Diabetes Technol Ther. 2014 Apr;16(4):208-18.

Target attainment through algorithm design during intravenous insulin infusion.

Devi R, Zohra T, Howard BS, Braithwaite SS.

St. Francis Hospital , Evanston, Illinois.



BACKGROUND: Algorithms were designed under a single model, to attain differing designated glycemic targets during intravenous insulin infusion, and evaluated in order to justify computerization of the model. The approximate maintenance rate (MR) of insulin infusion is discovered according to rate of change of blood glucose (BG) and previous insulin infusion rate (IR). During treatment, re-assignment of IR depends on MR and BG. For each MR, a roughly sigmoidal relationship between BG and IR is specified, such that the inflection point falls approximately at a true target BG.

MATERIALS AND METHODS: Performance at St. Francis Hospital, Evanston, IL, was examined during use of tabular algorithms targeting three distinct BG ranges, appropriate for the treatment of hyperglycemic hyperosmolar state, diabetic ketoacidosis, or hyperglycemia accompanying other critical illness. Group membership was defined according to algorithm used for patient treatment during the first 6 months of 2012. The group geometric mean (GGM) and multiplicative surrogate standard deviation (MSSD) are reported as group measures, respectively typifying the central tendency and variability of individual patient BG distributions.

RESULTS: Between first attainment of target range BG control and a data collection end point, BG data were evaluable during treatment courses for 58 patients. During this time frame, in the group treated with target 100-149 mg/dL, there were five episodes of BG <70 mg/dL for each of five patients, with the lowest being 57 mg/dL. The GGM (with multiplicative standard deviation) was 269.4 (÷/× 1.06) mg/dL for the algorithm having target 200-299 mg/dL (n = 3 treatment courses), 172.6 (÷/× 1.15) mg/dL for target 150-199 mg/dL (n = 7), and 131.3 (÷/× 1.19) mg/dL for target 100-149 mg/dL (n = 48). The values of MSSD for the three groups were (÷/× 1.14), (÷/× 1.20), and (÷/× 1.20), respectively.

CONCLUSIONS: The pilot series suggests that once target range BG is attained, maintenance of control within each of three distinct BG target ranges is achievable, according to choice of algorithm.

PMID: 24354344



Efforts to arrive at evidence-based professional consensus about the glycemic targets for intravenous insulin infusion therapy have been impeded by lack of technology that would achieve and maintain glucose values within specified target ranges with safety.  Furthermore, glycemic targets for hospitalized patients may differ depending upon patient medical condition, site of care, and presence or absence of uncontrolled diabetes prior to admission (1-3).

Patients treated for hyperglycemia in the intensive care unit generally should receive insulin by intravenous insulin infusion.  Proprietary devices and institutional insulin infusion protocols under some designs may rely upon discovery of an intermediary parameter, related to patient insulin resistance and carbohydrate exposure, from which computation of intravenous insulin infusion rate (IR) is performed.   The essential parameter is called the “maintenance rate” (MR) in our algorithms, or “multiplier” in traditional multiplier algorithms.  At any given time during the treatment course, the recommended IR over the range of BG that might be encountered will depend upon the MR or the multiplier.  The value of the MR or the multiplier will be re-determined repeatedly after initiation of treatment, by the response to previous IR assignments.  Thus the algorithms described in our publication and the standard multiplier algorithms are similar in that each provides dynamic rules, by which an essential parameter is revised repeatedly during the course of therapy.

The rule for IR as a function of multiplier, in commonly-used multiplier algorithms, is:

IR = (BG – 60 mg/dL) x (multiplier)

In our algorithm, the rule for IR as a function of MR is a more complex sigmoidal rule, shown as a step function giving rounded-off values, when expressed in tabular form as a paper protocol.

At BG 130-149 mg/dL, our standard default insulin infusion algorithm recommends that IR = MR.   Suppose caregivers judge that BG = 130-149 mg/dL is appropriate for a patient.  During the course of treatment, suppose further that the MR necessary to hold BG of the patient in that range is variably estimated to be 2, 3, or 4 units/hr.  In order to illustrate a comparison between our standard default insulin infusion algorithm and a typical multiplier algorithm, multipliers can be identified that would recommend IR = 2, 3, or 4 units/hr for BG = 140/mg/dL (Figures 1, 2 and 3 respectively).



Figure 1.  Comparison of algorithms that would recommend IR = 2 units/hr for BG = 140 mg/dL.  Abbreviations:  Insulin infusion rate (IR), maintenance rate (MR), and blood glucose (BG).  For excessive upward or downward trending of BG, revision of MR or multiplier is recommended.  Some implementations recommend not only multiplier reduction, but also temporary suspension of insulin infusion at a threshold BG value considered to signify or portend hypoglycemia.  Overt hypoglycemia is treated with concentrated dextrose.


We had two principal motives to attempt to improve upon the linear design of multiplier algorithms.  First, it was speculated that oscillations of blood glucose (BG) could be reduced by a nearly-sigmoidal design, relating IR to BG, possibly with reduction of both hypoglycemia and hyperglycemia.  The sigmoidal curve would be “centered” on the target BG value, the value at which the curve would have its inflection point.  Second, it was speculated that attainment of specific targets could be improved by a nearly-sigmoidal design.

We reasoned that the linear relationship between IR and BG as seen in multiplier algorithms could promote hypoglycemia.  Engineering of insulin therapy is complicated by the delay between administration and final biologic effect, so that failure to damp incremental upward adjustments of IR at highest BG levels could leave the patient later with a reservoir of excessive insulin effect.  The risk of delayed excessive effect might be especially likely to be realized if the rate of insulin infusion had been “ramped up” over several hours of initial insulin resistance.

In case of excessive downward trending of BG, the multiplier design relies upon temporary suspension of insulin infusion, as a strategy to allow abatement of insulin effect, prior to resumption of the infusion. Under the rules of some implementations, such suspension may be not recommended until the glucose is as low as 3.5 mmol/L  or 63 mg/dL (4). Prolongation of the suspension, either by protocol design or through inadvertent inattention of caregivers, could contribute to oscillations of glycemic control. We reasoned that if the provider intends to continue intravenous insulin infusion, a sharp abatement of insulin infusion responsive to excessive downward trend of BG could be superior to complete suspension.  Overt hypoglycemia should be treated, followed by re-testing, but then after recovery from hypoglycemia, a negligible rate of insulin infusion could be continued until the patient exhibits a clearcut further rise of glucose.



Figure 2.  Comparison of algorithms that would recommend IR = 3 units/hr for BG = 140 mg/dL.


The multiplier design, relying upon temporary suspensions followed by timed resumptions of insulin infusion, may lack a sound method of attaining and maintaining various target ranges of BG.  A sigmoidal design places the target range in the “center “ of the sigmoidal curve, at its inflection point.

Based on the preliminary pilot data mentioned in the abstract cited above, design and implementation of a programmable algorithm is moving forward, that will express IR for each MR as a strictly ascending, continuous, and differentiable function of BG (5).  Each iso-MR curve, showing IR as function of MR and BG, will be quadruply asymmetric, having a relatively flat mid-portion.  The mid-portion will correspond to the target range of BG.  Although the importance and difficulty of identifying the MR should not be underestimated, assuming it is possible to approximately identify the MR, then it might be hoped that target attainment can be safely achieved for each of a variety of target ranges.  If differing BG targets can be safely achieved, we will have a rational approach to future investigation of the impact of glycemic control upon outcomes.



Figure 3.  Comparison of algorithms that would recommend IR = 4 units/hr for BG = 140 mg/dL.



  1. Jacobi J, Bircher N, Krinsley J, Agus M, Braithwaite SS, Deutschman C, et al. Guidelines for the use of an insulin infusion for the management of hyperglycemia in critically ill patients. Crit Care Med. 2012;40(12):3251-76.
  2. Plummer MP, Bellomo R, Cousins CE, Annink CE, Sundararajan K, Reddi BA, et al. Dysglycaemia in the critically ill and the interaction of chronic and acute glycaemia with mortality. Intensive Care Med. 2014;40(7):973-80.
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  4. Yamashita S, Ng E, Brommecker F, Silverberg J, Adhikari NK. Implementation of the glucommander method of adjusting insulin infusions in critically ill patients. Can J Hosp Pharm. 2011;64(5):333-9.
  5. Braithwaite DT, Umpierrez GE, Braithwaite SS. A quadruply-asymmetric sigmoid to describe the insulin-glucose relationship during intravenous insulin infusion. J Healthc Eng. 2014;5(1):23-53.


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