Characterization of age-related variation in corneal biomechanical properties

Abstract

An experimental study has been conducted to determine the stress-strain behaviour of human corneal tissue and how the behaviour varies with age. Fifty-seven well-preserved ex vivo donor corneas aged between 30 and 99 years were subjected to cycles of posterior pressure up to 60 mm Hg while monitoring their behaviour. The corneas were mechanically clamped along their ring of scleral tissue and kept in physiological conditions of temperature and hydration. The tissue demonstrated hyper-elastic pressure-deformation and stress-strain behaviour that closely matched an exponential trend. Clear stiffening (increased resistance to deformation) with age was observed in all loading cycles, and the rate of stiffness growth was nonlinear with bias towards older specimens. With a strong statistical association between stiffness and age (p < 0.05), it was possible to develop generic stress-strain equations that were suitable for all ages between 30 and 99 years. These equations, which closely matched the experimental results, depicted corneal stiffening with age in a form suitable for implementation in numerical simulations of ocular biomechanical behaviour.

Figure 1.

Inflation rig used for cornea testing. (a) Shows [1] the pressure chamber, [2] the laser beam used to monitor cornea apical displacement, [3] pressure transducer that monitors the posterior pressure acting on corneal specimens, [4] temperature controller to enable conduct of tests at 37°C, [5] pressure vessel, [6] fitting for a camera used to monitor corneal profile during test—cameras are not shown for clarity. (b) Shows a cross section through the front piece of the pressure chamber.

Figure 2.

Example results of a cornea specimen obtained from a 79-year-old donor. The results include: (a) the pressure–apical behaviour under 10 load cycles, (b) stress–strain behaviour based on the results of the first (grey line) and fourth (black line) load cycles, (c) the relationship between the tangent modulus, E, and stress within the first (grey) and fourth (black) load cycles and (d) the variation of E at different stress levels (filled squares, stress = 0.01 MPa; filled triangles, stress = 0.02 MPa; filled circles, stress = 0.03 MPa) with the progression of load cycles.

Figure 3.

Stress–strain behaviour of corneas as obtained from (a,c,e) first loading cycle and (b,d,f) fourth loading cycle. The results include: (a,b) the results of all corneas, (c,d) the results of corneas aged 40–59 years and (e,f) the results of corneas aged 80–99 years. Black lines represent the average behaviour in each case.

Figure 4.

Variation of stress with age at strain = 0.008 (which corresponds to an IOP of 15 mm Hg for a cornea with average dimensions and material properties) showing the nonlinear polynomial relationship between the two parameters. (a) First loading cycle (y =1 × 10⁻⁷x² +2 × 10⁻⁶x + 0.0011, R² = 0.1444) and (b) fourth loading cycle (y =5 × 10⁻⁷x² −1 × 10⁻⁵x + 0.0017, R² = 0.2866).

Figure 5.

Comparisons between the stress–strain constitutive models obtained using equation (3.4) and the average experimental behaviour of corneas aged between (a) solid line, 50 and 59 years; dashed line, equation 55 years; (b) solid line, 60 and 69 years; dashed line, equation 65 years; (c) solid line, 70 and 79 years; dashed line, equation 75 years; (d) solid line, 80 and 89 years; dashed line, equation 85 years; (e) solid line, 90 and 99 years; dashed line, equation 95 years. The results of equation (3.4) for different age groups are compared in (f): solid line, equation 55 years; dash dotted line, equation 65 years; long-dashed line, equation 75 years; short-dashed line, equation 85 years; dashed-double dotted line, equation 95 years. The error bars represent the standard deviation of stress values.

Figure 6.

Correlation between the conditioning behaviour and specimen age assessed by comparing the final tangent modulus of the first three cycles, E₁ to E₃, against the average of the final modulus values obtained over cycles 4–10, E_4–10 ((a) y = 0.0014x + 0.7695; (b) y = 0.0006x + 0.9187; (c) y = 0.0000x + 1.0055).