DEPLETION EFFECTS IN TOPICAL PREPARATIONS 169 application for test and standard preparations, also the thickness of the preparation. After elimination of the ointment film thickness, the resulting bioavailability factors are called fh: log fh = log CResp%S T - log CResp%T (Eq. 3a) fh = CResp%ST/CResp%T (Eq. 3b) fh = RT ' hT/(RsT hST) = PBT/PBsT (Eq. 3c) From measurements of the permeant, penetration rate bioavailability factors may there- fore be determined as the ratio of the permeant permeabilities PB = Dn' PCn/v/d n obtained with the test vehicles and the standard vehicle. The permeant permeability PB is calculated as the steady-state permeant penetration rate multiplied by the preparation thickness (=V/A) and divided by the permeant amount in the vehicle. Enhancement factor EF. Enhancement factors may be calculated by dividing the bioavail- ability factors fh by the relative effective activity coefficient •/T/ST (Eq. 4a), which is defined as the ratio of the permeant partition coefficients ST/reference phase and T/ref- erence phase (13). Procedures to determine these partition coefficients have been de- scribed (10,13). EF --- fh/YT/ST = fa (Eq. 4a) In absence of penetration enhancement and permeant depletion, fh equals •T/ST' En- hancement factors EF, which sometimes are called activity-standardized bioavailability factors fa (14), may be calculated from the horizontal distance between activity-response curves, where the relative permeant activity a is the product of the permeant concen- tration in the vehicle and •/T/ST' log EF = log aResp%S T - log aResp%T (Eq. 4b) EF = aResp%ST/aResp%T (Eq. 4c) With activity-response curves, not only the influence of the preparation thickness h but also the influence of the permeant solubility in the vehicle CsB on the bioavailability factor f is mathematically eliminated. Provided that the thickness of the stratum cor- neum is not affected by the ointment bases, enhancement factors are only dependent on the permeant diffusion coefficient DB and the permeant solubility in the barrier CsB and may therefore be written as EF = DB T ß CSBT/(DBsT ' CSBsT ) (Eq. 4d) In the case of the penetration rate data, EF values may also be calculated as the ratio of the steady-state permeant penetration rates from a test vehicle (ssPRaT) and the standard vehicle (ssPRasT) , provided that the permeant activity a is the same in all vehicles and again assuming equal application areas for test and standard preparations. EF = ssPRaT/ssPRasT (Eq. 4e) Equal permeant activities in the vehicles may be obtained if the initial permeant con- centration in the standard vehicle is divided by the 3'T/ST value of the test vehicles. The direct influence of the factors A, V, and csv on the bioavailability factor f may be eliminated by the above-mentioned mathematical procedures. However, it has to be taken into consideration that the contribution of all of these factors to permeant deple- tion cannot be eliminated by these calculations, a fact which may lead to a false

170 JOURNAL OF COSMETIC SCIENCE estimation of the relative bioavailability as a result of an insufficient parallelism of the dose-response curves resp. a reduction in the penetration rate. If an enhancement effect is mainly caused by an increase of the permeant diffusion coefficient in the stratum comeurn, it has to be considered that the lag time, which depends not only on the thickness of the barrier but also on the permeant diffusion coefficient in the barrier (15), may also influence the shape of the dose-, concentration-, or activity-response curves, particularly those obtained with the response parameter 1/LT: the resulting curves do not run parallel to each other and different plateau values may be reached. In this case a correct estimation of the bioavailability factor from the distance of the curves is impossible. However, it has been found that pronounced penetration enhancement is mainly caused by an increase of the permeant solubility in the barrier csn rather than by an increase of the permeant diffusion coefficient Dn (16). Depletion factor DF. Any increase of R leads to a more or less pronounced permeant depletion. This phenomenon is not described by the above-mentioned equations. With the data of both in vivo studies, permeant depletion, which usually occurs under finite- dose conditions and which manifests itself in a significant decrease of the permeant penetration rate and thus in an insufficient parallelism of the dose-, concentration-, or activity-response curves, can be quantified. In order to do so, a so-called depletion factor DF is introduced and can be calculated from the infinite-dose (inf) and finite-dose (fin) enhancement factors EF as follows: DF = EFinf/EFoein (Eq. 5) Depending on which vehicle is chosen as standard, these depletion factors can reach values greater or smaller than unity. A standard vehicle that shows pronounced pen- etration-enhancing properties leads to values • 1, whereas an inert standard vehicle leads to values • 1. It again has to be mentioned that not only Dn and csn as described by the enhancement factor but every single factor included in R contributes to the extent of permeant depletion. RESULTS AND DISCUSSION The bioavailability factors fh resulting from the in vivo studies are shown in Figure 3. As the extent of permeant input can be assumed to be 100% with all three methods, any differences in fh are attributable to differences in the rate of permeant input. In absence of penetration enhancement and depletion effects, all data points should be located on the theoretical straight line described by the equation fh = •/T/S•:' Deviations from the straight line may be interpreted as follows: higher values as in the case of IPM result from penetration enhancement, whereas lower values indicate MN depletion of the preparations, which is particularly obvious in the case of the response parameter duration of the erythema. Permeant depletion manifests itself in an insufficient parallelism of the concentration-response curves, which may lead to an underestimation of fh if the stan- dard vehicle is inert with regard to penetration enhancement and shows the highest MN solubility as compared to the test vehicles. As in the case of the time of onset, the duration of the effect, i.e., the time period during which the MN concentration at the receptor site is above the threshold concentration required for an effect to become obvious, depends on the permeant penetration rate and thus on R and the applied permeant dose. If the penetration rate decreases rapidly over time as in the case of high