Diffusion in the Vitreous Cavity Is Related to the Viscosity of the Medium According to the Stokes Einstein Equation

Abstract

 

Purpose:

 

The laws of Stokes Einstein, Fick and Hagen-Poiseuille postulate that the rate of transport of any substance by diffusion or in convection currents, is inversely related to the viscosity of the medium. The viscosity of vitreous gel is greater than water. In vitrectomy, when the vitreous gel is removed and replaced with water, the diffusion coefficient and the rate of transport by diffusion or convection within the vitreous cavity is increased. This change influences the transport of all molecules.

 

Methods:

 

Specially designed diffusion cells were used, with a middle chamber filled with either saline solution or porcine vitreous humour, between layers of cellophane membranes (MWCO 12,000-14,000). Dexamethasone was used as a reference molecule. HPLC was used to measure the flux of dexamethasone through the saline or vitreous gel filled chamber under standardized conditions. The diffusion coefficient of the vitreous gel and saline solution were calculated, using Fick's law and Stokes-Einstein equation.

 

Results:

 

Figure 1 shows the concentration of dexamethasone in the receptor phase with the vitreous gel (n=4) and saline solution (n=4). Double membrane was used as a reference (n=3). The lines show the mean concentration of dexamethasone (mg/ml) ±SD over time.At 24 hours, the mean concentration of dexamethasone in the receptor chamber was 0.087±0.008 mg/ml with the vitreous gel and 0.143± 0.017 mg/ml with the saline solution (figure 1).The mean flux of dexamethasone through the saline filled chamber was 16.5 µg/(hour*cm²) and 4.2 µg/(hour*cm²) with the vitreous gel. The diffusion coefficient in porcine vitreous gel is 0.00308 cm²/hour and 0.01206 cm²/hour in physiological saline solution.

 

Conclusions:

 

These preliminary results indicate that diffusion is faster in physiological saline than in vitreous humour. This finding, which is predicted by classic laws of physics can help explain some of the physiological, pharmacological and clinical consequences of vitrectomy.  

 

Keywords: vitreous • vitreoretinal surgery • vitreous substitutes