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

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.


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


[1] Couto, A, Fernandes, R, Cordeiro, M, et al. Dermic diffusion and stratum corneum: a state of the art review of mathematical models. J Controlled Release 2013; 177: 74-83.
[2] Anissimov, Y, Jepps, O, Dancik, Y, et al. Mathematical and pharmacokinetic modelling of epidermal and dermal transport processes. Adv Drug Delivery Rev 2013; 65: 169-190.
[3] Chen, L, Han, L, Lian, G. Recent advances in predicting skin permeability of hydrophilic solutes. Adv Drug Delivery Rev 2013; 65: 295-305.
[4] Dancik, Y, Miller, M, Jaworska, J, et al. Design and performance of a spreadsheet-based model for estimating bioavailability of chemicals from dermal exposure. Adv Drug Delivery Rev 2013; 65: 221-236.
[5] Frasch, H, Barbero, A. Application of numerical methods for diffusion-based modeling of skin permeation. Adv Drug Delivery Rev 2013; 65: 208-220.
[6] Jepps, O, Dancik, Y, Anissimov, Y, et al. Modeling the human skin barrier – towards a better understanding of dermal absorption. Adv Drug Delivery Rev 2013; 65: 152-168.
[7] Mitragotri, S, Anissimov, YG, Bunge, AL, et al. Mathematical models of skin permeability: an overview. Int J Pharm 2011; 418(1): 115-129.
[8] Naegel, A, Heisig, M, Wittum, G. Detailed modeling of skin penetration – an overview. Adv Drug Delivery Rev 2013; 65: 191-207.
[9] Adams, M, Mallet, D, Pettet, G. Towards a quantitative theory of epidermal calcium profile formation in unwounded skin. PLOS One 2015; 10: e0116751.
[10] Nitsche, J, Kasting, G. A microscopic multiphase diffusion model of viable epidermis permeability. Biophys J 2013; 104(10): 2307-2320.
[11] Cleek, RL, Bunge, AL. A new method for estimating dermal absorption from chemical exposure. 1. General approach. Pharm Res 1993; 10: 497-506.
[12] Matzke, EB. An analysis of the orthic tetrakaidecahedron. Bull Torrey Bot Club 1927; 54(4): 341-348.
[13] Yokouchi, M, Atsugi, T, van Logtestijn, M, et al. Epidermal cell turnover across tight junctions based on Kelvin’s tetrakaidecahedron cell shape. eLIFE 2016; 5: e19593.
[14] Kelvin, WT. On the division of space with minimal partitional area. Philos Mag 1887; 24: 503-514. · JFM 19.0520.02
[15] Naegel, A, Heisig, M, Wittum, G. A comparison of two- and three-dimensional models for the simulation of the permeability of human stratum corneum. Eur J Pharm Biopharm 2009; 72(2): 332-338.
[16] Muha, I, Naegel, A, Stichel, S, et al. Effective diffusivity in membranes with tetrakaidekahedral cells and implications for the permeability of human stratum corneum. J Membr Sci 2011; 368(1-2): 18-25.
[17] Feuchter, D, Heisig, M, Wittum, G. A geometry model for the simulation of drug diffusion through the stratum corneum. Comput Visual Sci 2006; 9: 117-130.
[18] Fick, A. Über Diffusion. Poggendorff’s Annalen der Physik 1855; 94: 59-86.
[19] Feuchter, D. Geometrie- und Gittererzeugung für anisotrope Schichtengebiete. PhD Thesis, Ruprecht-Karls-Universität, Germany, 2008.
[20] Scherer, M. Modellierung des Schwellens von Korneozyten im Stratum Corneum. PhD Thesis, Johann Wolfgang Goethe-Universität, Germany, 2012.
[21] Wittum, R. Modeling diffusion through cellular membranes. Master’s Thesis, Karlsruhe Institute of Technology, Germany, 2016.
[22] Vogel, A, Reiter, S, Rupp, M, et al. UG4: a novel flexible software system for simulating PDE based models on high performance computers. Comput Visual Sci 2014; 16: 165-179. · Zbl 1375.35003
[23] Li, XS. An overview of SuperLU: algorithms, implementation, and user interface. ACM Trans Math Software 2005; 31: 302-325. · Zbl 1136.65312
[24] Brandner, JM. Tight junctions and tight junction proteins in mammalian epidermis. Eur J Pharm Biopharm 2009; 72(2): 289-294.
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