Algorithms for intravenous insulin delivery

Insulin infusion therapy in critically ill patients

While dysglycemia (hyperglycemia, hypoglycemia and glucose variability) is clearly associated with increased mortality in critically ill patients, target range of blood glucose control remains controversial. Standardized insulin infusion protocols constitute the basis of treatment of these patients. The choice of protocol and its implementation is a great challenge. In this article, we review the published data to help define the essential elements that compose a good protocol and apply the right conditions to make it safe and effective.

A quadruply-asymmetric sigmoid to describe the insulin-glucose relationship during intravenous insulin infusion

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.

Target attainment through algorithm design during intravenous insulin infusion

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.

Intermediary variables and algorithm parameters for an electronic algorithm for intravenous insulin infusion

BACKGROUND

Algorithms for intravenous insulin infusion may assign the infusion rate (IR) by a two-step process. First, the previous insulin infusion rate (IR(previous)) and the rate of change of blood glucose (BG) from the previous iteration of the algorithm are used to estimate the maintenance rate (MR) of insulin infusion. Second, the insulin IR for the next iteration (IR(next)) is assigned to be commensurate with the MR and the distance of the current blood glucose (BG(current)) from target. With use of a specific set of algorithm parameter values, a family of iso-MR curves is created, each giving IR as a function of MR and BG.

METHOD

To test the feasibility of estimating MR from the IR(previous) and the previous rate of change of BG, historical hyperglycemic data points were used to compute the "maintenance rate cross step next estimate" (MR(csne)). Historical cases had been treated with intravenous insulin infusion using a tabular protocol that estimated MR according to column-change rules. The mean IR on historical stable intervals (MR(true)), an estimate of the biologic value of MR, was compared to MR(csne) during the hyperglycemic iteration immediately preceding the stable interval. Hypothetically calculated MR(csne)-dependent IR(next) was compared to IR(next) assigned historically. An expanded theory of an algorithm is developed mathematically. Practical recommendations for computerization are proposed.

RESULTS

The MR(true) determined on each of 30 stable intervals and the MR(csne) during the immediately preceding hyperglycemic iteration differed, having medians with interquartile ranges 2.7 (1.2-3.7) and 3.2 (1.5-4.6) units/h, respectively. However, these estimates of MR were strongly correlated (R(2) = 0.88). During hyperglycemia at 941 time points the IR(next) assigned historically and the hypothetically calculated MR(csne)-dependent IR(next) differed, having medians with interquartile ranges 4.0 (3.0-6.0) and 4.6 (3.0-6.8) units/h, respectively, but these paired values again were correlated (R(2) = 0.87). This article describes a programmable algorithm for intravenous insulin infusion. The fundamental equation of the algorithm gives the relationship among IR; the biologic parameter MR; and two variables expressing an instantaneous rate of change of BG, one of which must be zero at any given point in time and the other positive, negative, or zero, namely the rate of change of BG from below target (rate of ascent) and the rate of change of BG from above target (rate of descent). In addition to user-definable parameters, three special algorithm parameters discoverable in nature are described: the maximum rate of the spontaneous ascent of blood glucose during nonhypoglycemia, the glucose per daily dose of insulin exogenously mediated, and the MR at given patient time points. User-assignable parameters will facilitate adaptation to different patient populations.

CONCLUSIONS

An algorithm is described that estimates MR prior to the attainment of euglycemia and computes MR-dependent values for IR(next). Design features address glycemic variability, promote safety with respect to hypoglycemia, and define a method for specifying glycemic targets that are allowed to differ according to patient condition.