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Plasma Insulin Cognizant Predictive Control for Artificial Pancreas

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In the present work, an adaptive model predictive control (MPC) algorithm is designed to effectively compute the optimal exogenous insulin delivery for artificial pancreas systems. The proposed MPC is designed using adaptive models that are recursively identified through subspace-based techniques to characterize the transient dynamics of glycemic measurements without requiring any information on the time and amount of carbohydrate consumption. A dynamic safety constraint derived from the estimation of plasma insulin concentration (PIC) is incorporated in the proposed MPC algorithm for the efficacy and reliability of the artificial pancreas system. The MPC algorithm, cognizant of the PIC, computes the optimal control solution to regulate blood glucose concentration while mitigating aggressive control actions (excessive insulin doses) when sufficient insulin is present in the bloodstream, thereby minimizing the risk of hypoglycemia. The efficiency of the proposed MPC algorithm is demonstrated using simulation studies.
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Plasma Insulin Cognizant Predictive Control for Artificial Pancreas
Mudassir Rashid, Iman Hajizadeh and Ali Cinar
Abstract In the present work, an adaptive model predictive
control (MPC) algorithm is designed to effectively compute the
optimal exogenous insulin delivery for artificial pancreas sys-
tems. The proposed MPC is designed using adaptive models that
are recursively identified through subspace-based techniques to
characterize the transient dynamics of glycemic measurements
without requiring any information on the time and amount
of carbohydrate consumption. A dynamic safety constraint
derived from the estimation of plasma insulin concentration
(PIC) is incorporated in the proposed MPC algorithm for the
efficacy and reliability of the artificial pancreas system. The
MPC algorithm, cognizant of the PIC, computes the optimal
control solution to regulate blood glucose concentration while
mitigating aggressive control actions (excessive insulin doses)
when sufficient insulin is present in the bloodstream, thereby
minimizing the risk of hypoglycemia. The efficiency of the
proposed MPC algorithm is demonstrated using simulation
studies.
I. Introduction
Type 1 diabetes mellitus (T1DM) is a chronic disease
characterized by the autoimmune destruction of insulin-
producing pancreatic beta cells, resulting in the inability
of the pancreas to produce sufficient insulin to maintain
euglycemia. As a result, people with T1DM depend on
exogenous insulin that is administered either by multiple daily
insulin injections or by a continuous subcutaneous insulin
infusion pump to control their blood glucose concentration
(BGC). Recent advances in T1DM therapy involve the
development of fully automated insulin delivery systems,
called the artificial pancreas (AP), that use appropriate control
algorithms to compute the insulin dose based on recurrent
measurements from continuous glucose monitoring (CGM)
sensors. Computing the exogenous insulin infusion rates
exclusively on feedback from lagged measurements of glucose
concentration in the interstitial fluid without considering
the previously administered insulin administration may lead
to hypoglycemia (
BGC <
70
mg/dL
) as a result of over-
correction. Therefore, a critical element of a safe and
effective fully automated AP system is a feedback control
law that is cognizant of the previously administered insulin.
A number of AP systems are proposed based on a variety of
control algorithms, such as proportional-integral-derivative
(PID) control [1]–[3], fuzzy logic (FL) control [4], adaptive
neural networks, and model predictive control (MPC) [5]–
[14]. Among these control techniques, MPC is particularly
Department of Chemical and Biological Engineering, Illinois In-
stitute of Technology, Chicago, IL 60616.
mrashid3@iit.edu
,
ihajizad@hawk.iit.edu and cinar@iit.edu
Financial support from the National Institutes of Health (NIH) under the
grants 1DP3DK101075-01 and 1DP3DK101077-01 is gratefully acknowl-
edged.
attractive because it can explicitly consider constraints in
the computation of the optimal control actions. Moreover,
in contrast to PID and FL control [15], the formulation
of MPC algorithms is not restricted by the type of model,
objective function, or constraints. This inherent flexibility
of MPC is exploited to design controllers that predict the
future dynamic glycemic evolution over a finite-time horizon
to determine the optimal insulin infusion rate with respect
to a specified performance index. Despite the theoretical
advantages of MPC techniques, the closed-loop performance
of predictive control algorithms is predicated on definitive
models of the glucose–insulin dynamics. High fidelity
glycemic predictive models are not readily available, however,
due to the significant inter- and intra-subject variability of
human physiology. The model accuracy notwithstanding, the
performance of feedback control algorithms is also inhibited
by the CGM measurements that are affected by varying sensor
errors and distortions as well as uncertain time-delays in
CGM response to carbohydrate consumption. Consequently,
the risk of hypoglycemia is a concern in closed-loop insulin
therapy.
Effective feedback control is necessary to maintain eug-
lycemia, and the greater time spent in a safe glycemic range
can effectively delay the onset and slow the progression of
serious diabetes related complications. Although advances in
diabetes therapeutics have improved glucose regulation, peo-
ple with T1DM still suffer from long-term ailments as a result
of prolonged hyperglycemia (
BGC >
180
mg/dL
), including
cardiovascular complications, nephropathy, neuropathy, and
retinopathy. To alleviate such adversity, it is desirable to
maintain BGC levels closer to the lower values within a
safe glycemic range, though suppressing the blood glucose
levels towards the lower end of the allowable range increases
the probability of hypoglycemic episodes. The risk of hypo-
glycemic episodes, however, can be attenuated by formulating
controllers cognizant of the previously administered unreacted
insulin still present in the body [16].
The injected insulin (basal or bolus) gradually accumulates
in the bloodstream and is eventually utilized by the body. One
factor that prolongs the utilization of administered insulin
is the significant time delays involved in the diffusion and
absorption of the subcutaneously injected insulin analogues.
The amount of previously administered insulin that is present
in the blood or the subcutaneous space is referred to as the
insulin on board (IOB) [17], [18]. The IOB is typically
determined in insulin pumps through static approximations of
the insulin action curves. The significant time-varying delays
induced by the unsteady rates of insulin diffusion, absorption
and utilization and the diurnal variations in the metabolic state
2018 Annual American Control Conference (ACC)
June 27–29, 2018. Wisconsin Center, Milwaukee, USA
978-1-5386-5427-9/$31.00 ©2018 AACC 3589
of individuals have significant effects on the dynamics of the
glucose–insulin system. Therefore, the insulin decay profiles
and action curves used in the calculation of the IOB are
not accurate enough over the diverse conditions encountered
throughout the day to be reliably used in an AP control system
[19].
In contrast to the conventional IOB calculations based
on approximated insulin decay curves, accurate estimates
of the concentration of insulin in the bloodstream, termed
plasma insulin concentration (PIC), can be obtained by using
CGM measurements with adaptive observers designed for
simultaneous state and parameter estimation [19]. Such PIC
estimation approaches typically incorporate reliable glucose–
insulin dynamic models with nonlinear filtering algorithms.
The estimated PIC can be subsequently used to design a
predictive control algorithm that is dynamically constrained
by the estimated PIC and thus considers the insulin concentra-
tion in the bloodstream as part of the optimal control solution.
Incorporating PIC constraints in the optimal control problems
can prevent insulin stacking that may lead to hypoglycemia.
Avoiding extreme glycemic excursions can thus yield a safe
and reliable AP system even in the presence of significant
uncertainty in the system.
Motivated by the above considerations, an MPC algorithm
that is cognizant of the estimated PIC is proposed in this work
for use in AP systems. A recursive subspace-based system
identification approach is used to identify a linear, time-
varying state-space model to characterize the glycemic dy-
namics without requiring onerous and obscure information on
the time and amount of carbohydrate consumption [20]. The
identified adaptive model with an insulin compartment model
that translates insulin to PIC for use in the predictive model is
employed to design the MPC algorithm. The large degree of
design flexibility afforded by MPC algorithms is leveraged to
develop a glycemic controller that manipulates the exogenous
insulin delivery while satisfying a dynamic safety constraint
that limits the insulin infusion rate when PIC levels are high.
The control algorithm also manipulates the objective penalty
weights in response to hypo- and hyperglycemic excursions to
improve control performance. The efficacy of the proposed
PIC cognizant MPC is demonstrated using the University of
Virginia/Padova (UVa/Padova) metabolic simulator [21].
II. Plasma Insulin Concentration Cognizant
Model Predictive Control
In this section, we briefly describe the state and pa-
rameter estimation approach for determining the values of
time-varying parameters and the meal effect for consumed
carbohydrates [19]. Then, the structure of the model deter-
mined through the recursive system identification approach
is outlined. Finally, a detailed description of the risk indexes
for negotiating the penalty weights in the objective function
of the optimal control problem is provided, followed by the
formulation of the MPC algorithm.
A. Plasma Insulin Concentration Estimation
The PIC and the uncertain model parameters, including
the effects of carbohydrates consumed, are simultaneously
estimated using the infused insulin inputs and CGM output
measurements. To this end, Hovorka’s glucose–insulin dy-
namic model is utilized to design the joint state and parameter
estimator [22]. The model is of the general form
xk+1=f(xk,uk, θk)+wk,w∼ N (0,Rw)
yk=g(xk,uk, θk)+vk,v∼ N (0,Rv)(1)
where
xRn
,
uRm
and
yRp
denote the vectors of state,
input, and output variables, respectively, with
f:Rn×mRn
and
g:Rn×mRp
obtained from Hovorka’s model [22]. In
this work, the outputs are the CGM measurements and the
input variable is the infused insulin. Further,
wRn
and
vRp
denote the vectors of process and measurement noises,
respectively, and
θ
denotes the uncertain model parameters.
In the simultaneous state and parameter estimation approach,
the unscented Kalman filter algorithm is used to recursively
compute both the state and parameter estimates
ˆxi,ˆ
θi
at the
i
th sampling instance. To achieve the simultaneous estimation,
the original problem is transformed by treating the parameters
to be estimated as additional states as follows:
x0
k+1=f0x0
k,uk
yk=g0x0
k,uk(2)
where x0
kBhxT
kθT
kiT
is the augmented state vector and
f0x0
k,ukBf(xk,uk, θk)
θk
g0x0
k,ukBg(xk,uk, θk)
Furthermore, the augmented process and measurement noise
covariances are defined as
R0
wBdiag {Rw,Rθ}
and
R0
vBR
,
respectively, as well as the augmented state estimation error
covariance
P0
kBdiag nPx
k,Pθ
ko
. Bounds on the states and pa-
rameters can be similarly augmented as
x0
Lx0
kx0
U
, where
x0
LBxT
LθT
LT
and
x0
UBhxT
UθT
UiT
. The augmented
quantities can be used with the standard UKF state estimator
framework to perform simultaneous state and parameter
estimation. Employing the state and parameter estimation
approach with Hovorka’s model allows for simultaneously
estimating the PIC, which is a state variable in the model,
and the meal effect, along with other time-varying parameters.
B. Recursive System Identification Algorithm
In this work, a recursive subspace-based empirical model-
ing algorithm based on the predictor-based subspace identifi-
cation (PBSID) method is used to determine linear dynamic
models for designing the predictive controller [20], [23]. The
proposed system identification method is able to provide a
stable, time-varying, and individualized state-space model
for predicting the future CGM measurement outputs with
the insulin infusion rate and biometric variables as inputs.
3590
Adaptive identification allows the model to be valid over
various daily life conditions without requiring onerous and
obscure information on carbohydrate consumption. The
identified model is of the form
˜xk+1=Ak˜xk+Bkukd3+˜wk,˜w∼ N 0,˜
Rw
yk=Ck˜xk+˜vk,˜v∼ N 0,˜
Rv(3)
where
˜xR˜n
denotes the vector of state variables for the
identified system, and the delayed input is
ukd3
. Note that
the abrupt and discrete insulin variations are challenging
for empirical modeling, thus complicating the direct use
of the administered insulin in the subspace identification
approach. Therefore, to improve the prediction ability of the
identified model, the administered insulin is filtered through
a compartment model extracted from Hovorka’s model with
time-varying model parameters estimated using the UKF
algorithm. This results in the past administered insulin
ukd4
being translated to
PICkd1
as a variable of the state
vector
˜xk
, resulting in the predicted CGM
ˆyk
. Accordingly,
given
uk1
and thus
PICk+3
, the prediction
ˆyk+d+3
can be
determined off-line. Therefore, the off-line calculated CGM
prediction of
ˆyk+d+3
is used in this work to determine the
appropriate values for the PIC bounds and the risk indexes.
C. Glycemic and Plasma Insulin Risk Indexes
1) Glycemic Risk Index: A glycemic risk index (GRI) is
used to determine the weighting matrix, denoted
Qˆyk+d+3
,
for penalizing the deviations of the outputs from their nominal
set-point [24]. To this end, the time-varying positive semi-
definite weighting matrix
Qk
is defined as
QkBQˆyk+d+3
.
The glycemic risk index asymmetrically increases the set-
point tracking weight when the off-line predicted CGM
ˆyk+d+3
diverges from the target range. Since hypoglycemic
events have serious short-term implications, the set-point
penalty increases rapidly in response to hypoglycemic ex-
cursions and more gradually in hyperglycemic excursions. A
plot of the glycemic risk index is given in Fig. 1.
2) Plasma Insulin Risk Index: A plasma insulin risk
index (PIRI), denoted
γk+d+3
, is defined to manipulate the
weighting matrix for penalizing the amount of input actuation
(aggressiveness of insulin dosing) depending on the estimated
PIC, thus suppressing the infusion rate if sufficient insulin
is present in the bloodstream. To this end, the time-varying
positive definite weighting matrix
Rk
is developed from the
0 50 80 140 180 220 300 400
CGM (mg/dL)
0
0.2
0.4
0.6
0.8
1
Glycemic penalty index (GPI)
Fig. 1. Plot of the glycemic risk index
PIRI as RkBRγk+d+3, with γk+d+3defined as
γk+d+3BPICk+d+3
PICbasal,k+d+32
(4)
where
PICbasal,k+d+3BIdb,k+d+3
VI·ke,k
(5)
and
Idb
is the patient specific (possibly time-varying) basal
insulin rate that is known in practice, and
VI
and
ke
are
parameters of Hovorka’s model. Furthermore, the parameter
ke
is estimated on-line using the UKF and the CGM output
measurements. A plot of the plasma insulin risk index is
given in Fig. 2. Note that as the penalty weight on the input
action increases, and dosing becomes less aggressive, if the
estimated PIC in high.
D. Plasma Insulin Concentration Bounds
In the proposed MPC, the estimated future PIC is dynam-
ically bounded with updated constraints at each sampling
time depending on the value of the CGM measurements.
For instance, if the CGM measurement values are elevated,
the bounds on the PIC are increased to ensure sufficient
insulin is administered to regulate the glucose concentration.
Furthermore, the PIC bounds also constrain the search
space in the optimization problem, thus reducing the search
space and convergence of the optimization in the proposed
MPC. The PIC bounds are determined based on the CGM
measurements as
hd
PICL,kd
PICU,kiBΓˆyk+d+3(6)
where the function
Γˆyk+d+3
defines the lower and upper
bounds on the normalized PIC values, denoted
d
PICL
and
d
PICU
(respectively), through the estimated CGM
ˆyk+d+3
. The
nominal PIC bounds can be determined from the normalized
PIC bounds as
PICL,kPICU,kBhd
PICL,kd
PICU,ki·PICbasal,k+d+3(7)
Therefore, appropriate PIC bounds can be determined based
on each subject’s basal rate and the CGM measurement. A
plot of the PIC bounds is given in Fig. 3.
E. Model Predictive Control Formulation
In this subsection, we propose a novel adaptive MPC algo-
rithm cognizant of the PIC for computing the optimal insulin
infusion rate. The proposed MPC formulation employs the
0 0.5 1 1.5 2 2.5 3 3.5 4
Scaled PIC (PICk/PIC b asal )
0
5
10
15
PIC penalty index
Fig. 2. Plot of the plasma insulin risk index
3591
Fig. 3. Plot of the plasma insulin concentration bounds
glycemic and PIC risk indexes that manipulate the penalty
weighting matrices in the cost function. To this end, the MPC
computes the optimal insulin infusion over a finite horizon
using the identified time-varying subspace-based models by
solving at each
i
th sampling instance the following quadratic
programming problem
u
knPd4
k=0Barg min
u∈U
J
nP,iˆyi+d+3, γk+d+3,{uk}nPd4
k=0
s.t.
ˆ
˜xk+1=Akˆ
˜xk+Bkukd3,kZnP1
0
ˆyk=Ckˆ
˜xk,kZnP
0
ˆ
˜x0=ˆ
˜xix∈ X
(8)
with the objective function
J
nP,i(·)B
nP
Õ
k=0
eT
kQiek+
nPd4
Õ
k=0
uT
kRiuk
where
ˆ
˜x
and
ˆy
denote the predicted states and outputs,
respectively, for the prediction/control horizon
nP
,
uRm
denotes the vector of constrained input variables, taking
values in a nonempty convex set
U ⊆ Rm
with
UB
{uRm:umin uumax}
,
umin Rm
and
umax Rm
denote the lower and upper bounds on the manipulated input,
respectively, and
ekBˆykysp
. The index
ZnP
0
represents
all integers in a set as
ZnP
0B{0, . . . , nP}
. The nonempty
convex set
X ⊆ R˜n
with
XBxR˜n:xmin xxmax
,
xmin R˜n
and
xmax R˜n
denote the lower and upper bounds
on the state variables, respectively, with one of the states
as the estimated PIC that is constrained through the PIC
bounds. Furthermore,
ˆ
˜xi
provides an initialization of the
state vector,
Q
0,
QkBQˆyk+d+3
is a positive semi-
definite symmetric matrix used to penalize the deviations
of the outputs from their nominal set-point, and
R>
0,
RkBRγk+d+3
is a strictly positive definite symmetric
matrix to penalize the manipulated input variables.
III. Results
The efficacy of the proposed PIC cognizant MPC is
demonstrated using the UVa/Padova metabolic simulator [21].
The subjects are simulated for three days with varying times
and quantities of meals consumed on each day, as detailed
in Table I. The meal information is not utilized in the MPC
algorithm as the controller is designed to regulate BGC in
the presence of significant disturbances such as unannounced
meals. The controller set-point is specified to be 110
mg/dL
.
In practice, such low glycemic set-points are avoided due to
fear of hypoglycemia, though a controller that is aware of
the previously administered insulin will moderate aggressive
inputs (decrease insulin dosing) when sufficient insulin has
been delivered. The model is designed with a delay of order
d=1with regards to the effect of PIC on CGM.
The quantitative evaluation of the closed-loop results based
on the proposed MPC algorithm are presented in Table II,
which gives the percentage of samples in defined glycemic
ranges and selected statistics for the glucose measurements. It
is readily observed that no hypoglycemia occurs as the BGC is
never below 70
mg/dL
. Furthermore, the average percentage
of time spent in the target range (
BGC [70,180]mg/dL
)
and the higher tier of
BGC [180,250]mg/dL
are 71
.
14%
and 27
.
79%, respectively. The minimum and maximum
observed BGC values across all experiments are 72 and
267
ml/dL
, respectively. Therefore, for the majority of time
BGC is tightly controlled to be within the safe range. Overall,
the results demonstrate that the proposed PIC cognizant
MPC is able to regulate BGC effectively without requiring
meal announcement, as shown by the significant disturbances
caused by the diverse timing and amounts of meals, while
mitigating severe hypo- and hyperglycemic excursions.
A representative glycemic trajectory and corresponding
insulin dosing decisions made by the proposed PIC cognizant
MPC are shown in Fig. 4. It is evident that the glucose
values stay within or close to the target range for most of the
duration of the experiment. Notice that the basal insulin, a
constant low dose of insulin continuously infused to regulate
blood glucose levels at a consistent level during periods of
fasting, is sometimes reduced or even completely shutoff.
This is done automatically by the controller when the PIC
is higher than the upper limit and thus no additional insulin
infusion is necessary, while the continuation of the basal
rate may result in hypoglycemia as a result of overcorrection.
Furthermore, the insulin boluses, typically a single large
dose of insulin administered before meal consumption to
counteract the postprandial rise blood glucose levels, occur
in in close proximity to the unannounced meals. Therefore,
the proposed PIC cognizant MPC is aware of the insulin
concentration in the bloodstream to avoid overcorrection yet
capable of effectively regulating the glucose levels.
IV. Discussion
The PIRI is used to manipulate the penalty weights of the
objective function and is specified using the CGM value of
TABLE I
Meal scenario for three days closed-loop experiment
using the UVa/Padova metabolic simulator
Meal First day Second day Third day
Time Amount Time Amount Time Amount
Breakfast 09:45 53 g 09:10 61 g 09:00 83 g
Lunch 13:30 63 g 13:45 77 g 14:00 44 g
Dinner 17:45 83 g 18:00 72 g 18:20 75 g
Snack 21:30 34 g 22:00 22 g 22:30 28 g
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TABLE II
Results for percentage time spent in different BGC ranges and various statistics for closed-loop experiment using the
UVA/Padova metabolic simulator
Subject Percent of time in range Statistics
<55 [55,70) [70,180) [180,250)>250 Mean SD Min Max
Adult 1 0.0 0.0 81.2 18.8 0.0 143.0 35.9 96.0 210.0
Adult 2 0.0 0.0 64.0 34.2 1.7 156.5 48.6 91.0 263.0
Adult 3 0.0 0.0 75.8 24.2 0.0 157.2 33.4 91.0 242.0
Adult 4 0.0 0.0 61.8 36.6 1.5 160.7 48.5 76.0 258.0
Adult 5 0.0 0.0 65.7 30.8 3.6 157.9 48.5 72.0 267.0
Adult 6 0.0 0.0 69.4 29.9 0.7 151.7 46.5 87.0 253.0
Adult 7 0.0 0.0 65.1 31.7 3.2 160.1 47.9 100.0 262.0
Adult 8 0.0 0.0 71.7 28.3 0.0 148.8 45.6 88.0 242.0
Adult 9 0.0 0.0 75.3 24.7 0.0 146.5 40.0 92.0 223.0
Adult 10 0.0 0.0 81.4 18.6 0.0 141.6 37.0 90.0 214.0
Average 0.0 0.0 71.14 27.79 1.07 152.4 43.19 88.3 243.4
Fig. 4. Closed-loop results of PIC cognizant MPC for a selected subject (Adult 1) of the UVa/Padova metabolic simulator
ˆyk+d+3
. The daily basal insulin rate for each patient should
be specified appropriately as it affects the weightings of the
MPC objective function through the PIRI. Furthermore, the
daily basal insulin rate is also used to define the bound
constraints for the estimated PIC. The PIC bounds, along with
the risk indexes, govern the aggressiveness of the controller.
A minimum bound for the PIC is considered in the MPC
formulation to enforce the controller to suggest a safe amount
of insulin to derive the CGM towards the specified set-point
target value in a reasonable amount of time. A maximum
bound is considered to avoid giving large doses of insulin
that may cause hypoglycemia as a result of overcorrection.
By bounding the PIC estimates, the insulin doses are also
constrained.
The insulin concentration in the bloodsteam should be
maintained within a safe range. If the PIC decreases
to extreme low values (less than the
PI Cbasal
value that
characterizes the PIC without disturbances and only steady
basal insulin infusion), then the BGC may rise rapidly in
response to meal consumption. The low PIC value may cause
hyperglycemia, and consequently a large bolus to derive the
high BGC towards the set-point. However, the significant
delays in the glucose–insulin dynamics may result in an
overcorrection of the high glucose values, which may ad-
versely lead to hypoglycemia. Such abrupt and counteracting
behavior should be avoided for effective glucose regulation.
One approach to ensure such unfavorable dynamics are
avoided is to effectively negotiate the trade-offs between
the opposing criteria of the cost function. To this end,
the glycemic and plasma insulin risk indexes are defined to
maintain PIC close to the basal value under normal conditions
and thus increase the effectiveness of the AP therapy.
Since bound constraints are considered for the PIC, and
as PIC is one of states in the model used in designing the
predictive controller, the MPC prediction horizon should be
specified sufficiently large to capture the prolonged effects of
insulin on the glucose measurements. Specifically, the pre-
diction horizon should be large enough that the peak effect of
3593
the administered insulin is evident in the predicted future PIC
values. The
tmax,I
parameter in Hovorka’s model characterizes
the time duration of PIC reaching its peak value in response
to administered insulin. Therefore, the prediction horizon of
the predictive controller should be defined according to the
time duration of the insulin subsystem. The adaptive and per-
sonalized PIC estimator is able to provide accurate estimates
of the insulin present in the bloodstream for direct use in the
control algorithm. The presented results are based on an MPC
controller without incorporating any additional AP modules
like the meal detection module that automatically recognizes
carbohydrate consumption and suggests appropriate boluses.
Such modules have the potential to further improve the closed-
loop performance of the proposed PIC cognizant MPC for
use in safe and reliable AP systems.
V. Conclusions
In this work, an adaptive MPC algorithm is designed to
effectively compute the optimal exogenous insulin delivery for
AP systems. The proposed MPC is designed using adaptive
models that are recursively identified through subspace-based
techniques to characterize the transient dynamics of glycemic
measurements without requiring any information on the time
and amount of carbohydrate consumption. A dynamic safety
constraint derived from the estimation of PIC is incorporated
in the proposed MPC algorithm for the efficacy and reliability
of the AP system. The MPC algorithm, cognizant of the PIC,
computes the optimal control solution to regulate BGC while
mitigating aggressive control actions (excessive insulin doses)
when sufficient insulin is present in the bloodstream, thereby
minimizing the risk of hypoglycemia.
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... Glycemic Risk Index A glycemic risk index (GRI) is used to determine the weighting matrix, denoted Q (ŷ k+d+3 ), for penalizing the deviations of the outputs from their nominal set-point (Rashid et al., 2018). The glycemic risk index asymmetrically increases the set-point tracking weight when the off-line predicted CGMŷ k+d+3 diverges from the target range. ...
... A plasma insulin penalty index (PIRI), denoted γ k+d+3 , is defined to manipulate the weighting matrix for penalizing the amount of input actuation (aggressiveness of insulin dosing) depending on the estimated PIC, thus suppressing the infusion rate if sufficient insulin is present in the bloodstream (Rashid et al., 2018). To this end, the time-varying positive definite weighting matrix R k := R (γ k+d+3 ) is developed from the PIRI as R (γ k+d+3 ) := γ k+d+3 · R, with R as a nominal weight and γ k+d+3 defined as ...
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An adaptive model predictive control (MPC) formulation is proposed in this work for optimal insulin dosing decisions in artificial pancreas (AP) systems. To this end, a recursive subspace-based system identification approach is used to characterize the transient dynamics of biological systems, specifically the metabolic processes involved in diabetes. Subsequent to system identification, an adaptive MPC algorithm is designed using the recursively identified models to effectively compute the optimal insulin delivery for AP systems. A feature extraction method based on glucose measurements is used to detect rapid deviations from the desired set-point caused by significant disturbances and subsequently modify the constraints of the optimization problem for negotiating between the aggressiveness and robustness of the controller to suggest the required amount of insulin. The efficacy of the proposed adaptive MPC is demonstrated using simulation case studies.
... An adaptive glycemic risk index (GRI) is used to determine the weighting matrix for penalizing the deviations of the outputs from their nominal set-point 38,57 . To this end, the time-varying positive semi-denite weighting matrix Q k := Q (ȳ k ) is dened as Q (ȳ k ) := α (ȳ k ) · Q nom where Q nom denotes a nominal weight and ...
... A plasma insulin risk index (PIRI) is dened to manipulate the weighting matrix for penalizing the amount of input actuation (aggressiveness of insulin dosing) depending on the estimated PIC, thus suppressing the infusion rate if sucient insulin is present in the bloodstream 38,57 . To this end, the time-varying positive denite weighting matrix ...
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A controller performance assessment algorithm is developed to analyze the closed-loop behavior and modify the parameters of a control system employed in automated insulin delivery. To this end, various performance indices are dened to quantitatively evaluate the controller efficacy in real-time. The controller assessment and modication module also incorporates on-line learning from historical data to anticipate impending disturbances and proactively counteract their effects. A dynamic safety constraint derived from estimates of the physiological states ensures safety of the controlled drug dosing. Using a multivariable simulation platform for type 1 diabetes mellitus, the controller assessment and modication module is applied to the problem of regulating glucose concentrations in people with diabetes by means of automated insulin delivery with an artificial pancreas, and the results demonstrate the improvement in controller performance using the performance assessment module.
... Glycemic Risk Index A glycemic risk index (GRI) is used to determine the weighting matrix, denoted Q (ŷ k+d+3 ), for penalizing the deviations of the outputs from their nominal set-point (Rashid et al., 2018). The glycemic risk index asymmetrically increases the set-point tracking weight when the off-line predicted CGMŷ k+d+3 diverges from the target range. ...
... A plasma insulin penalty index (PIRI), denoted γ k+d+3 , is defined to manipulate the weighting matrix for penalizing the amount of input actuation (aggressiveness of insulin dosing) depending on the estimated PIC, thus suppressing the infusion rate if sufficient insulin is present in the bloodstream (Rashid et al., 2018). To this end, the time-varying positive definite weighting matrix R k := R (γ k+d+3 ) is developed from the PIRI as R (γ k+d+3 ) := γ k+d+3 · R, with R as a nominal weight and γ k+d+3 defined as ...
Conference Paper
Full-text available
An adaptive model predictive control (MPC) formulation is proposed in this work for optimal insulin dosing decisions in artificial pancreas (AP) systems. To this end, a recursive subspace-based system identification approach is used to characterize the transient dynamics of biological systems, specifically the metabolic processes involved in diabetes. Subsequent to system identification, an adaptive MPC algorithm is designed using the recursively identified models to effectively compute the optimal insulin delivery for AP systems. A feature extraction method based on glucose measurements is used to detect rapid deviations from the desired set-point caused by significant disturbances and subsequently modify the constraints of the optimization problem for negotiating between the aggressiveness and robustness of the controller to suggest the required amount of insulin. The efficacy of the proposed adaptive MPC is demonstrated using simulation case studies.
... Previous studies integrated an adaptive and personalized physiological insulin compartment model (to translate the abrupt bolus and infrequent basal changes into PIC estimates) with a timevarying linear state-space model obtained through the recursive PBSID approach, which provided good prediction accuracy of the glucose trajectory [41,42]. The identified adaptive models were used to design an adaptive MPC with a feature extraction method using CGM data to detect rapid glycemic deviations from the desired set-point caused by significant disturbances (such as meal consumption) and subsequently adjust the controller constraints. ...
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An adaptive model predictive control (MPC) algorithm with dynamic adjustments of constraints and objective function weights based on estimates of the plasma insulin concentration (PIC) is proposed for artificial pancreas (AP) systems. A personalized compartment model that translates the infused insulin into estimates of PIC is integrated with a recursive subspace-based system identification to characterize the transient dynamics of glycemic measurements. The system identification approach is able to identify stable, reliable linear time-varying models from closed-loop data. An MPC algorithm using the adaptive models is designed to compute the optimal exogenous insulin delivery for AP systems without requiring any manually-entered meal information. A dynamic safety constraint derived from the estimation of PIC is incorporated in the adaptive MPC to improve the efficacy of the AP and prevent insulin overdosing. Simulation case studies demonstrate the performance of the proposed adaptive MPC algorithm.
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Objective: As artificial pancreas (AP) becomes standard of care, consideration of extended use of insulin infusion sets (IIS) and continuous glucose monitors (CGMs) becomes vital. We conducted an outpatient randomized crossover study to test the safety and efficacy of a zone model predictive control (zone-MPC)-based AP system versus sensor augmented pump (SAP) therapy in which IIS and CGM failures were provoked via extended wear to 7 and 21 days, respectively. Research design and methods: A smartphone-based AP system was used by 19 adults (median age 23 years [IQR 10], mean 8.0 ± 1.7% HbA1c) over 2 weeks and compared with SAP therapy for 2 weeks in a crossover, unblinded outpatient study with remote monitoring in both study arms. Results: AP improved percent time 70-140 mg/dL (48.1 vs. 39.2%; P = 0.016) and time 70-180 mg/dL (71.6 vs. 65.2%; P = 0.008) and decreased median glucose (141 vs. 153 mg/dL; P = 0.036) and glycemic variability (SD 52 vs. 55 mg/dL; P = 0.044) while decreasing percent time <70 mg/dL (1.3 vs. 2.7%; P = 0.001). AP also improved overnight control, as measured by mean glucose at 0600 h (140 vs. 158 mg/dL; P = 0.02). IIS failures (1.26 ± 1.44 vs. 0.78 ± 0.78 events; P = 0.13) and sensor failures (0.84 ± 0.6 vs. 1.1 ± 0.73 events; P = 0.25) were similar between AP and SAP arms. Higher percent time in closed loop was associated with better glycemic outcomes. Conclusions: Zone-MPC significantly and safely improved glycemic control in a home-use environment despite prolonged CGM and IIS wear. This project represents the first home-use AP study attempting to provoke and detect component failure while successfully maintaining safety and effective glucose control.
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This paper presents an individualized model predictive control (MPC) algorithm for overnight blood glucose stabilization in people with type 1 diabetes (T1D). The MPC formulation uses an asymmetric objective function that penalizes low glucose levels more heavily. We compute the model parameters in the MPC in a systematic way based on a priori available patient information. The model used by the MPC algorithm for filtering and prediction is an autoregressive integrated moving average with exogenous input (ARIMAX) model implemented as a linear state space model in innovation form. The control algorithm uses frequent glucose measurements from a continuous glucose monitor (CGM) and its decisions are implemented by a continuous subcutaneous insulin infusion (CSII) pump. We provide guidelines for tuning the control algorithm and computing the Kalman gain in the linear state space model in innovation form. We test the controller on a cohort of 100 randomly generated virtual patients with a representative inter-subject variability. We use the same control algorithm for a feasibility overnight study using 5 real patients. In this study, we compare the performance of this control algorithm with the patient's usual pump setting. We discuss the results of the numerical simulations and the in vivo clinical study from a control engineering perspective. The results demonstrate that the proposed control strategy increases the time spent in euglycemia.
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Objective: A fully closed-loop insulin-only system was developed to provide glucose control in patients with type 1 diabetes without requiring announcement of meals or activity. Our goal was to assess initial safety and efficacy of this system. Research design and methods: The multiple model probabilistic controller (MMPPC) anticipates meals when the patient is awake. The controller used the subject's basal rates and total daily insulin dose for initialization. The system was tested at two sites on 10 patients in a 30-h inpatient study, followed by 15 subjects at three sites in a 54-h supervised hotel study, where the controller was challenged by exercise and unannounced meals. The system was implemented on the UVA DiAs system using a Roche Spirit Combo Insulin Pump and a Dexcom G4 Continuous Glucose Monitor. Results: The mean overall (24-h basis) and nighttime (11 PM-7 AM) continuous glucose monitoring (CGM) values were 142 and 125 mg/dL during the inpatient study. The hotel study used a different daytime tuning and manual announcement, instead of automatic detection, of sleep and wake periods. This resulted in mean overall (24-h basis) and nighttime CGM values of 152 and 139 mg/dL for the hotel study and there was also a reduction in hypoglycemia events from 1.6 to 0.91 events/patient/day. Conclusions: The MMPPC system achieved a mean glucose that would be particularly helpful for people with an elevated A1c as a result of frequent missed meal boluses. Current full closed loop has a higher risk for hypoglycemia when compared with algorithms using meal announcement.
Article
Objective: The development of artificial pancreas (AP) technology for deployment in low-energy, embedded devices is contingent upon selecting an efficient control algorithm for regulating glucose in people with type 1 diabetes mellitus. In this paper, we aim to lower the energy consumption of the AP by reducing controller updates, that is, the number of times the decision-making algorithm is invoked to compute an appropriate insulin dose. Methods: Physiological insights into glucose management are leveraged to design an event-triggered model predictive controller (MPC) that operates efficiently, without compromising patient safety. The proposed event-triggered MPC is deployed on a wearable platform. Its robustness to latent hypoglycemia, model mismatch, and meal misinformation is tested, with and without meal announcement, on the full version of the US-FDA accepted UVA/Padova metabolic simulator. Results: The event-based controller remains on for 18 h of 41 h in closed loop with unannounced meals, while maintaining glucose in 70-180 mg/dL for 25 h, compared to 27 h for a standard MPC controller. With meal announcement, the time in 70-180 mg/dL is almost identical, with the controller operating a mere 25.88% of the time in comparison with a standard MPC. Conclusion: A novel control architecture for AP systems enables safe glycemic regulation with reduced processor computations. Significance: Our proposed framework integrated seamlessly with a wide variety of popular MPC variants reported in AP research, customizes tradeoff between glycemic regulation and efficacy according to prior design specifications, and eliminates judicious prior selection of controller sampling times.
Article
Background: Postprandial (PP) control remains a challenge for closed-loop (CL) systems. Few studies with inconsistent results have systematically investigated the PP period. Objective: To compare a new CL algorithm with current pump therapy (open loop [OL]) in the PP glucose control in type 1 diabetes (T1D) subjects. Methods: A crossover randomized study was performed in two centers. Twenty T1D subjects (F/M 13/7, age 40.7 ± 10.4 years, disease duration 22.6 ± 9.9 years, and A1c 7.8% ± 0.7%) underwent an 8-h mixed meal test on four occasions. In two (CL1/CL2), after meal announcement, a bolus was given followed by an algorithm-driven basal infusion based on continuous glucose monitoring (CGM). Alternatively, in OL1/OL2 conventional pump therapy was used. Main outcome measures were as follows: glucose variability, estimated with the coefficient of variation (CV) of the area under the curve (AUC) of plasma glucose (PG) and CGM values, and from the analysis of the glucose time series; mean, maximum (Cmax), and time to Cmax glucose concentrations and time in range (<70, 70-180, >180 mg/dL). Results: CVs of the glucose AUCs were low and similar in all studies (around 10%). However, CL achieved greater reproducibility and better PG control in the PP period: CL1 = CL2<OL1<OL2 (PGmean 123 ± 47 and 125 ± 44 vs. 152 ± 53 and 159 ± 54 mg/dL) and Cmax OL 217.1 ± 67.0 mg/dL versus CL 183.3 ± 63.9 mg/dL, P < 0.0001. Time-in-range was higher with CL versus OL (80% vs. 64%; P < 0.001). Neither the time below 70 mg/dL (CL 6.1% vs. OL 3.2%; P > 0.05) nor the need for oral glucose was significantly different (CL 40.0% vs. OL 22.5% of meals; P = 0.054). Conclusions: This novel CL algorithm effectively and consistently controls PP glucose excursions without increasing hypoglycemia. Study registered at ClinicalTrials.gov : study number NCT02100488.
Article
Objective: To evaluate two widely used control algorithms for an artificial pancreas (AP) under nonideal but comparable clinical conditions. Research design and methods: After a pilot safety and feasibility study (n = 10), closed-loop control (CLC) was evaluated in a randomized, crossover trial of 20 additional adults with type 1 diabetes. Personalized model predictive control (MPC) and proportional integral derivative (PID) algorithms were compared in supervised 27.5-h CLC sessions. Challenges included overnight control after a 65-g dinner, response to a 50-g breakfast, and response to an unannounced 65-g lunch. Boluses of announced dinner and breakfast meals were given at mealtime. The primary outcome was time in glucose range 70-180 mg/dL. Results: Mean time in range 70-180 mg/dL was greater for MPC than for PID (74.4 vs. 63.7%, P = 0.020). Mean glucose was also lower for MPC than PID during the entire trial duration (138 vs. 160 mg/dL, P = 0.012) and 5 h after the unannounced 65-g meal (181 vs. 220 mg/dL, P = 0.019). There was no significant difference in time with glucose <70 mg/dL throughout the trial period. Conclusions: This first comprehensive study to compare MPC and PID control for the AP indicates that MPC performed particularly well, achieving nearly 75% time in the target range, including the unannounced meal. Although both forms of CLC provided safe and effective glucose management, MPC performed as well or better than PID in all metrics.