{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T16:13:45Z","timestamp":1760890425613,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,8]],"date-time":"2022-01-08T00:00:00Z","timestamp":1641600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym14010109","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:35:09Z","timestamp":1641771309000},"page":"109","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples\u2014Part 2"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1733-5240","authenticated-orcid":false,"given":"Roman","family":"Cherniha","sequence":"first","affiliation":[{"name":"Institute of Mathematics, NAS of Ukraine, 3, Tereshchenkivs\u2019ka Street, 01004 Kyiv, Ukraine"}]},{"given":"Vasyl\u2019","family":"Davydovych","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, NAS of Ukraine, 3, Tereshchenkivs\u2019ka Street, 01004 Kyiv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2148-6316","authenticated-orcid":false,"given":"Joanna","family":"Stachowska-Pietka","sequence":"additional","affiliation":[{"name":"Nalecz Institute of Biocybernetics and Biomedical Engineering, PAS, Ks. Trojdena 4, 02 109 Warsaw, Poland"}]},{"given":"Jacek","family":"Waniewski","sequence":"additional","affiliation":[{"name":"Nalecz Institute of Biocybernetics and Biomedical Engineering, PAS, Ks. Trojdena 4, 02 109 Warsaw, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,8]]},"reference":[{"key":"ref_1","unstructured":"Hall, J.E. (2016). Guyton and Hall Textbook of Medical Physiology, Elsevier. [13th ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Loret, B., and Simoes, F.M.F. (2017). Biomechanical Aspects of Soft Tissue, CRC Press.","DOI":"10.1201\/9781315110783"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"H1501","DOI":"10.1152\/ajpheart.00925.2014","article-title":"Concomitant bidirectional transport during peritoneal dialysis can be explained by a structured interstitium","volume":"310","author":"Waniewski","year":"2016","journal-title":"Am. J. Physiol. Heart Circ. 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