Shock Propagation in a Hollow-Fiber Hemodialyzer

Shock Propagation in a Hollow-Fiber Hemodialyzer

Edward K. Boamah

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Shock Propagation in a Hollow-Fiber Hemodialyzer

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Abstract

Hemodialysis (HD) is one type of procedure for eliminating toxic chemicals and infusing bicarbonate in patients with end-stage renal disease (ESRD). We have developed a comprehensive mathematical model to describe the dynamic exchange process of solutes in a prototype hemodialyzer. The model, which is represented by a coupled set of transport equations, delineates the blood and dialyzate compartments of the hemodialyzer, and includes bicarbonate-buffering reaction in the blood channel and bicarbonate replenishment mechanism in the dialyzate. In a paper submitted by the author, we ignored the inherent velocity discontinuity in the blood channel as the radius of the blood channel 𝑟𝑟 approaches the semi-permeable membrane 𝑅𝑅𝐵𝐵, that is, 𝑟𝑟→𝑅𝑅𝐵𝐵. In this paper, we will investigate the evolution of bicarbonate and carbon dioxide in the blood compartment as the radius of the blood channel approaches the semi-permeable membrane. That is, we will investigate the solutions to the simplified form of the model in the blood compartment near the velocity shock vector, which manifests a discontinuity when 𝑣𝑣𝑧𝑧(𝑟𝑟)=0 of the simplified non-steady state model. We will investigate the cases of analytical solutions of the model in the blood channel with negligible diffusion and also shock solutions with diffusion.

References

9 Cites in Article

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

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Not applicable for this article.

How to Cite This Article

Edward K. Boamah. 2020. \u201cShock Propagation in a Hollow-Fiber Hemodialyzer\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 20 (GJSFR Volume 20 Issue F8).

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GJSFR Volume 20 Issue F8

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification MSC 2010: 00A05

Submission ReceivedSeptember 22, 2020
Peer Review Double Blind
Handling Editor
Accepted October 21, 2020
Published November 2, 2020

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v1.2

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December 15, 2020

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