The skin forms much of its bartrier function by having the complex arrangement of nearly impermeable corneocyte blocks. It is known that in the skin these corneocytes are actually like hexagonal paving slabs, with a height of about 1 micrometre, and a width of 40 micrometres. How these sheets of corneocytes (or patios) stack on top of each other is not so well prescribed. In some places on some mammals, they may be fully aligned, in others they may be fully staggered. The effect of this staggering is one issue we have been working on.

Consider the two dimensional equivalent of the hexes - the so called brick-and-mortar model. In this we have three cases of interest, namely fully aligned, fully staggered, and those that fall between the two which we call partially staggered. We measure this using the parameter K to indicate the offset from fully aligned.

K=0

K=1/6

K=1/3

K=1/2

The use of periodicity with unstructured tetrahedral meshes means that the initial mesh must be suitably constructed, and that the underlying solver must be able to handle this continuity. The mesh generator used in this project is Netgen. This allows us to specify the initial geometry in terms of geometric shapes, for which we use the corneocytes as replicated blocks inside a domain we term the unit cell. We can then identify faces on the unit cell as being periodic with each other, hence meaning that the vertices generated during the surface meshing stage and coincident across the periodic boundaries.

An example of this periodicity in action can be seen in the following example of chemical diffusing between partly 2-d staggered corneocytes with thick lipid layers. The chemical is applied on the top of the domain in the centre, although it does not fully cover the corneocyte, but is centred just to the left of the first route down to the next layer. This is clearly a very artifical example as we are imagining an identical application of chemical on the next corneoctye across in each direction. The image to the right shows the concentration of chemical in the domain at steady state, with red indicating low concentration, up to magenta with high concentration. There is also a movie of how we get here.

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