses were assumed to have constant thickness (h=100μm) and radius of curvature (R=7.68mm). The indenter surface and the top surface of contact lens were defined as potential contact surfaces. The mesh consisted of ∼1600 nine-node rectangular elements.

Figure 4

Fitting between computational and experimental curves at different indenter velocities (1.2 and 20μm∕s). The values used are E=150kPa, k=2.5×10−15m4∕Ns, and v=0.3.

Figure 5

Changes in the AUC correspond to changes in F-D behavior (A). Sensitivity of F-D curves to (B) indenter velocity and (C) permeability. Normalized AUC was calculated by dividing AUC with the asymptotic limit of AUC determined at high loading rate in (B) and at low permeability in (C) (E=270kPa, v=0.3).

Figure 6

MSE map generated to compare experimental and simulated F-D response for varying E and k. A node on the mesh represents a combination of (E,k) used in the FEM biphasic model. This map (at a fixed v=0.3) compares experimental data at single indenter velocity of 1.2μm∕s. Minimum values represent best fit with the experimental F-D data. Nonunique optimal values are found.

Figure 7

MSE maps generated to compare simulated and experimental F-D responses at indenter velocities of 1.2 and 20μm∕s. A node on the mesh represents a combination of (E,k) used in the FEM biphasic model. Best-fit parameter values of E and k minimize the MSE at different Poisson ratio, v=0.1, 0.2, 0.3, and 0.4.

Figure 8

Predicted pore pressure distribution for different indenter velocities using optimal parameters: E=140kPa, k=2.5×10−15m4∕Ns, v=0.3, u0=20μm, where u0 is the maximum indenter depth. t0 is the ramping time to reach u0. The pink arc is the indenter. For t0=1, 16, and 400s (corresponding to indenter velocities of 20, 1.2, and 0.05μm∕s, respectively), the magnitude of maximum pore pressure are 50.9, 26.4, and 1.9kPa, respectively, and the effective stress of the solid are approximately 47.9, 37.7, and 27.1kPa, respectively.

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