# Modelling Transdermal Permeation of Volatiles from Complex Product Formulations

## TL;DR

This study creates a new model to predict how volatile ingredients in topical products evaporate and penetrate the skin, improving predictions of their bioavailability.

## Contribution

A novel framework couples evaporation and permeation dynamics using activity coefficients and UNIFAC for volatile activity computation.

## Key findings

- The model predicted transdermal permeation of 4-Tolunitrile and Nitrobenzene with reasonable accuracy after optimizing evaporation coefficients.
- Initial FSG-based evaporation estimates were higher than optimized values, which were still significantly larger than SE-derived values.
- The model's accuracy improved with optimized evaporation coefficients but showed limited gains from tuning internal skin parameters.

## Abstract

Background: The evaporation of volatile ingredients from topical formulations strongly influences transdermal permeation and overall bioavailability, yet coupled evaporation–permeation dynamics are mostly simplified or neglected in existing models. Methods: We developed a mechanistic framework that couples Fickian gas-phase evaporation and transdermal permeation, both driven by the activity coefficients of volatiles. The model equations are implemented in a hybrid MATLAB–Python architecture with the volatile activity computed on-the-fly using UNIFAC and the gas-phase diffusivity calculated by the kinetic equation of Fuller–Schettler–Giddings (FSG). Initial validation used published IVPT data for 4-Tolunitrile and Nitrobenzene. Results: For 4-Tolunitrile, the FSG-based model estimated an initial evaporation coefficient of Kevap,i = 7.9348 × 10−10 mol·cm−2·s−1, and parameter optimization converged to 8.3929 × 10−11 mol·cm−2·s−1 (≈1/10 of the FSG estimate). The optimized model predicted an accumulation amount of 19.15% versus an experimental value of 16.97% in the receptor fluid (RF) at 24 h. For Nitrobenzene, the FSG initial estimation value of Kevap,i = 6.6480 × 10−10 mol·cm−2·s−1 was optimized to 8.1174 × 10−11 mol·cm−2·s−1 (≈1/8 of the FSG value), and the predicted amount of 24 h RF is 27.61% (experimental 23.19%). Both optimized Kevap,i values are roughly one order of magnitude lower than the initial FSG estimates, but >20× larger than Stokes–Einstein (SE)-derived values. Sensitivity scans show that further tuning of internal skin parameters (e.g., diffusion coefficient (DSC,i) and partition coefficient (PSCw,i)) produced only marginal improvements in RF prediction once Kevap,i was optimized. Conclusions: The coupled evaporation–permeation framework reproduces key IVPT kinetics for volatile solutes when the effective evaporation coefficient is calibrated. The kinetic-theory estimates (FSG-based) are a reasonable starting point, but typically overestimate the evaporation rate constant under finite-dose unoccluded IVPT conditions. By implementing the on-the-fly computation of volatile activity using UNIFAC, the approach is extensible to modelling transdermal permeation of volatiles from multicomponent/non-ideal formulations.