| New mathematical model for fluid-glucose-albumin transport in peritoneal dialysis |
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| Written by seminaire |
| Wednesday, 02 November 2011 10:15 |
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There are no translations available. Mercredi 2 novembre à 11h LPTMC salle de réunion du couloir 13-23
Roman Cherniha Institute of Mathematics (Kiev, Ukraine)New mathematical model for fluid-glucose-albumin transport in peritoneal dialysis
invité par Richard Kerner
Résumé: Mathematical description of fluid and solute transport between blood and dialysis fluid in the peritoneal cavity has not been formulated fully yet, in spite of the well known basic physical laws for such transport. Recent mathematical, theoretical and numerical studies introduced new concepts on peritoneal transport and yielded better results for the transport of fluid and osmotic agent [1, 2, 3]. However, the problem of a combined description of osmotic ultrafiltration to the peritoneal cavity, absorption of osmotic agent from the peritoneal cavity and leak of macromolecules (proteins, e.g., albumin) from blood to the peritoneal cavity has not been addressed yet. Therefore, we present here a new extended model for these phenomena and investigate its mathematical structure [4]. The model is based on a three-component nonlinear system of two-dimensional partial differential equations with the relevant boundary and initial
conditions. The non-constant steady-state solutions of the model are studied. The restrictions on the parameters arising in the model were established with the aim to obtain exact formulae for non-constant steady-state solutions. As the result, exact formulae for the density of fluid flux from blood to tissue and the volumetric flux across the tissue were constructed and two linear autonomous ordinary differential equations for glucose and albumin concentrations were derived. The analytical results were checked for their applicability for the description of fluid- glucose-albumin transport in peritoneal dialysis. References [1] Cherniha, R., Waniewski, J.: Exact solutions of a mathematical model for fluid transport in peritoneal dialysis. Ukrainian Math. J., 57, 1112{1119 (2005) [2] R. Cherniha, V.Dutka, J.Stachowska-Pietka and J.Waniewski. Fluid transport in peritoneal dialysis: a mathematical model and numerical solutions. //Mathematical Modeling of Biological Systems, Vol.I. Ed. by A.Deutsch et al., Birkhaeuser, P.291-298, 2007 [3] Waniewski J, Dutka V, Stachowska-Pietka J, Cherniha R: Distributed modeling of glucose-induced osmotic °ow. Adv Perit Dial 2007;23:2-6. [4] Cherniha, R., Waniewski, J.:New mathematical model for °uid-glucose-albumin transport in peritoneal dialysis (submitted) Lieu du séminaire: salle de réunion du LPTMC, couloir 13-23, 5ème étage, 4 Place Jussieu, Paris
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| Last Updated on Wednesday, 02 November 2011 10:28 |