ABSTRACT
The objective of any mathematical model describing dermal absorption is to
represent the processes associated with solute partitioning into and penetration
through stratum corneum (SC) accurately, model various experimental data and
predict outcomes under varying conditions or, in the context of this chapter, under
different exposure scenarios. As mathematical modelling in percutaneous absorp-
tion has been described in some detail in Ref. 1, we have concentrated here on
elaborating the mathematical approach presented in Ref. 1 to account for different
exposure scenarios (Fig. 1). In mathematical modelling, some solutions often suffer
from being too complex to be practically useful; therefore, in this work we give
priority to simple approximations and consider simplifying assumptions. Solutions
in the time domain are presented only when they could be expressed in a simple
form. The emphasis in this chapter is on using Laplace domain solutions, which
often are presented in simple closed form (no infinite series involved) and allow
derivation of equations for some important model outcomes (e.g., total amount of
solute absorbed, amount absorbed over long periods of time). The attractiveness of
Laplace domain solutions is enhanced by the existence of standard nonlinear
regression programs such as MULTI FILT, MINIM, and SCIENTIST, which enable
fast analysis of experimental data using Laplace domain solutions directly, and
avoid computational complexities associated with infinite series solutions,
especially those involving solving transcendental equations. For a complex
exposure scenario, analytical solutions, even in the Laplace domain, are often
nonattainable or far too complex. In order to deal with such situations, in this
chapter we outline a simple numerical approach to computationally model these
complex exposure conditions.
