Diffusion of Oxygen is Slower in Vitreous Gel Than in Saline in Agreement With the Stokes Einstein Equation

Abstract

Purpose: : The laws of Stokes-Einstein and Fick postulate that the rate of diffusion is inversely related to the viscosity of the medium. The viscosity of vitreous gel is greater than water. In vitrectomy the vitreous gel is removed and replaced with saline and the diffusion coefficient and the rate of transport by diffusion within the vitreous cavity is increased. We test this hypothesis in vitro using O₂ as the signal molecule.

Methods: : Specially designed diffusion cells were used (PermeGear, Inc, Hellertown, PA, USA) with a middle chamber filled with either saline solution or porcine vitreous humour, separated by cellophane membranes (MWCO 12,000-14,000). The decreasing pO₂ was measured in a lower chamber as oxygen diffused through vitreous humour or saline solution to an upper chamber, where pure N₂ bubbled. A double layer of cellophane membranes was used as a reference, with no middle chamber. An oxygen sensor, OxyLab pO2 (Oxford Optronix Ltd., Oxford, UK) was used to measure the concentration of oxygen under standardized conditions. The diffusion coefficient of the vitreous gel and saline solution were calculated, using Fick’s law. The resistance of the membranes was subtracted in order to find the diffusion coefficient for the vitreous gel or saline solution only.

Results: : The average pO₂ in the lower chamber decreased over 2 hours from 149.2±3.3 mmHg to 138.6±6.0 mmHg (n=8) with vitreous gel in the middle chamber. With saline solution in the middle chamber the pO₂ dropped from 146.1±3.4 mmHg to 136.8±2.7 mmHg in 1 hour (n=8). The double membrane reference showed a decrease in pO₂ from 145.2±5.8 mmHg to 136.3±5.2 mmHg in 30 minutes (n=9). The diffusion coefficient for the vitreous gel was calculated as 0.0045±0.0016 mmHg/hour*cm² (n=8) and for the saline solution 0.020 ± 0.0055 mmHg/hour*cm² (n=8, p=0.000, Student's t-test). According to this, oxygen diffuses about 4 times faster through physiological saline solution than vitreous gel.

Keywords: vitreous • vitreoretinal surgery • vitreous substitutes