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10-09-2022 | Review Paper

Application of mathematical analysis on dialysis

Authors: Takehiro Miyasaka, Kiyotaka Sakai

Published in: Journal of Artificial Organs | Issue 1/2023

Abstract

Hemodialysis is a blood purification method based on solute removal by diffusion and incorporates filtration to improve the efficiency of water removal and removal of high molecular weight substances. It is now a well-established treatment, due to the improved performance of dialyzers. This review outlines the development process of dialyzers, focusing on the application based on the mathematical analysis. First, phenomena occurring in the vicinity of the dialysis membrane are explained using a film model for diffusion and a gel polarization model for filtration. Then, currently established dialyzer designs are introduced using mathematical analysis. Furthermore, the design of dialyzers to promote internal filtration, the designs of hemodiafilters suitable for online hemodiafiltration (HDF), and the design of compact dialyzer for are also presented.

Smith KA, Colton CK, Merrill EW, Evans LB. Convective transport in a batch dialyzer: determination of true membrane permeability from a single measurement. Chem Eng Prog Symp Ser Artif Kidney. 1968;64:45–58.

Babb AL, Maurer CJ, Fry DL, Popovich RP, McKee RE. The determination of membrane permeabilities and solute diffusivities with applications to hemodialysis. Chem Eng Prog Symp Ser Artif Kidney. 1968;64:59–68.

Hershey D, Cho SJ. Laminar flow of suspensions (blood): thickness and effective slip velocity of the film adjacent to the wall. Chem Eng Prog Symp Ser Chem Eng Med. 1966;62:140–5.

Kanamori T, Sakai K. Effect of mass transfer between plasma and erythrocyte interior on evaluating dialyzer performance: Artif. Organs Today. 1995;5:101–12.

Lightfoot EN. A formal description of ultrafiltration. Chem Eng Prog Symp Ser Artif Kidney. 1968;64:79–84.

Keshaviah P. Hemofiltration. AIChE Symp Ser Chron Replace Kidney Funct. 1979;75:24–30.

Yoshida F. Rates of blood filtration. A brief review. Ind Eng Chem Fundam. 1986;25:633–5.CrossRef

Zydney AL, Colton CK. Continuous flow membrane plasmapheresis: theoretical models for flux and hemolysis prediction. Trans Am Soc Artif Intern Organs. 1982;28:408–12.PubMed

Ohashi K, Tashiro K, Kushiya F, Matsumoto T, Yoshida S, Endo M, Horio T, Ozawa K, Sakai K. Rotation-induced Taylor vortex enhances filtrate flux in plasma separation. Trans Am Soc Artif Intern Organs. 1988;34:300–7.

10.

Okazaki M, Yoshida F. Ultrafiltration of blood: effect of hematocrit on ultrafiltration rate. Ann Biomed Eng. 1976;4:138–50.PubMedCrossRef

11.

Mochizuki S, Zydney AL. Dextran transport through asymmetric ultrafiltration membranes: comparison with hydrodynamic models. J Membr Sci. 1992;68:21–41.CrossRef

12.

Mochizuki S, Zydney AL. Effect of protein adsorption on the transport characteristics of asymmetric ultrafiltration membranes. Biotechnol Prog. 1992;8:553–61.PubMedCrossRef

13.

Abel JJ, Rowntree LG, Turner BB. On the removal of diffusible substances from the circulating blood of living animals by dialysis. J Pharmacol Exp Ther. 1914;5:275–316.

14.

Grimsrud L, Babb AL. Velocity and concentration profiles for laminar flow of a Newtonian fluid in a dialyzer. Chem Eng Prog Symp Ser Chem Eng Med. 1966;62:20–31.

15.

Wolf L Jr, Zaltzman S. Optimum geometry for artificial kidney dialyzers. Chem Eng Prog Symp Ser Artif Kidney. 1968;64:104–11.

16.

Shimizu S, Okazaki M, Yoshida F. Mass transfer in hemodialyzers. Jpn J Artif Organs. 1978;7:317–8 (in Japanese).

17.

Sakai K. Technical determination of optimal dimensions of hollow fibre membranes for clinical dialysis. Nephrol Dial Transp. 1989;4:73–7.

18.

Suzuki Y, Kohori F, Sakai K. Computer-aided design of hollow-fiber dialyzers. J Artif Organs. 2001;4:326–30.CrossRef

19.

Noda I, Gryte CC. Mass transfer in regular arrays of hollow fibers in countercurrent dialysis. AIChE J. 1979;25:113–22.CrossRef

20.

Fukuda M, Hosoya N, Kanamori T, Sakai K, Nishikido J, Watanabe T, Fushimi F. Determination of optimal fiber density of conventional and high performance dialyzers. Artif Organs Today. 1992;2:205–14.

21.

Takesawa S, Terasawa M, Sakagami M, Kobayashi T, Hidai H, Sakai K. Nondestructive evaluation by X-ray computed tomography of dialysate flow pattern in capillary dialyzers. Trans Am Soc Artif Intern Organs. 1988;34:794–9.

22.

Osuga T, Obata T, Ikehira H, Tanada S, Sasaki Y, Naito H. Dialysate pressure isobars in a hollow-fiber dialyzer determination from magnetic resonance imaging and numerical simulation of dialysate flow. Artif Organs. 1998;22:907–9.PubMedCrossRef

23.

Osuga T, Ikehira H, Obata T, Homma K, Yamane S, Naito H. Numerical simulation of dialysate flow in a hollow-fiber dialyzer. Johosyorigakkai Ronbunshi. 2002;43:2687–96 (in Japanese).

24.

Osuga T, Obata T, Ikehira H. Detection of small degree of nonuniformity in dialysate flow in hollow-fiber dialyzer using proton magnetic resonance imaging. Magn Reson Imaging. 2004;22:417–20.PubMedCrossRef

25.

Yamamoto K, Matsuda M, Hirano A, Takizawa N, Iwashima S, Yakushiji T, Fukuda M, Miyasaka T, Sakai K. Computational evaluation of dialysis fluid flow in dialyzers with variously designed jackets. Artif Organs. 2009;33:481–6.PubMedCrossRef

26.

Zydney AL. Bulk mass transport limitations during high-flux hemodialysis. Artif Organs. 1993;17:919–24.PubMedCrossRef

27.

Kanamori T, Mizoguchi K. Analysis of solute transport by diffusion and convection in hollow-fiber hemodialyzer using the finite element method. Kagaku-Kogaku Ronbunsyu. 2011;37:91–5 (in Japanese).CrossRef

28.

Sano Y, Nakayama A. A porous media approach for analyzing a countercurrent dialyzer system. J Heat Transf. 2012;134:072602.CrossRef

29.

Sano Y. Operating conditions for hemodialysis treatment based on the volume averaging theory. Interdiscip Inf Sci. 2016;22:215–27.

30.

Donato D, Boschetti-de-Fierro A, Zweigart C, Kolb M, Eloot S, Storr M, Krause B, Leypoldt K, Segers P. Optimization of dialyzer design to maximize solute removal with a two-dimensional transport model. J Membr Sci. 2017;541:519–28.CrossRef

31.

Stiller S, Mann H, Brunner H. Backfiltration in hemodialysis with highly permeable membranes. Contr Nephrol. 1985;46:23–32.CrossRef

32.

Hosoya N, Kanamori T, Sakai K. Optimal design of a high-performance dialyzer involving backfiltration. Artif Organs Today. 1993;2:287–98.

33.

Mineshima M, Ishimori I, Ishida K, et al. Effects of internal filtration on the solute removal efficiency of a dialyzer. ASAIO J. 2000;46:456–60.PubMedCrossRef

34.

Sekino M, Yagi T, Tamamura N. New analytical model and its applications for hemodiafilter. Kagaku Kogaku Ronbunsyu. 2010;36:34–40 (in Japanese).CrossRef

35.

Rautenbach R. Albrecht R. 5.1 Tubular module. In: Membrane Processes. Wiley, New York, pp. 135–137. 1989

36.

Sekino M. Effect of ultrafiltration in hemodiafiltration system. Kagaku Kogaku Ronbunsyu. 2012;38:34–40 (in Japanese).CrossRef

37.

Yamashita AC. Development of the hemodialyzer and hemodiafilter of the near future. Jpn J Clin Dial. 2020;36:439–44 (in Japanese).

38.

Yamashita AC. Diafilters for predilution and postdilution on-line hemodiafiltration. Blood Purif. 2013;35:29–33.PubMedCrossRef

39.

Dorson A, Markovitz M. A pulsating ultrafiltration artificial kidney. Chem Eng Prog Symp Ser Artif Kidney. 1968;64:85–9.

40.

Bixler HJ, Nelsen LM, Besarab A. The Diaphron hemodiafilter: an alternative to dialysis for extracorporeal blood purification. Eng Prog Symp Ser Artif Kidney. 1968;64:90–103.

41.

Kokubo K, Kobayashi K, Yamane T, Yamamoto K, Matsuda K. Portable blood purification device available in the event of natural disaster. Jpn J Clin Dial. 2020;36:459–64 (in Japanese).

42.

Kokubo K, Kurihara Y, Kobayashi K, Moriguchi T, Matsuda K, Kobayashi H. Development of a blood purifier using thin hollow fiber membranes. Jpn J Artif Organs. 2014;43:238–41 (in Japanese).

43.

Kurihara Y, Kokubo K, Kobayashi K, Ushiroda Y, Tsukao H, Yanagisawa M, Goto J, Harii N, Moriguchi T, Matsuda K, Kobayashi H. Development of hemofilter using fine diameter fibers. Ther Eng. 2015;27:44–7 (in Japanese).

Title: Application of mathematical analysis on dialysis
Authors: Takehiro Miyasaka
Kiyotaka Sakai
Publication date: 10-09-2022
Publisher: Springer Nature Singapore
Published in: Journal of Artificial Organs / Issue 1/2023
Print ISSN: 1434-7229
Electronic ISSN: 1619-0904
DOI: https://doi.org/10.1007/s10047-022-01359-8

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Springer Medicine

Application of mathematical analysis on dialysis

Abstract

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Springer Medicine

Abstract

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