The process of percutaneous absorption involves several individual transport processes, some of which occur in series and others in parallel (see Fig. 3). The two key determinants for a solute crossing a membrane are solubility and diffusivity. The relative solubility of a solute in two phases determines its partition coefficient and, therefore, the likelihood of the solute being taken up into the SC from a vehicle. Also, solubility will determine whether a solute is likely to be desorbed from the SC into deeper layers. The diffusivity is a measure of the speed at which a solute crosses a given barrier and is affected by binding, viscosity of the environment, and the tortuosity of the path.
In the first step of the transport process, molecules must be in solution in the vehicle to partition from the vehicle into the lipids in the outermost part of the SC; they must then diffuse through it; partition back out of the SC and into the viable epidermis. Next, molecules diffuse through the viable epidermis and papillary dermis. At the capillary plexus a high percentage of molecules are transferred into the circulating blood and a lower percentage diffuses into deeper tissues (see Fig. 3). To predict the penetration of a given solute it is necessary (a) to define the skin barrier in terms of a mechanistic model, and (b) to relate transport to a physical property of the solute, such as its organic solvent-water partition coefficient. Scheuplein and Blank (5) suggested that an appropriate skin model is a multilayer barrier consisting of the SC (10 ¡m) (S1), the viable epidermis (100 ¡m) (S2), and the upper papillary layer of the dermis (100-200 ¡m) (Fig. 7). We now develop a steady-state model for skin transport consistent with this model and based on the theoretical considerations presented in Chapter 3.
A. Stratum Corneum-Vehicle Partition Coefficients
We first consider the partitioning between the SC and vehicle. The previous chapter recognized that the chemical potential gradient across a membrane is a major determinant of flux (J), the amount of solute passing through a unit area of membrane in unit time. The chemical potential of a solute in a phase is also a major determinant for its partitioning into another adjacent phase. In an ideal solution, the chemical potential of a solute jj is defined by the standard chemical potential state j0 for that solute, and its activity ai (defined as the product of its activity coefficient yi and concentration C,-, expressed as a mole fraction; i.e., at = y£), the gas constant R, and absolute temperature T:
The partitioning of a solute between the SC and vehicle is defined by the chemical potential difference between the solute in the SC jsc and that in the vehicle jv for which chemical potential is defined by Eq. (1) for each phase. At equilibrium, the chemical potential of the solute in the two phases is equal (i.e., jsc = jv) such that (55)
Rearranging and defining the ratios of yiCi as a SC-vehicle partition coefficient Kasc—v, based on activities, yields n C ! 0 — 0\
However, we could also define an SC-vehicle partition coefficient Ksc—v based on concentrations.
Ksc—V could also be defined in terms of the solubility of the solute in the SC (Ssc) and vehicle (Sv):
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