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International Journal for Multiscale Computational Engineering

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ISSN Печать: 1543-1649

ISSN Онлайн: 1940-4352

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

Том 8, Выпуск 1, 2010, pp. 81-102
DOI: 10.1615/IntJMultCompEng.v8.i1.70
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Краткое описание

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.

ЛИТЕРАТУРА
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ЦИТИРОВАНО В
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  2. Rohan Eduard, Naili Salah, Cimrman Robert, Lemaire Thibault, Hierarchical homogenization of fluid saturated porous solid with multiple porosity scales, Comptes Rendus Mécanique, 340, 10, 2012. Crossref

  3. Rohan Eduard, Shaw Simon, Whiteman John R., Poro-viscoelasticity modelling based on upscaling quasistatic fluid-saturated solids, Computational Geosciences, 18, 5, 2014. Crossref

  4. Chapelle D., Moireau P., General coupling of porous flows and hyperelastic formulations—From thermodynamics principles to energy balance and compatible time schemes, European Journal of Mechanics - B/Fluids, 46, 2014. Crossref

  5. Rohan E., Lukeš V., Modeling nonlinear phenomena in deforming fluid-saturated porous media using homogenization and sensitivity analysis concepts, Applied Mathematics and Computation, 267, 2015. Crossref

  6. Lee Jack, Nordsletten David, Cookson Andrew, Rivolo Simone, Smith Nicolas, In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion, Biomechanics and Modeling in Mechanobiology, 15, 6, 2016. Crossref

  7. Rohan Eduard, Lukeš Vladimír, Turjanicová Jana, Jiřík Miroslav, Towards Image-Based Analysis of the Liver Perfusion Using a Hierarchical Flow Model, in VipIMAGE 2017, 27, 2018. Crossref

  8. Rohan Eduard, Lukeš Vladimír, Jonášová Alena, Modeling of the contrast-enhanced perfusion test in liver based on the multi-compartment flow in porous media, Journal of Mathematical Biology, 77, 2, 2018. Crossref

  9. Gorguluarslan Recep M., Park Sang-In, Rosen David W., Choi Seung-Kyum, A Multilevel Upscaling Method for Material Characterization of Additively Manufactured Part Under Uncertainties, Journal of Mechanical Design, 137, 11, 2015. Crossref

  10. Chabiniok Radomir, Wang Vicky Y., Hadjicharalambous Myrianthi, Asner Liya, Lee Jack, Sermesant Maxime, Kuhl Ellen, Young Alistair A., Moireau Philippe, Nash Martyn P., Chapelle Dominique, Nordsletten David A., Multiphysics and multiscale modelling, data–model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics, Interface Focus, 6, 2, 2016. Crossref

  11. Cimrman Robert, Lukeš Vladimír, Rohan Eduard, Multiscale finite element calculations in Python using SfePy, Advances in Computational Mathematics, 45, 4, 2019. Crossref

  12. 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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  14. Rohan Eduard, Lukeš Vladimír, Modeling Tissue Perfusion Using a Homogenized Model with Layer-wise Decomposition, IFAC Proceedings Volumes, 45, 2, 2012. Crossref

  15. Rohan Eduard, Turjanicová Jana, Lukeš Vladimír, Multiscale modelling and simulations of tissue perfusion using the Biot-Darcy-Brinkman model, Computers & Structures, 251, 2021. Crossref

  16. Lukeš Vladimír, Rohan Eduard, Homogenization of large deforming fluid-saturated porous structures, Computers & Mathematics with Applications, 110, 2022. Crossref

  17. Tonar Zbyněk, Khadang Ismail, Fiala Pavel, Nedorost Lukáš, Kochová Petra, Quantification of compact bone microporosities in the basal and alveolar portions of the human mandible using osteocyte lacunar density and area fraction of vascular canals, Annals of Anatomy - Anatomischer Anzeiger, 193, 3, 2011. Crossref

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