Original Article
Evaluation of the Effect of Gain on the Meal Response of
an Automated Closed-Loop Insulin Delivery System
Antonios E. Panteleon, Mikhail Loutseiko, Garry M. Steil, and Kerstin Rebrin
A continuous closed-loop insulin delivery system using
subcutaneous insulin delivery was evaluated in eight diabetic canines. Continuous glucose profiles were obtained
by extrapolation of blood glucose measurements. Insulin
delivery rate was calculated, using a model of ␤-cell insulin
secretion, and delivered with a Medtronic MiniMed subcutaneous infusion pump. The model acts like a classic proportional-integral-derivative controller, delivering insulin
in proportion to glucose above target, history of past
glucose values, and glucose rate of change. For each dog, a
proportional gain was set relative to the open-loop total
daily dose (TDD) of insulin. Additional gains based on
0.5 ⴛ TDD and 1.5 ⴛ TDD were also evaluated (gain dose
response). Control was initiated 4 h before the meal with a
target of 6.7 mmol/l. At the time of the meal, glucose was
similar for all three gains (6.0 ⴞ 0.3, 5.2 ⴞ 0.3, and 4.9 ⴞ 0.5
mmol/l for 0.5 ⴛ TDD, TDD, and 1.5 ⴛ TDD, respectively;
P > 0.05) with near-target values restored at the end of
experiments (8.2 ⴞ 0.9, 6.0 ⴞ 0.6, and 6.0 ⴞ 0.5, respectively). The peak postprandial glucose level decreased
significantly with increasing gain (12.1 ⴞ 0.6, 9.6 ⴞ 1.0, and
8.5 ⴞ 0.6 mmol/l, respectively; P < 0.05). The data demonstrate that closed-loop insulin delivery using the subcutaneous site can provide stable glycemic control within a
range of gain. Diabetes 55:1995–2000, 2006
I
ntegration of glucose-sensing and insulin delivery
technologies can potentially lead to a fully ambulatory closed-loop insulin delivery system or “artificial
pancreas.” Such a system may achieve glucose and
insulin profiles near those observed in individuals with
normal glucose tolerance while at the same time decreasing the incidence of hypoglycemia and minimizing the
complications of diabetes.
Glucose-sensing technology has been rapidly advancing
(1– 6), and fast-absorbing insulin analogs (7,8) have been
available for several years; nonetheless, little data exist
demonstrating the feasibility of closed-loop insulin delivery using the subcutaneous route (overview in 9). Early
studies in the diabetic canine, using intravenous insulin
(10,11), showed promising results, delivering insulin in
proportion to glucose above or below target and its rate of
From Medtronic MiniMed, Northridge, California.
Address correspondence and reprint requests to Garry Steil, PhD,
Medtronic MiniMed, 18000 Devonshire Rd., Northridge, CA 91325. E-mail:
garry.steil@medtronic.com.
Received for publication 15 October 2005 and accepted in revised form 30
March 2006.
AUC, area under the curve; TDD, total daily dose.
DOI: 10.2337/db05-1346
© 2006 by the American Diabetes Association.
The costs of publication of this article were defrayed in part by the payment of page
charges. This article must therefore be hereby marked “advertisement” in accordance
with 18 U.S.C. Section 1734 solely to indicate this fact.
DIABETES, VOL. 55, JULY 2006
change, and later work extended these results with rapidacting insulin analogs and alternate sites of delivery (12–
14).
The current study was undertaken with three objectives.
The first was to evaluate the ability of a previously
proposed multiphasic model of ␤-cell secretion (15) to
provide adequate control when the relative amount of
insulin in each phase is adjusted to compensate for the
delay in subcutaneous insulin delivery. The second was to
assess the stability of the system as the closed-loop gain is
increased or decreased. The third objective was to assess
how well the in vivo closed-loop responses could be
described using standard metabolic models.
RESEARCH DESIGN AND METHODS
Experiments were performed on eight diabetic dogs (26.8 ⫾ 1.7 kg, range
20.3–35.3) housed at Medtronic MiniMed animal facilities. Diabetes was
induced by partial pancreatectomy. Dogs were treated with continuous
subcutaneous insulin infusion for at least 1 week before experiments to
determine the total daily dose (TDD) of insulin required for open-loop glucose
control. On the day before experiments began, a new insulin infusion catheter
was inserted. Closed-loop experiments were performed using Humalog. Dogs
were housed under controlled kennel conditions and used for experiments
only if judged to be in good condition (physical appearance, hematocrit, white
blood cell count, body temperature, and weight stability). The experimental
protocol was approved by the appropriate animal research committee.
Insulin delivery algorithm. Insulin delivery was calculated by an algorithm
that responds to glucose with three components: a proportional component
(P) that reacts to the difference between plasma glucose and basal glucose
(the putative ␤-cell set point for fasting glucose), an integral component (I)
that adapts to persistent hyper- or hypoglycemia, and a derivative component
(D) that acts in response to the rate of change of blood glucose. We have
previously shown the model to describe insulin secretion during hyperglycemic clamps performed in humans with normal glucose tolerance (16). The
model is identical to the well-known proportional-integral-derivative algorithm widely used in engineering (17). It is described by:
PID(t) ⫽ P(t) ⫹ I(t) ⫹ D(t); PID(t) ⱖ 0
P(t) ⫽ KP(G ⫺ GB)
冕
t
KP
I(t) ⫽
(G ⫺ GB) dt; I(0) ⫽ IDB
TI
(1)
0
D(t) ⫽ KPTD
dG
dt
where the proportional gain KP (units/h per mg/dl) determines the rate of
insulin delivery in response to glucose above the set point (GB; mmol/l), TI
(integral time; min) determines the rate at which the underlying basal rate
adapts, and TD (derivative time; min) determines the relative amount of insulin
delivered in response to the rate of change of glucose. GB was fixed at 6.7
mmol/l, and KP was set in relation to the TDD of insulin under open-loop
treatment:
KP ⫽ TDD ⫻
reference KP
reference TDD
(2)
Reference KP was 0.675 units/h per mg/dl, and reference TDD was 1.0 units 䡠
kg⫺1 䡠 day⫺1. TD and TI were fixed at 66 and 150 min, respectively. These
1995
AUTOMATED CLOSED-LOOP INSULIN DELIVERY
FIG. 1. Blood glucose (A), plasma insulin (B), and
algorithm output (C) during 10 h of closed-loop
insulin delivery (n ⴝ 8) for 0.5 ⴛ TDD (f), TDD (䡺),
and 1.5 ⴛ TDD (E).
values were based on a computer simulation (computer model in 18) and
preliminary experiments performed in dogs during the development of the
system. Using these nominal gains, we performed a dose response with KP
increased by 50% (1.5 ⫻ TDD) or decreased by 50% (0.5 ⫻ TDD).
At the time closed-loop control was initiated (approximately 8:00 A.M.), all
preprogrammed basal rates were set to 0, and the initial condition of the
integral term (IDB) (Eq. 1) was set to the 8:00 A.M. basal rate. Setting the initial
condition to the 8:00 A.M. basal rate allowed the animals starting closed-loop
control at target glucose [P(t) ⫽ 0] and stable rate of change of glucose
[D(t) ⫽ 0] to transfer onto closed-loop control with no change in insulin
delivery. For animals starting closed-loop control above target, the initial
condition (IDB) was also set to the 8:00 A.M. value basal rate, and the animals
received an insulin bolus calculated by the algorithm: (KP ⫻ TD) ⫻ (glucose ⫺
GB). If PID(t) was calculated to be ⬍0, insulin delivery was suspended, and no
changes were made in the integral component. Continuous glucose concentration was calculated by a linear extrapolation of the measured blood glucose
samples (referred to in engineering literature as a first-order hold) (19). Insulin
delivery was calculated with a discrete form of Eq. 1 and delivered with a
Medtronic MiniMed Paradigm 511 pump.
Experimental details. After an overnight period, during which euglycemia
was achieved with continuous subcutaneous insulin infusion, a blood-sampling catheter was inserted into a peripheral vein. Blood samples were
obtained every 20 min until noon, at which time the dog was fed a standard
meal of commercially available dog food (LabDiet). After the meal, blood
samples were drawn every 10 min for 3 h and every 20 min thereafter for an
additional 3 h. Experiments on the same dog were separated by at least 5 days,
and the order was randomized.
Insulin kinetic analysis. The plasma insulin concentration [Ip(t)] in response to a single subcutaneous bolus of insulin was assumed to follow a
biexponential curve [h(t)] with the response to multiple boluses linearly
summing:
1996
冕
t
Ip (t) ⫽
PID(t) ⫻ h(t ⫺ ␶)d␶
0
[
t
t
h(t) ⫽ B ⫻ e ⫺␶1 ⫺ e ⫺␶2
]
(3)
Eq. 3 is the solution to a standard two-compartment (subcutaneous and
plasma) insulin model (20). Parameters were identified by nonlinear least
squares (Civilized Software, Silver Spring, MD). From the parameters B, ␶1,
and ␶2, the time to peak insulin concentration after a subcutaneous bolus and
insulin clearance rate were calculated as ln(␶2/␶1)/(1/␶1 ⫺ 1/␶2) and 1/B/(␶1 ⫺
␶2), respectively.
Statistical analysis. Data are reported as the means ⫾ SE. Differences in
parameters were evaluated with either paired Student’s t tests or one-way
ANOVA (GraphPad Prism; GraphPad Software, San Diego, CA).
Assays. Blood glucose values were immediately ascertained, using a Chiron
865 automated analyzer (Chiron, Emeryville, CA). Additional blood was drawn
into heparinized tubes (⬃1 ml) and centrifuged, and the plasma was stored at
⫺20°C. Insulin was measured in duplicate, using an enzyme-linked immunosorbent assay kit (ALPCO Diagnostics, Windham, NH).
RESULTS
Closed-loop glucose control. Preprandial glucose levels
were similar for the different algorithm gains (6.0 ⫾ 0.3,
5.2 ⫾ 0.3, and 4.9 ⫾ 0.5 mmol/l for 0.5 ⫻ TDD, TDD, and
1.5 ⫻ TDD, respectively; P ⬎ 0.05) (Fig. 1A). Peak postprandial glucose significantly decreased as gain increased
(12.1 ⫾ 0.6, 9.6 ⫾ 1.0, and 8.5 ⫾ 0.6 mmol/l; P ⬍ 0.05).
Maximum plasma insulin levels were similar (224.5 ⫾ 50.8,
DIABETES, VOL. 55, JULY 2006
A.E. PANTELEON AND ASSOCIATES
FIG. 3. Blood glucose concentration (A), plasma insulin delivery (B),
and insulin concentration (C) before consuming a standard meal and
6 h after the meal, using closed-loop insulin delivery gains calculated
with 0.5 ⴛ TDD, TDD, and 1.5 ⴛ TDD (n ⴝ 8).
FIG. 2. Postprandial incremental AUC for glucose (A), postprandial
incremental AUC for insulin (B), and incremental area under the
insulin curve during the first 2 h after the meal (C). Results based on
closed-loop insulin delivery gain KP calculated as 0.5 ⴛ TDD, TDD, and
1.5 ⴛ TDD, respectively (n ⴝ 8 for all). *P < 0.05.
187.3 ⫾ 27.8, and 194.2 ⫾ 42.6 pmol/l; P ⬎ 0.05) (Fig. 1B)
as gain increased. Early-phase insulin delivery was substantially higher as gain increased (peak values 2.5 ⫾ 0.9,
4.2 ⫾ 0.8, and 10.1 ⫾ 3.5 units/h, respectively; P ⬍ 0.05)
(Fig. 1C). Insulin delivery 6 h postmeal was elevated at the
0.5 ⫻ TDD level compared with TDD and 1.5 ⫻ TDD (2.1 ⫾
0.3 vs. 0.6 ⫾ 0.2 and 0.7 ⫾ 0.4 units/h; P ⬍ 0.05). The lower
peak glucose levels achieved with increasing gain resulted
in dramatically lower postprandial incremental area under
the glucose curve (⌬AUCGLC) for the 6-h period after the
meal (2,009 ⫾ 143, 1,182 ⫾ 158, and 1,000 ⫾ 106 mmol/l ⫻
min, for 0.5 ⫻ TDD, TDD, and 1.5 ⫻ TDD, respectively; P ⬍
0.05) (Fig. 2A), particularly as the gain was increased from
0.5 ⫻ TDD to TDD. Insulin delivery over the same period
tended to increase with increasing gain, but this did not
achieve statistical significance (13.3 ⫾ 1.5, 14.0 ⫾ 0.9, and
DIABETES, VOL. 55, JULY 2006
15.5 ⫾ 1.1 units, respectively; P ⬎ 0.05). All gains resulted
in similar incremental insulin AUC (Fig. 2B), but the initial
rise in plasma insulin was more rapid with high gain
leading to significant differences in the 2-h incremental
AUC (P ⬍ 0.01) (Fig. 2C). Hypoglycemia (⬍3.3 mmol)
occurred in one experiment for 0.5 ⫻ TDD, three experiments for TDD, and two experiments for 1.5 ⫻ TDD. For
all gains, insulin concentration and insulin delivery remained substantially elevated 6 h after the meal, even
though glucose levels had, with the exception of the low
gain response, returned to preprandial basal levels by t ⫽
600 min (8.2 ⫾ 0.9, 6.0 ⫾ 0.6, and 6.0 ⫾ 0.5, respectively;
P ⬎ 0.05) (Fig. 3).
Insulin kinetic model analysis. Plasma insulin kinetics
were well described by the insulin kinetic model (Eq. 3)
for all gains (r2 ⫽ 0.77, 0.82, and 0.78 for 0.5 ⫻ TDD, TDD,
and 1.5 ⫻ TDD, respectively; correlation calculated between measured and model predicted insulin levels) (Fig.
4). No differences were observed in insulin clearance
(44.6 ⫾ 6.5, 48.3 ⫾ 5.0, and 46.9 ⫾ 6.1 ml 䡠 min⫺1 䡠 kg⫺1) or
kinetic time constants (␶1 ⫽ 48.6 ⫾ 7.0, 58.4 ⫾ 5.5, and
1997
AUTOMATED CLOSED-LOOP INSULIN DELIVERY
FIG. 4. Insulin kinetic model analysis and
residuals for 0.5 ⴛ TDD (A and B), TDD (C
and D), and 1.5 ⴛ TDD (E and F) gain (n ⴝ
8). Plasma insulin (F) is shown together with
model fit (in solid line) and algorithm output
(gray shaded area). Residual plots are shown
for each level of gain in subpanels.
53.4 ⫾ 7.5 min; ␶2 ⫽ 33.0 ⫾ 6.9, 31.3 ⫾ 6.0, and 36.2 ⫾ 6.1
min) as gain increased (P ⬎ 0.05 for all), with predicted
time-to-peak insulin concentration after a single bolus to
be ⬃40 – 44 min at all gains.
DISCUSSION
The current study has three main conclusions. First,
automated closed-loop glucose control, based on a model
of the ␤-cell, is achievable across a wide range of gains,
1998
using subcutaneous insulin delivery. Second, after meals,
high plasma insulin levels are required well past the
time when plasma glucose is normalized. Third, plasma
insulin kinetics during closed-loop insulin delivery are
well described by a simple two-compartment insulin
model.
The ␤-cell model/closed-loop algorithm used here (Eq.
1) reproduces the well-established pattern of ␤-cell insulin
secretion in response to a hyperglycemic clamp (16,21).
DIABETES, VOL. 55, JULY 2006
A.E. PANTELEON AND ASSOCIATES
Although the model used here has been shown to describe
hyperglycemic clamp data, other models of ␤-cell secretion have been proposed (22–30). The models are similar
insofar as each describes glucose-induced insulin secretion as the sum of components that react immediately to a
change in glucose, have a delayed reaction to a change in
glucose, and/or react to the rate of change of glucose. Of
these models, the one proposed by Cerasi et al. (29) is of
particular interest because it also produces a slowly rising
second phase without using an integral term per se.
Previous closed-loop studies in diabetic dogs have used
phases analogous to P(t) and D(t), with intravenous insulin delivery, to show that meal excursions could be obtained that were actually lower than those observed in
normal dogs (10,11). More recent studies using insulin
analogs have evaluated other administration routes (12–
14). The main difference between the algorithms in these
earlier studies (10 –14) and the algorithm used here is that
the proposed ␤-cell model has an integral component [I(t)]
(Eq. 1) that can theoretically adjust insulin delivery (using
transient periods of glucose concentration above or below
set point) to restore steady-state glucose in the case of
changes in insulin sensitivity or endogenous glucose production (result shown using computer simulations based
on the Bergman minimal model) (16). Similar adaptation
of the ␤-cell was demonstrated in rats undergoing chronic
glucose infusion, whereby an increase in basal insulin
secretion was observed without change in glucose (31).
The hypothesis is also consistent with earlier observation
in humans that adiposity affects fasting insulin concentration independent of fasting glucose (32).
In the PID algorithm, the integral component creates the
slow rise in second-phase insulin observed during hyperglycemic clamps (21). In the current study, the integral
component maintained an elevated insulin delivery rate
after meals, even though near normoglycemia was established (Figs. 1 and 3). The need for elevated insulin
delivery was likely caused by a prolonged rate of appearance of glucose after the meal, which has been shown in
canines receiving basal insulin alone to lead to elevated
plasma glucose levels for 16 –20 h (33). Although the
maintenance of target glycemia during periods of elevated
glucose appearance is desirable, it can be expected that
once glucose appearance returns to normal, the elevated
value of the integral component will result in a plasma
glucose excursion below target (a consideration when
deciding to use a high 6.7-mmol/l target rather than a more
physiological 5.5 mmol/l).
The reference gain used here was set in direct proportion to open-loop total daily insulin requirement (TDD) in
an attempt to keep the product of KP and insulin sensitivity constant. Underlying this approach is the hypothesis
that the ␤-cell has a similar relationship between insulin
secretion and insulin sensitivity—the so-called disposition
index (34,35). It is not clear, however, whether the “reference KP” was optimal or whether TDD is a suitable
surrogate for insulin sensitivity. The 50% increase in KP did
produce a lower meal excursion without postmeal hypoglycemia (Fig. 1), and it could be argued to be a more
optimal gain. However, at this gain, postprandial glucose
had a tendency to undershoot/overshoot in some individual experiments, suggesting that a further increase in gain
might lead to an oscillatory glucose response.
Also affecting stability was the choice of TD and TI.
During a hyperglycemic glucose clamp, TD determines the
amount of rapidly released first-phase insulin, and TI
DIABETES, VOL. 55, JULY 2006
determines the rate at which the second-phase response
linearly increases (16). For human subjects, we have
estimated ␤-cell secretion to be well described with values
of ⬃40 and 100 min (TD and TI, respectively) (16). Here,
the amount of insulin delivered as first phase was substantially increased (TD ⫽ 66 min), and the second-phase rate
of increase was substantially slower (TI ⫽ 150 min).
Although these changes were made to compensate for the
delays inherent in subcutaneous insulin delivery, they may
not be optimal.
Optimization of controller parameters (KP, TI, and TD),
can likely only be achieved using a metabolic model (18).
We attempted to describe the gain dose response with the
minimal model of insulin action (36) and meal models
proposed by Hovorka et al. (37) and by Lehmann et al.
(38). However, the large change in AUCGLC observed as
the gain was increased from 0.5 ⫻ TDD to TDD, versus the
much smaller change observed as the gain was further
increased to 1.5 ⫻ TDD (Fig. 1), could only be fit by
introducing nonlinearities, either in insulin-dependent gastric carbohydrate extraction or in minimal model metabolic parameters (data not shown). Support for both
mechanisms exists in the literature. Splanchnic glucose
uptake (39) and the amount of ingested carbohydrate that
is extracted by the gut (37,40) have both been argued to be
affected by plasma insulin. Conversely, nonlinearities in
insulin sensitivity and glucose effect have also been used
in different metabolic models (rev. in 41). Differentiating
between these two mechanisms and validating the resulting model describes the reference gain (TDD in this study)
response, and perturbations in gain (0.5 ⫻ TDD and 1.5 ⫻
TDD) will be essential if a model-based optimization of
control parameters (KP, TI, and TD) is to be performed. To
differentiate between the two mechanisms, it is likely that
closed-loop experiments, using glucose tracers, will need
to be performed.
Although we were not successful in describing the
complete closed-loop dose response, plasma insulin kinetics were well described by the simple two-compartment
approximation (r2 ⬎0.77) (Fig. 4). Time constants estimated from this approach suggest peak absorption times
between 40 and 44 min, similar to the peak time observed
in humans (42,43). Insulin clearance was not affected by
changes in insulin delivery (P ⬎ 0.05) (see RESULTS), and no
systematic residuals were observed in the fit of the simple
two-compartment model, suggesting that a more complicated insulin absorption model (20,44,45) is unnecessary.
The ability to describe plasma insulin concentration during closed loop allows for an insulin feedback term to be
added to the PID ␤-cell model. This would allow the
putative inhibition of ␤-cell insulin secretion by plasma
insulin (46 – 48) to be added to the artificial ␤-cell algorithm used here.
In summary, automated closed-loop insulin delivery,
based on a simple PID model of ␤-cell secretion combined
with subcutaneous insulin delivery, results in stable meal
response for a wide range of gain. This suggests that the
proposed closed-loop system can adjust to day-to-day
variability in metabolic processes. Further optimization of
algorithm tuning, either by adjusting the relative ratios of
the different insulin delivery phases or by inclusion of
insulin feedback, may lead to improved meal responses.
Optimization is likely to be facilitated by using a more
comprehensive metabolic model together with glucose
tracer information.
1999
AUTOMATED CLOSED-LOOP INSULIN DELIVERY
ACKNOWLEDGMENTS
This study was supported by National Institutes of Health
Research Grants DK57210 (to K.R.) and DK64567 (to G.M.S.).
The authors thank Natalie Kurtz, Vera Stafekhina, and
Gayane Voskanyan for their contribution to the experiments and subsequent laboratory analysis.
REFERENCES
1. Feldman B, Brazg R, Schwartz S, Weinstein R: A continuous glucose sensor
based on wired enzyme technology: results from a 3-day trial in patients
with type 1 diabetes. Diabetes Technol Ther 5:769 –779, 2003
2. Kovatchev BP, Gonder-Frederick LA, Cox DJ, Clarke WL: Evaluating the
accuracy of continuous glucose-monitoring sensors: continuous glucoseerror grid analysis illustrated by TheraSense Freestyle Navigator data.
Diabetes Care 27:1922–1928, 2004
3. Tansey MJ, Beck RW, Buckingham BA, Mauras N, Fiallo-Scharer R, Xing D,
Killman C, Tamborlane WV, Ruedy KJ: Accuracy of the modified continuous glucose monitoring system (CGMS) sensor in an outpatient setting:
results from a diabetes research in children network (DirecNet) study.
Diabetes Technol Ther 7:109 –114, 2005
4. Kerssen A, de Valk HW, Visser GH: The continuous glucose monitoring
system during pregnancy of women with type 1 diabetes mellitus: accuracy
assessment. Diabetes Technol Ther 6:645– 651, 2004
5. Steil GM, Rebrin K, Mastrototaro J, Bernaba B, Saad MF: Determination of
plasma glucose during rapid glucose excursions with a subcutaneous
glucose sensor. Diabetes Technol Ther 5:27–31, 2003
6. Steil GM, Rebrin K, Hariri F, Jinagonda S, Tadros S, Darwin C, Saad MF:
Interstitial fluid glucose dynamics during insulin-induced hypoglycaemia.
Diabetologia 48:1833–1840, 2005
7. Howey DC, Bowsher RR, Brunelle RL, Woodworth JR: [Lys(B28),
Pro(B29)]-human insulin: a rapidly absorbed analogue of human insulin.
Diabetes 43:396 – 402, 1994
8. Reynolds NA, Wagstaff AJ: Insulin aspart: a review of its use in the
management of type 1 or 2 diabetes mellitus. Drugs 64:1957–1974, 2004
9. Hovorka R: Continuous glucose monitoring and closed-loop systems.
Diabet Med 23:1–12, 2006
10. Rebrin K, Fischer U, von Woedtke T, Abel P, Brunstein E: Automated
feedback control of subcutaneous glucose concentration in diabetic dogs.
Diabetologia 32:573–576, 1989
11. Fischer U, Freyse EJ, Salzsieder E, Rebrin K: Artificial connection between
glucose sensing and insulin delivery: implications of peritoneal administration. Artif Organs 16:151–162, 1992
12. Shimoda S, Nishida K, Sakakida M, Konno Y, Ichinose K, Uehara M, Nowak
T, Shichiri M: Closed-loop subcutaneous insulin infusion algorithm with a
short-acting insulin analog for long-term clinical application of a wearable
artificial endocrine pancreas. Front Med Biol Eng 8:197–211, 1997
13. Sekigami T, Shimoda S, Nishida K, Matsuo Y, Ichimori S, Ichinose K,
Shichiri M, Sakakida M, Araki E: Comparison between closed-loop portal
and peripheral venous insulin delivery systems for an artificial endocrine
pancreas. J Artif Organs 7:91–100, 2004
14. Matsuo Y, Shimoda S, Sakakida M, Nishida K, Sekigami T, Ichimori S,
Ichinose K, Shichiri M, Araki E: Strict glycemic control in diabetic dogs
with closed-loop intraperitoneal insulin infusion algorithm designed for an
artificial endocrine pancreas. J Artif Organs 6:55– 63, 2003
15. Steil GM, Panteleon AE, Rebrin K: Closed-loop insulin delivery: the path to
physiological glucose control. Adv Drug Deliv Rev 56:125–144, 2004
16. Steil GM, Rebrin K, Janowski R, Darwin C, Saad MF: Modeling beta-cell
insulin secretion–implications for closed-loop glucose homeostasis. Diabetes Technol Ther 5:953–964, 2003
17. D’Azzo JJ, Houpis CH: Linear Control Systems: Analysis and Design. New
York, McGraw-Hill, 2002
18. Steil GM, Rebrin K: Closed-loop insulin delivery: what lies between where
we are and where we are going? Expert Opin Drug Deliv 2:353–362, 2005
19. Proakis JG, Manolakis DG: Digital Signal Processing: Principles, Algorithms, and Applications. Upper Saddle River, NJ, Prentice-Hall, 1996
20. Nucci G, Cobelli C: Models of subcutaneous insulin kinetics: a critical
review. Comput Methods Programs Biomed 62:249 –257, 2000
21. Elahi D: In praise of the hyperglycemic clamp: a method for assessment of
␤-cell sensitivity and insulin resistance. Diabetes Care 19:278 –286, 1996
22. Breda E, Toffolo G, Polonsky KS, Cobelli C: Insulin release in impaired
glucose tolerance: oral minimal model predicts normal sensitivity to glucose
but defective response times. Diabetes 51 (Suppl. 1):S227–S233, 2002
23. Breda E, Cavaghan MK, Toffolo G, Polonsky KS, Cobelli C: Oral glucose
tolerance test minimal model indexes of ␤-cell function and insulin
sensitivity. Diabetes 50:150 –158, 2001
24. Mari A, Camastra S, Toschi E, Giancaterini A, Gastaldelli A, Mingrone G,
2000
Ferrannini E: A model for glucose control of insulin secretion during 24 h
of free living. Diabetes 50 (Suppl. 1):S164 –S168, 2001
25. Mari A, Schmitz O, Gastaldelli A, Oestergaard T, Nyholm B, Ferrannini E:
Meal and oral glucose tests for assessment of beta-cell function: modeling
analysis in normal subjects. Am J Physiol 283:E1159 –E1166, 2002
26. Mari A, Tura A, Gastaldelli A, Ferrannini E: Assessing insulin secretion by
modeling in multiple-meal tests: role of potentiation. Diabetes 51 (Suppl.
1):S221–S226, 2002
27. Cretti A, Lehtovirta M, Bonora E, Brunato B, Zenti M, Tosi F, Caputo M,
Caruso B, Groop LC, Muggeo M, Bonadonna RC: Assessment of beta-cell
function during oral glucose tolerance test by minimal model of insulin
secretion. Exp Clin Endocrinol 31:405– 416, 2003
28. Hovorka R, Chassin L, Luzio SD, Playle R, Owens DR: Pancreatic beta-cell
responsiveness during meal tolerance test: model assessment in normal
subjects and subjects with newly diagnosed noninsulin-dependent diabetes mellitus. J Clin Endocrinol Metab 83:744 –750, 1998
29. Cerasi E, Fick G, Rudemo M: A mathematical model for the glucose
induced insulin release in man. Eur J Clin Invest 4:267–278, 1974
30. Nesher R, Cerasi E: Modeling phasic insulin release: immediate and
time-dependent effects of glucose. Diabetes 51 (Suppl. 1):S53–S59, 2002
31. Steil GM, Trivedi N, Jonas JC, Hasenkamp WM, Sharma A, Bonner-Weir S,
Weir GC: Adaptation of beta-cell mass to substrate oversupply: enhanced
function with normal gene expression. Am J Physiol 280:E788 –E796, 2001
32. Bagdade JD, Bierman EL, Porte D Jr: The significance of basal insulin
levels in the evaluation of the insulin response to glucose in diabetic and
nondiabetic subjects. J Clin Invest 46:1549 –1557, 1967
33. Goriya Y, Bahoric A, Marliss EB, Zinman B, Albisser AM: Responses to
mixed meals in pancreatectomized dogs deprived of postprandial insulin.
Am J Physiol 242:E335–E342, 1982
34. Bergman RN, Ader M, Huecking K, Van Citters G: Accurate assessment of
beta-cell function: the hyperbolic correction. Diabetes 51 (Suppl. 1):S212–
S220, 2002
35. Kahn SE, Prigeon RL, McCulloch DK, Boyko EJ, Bergman RN, Schwartz
MW, Neifing JL, Ward WK, Beard JC, Palmer JP, et al.: Quantification of the
relationship between insulin sensitivity and ␤-cell function in human
subjects. Evidence for a hyperbolic function. Diabetes 42:1663–1672, 1993
36. Bergman RN, Finegood DT, Ader M: Assessment of insulin sensitivity in
vivo. Endocr Rev 6:45– 86, 1985
37. Hovorka R, Canonico V, Chassin LJ, Haueter U, Massi-Benedetti M, Orsini
FM, Pieber TR, Schaller HC, Schaupp L, Vering T, Wilinska ME: Nonlinear
model predictive control of glucose concentration in subjects with type 1
diabetes. Physiol Meas 25:905–920, 2004
38. Lehmann ED, Deutsch T, Roudsari AV, Carson ER, Sonksen PH: Validation
of a metabolic prototype to assist in the treatment of insulin-dependent
diabetes mellitus. Med Inform (Lond) 18:83–101, 1993
39. Basu R, Basu A, Johnson CM, Schwenk WF, Rizza RA: Insulin doseresponse curves for stimulation of splanchnic glucose uptake and suppression of endogenous glucose production differ in nondiabetic humans and
are abnormal in people with type 2 diabetes. Diabetes 53:2042–2050, 2004
40. Dalla MC, Caumo A, Cobelli C: The oral glucose minimal model: estimation of
insulin sensitivity from a meal test. IEEE Trans Biomed Eng 49:419–429, 2002
41. Steil GM, Clark B, Kanderian S, Rebrin K: Modeling insulin action for
development of a closed-loop artificial pancreas. Diabetes Technol Ther
7:94 –108, 2005
42. Mudaliar SR, Lindberg FA, Joyce M, Beerdsen P, Strange P, Lin A, Henry
RR: Insulin aspart (B28 asp-insulin): a fast-acting analog of human insulin:
absorption kinetics and action profile compared with regular human
insulin in healthy nondiabetic subjects. Diabetes Care 22:1501–1506, 1999
43. Bolli GB, Di Marchi RD, Park GD, Pramming S, Koivisto VA: Insulin
analogues and their potential in the management of diabetes mellitus.
Diabetologia 42:1151–1167, 1999
44. Wilinska ME, Chassin LJ, Schaller HC, Schaupp L, Pieber TR, Hovorka R:
Insulin kinetics in type-I diabetes: continuous and bolus delivery of rapid
acting insulin. IEEE Trans Biomed Eng 52:3–12, 2005
45. Serne EH, IJzerman RG, Gans RO, Nijveldt R, De Vries G, Evertz R, Donker
AJ, Stehouwer CD: Direct evidence for insulin-induced capillary recruitment in skin of healthy subjects during physiological hyperinsulinemia.
Diabetes 51:1515–1522, 2002
46. Baynes C, Anyaoku V, Johnston DG, Elkeles RS: Feedback inhibition of
insulin secretion in type 2 diabetes. Clin Sci (Lond) 81:685– 690, 1991
47. DeFronzo RA, Binder C, Wahren J, Felig P, Ferrannini E, Faber OK:
Sensitivity of insulin secretion to feedback inhibition by hyperinsulinaemia. Acta Endocrinol (Copenh) 98:81– 86, 1981
48. Elahi D, Nagulesparan M, Hershcopf RJ, Muller DC, Tobin JD, Blix PM,
Rubenstein AH, Unger RH, Andres R: Feedback inhibition of insulin
secretion by insulin: relation to the hyperinsulinemia of obesity. N Engl
J Med 306:1196 –1202, 1982
DIABETES, VOL. 55, JULY 2006