Fourteen adult subjects with type 1 diabetes underwent 22 human closed-loop experiments lasting 21.5 ± 2.0 h as published previously.3
One subject withdrew early from the study because of repeated intravenous catheter failures, for a total of 21 closed-loop experiments in 13 subjects who received automated insulin and glucagon delivery. Hormone delivery rates were determined by the fading memory proportional derivative (FMPD) algorithm.13,14
Each subject wore two glucose sensors, and data from the more accurate sensor after a 2 h assessment period was used as the input into the FMPD algorithm. Arterialized venous blood glucose (VBG) levels were measured every 10 min for assessment of sensor accuracy, detection of hypoglycemia, and data analysis purposes. If neither glucose sensor was reading accurately, defined as deviating by more than 20% (for VBG 75 mg/dl or higher) or 20 mg/dl (<75 mg/dl) from the reference VBG value, then the VBG level was used as the input into the algorithm.
In addition to a basal component, the subcutaneous insulin delivery was dosed according to the difference between the glucose levels and the glucose target (proportional error) and the slope of glucose level (derivative error). The insulin delivery rate was modified by a fading memory (exponential decay) of past proportional and derivative errors, with more recent errors affecting the rate more heavily than remote errors.
Glucagon was delivered subcutaneously via a syringe pump and was given at times of impending hypoglycemia as determined by the FMPD algorithm, but in the opposite direction compared to insulin. Glucagon delivery was increased for negative proportional errors (glucose levels below target) and negative derivative errors (falling glucose levels) and was also modified by the glucose history. Seven subjects received glucagon delivered in a prolonged fashion, termed low-gain glucagon delivery, and six subjects received glucagon delivered in a short-lived but brisk fashion at times of impending hypoglycemia, termed high-gain glucagon delivery. Episodes of high-gain glucagon delivery that exceeded a dose of 0.5 mcg/kg were analyzed. The analysis was confined to glucagon delivery that was triggered by low and/or falling sensed glucose values and was separated from a meal by at least 1 h in either direction, yielding a total of 19 episodes. To be classified as a success (or failure), VBG did not (or did) fall below 70 mg/dl over a 60 min time period beginning at the start of glucagon delivery.
Insulin on board was estimated at the start of glucagon delivery and compared between successes and failures using a model that we derived from data published by Holmes and associates.15
From the time of delivery, the amount of insulin on board, in units, was modeled to rise in a linear fashion for 30 min and maintain constant at this peak level for an additional 60 min. After this 90 min period, the amount of insulin considered to be on board from a discrete time point was decreased using the exponential decay function: ae-kt
, where a
is the amount of insulin infused over a five minute time interval, e
is Euler’s number (2.717), k
is the decay constant (0.012 min-1
), and t
is the elapsed time in minutes since the end of the 60 min plateau. After 9 h, insulin was considered to be completely cleared. For comparison, serum free insulin levels were measured by ELISA (Mercodia) in seven subjects just prior to each episode of glucagon delivery, as well as 5, 20, and 40 min after glucagon delivery.
Data are expressed as mean ± standard error of the mean. Sensor accuracy was calculated by comparing sensor glucose to reference blood glucose values.16
If there was no VBG value available at the start of glucagon delivery, then the values done just prior to starting the glucagon and just after the initiation of glucagon were averaged. In general, these values were from blood drawn 5 min prior to and 5 min after the start of glucagon delivery, respectively. The same was true for calculating sensor bias at the start of glucagon delivery. Comparisons were made using unpaired t
tests. Calculations were performed using Excel 2007 version 12 (Microsoft Corporation, Redmond, WA).