Manual Closed-Loop Insulin Delivery Using a Saddle Point Model Predictive Control Algorithm: Results of a Crossover Randomized Overnight Study

Abstract

Background:

The purpose was to assess the efficacy of a new closed-loop algorithm (Saddle Point Model Predictive Control, SP-MPC) in achieving nocturnal normoglycemia while reducing the risk of hypoglycemia in patients with type 1 diabetes.

Method:

In this randomized crossover study, 10 adult patients (mean hemoglobin A1c 7.35 ± 1.04%) were assigned to be treated overnight by open loop using sensor-augmented pump therapy (open-loop SAP) or manual closed-loop delivery. During closed loop, insulin doses were calculated using the SP-MPC algorithm and administered as manual boluses every 15 minutes from 9:00 pm to 8:00 am. Patients consumed a self-selected meal (65-125 g of carbohydrates) at 7:00 pm accompanied by their usual prandial bolus. Blood glucose was measured every 30 minutes. The primary endpoints were the time spent in target (70-145 mg/dl) and time spent below 70 mg/dl from 11:00 pm to 8:00 am.

Results:

Time spent in target did not differ between closed-loop and open-loop SAP. The number of hypoglycemic events (<70 mg/dl) was reduced 2.8-fold in closed loop (n = 5, median = 0/patient/hour; interquartile range: 0-0.11) as compared to open-loop SAP (n = 14, median = 0.22/patient/hour, 0.02-0.22) (P = .02). The area under the curve for sensor glucose values >145 mg/dl was significantly lower during closed-loop than during open-loop SAP (P = .03) as well as HBGI (P = .02).

Conclusions:

This pilot study suggests that the use of the SP-MPC algorithm may improve mean overnight glucose control and reduce the number of hypoglycemic events as compared to SAP therapy.

Keywords

artificial pancreas closed loop model predictive control sensor-augmented pump therapy type 1 diabetes

Recent advances in insulin pumps, continuous glucose monitoring (CGM) devices, and control algorithms have resulted in an acceleration of progress in the development of an artificial pancreas.^1-3 One of the paramount goals of an artificial pancreas is to improve nocturnal glycemic control. Several control algorithms have been tested aiming at both reducing nocturnal hypoglycemia and increasing the time spent in normoglycemia. Among these we can mention PID (proportional integral derivative) controller, which computes the insulin dose by using an analytical function of the error between the current measured glycemia and the target.^4-6 The fuzzy logic approach determines relevant insulin doses by evaluating rules that emulate the expert (medical personnel) decision-making in providing treatment recommendations to patients.^7-10 Finally, there is the model predictive control (MPC) algorithm which belongs to the family of optimization-based controllers. It calculates an insulin profile which optimizes a glycemic trajectory forecast by the model.^11-16 MPC and PID algorithms were compared in a randomized crossover trial.¹⁷ Although both forms of closed loop algorithm provided safe and effective glucose management, MPC performed as well or better than PID.¹⁷

The performances of the MPC approach are strongly dependent on the ability of the model to describe the process to be controlled. This is an issue when dealing with type 1 diabetes since developing a model of insulin/glucose interactions is a complex process involving a large number of parameters. Identifying these parameters for a given patient using standard clinical data (eg, CGM data, daily insulin doses, carbohydrate contents, etc) remains a challenge. Moreover, these parameters are liable to evolve over time. Our approach consisted in developing a new MPC controller, called Saddle Point Model Predictive Control (SP-MPC)^18-20 which explicitly takes into account the fact that the model is uncertain. The aim is to control blood glucose despite the model’s uncertainties (eg, neglected dynamics or parameter uncertainties).

In this article we present results from the first clinical evaluation of closed-loop insulin delivery using SP-MPC algorithm in adults with type 1 diabetes. The aim of this study was to assess the ability of SP-MPC to maintain normal blood glucose levels overnight while reducing the risk of hypoglycemia compared with SAP therapy at inpatient setting.

Methods

Patients

The study protocol and consent form were approved by the local institutional ethics review committee. All participants provided informed written consent. The study was performed at the Clinical Investigation Unit at Rennes University hospital (CIC INSERM 1414).

Key inclusion criteria were adults with type 1 diabetes (C-peptide negative) diagnosed at least 3 years previously, treated with insulin pump therapy for at least 3 months, experienced in the use of real-time CGM. Exclusion criteria were concurrent illness, laboratory abnormalities, or medications that might affect study participation, current pregnancy, renal impairment, or a hemoglobin A1c value above 10%.

Ten patients were assigned to be treated with manual closed-loop delivery of insulin, and open loop using SAP therapy, over two different nights separated by an interval of one to six weeks. They were randomized to determine the order of open-loop SAP and closed loop. All 10 patients completed the study (five women; mean ± SD age 48.1 ±14.4 years; diabetes duration: 27.5 ± 10.6 years; body mass index: 25 ± 3 kg/m2; hemoglobin A1c: 7.35 ± 1.04%, daily insulin dose 43 ± 15 units/day). Six patients were known to be subject to a marked dawn phenomenon and their insulin pump was usually programmed to deliver an increased insulin basal rate during the last part of the night.

CGM and Insulin Delivery

The devices used were the Enlite™ sensor and the Paradigm® Veo™ insulin pump (Medtronic Minimed, Northridge, CA, USA). The pump delivered rapid acting insulin analogue Aspart (Novo Nordisk, Bagsvaerd, Denmark). The Freestyle Optium Neo (Abbott Diabetes Care, Alameda, CA, USA) was used to calibrate the CGM device.

Closed-Loop Algorithm

A new MPC algorithm was developed at CentraleSupélec and is referred to as “Saddle Point Model Predictive Control.” Its objective is to search for an insulin control input which leads to an optimal profile of a predicted blood glucose level while searching for disturbances having the most negative impact on the control objective (given the uncertainties of the patient model). This problem is solved using a game theory framework (for details, see Penet,¹⁸ Penet et al,¹⁹ and Penet et al²⁰).

The patient model chosen was a state space model with 8 parameters, aiming at describing both insulin and meal ingestion dynamics. Its inputs were given by basal insulin, insulin boluses and meal carbohydrate contents. For each patient, the model’s parameters were identified by a nonlinear least-squares method using 5 days of previously recorded data. These included CGM data, insulin doses, and meal carbohydrate contents.

The blood glucose level was predicted on a 5-hour basis. The control objective was to stabilize glucose level at 100 mg/dL while avoiding glycemia lower than 70 mg/dL.

Study Design

Two sensors were inserted 48 hours prior to each study visit. Patients were instructed to calibrate the sensors according to manufacturer instructions and to avoid unusual physical activities the day of each visit. At admission, one sensor was chosen based on its accuracy and reliability; the second one was kept as backup. An intravenous cannula was inserted to collect blood samples for glucose determination every 30 minutes from 8:30 pm to 8:00 am the following morning. Investigators were blinded to the plasma glucose results. Finger stick glucose measurements were performed before and two hours after dinner, at bedtime, at 4:00 pm, in case of hypoglycemic symptoms and when the sensor glucose value was <70 mg/dl or >250 mg/dl for more than 15 minutes. Hypoglycemia was diagnosed when capillary glucose was <70 mg/dl with or without symptoms recognized by the patient and was treated with 15 g of carbohydrate. When occurring in the same one-hour period, we counted two hypoglycemia events as being distinct when, following carbohydrate intake, capillary glucose after rising above 70 mg/dl subsequently fell below 70 mg/dl. Additional blood samples were collected at time of hypoglycemia and 15 minutes after carbohydrate intake.

On both visits, participants ate an identical evening meal at 7:00 pm. Its composition was calculated according to each patient’s habits. The median carbohydrate content was 70 g (range: 65-125 g). An insulin bolus was delivered before the meal, calculated according to the patients’ own insulin to carbohydrate ratio, corrector factor and premeal capillary glucose level.

During the closed-loop session, the algorithm was provided with the carbohydrate content of the meal, the premeal bolus and the glucose levels measured by the reference sensor during the four hours preceding the start of closed-loop delivery. The closed loop started at 9:00 pm and continued during the night until 8:00 am (11 hours). The insulin basal infusion was set to zero when the closed-loop period started. The CGM sample time was 5 minutes. Every 15 minutes, the investigators initiated a control cycle: the three previous sensor glucose values (T, T-5, and T-10 minutes) were provided to the SP-MPC algorithm. The computed insulin dose was then administered as a manual bolus after being validated. The sensors’ alarms were switched off.

During the open-loop SAP session, the participants applied their usual insulin pump settings. The CGM data were available for the patients. They were allowed to deliver a correction bolus or to modify their basal insulin rate if needed. The sensors’ alarms were set at 70 mg/dl and 250 mg/dl. If the sensor alarm was not heard, the research nurse checked capillary glucose and woke the patient in case of confirmed hypoglycemia. Consequently, the low glucose suspend function of the pump was switched off.

Statistical Analysis

Investigators and study statisticians agreed on the analysis plan in advance.

The primary endpoints were the percentage time plasma glucose concentrations were in the target range (70-145 mg/dl) and the percentage time spent below 70 mg/dl between 11:00 pm and 8:00 am.

Secondary endpoints were, between 11:00 pm and 8:00 am, the mean plasma and sensor glucose values; the percentage time sensor glucose concentrations were within, below, or above the target range; the percentage time plasma glucose values were above 145 mg/dl; the area above the curve for glucose values below 70 mg/dl and the area under the curve for glucose values above 145 mg/dl (plasma and sensor glucose values); the number of hypoglycemic events; total insulin doses delivered. CONGA, low blood glucose index (LBGI), high blood glucose index (HBGI), and blood glucose risk index were used as metrics of risk for hypo- and hyperglycemia and overall glucose variability.^21,22

Plasma glucose and sensor glucose values were linearly interpolated to compute times and areas spent under 70 mg/dl and above 145 mg/dl. All measures are reported in relation to the time period during which they were assessed. Median and interquartile range (IQR 25th-75th percentiles) are presented. Because of the paired design, median and interquartile range of the differences between the two procedures are reported. Differences were assessed with Wilcoxon’s non parametric test for paired data. Finally a linear mixed model was used to compare mean plasma glucose and mean sensor glucose values between the two procedures. Mean differences and their 95% confidence intervals are reported. Analyses were carried out by with R software.²³

Results

Accuracy of CGM and Adverse Events

The accuracy of the reference sensor, evaluated as the median relative absolute difference between sensor glucose levels and paired plasma glucose levels divided by plasma glucose levels, was 10.9% (IQR: 5.0-15.8).

During the closed-loop nights, a 20-minute period of reference sensor loss occurred in one patient during which the second sensor was temporarily used. For another patient, both main and spare sensors failed for one hour on the night of the closed-loop experiment, and reported erroneous data. Because they were aberrant measures, this hour was missing. The same period of open-loop SAP experiment was therefore censored for this patient, to restore comparability between the nights.

No hypoglycemia below 40 mg/dl occurred. Hyperglycemia greater than 280 mg/dl and ketonemia were not observed during the study.

During closed-loop session, no omissions or discrepancies were observed between insulin doses validated by the diabetologist and those really administered by manual boluses every 15 minutes.

Overnight Glycemic Control (from 11:00 pm to 8:00 am)

Individual data are presented in Table 1. Figure 1 depicts plasma glucose profiles for closed-loop versus open-loop SAP.

Table 1.

Individual Data of the Closed-Loop and the Open-Loop SAP Nights (11:00 pm to 8:00 am).

Patient		1	2	3	4	5	6	7	8	9	10
Dinner CHO content—g		125	65	65	85	65	85	65	65	85	75
Number of hypoglycemic events
	CL	0	0	0	1	0	1	1	0	2	0
	OL	2	2	0	2	0	2	2	0	3	1
Mean plasma glucose value (SD)—mg/dl
	CL	146 (42.6)	132 (17.9)	135 (11.5)	111 (21.8)	170 (53.1)	123 (42.0)	133 (61.0)	148 (14.1)	88 (21.2)	205 (13.7)
	OL	111 (37.4)	122 (45.7)	167 (9.3)	86 (27.3)	212 (29.1)	135 (56.2)	95 (38.2)	200 (34.4)	93 (24.7)	195 (66.9)
Mean sensor glucose value (SD)—mg/dl
	CL	123 (30.9)	132 (15.6)	133 (11.3)	112 (13.0)	146 (36.4)	118 (27.2)	124 (43.7)	136 (6.6)	87 (18.1)	170 (12.6)
	OL	126 (45.2)	117 (35.4)	161 (6.7)	89 (17.8)	175 (19.6)	126 (46.2)	114 (33.1)	164 (16.2)	94 (17.7)	178 (48.3)
MARD (median, IQR)—%
	CL	13 (9-18)	2 (2-2.5)	3 (1-5)	6 (4-9)	14 (8-16)	12 (8-14)	14 (10-16)	8 (6-13)	6 (3-9)	17 (14-19)
	OL	10 (7-18)	8 (5-13)	4 (3-5)	11 (8-16)	19 (15-20)	11 (8-18)	18 (11-32)	20 (16-21)	8 (3-12)	11 (7-16)
Time at plasma glucose level—%
<70 mg/dl	CL	0	0	0	5.9	0.0	10.9	19.8	0.0	21.2	0.0
<70 mg/dl	OL	14.3	8.0	0.0	38.7	0.0	8.7	26.9	0.0	18.0	1.5
70-145 mg/dl	CL	54.0	90.0	78.0	94.1	34.4	48.7	30.9	41.3	78.8	0.0
70-145 mg/dl	OL	50.5	52.0	0.0	61.3	0.0	46.5	56.3	5.2	82.0	23.1
>145 mg/dl	CL	46.0	10.0	22.0	0.0	65.6	40.4	49.3	58.7	0.0	100.0
>145 mg/dl	OL	35.2	40.0	100.0	0.0	100.0	44.8	16.9	94.8	0.0	75.4
Time at sensor glucose level—%
<70 mg/dl	CL	5.3	0.0	0.0	2.4	0.0	8.1	6.1	0.0	19.1	0.0
<70 mg/dl	OL	16.8	4.4	0.0	4.3	0.0	6.1	3.9	0.0	5.0	0.0
70-145 mg/dl	CL	74.7	92.0	80.6	97.6	46.9	71.3	49.4	95.9	80.9	0.0
70-145 mg/dl	OL	40.6	58.9	0.0	95.7	1.3	53.9	76.3	8.7	95.0	32.0
>145 mg/dl	CL	20.0	8.0	19.4	0.0	53.1	20.6	44.4	4.1	0.0	100.0
>145 mg/dl	OL	42.6	36.7	100.0	0.0	98.7	40.0	19.8	91.3	0.0	68.0
Area under the curve for plasma glucose values—mg.min/dl
<70 mg/dl	CL	0.0	0.0	0.0	0.5	0.0	1.2	1.0	0.0	2.0	0.0
<70 mg/dl	OL	2.3	0.3	0.0	2.2	0.0	0.7	3.6	0.0	0.9	0.1
>145 mg/dl	CL	19.6	1.8	1.1	0.0	36.7	8.0	23.9	8.3	0.0	59.3
>145 mg/dl	OL	1.6	11.6	22.5	0.0	69.2	20.1	2.6	57.9	0.0	66.3
Area under the curve for sensor glucose values—mg.min/dl
<70 mg/dl	CL	0.8	0.0	0.0	0.1	0.0	0.3	0.3	0.0	1.5	0.0
<70 mg/dl	OL	1.3	0.1	0.0	0.2	0.0	0.1	0.1	0.0	0.1	0.0
>145 mg/dl	CL	4.3	1.8	1.0	0.0	16.3	1.4	9.7	0.0	0.0	24.9
>145 mg/dl	OL	12.5	5.0	16.3	0.0	30.2	13.2	4.3	20.4	0.0	42.6
Insulin dose—UI/h
	CL	0.91	0.57	0.42	0.90	0.78	0.95	0.83	0.56	1.23	0.68
	OL	0.76	0.58	0.36	1.03	0.59	0.85	0.88	0.63	1.41	0.53
LBGI	CL	10.4	0.09	1.72	3.51	0.97	2.86	4.91	4.84	4.36	0
	OL	12.88	3.43	0	5.08	0	3.05	4.57	4.36	4.69	3.56
HBGI	CL	2.38	2.14	1.14	0.1	5.53	2.01	4.1	1.3	0.01	6.6
	OL	4.43	3.72	4.05	0.09	6.53	8.21	2.97	4.94	0.14	10.26
CONGA	CL	5.19	6.88	6.5	5.24	7.94	5.79	5.66	6.53	4.03	9.01
	OL	5.14	4.95	8.32	3.91	9	6.9	4.43	7.73	3.93	8.12

CHO, carbohydrates; CL, closed loop; CONGA, continuous overall net glycemic action; HBGI, high blood glucose index; LBGI, low blood glucose index; MARD, median relative absolute difference; OL, open loop; SAP, sensor-augmented pump therapy.

Figure 1.

Median (curves) and 25th-75th percentiles (shaded areas) of plasma glucose during closed-loop and open-loop SAP nights. The straight dotted lines show the target zone 70-145 mg/dl.

Time spent in the target range and the mean plasma glucose value were similar under the two regimens (Table 2). The mean interstitial glucose concentration was significantly lower during nights when the artificial pancreas was used (128 mg/dl; 95% CI: 112-144) than during nights when SAP was used (134 mg/dl; 95% CI: 118-151) (P < .001).

Table 2.

Percentage of Time Spent in Various Glucose Ranges, Area Above or Under the Curve, Mean Values (Plasma Glucose and Sensor Glucose), Number of Hypoglycemic Events, Variability Index (LBGI, HBGI, CONGA), and Total Insulin Dose Delivered With Open-Loop SAP and Closed-Loop SAP During the Overnight Period (11:00 pm-8:00 am).

Variable	Open-loop SAP	Closed-loop SAP	Difference	p
Number of plasma glucose values	197	190
Number of sensor glucose values	1071	1072
Median time between 70-145 mg/dl (IQR)—%
Plasma glucose	48.5 (9.7 to 55.2)	51.4 (36.2 to 78.6)	0.2 (0.1 to 0.4)	.11
Sensor glucose	47.3 (14.5 to 71.9)	77.6 (54.9 to 89.2)	0.3 (−0.1 to 0.4)	.11
Median time below 70 mg/dl (IQR)—%
Plasma glucose	8.3 (0.4 to 17.1)	0.0 (0.0 to 9.7)	0.0 (−0.1 to 0.0)	.15
Sensor glucose	4.1 (0.0 to 4.9)	1.2 (0.0 to 5.9)	0.0 (0.0 to 0.0)	1.00
Median time above 145 mg/dl (IQR)—%
Plasma glucose	42.4 (21.4 to 90.0)	43.2 (13.0 to 56.3)	0.0 (−0.3 to 0.1)	.29
Sensor glucose	40.3 (24.0 to 85.5)	19.7 (5.0 to 38.5)	−0.2 (−0.4 to 0.0)	.18
Median area above the curve for glucose values <70 mg/dl (IQR)—mg.min/dl
Plasma glucose	0.5 (0.1 to 1.9)	0 (0.0 to 0.9)	−0.1 (−1.4 to 0.0)	.27
Sensor glucose	0.1 (0.0 to 0.1)	0.0 (0.0 to 0.3)	0.0 (0.0 to 0.1)	.67
Median area under the curve for glucose values >145 mg/dl (IQR)—mg.min/dl
Plasma glucose	15.9 (1.8 to 49.1)	8.1 (1.2 to 22.8)	−8.5 (−19.1 to 0.0)	.23
Sensor glucose	12.9 (4.5 to 19.4)	1.6 (0.3 to 8.3)	−10.0 (−14.9 to −0.8)	.03
Mean value—mg/dl (95% CI)
Plasma glucose	141 (118 to 165)	139 (115 to 163)	−2 (−10 to 5)	.54
Sensor glucose	134 (118 to 151)	128 (112 to 144)	−6 (9 to 4)	<.001
Hypoglycemic events (median (IQR))—n/patient/hour
	0.22 (0.02 to 0.22)	0 (0 to 0.11)	−0.11 (−0.11 to −0.03)	.02
LBGI (median (IQR))	4.0 (3.1 to 4.7)	3.2 (1.2 to 4.7)	−0.3 (−2.3 to 0.4)	.43
HBGI (median (IQR))	4.2 (3.2 to 6.1)	2.1 (1.2 to 3.7)	−1.8 (−3.5 to −0.3)	.02
CONGA (median (IQR))	6.0 (4.6 to 8.0)	6.1 (5.3 to 6.8)	0.1 (−1.1 to 1.1)	.77
Total insulin dose—UI/h (IQR)	0.69 (0.58 to 0.88)	0.8 (0.59 to 0.9)	0.03 (−0.07 to 0.13)	.62

CI, confidence interval; CONGA, continuous overall net glycemic action; HBGI, high blood glucose index; IQR, interquartile range; LBGI, low blood glucose index; SAP, sensor-augmented pump therapy.

Time spent below the target range and the area above the curve for glucose values below 70 mg/dl did not differ (Table 2). A total of 14 hypoglycemic events (7 patients) were observed using open-loop SAP and only 5 were recorded in 4 patients using closed loop (median 0.22/patient/hour, quartiles: 0.02-0.22 versus 0/patient/hour, 0-0.11) (P = .02). Hypoglycemic events lasted 15 to 35 minutes. Seven patients (6 in open loop and 1 in closed loop) experienced more than one hypoglycemic event. These episodes were generally separated by at least one and a half hours: only two occurred within the same hour. During open-loop SAP, seven hypoglycemias were detected after midnight thanks to glucose sensor alarms. In 4 cases, patients were woken by the alarm. In the 3 other cases, the alarm was not heard and patients were woken by the research nurse. Mean glycemia 1 hour after hypoglycemia treatment was a mean of 105 ± 16 mg/dl in closed-loop and 101 ± 30 mg/dl in open-loop SAP.

There was no significant difference between treatments in the time spent with plasma glucose or sensor glucose values above 145 mg/dl whereas the area under the curve for sensor glucose values above 145 mg/dl was lower during closed loop (Table 2). HBGI was reduced in closed loop (Table 2). The BG Risk index (LBGI+HBGI) was lower in closed-loop (5.5, IQR: 3.8-6.6) as compared to open-loop SAP (7.3, IQR: 5.5-10.7) (P = .01).

Insulin Doses

Total overnight insulin doses were similar during the two procedures (Table 2). During open-loop SAP, one patient decided to suspend basal rate during 30 minutes due to a hypoglycemia and two other patients set temporary basal rate while glucose sensor values were measured between 75 and 80 mg/dl (decrease of 33% during 180 minutes from 11:45 pm and 280 minutes from 2:50 am, respectively).

Discussion

Our randomized crossover pilot study has shown a significant 2.8-fold reduction in the number of nocturnal hypoglycemic events during closed loop using the SP-MPC algorithm while the percentage of time spent in the target range was not different, when compared to open-loop SAP.

Mean sensor glucose level, BG risk index and the extent of hyperglycemic events, measured by the sensor glucose area below the curve, were significantly lower during the closed loop when compared to open loop. However, despite a similar trend, these parameters were not significantly different when considering plasma glucose. The lack of significance of the plasma data may be explained at least in part because there were 5.5 times as many interstitial glucose values as compared to the number of plasma glucose values. In particular, the calculations of area and time passed in the different intervals are less precise in the sampling of plasma measures, carried out every 30 minutes, as against every 5 minutes for interstitial glucose measures.

Pilot closed-loop studies have generally shown dissociated metabolic results: either fewer hypoglycemic events without greater time spent in target range, or increased time in target range without a reduction in hypoglycemia. For instance, Hovorka et al compared a MPC closed-loop delivery with continuous subcutaneous insulin infusion in two randomized cross-over studies concerning 12 and 9 young patients with type 1 diabetes respectively.¹⁴ Analysis of pooled data of both studies documented increased time in target range from midnight to 8:00 am (P = .0025). This improvement of time spent in target after midnight was confirmed using the same algorithm in 12 adolescents undertaking moderate intensity exercise,²⁴ but without a significant reduction either in time below target (<70 mg/l) or in the number of hypoglycemias. A reduced risk of hypoglycemia was revealed in a later study on a greater number of adult patients.¹⁵ Breton et al, using a standard control to range algorithm during a multicentric study on 15 adults and 11 adolescents, reported a 6-fold reduction in hypoglycemia overnight with an increase of time in near normoglycemia (3.9-10 mmol/l) but not in tight glycemic range (4.4-7.8 mmol/l).¹¹ The authors also tested an enhanced control to range algorithm which allowed a significant decrease in average plasma glucose and a significant increase of time in tight control overnight. The most recent studies, carried out on outpatients, report an increase in time spent in target range (70-140 mg/dl or 70-180 mg/dl), together with a reduction in hypoglycemic range.^10,25-27 The highly encouraging results of these inpatient and outpatient studies made it possible to carry out studies at home.^26-31

In our study, the patients were placed in a setting where tight glucose control was their primary assignment during open-loop SAP night. They had all been given specific training in dynamic and motivated use of the sensor data. They had full access to CGM data and both hypoglycemic and hyperglycemic alarms were turned on. The low glucose suspend function of the pump was switched off but patients were woken by the nurse in case of hypoglycemia. They could then adjust their insulin delivery more precisely than by a basic threshold-based insulin-pump interruption. In spite of these drastic conditions, the number of hypoglycemic events was lower during closed loop while the time in tight target range did not differ between closed-loop and open-loop SAP.

The novelty of this closed-loop study lies in the SP-MPC algorithm. The MPC methodology relies on a model of the process to be controlled. The patient’s model is at the heart of the control performances. However, models of the glucose metabolism are imprecise or not completely accurate. In the SP-MPC, uncertainties on the parameters of the model and the impact of meals and exercise appear themselves as perturbations on the model. As a consequence, where the standard MPC only seeks to optimize glycemia for a given model, the SP-MPC defines the insulin profile which allows optimal regulation of glycemia in the most unfavorable circumstances. It makes a kind of compromise between a standard MPC algorithm and a min-max MPC.³² A standard MPC algorithm can be quite sensitive to uncertainties but will always try to regulate the glucose rate accurately. On the contrary a min-max MPC is not at all sensitive to uncertainties but will be satisfied with moderately accurate control performances. The SP-MPC control strategy does not prevent the controller being under-reactive in some situations, but would tend to be more accurate than a min-max MPC controller. One of the striking findings in our study is the ability of the SP-MPC algorithm to maintain glucose levels in the normal range during the last part of the closed-loop night even in the six patients who usually experienced a dawn phenomenon. Improved blood glucose levels in the second part of the night during the closed loop compared to the open loop has been highlighted by several authors and contributes to better glycemic control over the rest of the day.³³

There are limits to our study. The number of patients was small, but nonetheless comparable in size to those used in pilot studies. The closed loop was not automated. Nevertheless, we noted no discrepancies between the values recorded by the program using the integrated algorithm and those obtained by downloading the insulin pumps. Future studies will use an automated solution. We used two sensors, as is the case in the majority of inpatient studies. Despite these precautions we experienced hour-long failures of both main and spare sensors, resulting in data that could not be analyzed. Our study was carried out on inpatients, and in spite of our efforts to respect their habits and limit the disturbance caused by the comings and goings of investigators, patients’ sleep may have been disturbed, which would impact on the quality of their glycemic control. However, the disturbances resulting from venous blood sampling were equally frequent and thus equally disturbing in open loop and in closed loop. Programming of a low predictive alert in open loop could have warned the patients before the occurrence of a hypoglycemia. In addition, letting patients sleep through alarms would have been more reflective of real life. This may have influenced open loop results, but we chose to use the same pump programming and to apply the same procedures in open loop and closed loop. Indeed, the purpose of this study was to assess the potential benefits of our algorithm and not to compare it to the algorithm incorporated in the Veo pump.

Conclusions

Overnight manual closed loop using the novel algorithm SP-MPC was safe and effective in maintaining glucose in target while reducing the occurrence of hypoglycemia events, mean sensor glucose and the extent of hyperglycemia events when compared with optimized SAP therapy. An optimized SP-MPC controller including a supervision layer will be tested in a longer study concerning a larger number of patients.

Footnotes

Acknowledgements

We should like to thank the patients for their enthusiastic participation in this trial, the team of the Department of Endocrinology, Diabetes and Nutrition (Rennes University hospital), and the nurses of the Clinical Investigation Unit for technical support, Doctor Fabrice Lainé (CIC INSERM 1414) and Professor Hervé Guéguen (CentraleSupélec/I.E.T.R, Hybrid System Control Team, 35510 Cesson-Sévigné) for fruitful discussions.

Abbreviations

CGM, continuous glucose monitoring; CHO, carbohydrates; CI, confidence interval; CL, closed loop; CONGA, continuous overall net glycemic action; HBGI, high blood glucose index; IQR interquartile range; LBGI, low blood glucose index; MARD, median relative absolute difference; MPC, model predictive control; OL, open loop; PID, proportional integral derivative; SAP, sensor-augmented pump therapy; SP-MPC, Saddle Point Model Predictive Control.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: private funding

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