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

Braithwaite, Daniel T.; Umpierrez, Guillermo E.; Braithwaite, Susan S.

doi:https://doi.org/10.1260/2040-2295.5.1.23

Journal of Healthcare Engineering

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Research Article | Open Access

Volume 5 | Article ID 478409 | https://doi.org/10.1260/2040-2295.5.1.23

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

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

Received01 Jul 2013

Accepted01 Nov 2013

Abstract

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.

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