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

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 $130to170kPa$⁠.