Analysis

The analysis of the experimental diffusion data is based on the "constant gradient" assumption [7]. For relatively large vessel volumes and a relatively thin specimen, the concentration profile across the specimen, after a suitable initialization time, is nearly a straight line. Based on this assumption, the concentration gradient across the sample is a constant, equal to the difference between cell concentrations, divided by the sample thickness L. Under these ideal conditions, Fick's law (Eqn. 1) should apply. For vessel volumes v₁ and v₂ and sample area A, the difference in concentration $\Delta$ between the two vessels can be shown to decay exponentially [7,41]:

$$\frac{\Delta}{\Delta_0} = \exp\left[\frac{-D^a A}{L} \left(v_1^{-1}+v_2^{-1}\right)\,t\right]$$ (10)

The quantity $\Delta_0$₀ is the concentration difference at the onset of a linear concentration profile. Based on Eqn. 10, a semi-log plot of the concentration difference between the two vessels should appear as a straight line under ideal conditions; the magnitude of the slope being proportional to the apparent diffusion coefficient D^a. Deviations from a straight line will indicate behavior that cannot be modeled by Fick's law with a constant apparent diffusion coefficient.