Residual Modulus Calculation and Data Analysis

The apparent modulus as a function of time was defined as shear stress over shear strain and calculated through the following equation,

where τ(t) is the shear stress as a function of time, γ is the shear strain, and d is the step movement applied by the micromanipulator. The shear stress exerted on the corneal epithelial cell monolayers, τ(t), was defined as shear force over area, or F(t)/A. The shear strain exerted on the corneal epithelial cell monolayer, γ, was defined as the shear distance over the gap height in the normal direction, or d/d_gap. The gap, d_gap, was measured as the height difference between two focal planes, which varied between 5 and 8 µm. Figure 1 shows a graphical representation of shear stress and shear strain.

The peak modulus was defined as the first modulus value after the step strain was applied. The residual modulus was calculated as the mean modulus during the 20 seconds of the experiment before the retraction of the micromanipulator. Statistical analysis was performed using Welch's t-test owing to the unequal trial numbers among the samples and the small sample size compared with the time points collected for residual moduli.