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Application of mathematical analysis on dialysis

  • Review Paper
  • Artificial Kidney / Dialysis
  • Published:
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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.

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Authors and Affiliations

  1. Department of Human Environmental Science, Shonan Institute of Technology, 1-1-25 Tsujido-nishi-kaigan, Fujisawa, Kanagawa, 251-8511, Japan

    Takehiro Miyasaka

  2. Professor Emeritus of Waseda University, Tokyo, Japan

    Kiyotaka Sakai

Authors
  1. Takehiro Miyasaka
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  2. Kiyotaka Sakai
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Contributions

Both authors contributed to the idea for the review paper, and also collected the papers related. The first draft of the manuscript was written by TM, followed by KS’s revision. Both authors approved the final manuscript.

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Correspondence to Takehiro Miyasaka or Kiyotaka Sakai.

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This review paper is based on the Japanese version by Takehiro Miyasaka of Jpn J Artif Organs 2020;49(3):191–4.

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Miyasaka, T., Sakai, K. Application of mathematical analysis on dialysis. J Artif Organs 26, 1–11 (2023). https://doi.org/10.1007/s10047-022-01359-8

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  • DOI: https://doi.org/10.1007/s10047-022-01359-8

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