Publication de 6 numéros par an
ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352
Indexed in
Two-Scale Modeling of Tissue Perfusion Problem Using Homogenization of Dual Porous Media
RÉSUMÉ
This paper reports on application of the homogenization approach to the modeling of diffusion in a dual-porous deformable medium. As an important application, the coupled diffusion-deformation processes can describe the blood perfusion in biological tissues or fluid filtration phenomena in general. The micromodel to be homogenized is based on the Biot-type model for the incompressible medium. Because of the strong heterogeneity in permeability coefficients associated with three compartments of the representative microstructural cell (RMC), the homogenization of the model leads to the double diffusion phenomena. The resulting homogenized equations, involving a stress-equilibrium equation and two equations governing the mass redistribution, describe the parallel diffusion in two high-conducting compartments (arterial and venous sectors) separated by a low-conducting matrix, which represents the perfused tissue. To obtain the homogenized model, the method of periodic unfolding is applied. The homogenized coefficients are defined in terms of the characteristic response of the RMC. It is possible to identify the instantaneous and fading memory viscoelastic coefficients; other effective parameters, controlling the fluid redistribution between the compartments, are involved also in time convolutions. The numerical algorithms for the two-scale modeling are discussed and illustrative examples are introduced.
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Rohan Eduard, Camprová Turjanicová Jana, Liška Václav, Sequeira Adélia, Geometrical model of lobular structure and its importance for the liver perfusion analysis, PLOS ONE, 16, 12, 2021. Crossref
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Rohan Eduard, Turjanicová Jana, Lukeš Vladimír, Multiscale modelling and simulations of tissue perfusion using the Biot-Darcy-Brinkman model, Computers & Structures, 251, 2021. Crossref
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