The influence of hydration on different mechanical moduli of the cornea

Abstract

Purpose

To determine the interrelation of different elastic moduli of the cornea and to investigate their dependency on corneal hydration.

Methods

Rabbit eyes were divided into four groups. Corneas were excised and mounted into a Barron artificial anterior chamber. Various corneal hydration steady states were achieved with different dextran T-500 concentrations in the anterior chamber, as well as on the corneal anterior surface. The treatment-solutions of each group contained either 5, 10, 15, or 20% w/w dextran. Ultrasound pachymetry was used to measure central corneal thickness. Brillouin microscopy of the central cornea determined the longitudinal bulk modulus by means of Brillouin frequency shift. Subsequently, a 5-mm-wide central strip was taken for extensiometry to measure the tangential elastic modulus.

Results

The longitudinal bulk modulus was 1.2-times higher in corneas dehydrated with 20% dextran compared to those hydrated with 5% dextran. In contrast, the tangential elastic modulus increased by 4.4 times. The obtained longitudinal bulk moduli were two orders of magnitude bigger than the tangential elastic moduli. Regression analysis of longitudinal bulk modulus and tangential elastic modulus revealed a quadratic relation. The bulk modulus seemed to be independent of tension, whereas the elastic modulus was tension-dependent. Greater corneal hydration led to significantly thicker pachymetry.

Conclusion

Corneal biomechanics are highly dependent on the level of corneal hydration. Surprisingly, tangential elastic moduli were more sensitive to hydration changes than longitudinal bulk moduli. A quadratic relation was found between both moduli.

Appendix A: Brillouin frequency shift and elastic module

Bulk Brillouin scattering can be used to probe elastic properties of transparent materials because incident light is inelastically scattered by acoustic wavelets (phonons) whose velocity is related with the elasticity of the material. Photons of the incident light may take energy from the phonons leading to wavelength shift (Stokes shift) of the scattered light or may deliver energy to the phonons (anti-Stokes shift). Due to the experimental setup, measuring backscattered light perpendicular to the corneal surface, only longitudinal waves can be measured and in this case the Brillouin frequency shift Ω can be expressed by

$$ \Omega =\kern0.5em \frac{2n}{\uplambda}\kern0.50em v $$

(1)

where n = refractive index of the medium, λ = wavelength, v = velocity of the acoustic wave [31]. Longitudinal ultrasound velocity v in isotropic media, on the other hand, is related with the bulk modulus M

$$ M=\uprho \kern0.24em {v}^2 $$

(2)

where ρ = density of the medium. This bulk modulus M may not be confused with Young’s elastic modulus E that describes the elastic properties in the surface-parallel plane. Combining Eqs. 1 and 2, it is obvious that M ∝ Ω², in detail

$$ M=\uprho \kern0.5em \frac{\uplambda^2\kern.3em {\Omega}^2\kern.3em }{4\kern.3em {n}^2} $$

(3)

For a physiologically hydrated cornea (equivalent to 13% dextran) the frequency shift Ω was 5.564 GHz. A density of ρ = 1061 kg/m³, a laser wavelength of λ = 780 nm, and a refractive index of the corneal stroma n = 1.3672 yields for M a value of 2.673 GPa.