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Computational Modeling of the Skin Barrier

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Permeability Barrier

Part of the book series: Methods in Molecular Biology ((MIMB,volume 763))

Abstract

A simulation environment for the numerical calculation of permeation processes through human skin has been developed. In geometry models that represent the actual cell morphology of stratum corneum (SC) and deeper skin layers, the diffusive transport is simulated by a finite volume method. As reference elements for the corneocyte cells and lipid matrix, both three-dimensional tetrakaidecahedra and cuboids as well as two-dimensional brick-and-mortar models have been investigated. The central finding is that permeability and lag time of the different membranes can be represented in a closed form depending on model parameters and geometry. This allows a comparison of the models in terms of their barrier effectiveness at comparable cell sizes. The influence of the cell shape on the barrier properties has been numerically demonstrated and quantified. It is shown that tetrakaidecahedra in addition to an almost optimal surface-to-volume ratio also has a very favorable barrier-to-volume ratio. A simulation experiment was successfully validated with two representative test substances, the hydrophilic caffeine and the lipophilic flufenamic acid, which were applied in an aqueous vehicle with a constant dose. The input parameters for the simulation were determined in a companion study by experimental collaborators.

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References

  1. Scheuplein, R.J., Blank, I.H. (1971) Permeability of the skin. Physiol. Rev. 51, 702–747

    PubMed  CAS  Google Scholar 

  2. Barry B.W. (1991) Modern methods of promoting drug absorption through the skin. Mol. Aspects Med. 12, 195–241

    Article  PubMed  CAS  Google Scholar 

  3. Rim, J.E., Pinsky, P.M., van Osdol, W.W. (2007) Using the method of homogenization to calculate the effective diffusivity of the stratum corneum. J. Membr. Sci. 293, 174–182

    Article  CAS  Google Scholar 

  4. Rim, J.E., Pinsky, P.M., van Osdol, W.W. (2008) Using the method of homogenization to calculate the effective diffusivity of the stratum corneum with permeable corneocytes. J. Biomech. 41, 788–796

    Article  PubMed  Google Scholar 

  5. Wagner, C. (2008) Dreidimensionale digitale Rekonstruktion des humanen stratum corneum der Haut in Kombination mit Simulation substantieller Diffusion durch das stratum corneum, Veterinary University of Hannover, PhD thesis (in German).

    Google Scholar 

  6. Thomson, W., Lord Kelvin (1887) On the division of space with minimum partitional area. Phil. Mag. 24, 503

    Google Scholar 

  7. Feuchter, D., Heisig, M., Wittum, G. (2006) A geometry model for the simulation of drug diffusion through the stratum corneum. Comp. Visual. Sci. 9, 117–130

    Article  CAS  Google Scholar 

  8. Christophers, E., Wolff, H.H., Laurence, E.B. (1974) The formation of epidermal cell columns. J. Invest. Dermatol. 62, 555–559

    Article  PubMed  CAS  Google Scholar 

  9. Menton, D.N. (1976) A liquid film model of tetrakaidecahedral packing to account for the establishment of epidermal cell columns. J. Invest. Dermatol. 66, 283–291

    Article  PubMed  CAS  Google Scholar 

  10. Allen, T.D., Potten, C.S. (1976) Significance of cell shape in tissue architecture. Nature 264, 545–547

    Article  PubMed  CAS  Google Scholar 

  11. Feuchter, D. (2008) Geometrie- und Gittererzeugung fuer anisotrope Schichtengebiete, University of Heidelberg, PhD thesis (in German).

    Google Scholar 

  12. Richter, T., Mueller, J.H., Schwarz, U.D., Wepf, R., Wiesendanger, R. (2001) Investigation of the swelling of human skin cells in liquid media by tapping mode scanning force microscopy. Appl. Phys. A 72, 125–128

    Article  Google Scholar 

  13. Richter, T., Peuckert, C., Sattler, M., Koenig, K., Riemann, I., Hintze, U., Wittern, K-P., Wiesendanger, R., Wepf, R. (2004) Dead but highly dynamic – The stratum corneum is divided into three hydration zones. Skin Pharmacol. Physiol. 17, 246–257

    Article  PubMed  CAS  Google Scholar 

  14. Bouwstra, J.A., de Graaff, A., Gooris, G.S., Nijsse, J., Wiechers, J.W., van Aelst, A. C. (2003) Water distribution and related morphology in human stratum corneum at different hydration levels. J. Invest. Dermatol. 120, 750–758

    Article  PubMed  CAS  Google Scholar 

  15. Kashibuchi, N., Hirai, Y., O’Goshi, K., Tagami, H. (2002) Three-dimensional analyses of individual corneocytes with atomic force microscope: morphological changes related to age, location and to the pathologic skin conditions. Skin Res. Technol. 8, 203–211

    Article  PubMed  Google Scholar 

  16. Mihara, M. (1988) Scanning electron microscopy of skin surface and the internal structure of corneocyte in normal human skin. An application of the osmium-dimethyl sulfoxide-osmium method. Arch. Dermatol. Res. 288, 293–299

    Google Scholar 

  17. Anderson, R.L., Cassidy, J.M. (1973) Variation in physical dimensions and chemical composition of human stratum corneum. J. Invest. Dermatol. 61, 30–32

    Article  PubMed  CAS  Google Scholar 

  18. Raykar, P.V., Fung, M.C., Anderson, B.D. (1988) The role of protein and lipid domains in the uptake of solutes by human stratum corneum. Pharm. Res. 5, 140–150

    Article  PubMed  CAS  Google Scholar 

  19. Heisig, M., Lieckfeldt, R., Wittum, G., Mazurkevich, G., Lee, G. (1996) Non steady-state descriptions of drug permeation through stratum corneum. I. The biphasic brick-and-mortar model. Pharm. Res. 13, 421–426

    CAS  Google Scholar 

  20. Johnson, M.E., Blankschtein, D., Langer, R. (1997) Evaluation of solute permeation through the stratum corneum: lateral bilayer diffusion as the primary transport mechanism. J. Pharm. Sci. 86, 1162–1172

    Article  PubMed  CAS  Google Scholar 

  21. Barbero, A.M., Frasch, H.F. (2006) Transcellular route of diffusion through stratum corneum: Results from finite element models. J. Pharm. Sci. 95, 2186–2194

    Article  PubMed  CAS  Google Scholar 

  22. Wang, T.-F., Kasting, G.B., Nitsche, J.M. (2006) A multiphase microscopic diffusion model for stratum corneum permeability. I. Formulation, solution, and illustrative results for representative compounds. J. Pharm. Sci. 95, 620–648

    Article  PubMed  CAS  Google Scholar 

  23. COMSOL is a multiphysics software package for performing finite-element-method (FEM) simulations. See COMSOL AB, http://www.comsol.com/.

  24. Bastian, P., Wittum, G. (1994) Robustness and adaptivity: The UG concept. In: Hemker, P., Wesseling, P. (eds.): Multigrid Methods IV, Birkhäuser, Basel.

    Google Scholar 

  25. Lang, S., Wittum, G. (2005) Large scale density driven flow simulations using parallel unstructured grid adaptation and local multigrid methods. Concurrency Computat. 17, 1415–1440

    Article  Google Scholar 

  26. Bank, R.E., Rose, D.J. (1987) Some error-estimates for the box method. SIAM J. Numer. Anal. 24(4), 777–787

    Article  Google Scholar 

  27. Cai, Z. (1991) On the finite volume element method. Numer. Math. 58, 713–735

    Google Scholar 

  28. Michev, I.D. (1996) Finite Volume and Finite Volume Element Methods for Nonsymmetric Problems. PhD thesis, Texas A&M Univ., Inst. for Scientific Computation, 612 Blocker, College Station, Texas 77843–3404, USA. Also available as Technical Report ISC-96-04-MATH.

    Google Scholar 

  29. Bensoussan, A., Lions, J. L., Papanicolaou, G. (1978) Asymptotic analysis for periodic structures. North-Holland Publishing. Amsterdam, New York, Oxford.

    Google Scholar 

  30. Neuss, N. (1996) Homogenisierung und Mehrgitter, University of Heidelberg, PhD thesis (in German).

    Google Scholar 

  31. Muha, I., Naegel, A., Stichel, S., Grillo, A., Heisig, M., Wittum, G. (2011) Effective diffusivity in membranes with tetrakaidekahedral cells and implications for the permeability of human stratum corneum. J. Membr. Sci. 368, 18–25

    Google Scholar 

  32. Michaels, A.S., Chandrasekaran, S.K., Shaw, J.E. (1975) Drug permeation through human skin: theory and in vitro experimental measurement. AIChE J. 21, 985–996.

    Article  CAS  Google Scholar 

  33. Albery, W.J., Hadgraft, J. (1979) Percutaneous absorption: theoretical description. J. Pharm. Pharmacol. 31,129–139.

    Article  PubMed  CAS  Google Scholar 

  34. Gienger, G., Knoch, A., Merkle, H.P. (1986) Modeling and numerical computation of drug transport in laminates: model case evaluation of transdermal delivery system. J. Pharm. Sci. 75 (1) 9–15.

    Article  PubMed  CAS  Google Scholar 

  35. Tojo, K. (1987) Random brick model for drug transport across stratum corneum. J. Pharm. Sci. 76, 889–891.

    Article  PubMed  CAS  Google Scholar 

  36. Edwards, D.A., Langer R. (1994) A linear theory of transdermal transport phenomena. J. Pharm. Sci. 83, 1315–1334

    Article  PubMed  CAS  Google Scholar 

  37. Lee, A.J., King, J.R., Barrett D.A. (1997) Percutaneous absorption: a multiple pathway model. J. Control. Rel. 45, 141–151

    Article  CAS  Google Scholar 

  38. Manitz, R., Lucht, W., Strehmel, K., Weiner, R., Neubert, R. (1998) On mathematical mode­ling of dermal and transdermal drug delivery. J. Pharm. Sci. 87, 873–879

    Article  PubMed  CAS  Google Scholar 

  39. Anissimov, Y.G., Roberts, M.S. (1999) Diffusion modeling of percutaneous absorption kinetics. 1. Effects of flow rate, receptor sampling rate, and viable epidermal resistance for a constant donor concentration. J. Pharm. Sci. 88, 1201–1209

    Article  PubMed  CAS  Google Scholar 

  40. Charalambopoulou, G.Ch., Karamertzanis, P., Kikkinides, E.S., Stubos, A.K., Kanellopoulos, N.K., Papaioannou, A.Th. (2000) A study on structural and diffusion properties of porcine stratum corneum based on very small angle neutron scattering data. Pharm. Res. 17, 1085–1091

    Google Scholar 

  41. Anissimov, Y.G., Roberts, M.S. (2001) Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids. J. Pharm. Sci. 90, 504–520

    Google Scholar 

  42. Frasch, H.F. (2002) A random walk model of skin permeation. Risk Analysis 22, 265–276

    Article  PubMed  Google Scholar 

  43. Kubota, K., Dey, F., Matar, S.A., Twizell, E.H. (2002) A repeated-dose model of ­percutaneous drug absorption. Appl. Math. Modelling 26, 529–544

    Article  Google Scholar 

  44. Mitragotri, S. (2003) Modeling skin permeability to hydrophilic and hydrophobic solutes based on four permeation pathways. J. Contr. Rel. 86, 69–92

    Article  CAS  Google Scholar 

  45. Frasch, H.F., Barbero, A.M. (2003) Steady-state flux and lag time in the stratum corneum lipid pathway: results from finite element models. J. Pharm. Sci. 92, 2196–2207

    Article  PubMed  CAS  Google Scholar 

  46. Anissimov, Y.G., Roberts, M.S. (2004) Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics. J. Pharm. Sci. 93, 470–487

    Article  PubMed  CAS  Google Scholar 

  47. George, K., Kubota, K., Twizell, E.H. (2004) A two-dimensional mathematical model of percutaneous drug absorption. BioMedical Engineering OnLine 3,18

    Google Scholar 

  48. George, K. (2005) A two-dimensional mathematical model of non-linear dual-sorption of percutaneous drug absorption. BioMedical Engineering OnLine 4,40

    Article  PubMed  CAS  Google Scholar 

  49. Rim, J.E., Pinsky, P.M., van Osdol, W.W. (2005) Finite element modeling of coupled diffusion with partitioning in transdermal drug delivery. Ann. Biomed. Eng. 33, 1422–1438

    Article  PubMed  Google Scholar 

  50. Barbero, A.M., Frasch, H.F. (2005) Modeling of diffusion with partitioning in stratum corneum using a finite element model. Ann. Biomed. Eng. 33, 1281–1292

    Article  PubMed  Google Scholar 

  51. Mollee, T.R., Bracken, A.J. (2007) A model of solute transport through stratum corneum using solute capture and release. Bull. Math. Biol. 69, 1887–1907

    Article  PubMed  CAS  Google Scholar 

  52. Chen, L., Lian, G., Han, L. (2008) Use of “bricks and mortar” model to predict transdermal permeation: model development and initial validation. Ind. Eng. Chem. Res. 47 (17), 6465–6472

    Article  CAS  Google Scholar 

  53. Naegel, A., Hansen, S., Neumann, D.,, Lehr, C.M., Schaefer, U.F., Wittum, G., Heisig, M. (2008) In-silico model of skin penetration based on experimentally determined input parameters. Part II: Mathematical modelling of in-vitro diffusion experiments. Identification of critical input parameters. Eur. J. Pharm. Biopharm. 68, 368–379

    Google Scholar 

  54. Hansen, S., Henning, A., Naegel, A., Heisig, M., Wittum, G., Neumann, D., Kostka, K.- H., Zbytovska, J., Lehr, C.M., Schaefer, U. F. (2008) In-silico model of skin penetration based on experimentally determined input parameters. Part I: Experimental determination of partition and diffusion coefficients. Eur. J. Pharm. Biopharm. 68, 352–367

    Google Scholar 

  55. Anissimov, Y.G., Roberts, M.S. (2009) Diffusion modeling of percutaneous absorption kinetics: 4. Effects of a slow equilibration process within stratum corneum on absorption and desorption kinetics. J. Pharm. Sci. 98, 772–781

    Google Scholar 

  56. Rim, J.E., Pinsky, P.M., van Osdol, W.W. (2009) Multiscale modeling framework of transdermal drug delivery. Ann. Biomed. Eng. 37, 1217–1229

    Article  PubMed  Google Scholar 

  57. Naegel, A., Heisig, M., Wittum, G. (2009) A comparison of two- and three-dimensional models for the simulation of the permeability of human stratum corneum. Eur. J. Pharm. Biopharm. 72, 332–338

    Google Scholar 

  58. Goodyer, C.E., Bunge, A.L. (2009) Comp­arison of numerical simulations of barrier membranes with impermeable flakes. J. Membr. Sci. 329, 209–218

    Google Scholar 

  59. Mitragotri, S., Anissimov, Y.G., Bunge, A.L., Frasch, H.F., Guy, R.H., Hadgraft, J., Kasting, G.B., Lane, M.E., Roberts, M.S. (2011) Mathematical models of skin permeability: An overview. Int. J. Pharm. in press doi:10.1016/j.ijpharm.2011.02.023

    Google Scholar 

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Acknowledgments

The authors thank Steffi Hansen, Claus-Michael Lehr, Dirk Neumann and Ulrich Schaefer for conducting the experiments and for providing experimental input parameters. Further, the authors thank Dirk Feuchter, Yu-Hong Liu and Christine Wagner for providing the software TKD Modeller and the Cuboid Modeller, respectively. Parallel computations were performed on the SGI Altix 4700 system at the Leibniz-Rechenzentrum, Munich. Parts of this work were funded by the ZEBET division of the Federal Institute for Risk Assessment, Berlin under Contract No. BfR-ZEBET-1328-177.

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Authors and Affiliations

  1. Goethe-Center for Scientific Computing, Goethe-University, Frankfurt am Main, Germany

    Arne Naegel, Michael Heisig & Gabriel Wittum

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  1. Arne Naegel
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  2. Michael Heisig
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  3. Gabriel Wittum
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Correspondence to Gabriel Wittum .

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  1. Sprott Centre for Stem Cell Research, Regenerative Medicine Program, Ottawa Hospital Research Institute, Smyth Road 501, Ottawa, K1Y 8L6, Canada

    Kursad Turksen

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Naegel, A., Heisig, M., Wittum, G. (2011). Computational Modeling of the Skin Barrier. In: Turksen, K. (eds) Permeability Barrier. Methods in Molecular Biology, vol 763. Humana Press. https://doi.org/10.1007/978-1-61779-191-8_1

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  • DOI: https://doi.org/10.1007/978-1-61779-191-8_1

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  • Publisher Name: Humana Press

  • Print ISBN: 978-1-61779-190-1

  • Online ISBN: 978-1-61779-191-8

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