Effective diffusivity in membranes with tetrakaidekahedral cells and implications for the permeability of human stratum corneum

Muha, Ivo; Naegel, Arne; Stichel, S.; Grillo, Alfio; Heisig, Michael; Wittum, Gabriel

doi:10.1016/j.memsci.2010.10.020

Cited by 27 publications

(15 citation statements)

References 40 publications

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“…However, with the help of mathematical homogenization it is possible to preserve material characteristics such as anisotropy on a macroscopic scale when dealing with repetitive microstructures such as the brick-and-mortal-like structure of the stratum corneum. Basically, this technique allows for deriving effective (macroscopic) transport parameters from microscopic models without having to use models with a high spatial resolution [75,102].…”

Section: Skin-concentration Depth Profilesmentioning

confidence: 99%

Mathematical models for dermal drug absorption

Selzer

Neumann

Schaefer

2015

Expert Opinion on Drug Metabolism & Toxicology

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Section: Skin-concentration Depth Profilesmentioning

confidence: 99%

Mathematical models for dermal drug absorption

Selzer

Neumann

Schaefer

2015

Expert Opinion on Drug Metabolism & Toxicology

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“…Two-dimensional treatments of the tissue as seen in cross-section [7][8][9][10][11][12][13][14][15][16][17][18][19] ("ribbon models" 20 ) and analytical approximations for the tortuosity associated with staggered square flakes 21 have given way to sophisticated, fully 3-dimensional numerical analyses representing corneocytes as flattened cuboids 20,22,23 and tetrakaidecahedra. 20,24 A particularly useful application of such analyses is the calculation of effective (average, homogenized, coarse-grained) diffusion coefficients of the tissue by solution of a well-defined steady-state diffusion problem posed in one unit cell of the microstructure. 6,8,9,20,[22][23][24] These calculated coefficients can be slotted into macroscopic calculators that solve for the transient distribution of solute within the SC (and also viable epidermis and dermis layers underneath) treated as homogenized slabs, assuming the geometry of the unit cell has been agreed upon.…”

Section: Introductionmentioning

confidence: 99%

“…20,24 A particularly useful application of such analyses is the calculation of effective (average, homogenized, coarse-grained) diffusion coefficients of the tissue by solution of a well-defined steady-state diffusion problem posed in one unit cell of the microstructure. 6,8,9,20,[22][23][24] These calculated coefficients can be slotted into macroscopic calculators that solve for the transient distribution of solute within the SC (and also viable epidermis and dermis layers underneath) treated as homogenized slabs, assuming the geometry of the unit cell has been agreed upon. Subsequently, the fraction of an applied drug or deposited chemical dose residing in the skin, or having been cleared into the systemic circulation, can be calculated as a function of time.…”

Section: Introductionmentioning

confidence: 99%

Microscopic Models of Drug/Chemical Diffusion Through the Skin Barrier: Effects of Diffusional Anisotropy of the Intercellular Lipid

Nitsche

Kasting

Nitsche

2019

Journal of Pharmaceutical Sciences

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Owing to the systematic alignment and ordering of fatty acid and ceramide chains, lipid layers in biological membranes have strongly anisotropic diffusion properties. The diffusivity D lip k for solute transport in the direction parallel to the lipid layer is typically 10 3-10 5 times the diffusivity D lip ⊥ for the perpendicular direction. This article explores the consequences of this strong degree of anisotropy on solute diffusion through the stratum corneum (barrier) layer of the skin based on a realistic representation of a unit cell of the microstructure. Complementary numerical methods (smoothed particle hydrodynamics, finite differences) are used to solve the steady-state unit-cell diffusion problem leading to the average (homogenized, coarse-grained) diffusion tensor characterizing the tissue as an effective continuum. A parametric study is presented characterizing solute concentration profiles in detail for testosterone-and caffeine-like permeants, and it is shown that the results cannot be mimicked by calculations based on an isotropic lipid-phase diffusivity. The ratio of lateral to transdermal effective diffusivities calculated by the present model is of the order of 40 and 300 for fully hydrated (in vitro) and partially hydrated (in vivo) states, respectively. These values compare favorably with the results of recent experiments.

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“…For the SC advanced models with cellular resolution are available [7,8]. The development of computational models for the living epidermis has yet just started.…”

Section: Introductionmentioning

confidence: 99%

Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes

Nägel

Schulz

Siebenborn

et al. 2015

Comput. Visual Sci.

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In this work we consider inverse modeling of the shape of cells in the outermost layer of human skin. We propose a novel algorithm that combines mathematical shape optimization with high-performance computing. Our aim is to fit a parabolic model for drug diffusion through the skin to data measurements. The degree of freedom is not the permeability itself, but the shape that distinguishes regions of high and low diffusivity. These are the cells and the space in between. The key part of the method is the computation of shape gradients, which are then applied as deformations to the finite element mesh, in order to minimize a tracking type objective function. Fine structures in the skin require a very high resolution in the computational model. We therefor investigate the scalability of our algorithm up to millions of discretization elements.

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Effective diffusivity in membranes with tetrakaidekahedral cells and implications for the permeability of human stratum corneum

Cited by 27 publications

References 40 publications

Mathematical models for dermal drug absorption

Mathematical models for dermal drug absorption

Microscopic Models of Drug/Chemical Diffusion Through the Skin Barrier: Effects of Diffusional Anisotropy of the Intercellular Lipid

Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes

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