Fick’s Second Law of Diffusion has long been employed to describe in vitro percutaneous permeation experiments: Numerical solution in percutanous drug absorption Thesis, USM, Malaysia

1. Introduction

Fick’s Second Law of Diffusion has long been employed to describe in vitro percutaneous permeation experiments where the steady state is eventually attained (see [27–29]). When the donor cell concentration, C, is maintained at a constant value, the drug flux per unit area from the donor cell to the receptor cell, through the skin, approaches the steady-state flux, Jss , which is

related to C by the formula
Jss ¼ Kp C;

where Kp is the permeability coefficient. When Fick’s Law prevails, and provided the skin may be regarded as a simple diffusion membrane and the skin–receptor cell-boundary clearance may be assumed to be very large, the permeability coefficient may also be written in the form
Kp ¼ KmDs=Ls; ð2Þ

where Km is the vehicle (donor cell)-skin partition coefficient and Ds is the diffusion coefficient of a drug through the skin which has thickness Ls . Experimental values for Km and Ds for various compounds have been estimated using (1) and (2) in [27–29].

It is only recently, however, that this simple diffusion membrane model has been applied to processes in which a finite dose is applied topically [1,5,8,10,18,20,26,30] as well as to processes after removal [16,17,20,32]. I

n finite-dose processes, two parameters, the diffusion parameter, kd, and the partition parameter, ‘d , [25] (called the apparent length of diffusion in [18]), are employed.
These are defined by
kd ¼ Ds=L2
and
‘d ¼ KmLs;
respectively, and are used in pharmacokinetics when a process approaching the steady state is under consideration. The lag-time, TL , has been estimated to be TL ¼ 1=ð6kdÞ; this estimate was used by Barry [2], Crank [6] and Kubota and Twizell [21]. The parameters kd and ‘d are connected to Kp by the formula
Kp ¼ kd‘d.

Sometimes, in the description of finite-dose percutaneous-absorption kinetics, the diffusivity of a drug in the vehicle, of which the thickness is Lv , is taken to be very large and the skin-receptor cell clearance (or skin-capillary clearance for in vivo conditions) to be very large also [1,5,10,20,26,30]. A few papers describe the diffusion processes of finite doses of a drug, assuming
that the diffusion coefficient of the drug, Dv , through the vehicle has a finite value (see [13,18,19,22]) and that the skin-receptor cell (capillary) clearance per unit area, per unit con- centration excess at the skin surface, CL, also has a finite value [9,13,15–19,32]. When this clearance process is incorporated into the model the normalized skin-capillary clearance, kc , found by the formula
kc ¼ CL=Ls,

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