Numerical simulation of skin transport using Parareal

In silico investigation of skin permeation is an important but also computationally demanding problem. To resolve all scales involved in full detail will not only require exascale computing capacities but also suitable parallel algorithms. This article investigates the applicability of the time-parallel Parareal algorithm to a brick and mortar setup, a precursory problem to skin permeation. The C++ library Lib4PrM implementing Parareal is combined with the UG4 simulation framework, which provides the spatial discretization and parallelization. The combination’s performance is studied with respect to convergence and speedup. It is confirmed that anisotropies in the domain and jumps in diffusion coefficients only have a minor impact on Parareal’s convergence. The influence of load imbalances in time due to differences in number of iterations required by the spatial solver as well as spatio-temporal weak scaling is discussed

A Micro-Macro parallel-in-time Implementation for the 2D Navier-Stokes Equations

In this paper the Micro-Macro Parareal algorithm was adapted to PDEs. The parallel-in-time approach requires two meshes of different spatial resolution in order to compute approximations in an iterative way to a predefined reference solution. When fast convergence in few iterations can be accomplished the algorithm is able to generate wall-time reduction in comparison to the serial computation. We chose the laminar flow around a cylinder benchmark on 2-dimensional domain which was simulated with the open-source software OpenFoam. The numerical experiments presented in this work aim to approximate states local in time and space and the diagnostic lift coefficient. The Reynolds number is gradually increased from 100 to 1,000, before the transition to turbulent flows sets in. After the results are presented the convergence behavior is discussed with respect to the Reynolds number and the applied interpolation schemes.Comment: 17 pages, 28 figure

J Control Release

The impact of the complex structure of the stratum corneum on transdermal penetration is not yet fully described by existing models. A quantitative and thorough study of skin permeation is essential for chemical exposure assessment and transdermal delivery of drugs. The objective of this study is to analyze the effects of heterogeneity, anisotropy, asymmetry, follicular diffusion, and location of the main barrier of diffusion on percutaneous permeation. In the current study, the solution of the transient diffusion through a two-dimensional-anisotropic brick-and-mortar geometry of the stratum corneum is obtained using the commercial finite element program COMSOL Multiphysics. First, analytical solutions of an equivalent multilayer geometry are used to determine whether the lipids or corneocytes constitute the main permeation barrier. Also these analytical solutions are applied for validations of the finite element solutions. Three illustrative compounds are analyzed in these sections: diethyl phthalate, caffeine and nicotine. Then, asymmetry with depth and follicular diffusion are studied using caffeine as an illustrative compound. The following findings are drawn from this study: the main permeation barrier is located in the lipid layers; the flux and lag time of diffusion through a brick-and-mortar geometry are almost identical to the values corresponding to a multilayer geometry; the flux and lag time are affected when the lipid transbilayer diffusivity or the partition coefficients vary with depth, but are not affected by depth-dependent corneocyte diffusivity; and the follicular contribution has significance for low transbilayer lipid diffusivity, especially when flux between the follicle and the surrounding stratum corneum is involved. This study demonstrates that the diffusion is primarily transcellular and the main barrier is located in the lipid layers.CC999999/Intramural CDC HHS/United States2019-03-22T00:00:00Z28596104PMC64295526076vault:3178

Numerical simulation of skin transport using Parareal

In silico investigation of skin permeation is an important but also computationally demanding problem. To resolve all scales involved in full detail will not only require exascale computing capacities but also suitable parallel algorithms. This article investigates the applicability of the time-parallel Parareal algorithm to a brick and mortar setup, a precursory problem to skin permeation. The C++ library Lib4PrM implementing Parareal is combined with the UG4 simulation framework, which provides the spatial discretization and parallelization. The combination's performance is studied with respect to convergence and speedup. It is confirmed that anisotropies in the domain and jumps in diffusion coefficients only have a minor impact on Parareal's convergence. The influence of load imbalances in time due to differences in number of iterations required by the spatial solver as well as spatio-temporal weak scaling is discussed