The Open Biomedical Engineering Journal

ISSN: 1874-1207 ― Volume 9, 2015

A Non-Dimensional Analysis of Hemodialysis

Michael Bonert1, Bradley A Saville*, 2
1 Department of Laboratory Medicine and Pathobiology, University of Toronto, Canada
2 Department of Chemical Engineering, University of Toronto, Canada



Non-dimensional analysis is a powerful approach that can be applied to multivariate problems to better understand their behaviour and interpret complex interactions of variables. It is has not been rigorously applied to the parameters that define renal dialysis treatments and may provide insight into the planning of hemodialysis treatments.


Buckingham’s non-dimensional approach was applied to the parameters that define hemodialysis treatments. Non-dimensional groups were derived with knowledge of a mass transfer model and independent of it. Using a mass transfer model, the derived non-dimensional groups were plotted to develop an understanding of key relationships governing hemodialysis and toxin profiles in patients with end-stage renal disease.


Three non-dimensional groups are sufficient to describe hemodialysis, if there is no residual renal function (RRF). The non-dimensional groups found represent (1) the number of half-lives that characterize the mass transfer, (2) the toxin concentration divided by the rise in toxin concentration without dialysis for the cycle time (the inverse of the dialysis frequency), and (3) the ratio of dialysis time to the cycle time. If there is RRF, one additional non-dimensional group is needed (the ratio between cycle time and intradialytic elimination rate constant). Alternate non-dimensional groups can be derived from the four unique groups.


Physical interpretation of the non-dimensional groups allows for greater insight into the parameters that determine dialysis effectiveness. This technique can be applied to any toxin and facilitates a greater understanding of dialysis treatment options. Quantitative measures of dialysis adequacy should be based on dimensional variables.

Keywords: Dialysis adequacy, non-dimensional analysis, dimensionless groups, hemodialysis, peritoneal dialysis, dialysis dose, Buckingham Pi theorem, Kt/V..

Identifiers and Pagination:

Year: 2010
Volume: 4
First Page: 138
Last Page: 155
Publisher Id: TOBEJ-4-138
DOI: 10.2174/1874120701004010138

Article History:

Received Date: 11/2/2010
Revision Received Date: 13/5/2010
Acceptance Date: 18/5/2010
Electronic publication date: 9/7/2010
Collection year: 2010

Article Information:

© Bonert and Saville; Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address correspondence to this author at the Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street, Toronto, Ontario, M5S 3E5, Canada; Tel: 416-978-7745; Fax: 416-978-8605; E-mail:

SCImago Journal Ranking

SCImago Journal & Country Rank

Browse Contents

Webmaster Contact:
Copyright © 2015 Bentham Open