We present a three-dimensional geometry model with tetrakaidecahedra for the biphasic model stratum corneum (SC) membrane ΩSC consisting of corneocytes embedded in a lipid matrix. Two practical domains for ΩSC are realized: the simple model SC-membrane ΩsSC and a realistic model SC-membrane ΩrSC with dimensions for abdominal human SC. The new geometry model uses tetrakaidecahedra as basic units. It is possible to assemble the tetrakaidecahedra one upon the other and side by side without gaps in a densest packing and with minimal area for all required interfaces. Geometric characteristics such as length, depth, height and angles of the corneocytes as well as the thickness of the lipid channels can be chosen arbitrarily. Furthermore, we are able to control the shift of the corneocytes and our concept allows to assemble many corneocytes in rows, columns and layers all embedded in a lipid matrix. With the aid of this concept the non-steady-state problem of drug diffusion within a three-dimensional, biphasic model SC-membrane, such as ΩsSC or ΩrSC, having homogeneous lipid and corneocyte phases is solved numerically with a multigrid method. The numerical computations are done with our simulation system UG. Our method for solving the diffusion problem is validated with homogeneous model SC-membranes with varying size of corneocytes and lipid channels, different numbers of corneocytes, and corneocyte alignment. Several time-dependent drug concentration profiles within the heterogeneous model SC-membranes are calculated and graphically shown for different values of relative corneocyte permeability ε =D cor/D lip.
ASJC Scopus subject areas
- Theoretical Computer Science
- Modeling and Simulation
- Computer Vision and Pattern Recognition
- Computational Theory and Mathematics