Modeling Temperature-Dependent Dermal Absorption and Clearance for Transdermal and Topical Drug Applications

Abstract

A computational model was developed to better understand the impact of elevated skin temperatures on transdermal drug delivery and dermal clearance. A simultaneous heat and mass transport model with emphasis on transdermal delivery system (TDS) applications was developed to address transient and steady-state temperature effects on dermal absorption. The model was tested using representative data from nicotine TDS applied to human skin either in vitro or in vivo. The approximately 2-fold increase of nicotine absorption with a 10°C increase in skin surface temperature was consistent with a 50–65 kJ/mol activation energy for diffusion in the stratum corneum, with this layer serving as the primary barrier for nicotine absorption. Incorporation of a dermal clearance component into the model revealed efficient removal of nicotine via the dermal capillaries at both normal and elevated temperatures. Two-compartment pharmacokinetic simulations yielded systemic drug concentrations consistent with the human pharmacokinetic data. Both in vitro skin permeation and in vivo pharmacokinetics of nicotine delivered from a marketed TDS under normal and elevated temperatures can be satisfactorily described by a simultaneous heat and mass transfer computational model incorporating realistic skin barrier properties and dermal clearance components.

Appendix. Steady-state temperature profile in the skin and subcutaneous tissues

Following the analysis of Wilson and Spence (49), steady-state temperatures in the tissue and TDS layers can be calculated by solving Eq. 6 and simplifications thereof with appropriate boundary conditions and blood flows in the various layers. The solution for the case in which the upper boundary of the SC (z = 0) is held at temperature T₀ and the lower boundary of the muscle layer (z = z₅) is assumed to be equal to the core temperature T_c is given below.

Stratum corneum (q = 0, ω = 0; i = 1):

$$ {T}_1(z)={A}_1+{A}_2z\kern0.75em 0\le z\le z1 $$

(16)

Viable epidermis (ω = 0; i = 2):

$$ {T}_2(z)={A}_3+{A}_4z-\frac{q_2}{k_2}\cdotp \frac{z_2}{2}\kern0.5em z1\le z\le z2 $$

(17)

Dermis, subcutaneous fat and muscle (i = 3, 4, 5):

$$ {T}_i(z)={T}_a-{A}_{2i-1}\cosh \left(\gamma \xi \right)-{A}_{2i}\sinh \left(\gamma \xi \right)+\frac{\phi }{\gamma^2};{z}_{i-1}\le z\le {z}_i; $$

(18)

$$ \gamma ={\left(\frac{\omega_i{c}_b}{k_i}\right)}^{1/2}{h}_i;\xi =\left({z}_3-z\right)/{h}_i;\phi =\frac{q_i}{k_i}{h}_i^2 $$

(19)

There are 10 constants of integration, A_i, two for each layer. The boundary conditions at z = 0 and z = z₅ give A₁ = T₀ and A₉ = ϕ₅ / ${\gamma}_5^2$. The other 8 constants are determined by the continuity conditions on temperature and heat flux at the four internal interfaces. The non-linear system of 8 equations and 8 unknowns can be solved by standard methods. We found that the Solver add-in to Microsoft Excel™, set to the GRG non-linear option, worked very well. Note that this method of solution differs from the sequential optimization routine described by Wilson and Spence (49).