{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:31:36Z","timestamp":1759336296592,"version":"3.37.3"},"reference-count":29,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p><jats:italic>Objective.<\/jats:italic>To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis.<jats:italic>Methods.<\/jats:italic>A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues<jats:italic>\u03bb<\/jats:italic>, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation.<jats:italic>Results.<\/jats:italic>For urea two out of four eigenvalues describing the changes of concentrations in time are about 10<jats:sup>5<\/jats:sup>times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 10<jats:sup>2<\/jats:sup>between the largest and the smallest eigenvalue) indicating that all four compartments contribute to creatinine kinetics in hemodialysis.<jats:italic>Interpretation.<\/jats:italic>Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.<\/jats:p>","DOI":"10.1155\/2013\/654726","type":"journal-article","created":{"date-parts":[[2013,11,6]],"date-time":"2013-11-06T21:08:06Z","timestamp":1383772086000},"page":"1-11","source":"Crossref","is-referenced-by-count":5,"title":["Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8768-012X","authenticated-orcid":true,"given":"Przemys\u0142aw","family":"Korohoda","sequence":"first","affiliation":[{"name":"AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Department of Electronics, al. 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Mickiewicza 30, 30-059 Krakow, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Schneditz","sequence":"additional","affiliation":[{"name":"Institute of Physiology, Center for Physiological Medicine, Medical University of Graz, Harrachgasse 21\/5, 8010 Graz, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1991","key":"1"},{"volume-title":"Kinetic modeling in hemodialysis","year":"2005","first-page":"153","key":"2"},{"doi-asserted-by":"publisher","key":"3","DOI":"10.1159\/000093199"},{"year":"1995","key":"4"},{"issue":"3","key":"5","doi-asserted-by":"crossref","first-page":"M667","DOI":"10.1097\/00002480-199407000-00082","volume":"40","year":"1994","journal-title":"ASAIO Journal"},{"doi-asserted-by":"publisher","key":"6","DOI":"10.1016\/0010-4825(95)00040-0"},{"doi-asserted-by":"publisher","key":"7","DOI":"10.1053\/j.ajkd.2007.05.009"},{"doi-asserted-by":"publisher","key":"8","DOI":"10.1111\/j.1542-4758.2009.00351.x"},{"doi-asserted-by":"publisher","key":"9","DOI":"10.1159\/000245924"},{"doi-asserted-by":"publisher","key":"10","DOI":"10.1007\/s10439-011-0383-5"},{"issue":"6","key":"11","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1097\/MAT.0000436714.72752.13","volume":"59","year":"2013","journal-title":"ASAIO Journal"},{"doi-asserted-by":"publisher","key":"12","DOI":"10.1093\/ndt\/gfp023"},{"year":"2007","key":"13"},{"year":"2008","key":"14"},{"issue":"1","key":"15","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/S0272-6386(99)70107-1","volume":"34","year":"1999","journal-title":"American Journal of Kidney Diseases"},{"doi-asserted-by":"publisher","key":"16","DOI":"10.1111\/j.1525-1594.2009.00873.x"},{"issue":"3","key":"17","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1093\/ndt\/gfr413","volume":"27","year":"2012","journal-title":"Nephrology Dialysis Transplantation"},{"doi-asserted-by":"publisher","key":"18","DOI":"10.1053\/j.ajkd.2009.06.033"},{"doi-asserted-by":"publisher","key":"19","DOI":"10.1371\/journal.pcbi.1000696"},{"issue":"5","key":"20","doi-asserted-by":"crossref","first-page":"1360","DOI":"10.1681\/ASN.V651360","volume":"6","year":"1995","journal-title":"Journal of the American Society of Nephrology"},{"doi-asserted-by":"publisher","key":"21","DOI":"10.1097\/00002480-199307000-00085"},{"doi-asserted-by":"publisher","key":"22","DOI":"10.2215\/CJN.03360807"},{"doi-asserted-by":"publisher","key":"23","DOI":"10.1093\/ndt\/gfh102"},{"doi-asserted-by":"publisher","key":"24","DOI":"10.1111\/j.1542-4758.2008.00302.x"},{"doi-asserted-by":"publisher","key":"25","DOI":"10.1159\/000274460"},{"doi-asserted-by":"publisher","key":"26","DOI":"10.1088\/0031-9155\/40\/12\/001"},{"year":"1545","key":"27"},{"year":"2001","key":"28"},{"year":"1545","series-title":"G. 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