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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i1.70
pages 81-102

Two-Scale Modeling of Tissue Perfusion Problem Using Homogenization of Dual Porous Media

Eduard Rohan
Department of Mechanics, Faculty of Applied Sciences, University of West Bohemia in Pilsen, Univerzitni 22, 30614 Plzen, Czech Republic
Robert Cimrman
Department of Mechanics, Faculty of Applied Sciences, University of West Bohemia in Pilsen, Univerzitni 22, 30614 Plzen, Czech Republic

ABSTRAKT

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.

REFERENZEN

  1. Cimrman, R. et al., SfePy: Simple Finite Elements in Python.

  2. Cimrman, R. and Rohan, E., Modeling heart tissue using a composite muscle model with blood perfusion. DOI: 10.1016/B978-008044046-0.50400-0

  3. Cimrman, R. and Rohan, E., On modelling the parallel diffusion flow in deforming porous media. DOI: 10.1016/j.matcom.2007.01.034

  4. Cioranescu, D., Damlamian, A., and Griso, G., Periodic unfolding and homogenization.

  5. Cioranescu, D., Damlamian, A., and Griso, G., The periodic unfolding method in homogenization. DOI: 10.1137/080713148

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  7. Coussy, O., Mechanics of Porous Continua.

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  9. Griso, G. and Rohan, E., On the homogenization of diffusion-deformation problem in strongly heterogeneous media. DOI: 10.1007/s11587-007-0011-8

  10. Griso, G. and Rohan, E., Homogenization of double-porous fluid saturated biot-type medium with pressure discontinuity on interfaces.

  11. Hornung, U., Homogenization and Porous Media.

  12. Lukeš, V., Two scale computational modelling of soft biological tissues.

  13. Murad, M. A. and Cushman, J. H., Multiscale flow and deformation in hydrophilic swelling media. DOI: 10.1016/0020-7225(95)00057-7

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