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Journal of Healthcare Engineering
Volume 5 (2014), Issue 1, Pages 23-54
Research Article

A Quadruply-Asymmetric Sigmoid to Describe the Insulin-Glucose Relationship during Intravenous Insulin Infusion

Daniel T. Braithwaite,1 Guillermo E. Umpierrez,2 and Susan S. Braithwaite3

1Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL, USA
2Division of Endocrinology, Metabolism and Lipids, Emory University School of Medicine, Atlanta, Georgia, USA
3Division of Endocrinology, Diabetes and Metabolism, University of Illinois at Chicago, Chicago, IL, USA

Received 1 July 2013; Accepted 1 November 2013

Copyright © 2014 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For hospitalized patients requiring intravenous insulin therapy, an objective is to quantify the intravenous insulin infusion rate (IR) across the domain of blood glucose (BG) values at a single timepoint. The algorithm parameters include low BG (70 mg/dL), critical high BG, target range BG limits, and maintenance rate (MR) of insulin infusion, which, after initialization, depends on rate of change of blood glucose, previous IR, and other inputs. The restraining rate (RR) is a function of fractional completeness of ascent of BG (FCABG) from BG 70 mg/dL to target. The correction rate (CR) is a function of fractional elevation of BG (FEBG), in comparison to elevation of a critical high BG, above target. IR = RR + CR. The proposed mathematical model describing a sigmoidal relationship between IR and BG may offer a safety advantage over the linear relationship currently employed in some intravenous glucose management systems.