Mathematical modeling of the convectivediffusive mass transfer in a hemodialysis cell

1Bulat, AF, Eliseev, VI, Sovit, YP, Molchanov, RN, Blyuss, O
1M.S. Polyakov Institute of Geotechnical Mechanics of the NAS of Ukraine, Dnipropetrovsk
Dopov. Nac. akad. nauk Ukr. 2019, 2:40-44
Section: Mechanics
Language: Ukrainian

A mathematical model of a hemodialysis cell is proposed based on the theory of mass transfer and the analysis of the hemodialysis problem. Relative costs of the neutral components and their distributions in the calculated area are obtained with the hydrodynamic effect of a semipermeable membrane taken into account. The ability to regulate the costs of these components by profiling the membrane resistance is shown.

Keywords: diffusion, distribution of components, hemodialysis, mass transfer

1. Bryik, M. T. & Tsapyuk, E. A. (1989). Ultrafiltration. Kiev: Naukova Dumka (in Russian).
2. Bryik, M. T. Golubev, V. N. & Chagarovskiy, A. P. (1991). Membrane technology in the food industry. Kiev: Urozhay (in Russian).
3. Stetsyuk, E. A. (2001). Basics of hemodialysis. Moscow: GEOTARMED (in Russian).
4. Pallone, T. L., Hyver, S. & Petersen, J. (1989). The simulation of continuous arteriovenous hemodialysis with a mathematical model. Kidney Int., pp. 125-133. doi:
5. Eloot, S. (2004). Experimental and numerical modeling of dialysis (PhD dissertation). Ghent University, Gent (in Belgium).
6. Kagramanov, G. G. (2009). Diffusion membrane processes: tutorial. Moscow: RHTU im. Mendeleeva (in Russian).
7. Aniort, J., Chupin, L. & Cîndea, N. (2018). Mathematical model of calcium exchange during hemodialysis using a citrate containing dialysate. Math. Med. Biol., 35, suppl. 1, pp. 87-120. doi:
8. Annan, K. (2012). Mathematical modeling for hollow fiber dialyzer: blood and HCO3− dialysate flow characteristics. Int. J. Pure Appl. Math., 79, No. 3, pp. 425-452.
9. ErdeiGruz, T. (1986). Transfer phenomena in aqueous solutions. Moscow: Mir (in Russian).
10. Dyinerskiy, Yu. I. (1995). Processes and devices of chemical technology. Pt. 2. Mass transfer processes and devices. Moscow: Khimiya (in Russian).