|
|
Mathematical Model
for the Disposition of Volatile Compounds on Skin Following Topical
Application
Penpan Saiyasombati, University of Cincinnati, Cincinnati, OH, USA (Corresponding
Author)
Gerald B. Kasting, University of Cincinnati, Cincinnati, OH, USA
Purpose
To develop a mathematical model for predicting the absorption and evaporation
of volatile materials from skin, for use in dermal exposure assessment
and improved understanding of dose-related contact allergy.
Background
Allergy to perfume is known to be among the most common causes of cosmetic
contact dermatitis. Currently, 100% absorption (an overestimate for volatile
ingredients) is assumed for dermal exposure assessments. To improve the
current dermal risk assessment process for volatile materials, a mathematical
model for accurately estimating the actual fraction that will be dermally
absorbed is desired.
Methods
As a first step in this undertaking, we considered a first-order kinetic
approach, which is expected to be applicable for small doses applied to
skin. Skin penetration rate was calculated as a fraction of the maximum
flux estimated from the compound’s lipid solubility, Slip = KoctSw, and
molecular weight, MW [Koct = octanol/water partition coefficient, Sw =
water solubility]. Evaporation rates were estimated from a modified Henry’s
Law approach with a stagnant boundary layer whose thickness is a function
of surface airflow, v. At a given value of v, evaporation rate is proportional
to Pvp/Slip, where Pvp is the vapor pressure of the ingredient at skin
temperature. Values of Pvp were estimated from structure and normal boiling
points using a commercially available program.
Results
The model predicts a relationship for total evaporation from skin of the
form %evap = 100x/(k + x) where x = PvpMW2.7/(KoctSw) and k is a parameter
that varies inversely with v. Comparison with published data on perfume
evaporation from human skin in vivo (Vuilleumier et al., Int. J. Cosmet.
Sci., 1995) showed good agreement between theory and experiment for two
closely related perfume mixtures (r² = 0.52-0.74, s = 12-14%, n =
10).
Conclusions
The proposed model has a good prospect of providing skin absorption estimates
suitable for use in exposure assessment.
Next Steps
The current model assumes no ingredient interactions. Better predictions
may be attained by incorporating composition-dependent activity coefficients,
calculated according to the UNIFAC method, into the model. Results of
initial calculations of this nature will be reported.
|
