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Wittum, Rebecca; Naegel, Arne; Heisig, Michael; Wittum, Gabriel

Mathematical modelling of the viable epidermis: impact of cell shape and vertical arrangement. (English) Zbl 1480.92042

Math. Mech. Solids 25, No. 5, 1046-1059 (2020).
Summary: In-silico methods are valuable tools for understanding the barrier function of the skin. The key benefit is that mathematical modelling allows the interplay between cell shape and function to be elucidated. This study focuses on the viable (living) epidermis. For this region, previous works suggested a diffusion model and an approximation of the cells by hexagonal prisms. The work at hand extends this in three ways. First, the extracellular space is treated with full spatial resolution. This induces a decrease of permeability by about 10%. Second, cells of tetrakaidecahedral shape are considered, in addition to the original hexagonal prisms. For both cell types, the resulting membrane permeabilities are compared. Third, for the first time, the influence of cell stacking in the vertical direction is considered. This is particularly important for the stratum granulosum, where tight junctions are present.

MSC:

92C30 Physiology (general)
92C10 Biomechanics
92-10 Mathematical modeling or simulation for problems pertaining to biology

Keywords:

skin; in silico; mathematical model; viable epidermis

Software:

SuperLU; pcl; libAlgebra; libDiscretization; libGrid; UG4
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\textit{R. Wittum} et al., Math. Mech. Solids 25, No. 5, 1046--1059 (2020; Zbl 1480.92042)
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