Diffusion characteristics of vitreous humour and saline solution follow the Stokes Einstein equation

Abstract

PURPOSE: The Stokes-Einstein equation predicts that diffusion is inversely correlated with viscosity of the medium. This predicts that diffusion fluxes should be lower in vitreous humour than in saline solution with lower viscosity. We test this hypothesis, which has implications for vitrectomy. METHODS: Diffusion cells were used, with a middle chamber filled with saline solution with different concentrations of hyaluronic acid (0 microg/ml, 30 microg/ml, 90 microg/ml and 180 microg/ml) or porcine vitreous humour, between cellophane membranes. HPLC was used to measure the concentration of the diffusing molecule, dexamethasone, and calculate the flux through the chamber filled with the various media. The diffusion coefficients were calculated, using Fick's law. Viscosity was measured with a Brookfield digital DV-I+viscometer. RESULTS: The diffusion coefficient for dexamethasone in vitreous humour is 0.065 +/- 0.022 cm(2)/hour, 0.26 +/- 0.12 cm(2)/hour for saline alone, 0.17 +/- 0.04 cm(2)/hour for saline with 30 microg/ml hyaluronan, 0.076 +/- 0.009 cm(2)/hour with 90 microg/ml hyaluronan, and with 180 microg/ml hyaluronan 0.072 +/- 0.0018 cm(2)/hour (p < 0.001). The viscosity of liquid vitreous is 6.29 +/- 2.3 cp, and the viscosity of saline alone is 1.01 +/- 0.008 cp. For saline with 30 microg/ml of hyaluronan the viscosity is 1.04 +/- 0.015, with 90 microg/ml hyaluronan is 1.06 +/- 0.01, and with 180 microg/ml hyaluronan is 1.08 +/- 0.014 (p < 0.001). CONCLUSIONS: Dexamethasone diffuses four times faster through saline solution than vitreous humour. Liquid vitreous humour is about six times more viscous than saline. The results indicate that diffusion is faster in saline solution than in vitreous humour, in accordance to the Stokes-Einstein equation. This finding can help explain some of the physiological, pharmacological and clinical consequences of vitrectomy.