The Open Biomedical Engineering Journal

ISSN: 1874-1207 ― Volume 11, 2017

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..

Article Information

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 Metrics:

CrossRef Citations:

Total Statistics:

Full-Text HTML Views: 65
Abstract HTML Views: 64
PDF Downloads: 25
Total Views/Downloads: 154

Unique Statistics:

Full-Text HTML Views: 49
Abstract HTML Views: 44
PDF Downloads: 24
Total Views/Downloads: 117
Geographical View

© 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:


"Open access will revolutionize 21st century knowledge work and accelerate the diffusion of ideas and evidence that support just in time learning and the evolution of thinking in a number of disciplines."

Daniel Pesut
(Indiana University School of Nursing, USA)

"It is important that students and researchers from all over the world can have easy access to relevant, high-standard and timely scientific information. This is exactly what Open Access Journals provide and this is the reason why I support this endeavor."

Jacques Descotes
(Centre Antipoison-Centre de Pharmacovigilance, France)

"Publishing research articles is the key for future scientific progress. Open Access publishing is therefore of utmost importance for wider dissemination of information, and will help serving the best interest of the scientific community."

Patrice Talaga
(UCB S.A., Belgium)

"Open access journals are a novel concept in the medical literature. They offer accessible information to a wide variety of individuals, including physicians, medical students, clinical investigators, and the general public. They are an outstanding source of medical and scientific information."

Jeffrey M. Weinberg
(St. Luke's-Roosevelt Hospital Center, USA)

"Open access journals are extremely useful for graduate students, investigators and all other interested persons to read important scientific articles and subscribe scientific journals. Indeed, the research articles span a wide range of area and of high quality. This is specially a must for researchers belonging to institutions with limited library facility and funding to subscribe scientific journals."

Debomoy K. Lahiri
(Indiana University School of Medicine, USA)

"Open access journals represent a major break-through in publishing. They provide easy access to the latest research on a wide variety of issues. Relevant and timely articles are made available in a fraction of the time taken by more conventional publishers. Articles are of uniformly high quality and written by the world's leading authorities."

Robert Looney
(Naval Postgraduate School, USA)

"Open access journals have transformed the way scientific data is published and disseminated: particularly, whilst ensuring a high quality standard and transparency in the editorial process, they have increased the access to the scientific literature by those researchers that have limited library support or that are working on small budgets."

Richard Reithinger
(Westat, USA)

"Not only do open access journals greatly improve the access to high quality information for scientists in the developing world, it also provides extra exposure for our papers."

J. Ferwerda
(University of Oxford, UK)

"Open Access 'Chemistry' Journals allow the dissemination of knowledge at your finger tips without paying for the scientific content."

Sean L. Kitson
(Almac Sciences, Northern Ireland)

"In principle, all scientific journals should have open access, as should be science itself. Open access journals are very helpful for students, researchers and the general public including people from institutions which do not have library or cannot afford to subscribe scientific journals. The articles are high standard and cover a wide area."

Hubert Wolterbeek
(Delft University of Technology, The Netherlands)

"The widest possible diffusion of information is critical for the advancement of science. In this perspective, open access journals are instrumental in fostering researches and achievements."

Alessandro Laviano
(Sapienza - University of Rome, Italy)

"Open access journals are very useful for all scientists as they can have quick information in the different fields of science."

Philippe Hernigou
(Paris University, France)

"There are many scientists who can not afford the rather expensive subscriptions to scientific journals. Open access journals offer a good alternative for free access to good quality scientific information."

Fidel Toldrá
(Instituto de Agroquimica y Tecnologia de Alimentos, Spain)

"Open access journals have become a fundamental tool for students, researchers, patients and the general public. Many people from institutions which do not have library or cannot afford to subscribe scientific journals benefit of them on a daily basis. The articles are among the best and cover most scientific areas."

M. Bendandi
(University Clinic of Navarre, Spain)

"These journals provide researchers with a platform for rapid, open access scientific communication. The articles are of high quality and broad scope."

Peter Chiba
(University of Vienna, Austria)

"Open access journals are probably one of the most important contributions to promote and diffuse science worldwide."

Jaime Sampaio
(University of Trás-os-Montes e Alto Douro, Portugal)

"Open access journals make up a new and rather revolutionary way to scientific publication. This option opens several quite interesting possibilities to disseminate openly and freely new knowledge and even to facilitate interpersonal communication among scientists."

Eduardo A. Castro
(INIFTA, Argentina)

"Open access journals are freely available online throughout the world, for you to read, download, copy, distribute, and use. The articles published in the open access journals are high quality and cover a wide range of fields."

Kenji Hashimoto
(Chiba University, Japan)

"Open Access journals offer an innovative and efficient way of publication for academics and professionals in a wide range of disciplines. The papers published are of high quality after rigorous peer review and they are Indexed in: major international databases. I read Open Access journals to keep abreast of the recent development in my field of study."

Daniel Shek
(Chinese University of Hong Kong, Hong Kong)

"It is a modern trend for publishers to establish open access journals. Researchers, faculty members, and students will be greatly benefited by the new journals of Bentham Science Publishers Ltd. in this category."

Jih Ru Hwu
(National Central University, Taiwan)

Browse Contents

Webmaster Contact:
Copyright © 2017 Bentham Open