{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:53:28Z","timestamp":1760889208200,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,6,16]],"date-time":"2016-06-16T00:00:00Z","timestamp":1466035200000},"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 nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example) and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions) for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration) for a wide range of values of the model parameters.<\/jats:p>","DOI":"10.3390\/sym8060050","type":"journal-article","created":{"date-parts":[[2016,6,16]],"date-time":"2016-06-16T10:23:20Z","timestamp":1466072600000},"page":"50","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1733-5240","authenticated-orcid":false,"given":"Roman","family":"Cherniha","sequence":"first","affiliation":[{"name":"Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs\u2019ka Street, Kyiv 01004, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1473-5924","authenticated-orcid":false,"given":"Kateryna","family":"Gozak","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs\u2019ka Street, Kyiv 01004, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2705-504X","authenticated-orcid":false,"given":"Jacek","family":"Waniewski","sequence":"additional","affiliation":[{"name":"Institute of Biocybernetics and Biomedical Engineering, PAS, Ks. 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Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2554","DOI":"10.1097\/01.ASN.0000026492.83560.81","article-title":"Effect of increased dialysate volume on peritoneal surface area among peritoneal dialysis patients","volume":"13","author":"Chagnac","year":"2002","journal-title":"Journal of the American Society of Nephrology"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1177\/089686080002000108","article-title":"Discriminative impact of ultrafiltration on peritoneal protein transport","volume":"20","author":"Waniewski","year":"2000","journal-title":"Perit. Dial. 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