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Volume 14
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10.3390/sym14010109
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Article

A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples—Part 2

by
Roman Cherniha
1,*,
Vasyl’ Davydovych
1,
Joanna Stachowska-Pietka
2 and
Jacek Waniewski
2
1
Institute of Mathematics, NAS of Ukraine, 3, Tereshchenkivs’ka Street, 01004 Kyiv, Ukraine
2
Nalecz Institute of Biocybernetics and Biomedical Engineering, PAS, Ks. Trojdena 4, 02 109 Warsaw, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2022, 14(1), 109; https://doi.org/10.3390/sym14010109
Submission received: 1 December 2021 / Revised: 22 December 2021 / Accepted: 2 January 2022 / Published: 8 January 2022
(This article belongs to the Section B: Mathematics)
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Abstract

The model for perfused tissue undergoing deformation taking into account the local exchange between tissue and blood and lymphatic systems is presented. The Lie symmetry analysis in order to identify its symmetry properties is applied. Several families of steady-state solutions in closed formulae are derived. An analysis of the impact of the parameter values and boundary conditions on the distribution of hydrostatic pressure, osmotic agent concentration and deformation of perfused tissue is provided applying the solutions obtained in examples describing real-world processes.
Keywords: perfused tissue; fluid and solute transport; nonlinear PDE; Lie symmetry; steady-state solution; nonlinear stress tensor perfused tissue; fluid and solute transport; nonlinear PDE; Lie symmetry; steady-state solution; nonlinear stress tensor

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MDPI and ACS Style

Cherniha, R.; Davydovych, V.; Stachowska-Pietka, J.; Waniewski, J. A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples—Part 2. Symmetry 2022, 14, 109. https://doi.org/10.3390/sym14010109

AMA Style

Cherniha R, Davydovych V, Stachowska-Pietka J, Waniewski J. A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples—Part 2. Symmetry. 2022; 14(1):109. https://doi.org/10.3390/sym14010109

Chicago/Turabian Style

Cherniha, Roman, Vasyl’ Davydovych, Joanna Stachowska-Pietka, and Jacek Waniewski. 2022. "A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples—Part 2" Symmetry 14, no. 1: 109. https://doi.org/10.3390/sym14010109

APA Style

Cherniha, R., Davydovych, V., Stachowska-Pietka, J., & Waniewski, J. (2022). A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples—Part 2. Symmetry, 14(1), 109. https://doi.org/10.3390/sym14010109

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