Towards the Development of Intelligent Insulin Injection Controller For Diabetic Patients

Abstract

Diabetes Mellitus (DM) is a disease of the glucose-insulin regulatory system where the insulin producing beta-cells has been damaged thereby producing none to very little insulin leaving the body with no means of regulating glucose. DM has high socioeconomic costs because it needs long term monitoring and individual care to prevent or decrease complications. Uncontrolled or poorly controlled diabetes lead to evolution or development of microvascular and macrovascular complications. It has been shown that adequate or even tight glycaemic control can prevent or delay complications and finally can reduce these complications. One of this glycaemic control is insulin therapy, meanwhile, non-adherence to the therapy due to its sever pain is prevalent among patients. In this paper, a review of research efforts towards the development of automatic insulin injection from control engineering perspective is presented. The reviewed techniques are basically closed loop approach, which include PID controllers, Model Predictive Controllers and Adaptive Controller techniques using machine learning approaches.

Full text

15th International Conference on Electronics Computer and Computation (ICECCO 2019)
Towards the Development of Intelligent Insulin
Injection Controller For Diabetic Patients
Adeyinka P. ADEDIGBA∗, Abdul Razak ZUBAIR†, Abiodun M. AIBINU∗, Steve A. ADESHINA ‡
Olumide Okubadejo §, and Taliha A. FOLORUNSO ∗
∗Department of Mechatronics Engineering, Federal University of Technology, Minna, Nigeria
Email: adeyinka.adedigba@futminna.edu.ng
†University of Ibadan, Ibadan, Nigeria
‡Nile University of Nigeria, Abuja
§Audionamix, Paris, France
Abstract—Diabetes Mellitus (DM) is a disease of the glucose-
insulin regulatory system where the insulin producing beta-cells
has been damaged thereby producing none to very little insulin
leaving the body with no means of regulating glucose. DM has
high socioeconomic costs because it needs long term monitor-
ing and individual care to prevent or decrease complications.
Uncontrolled or poorly controlled diabetes lead to evolution or
development of microvascular and macrovascular complications.
It has been shown that adequate or even tight glycaemic control
can prevent or delay complications and finally can reduce these
complications. One of this glycaemic control is insulin therapy,
meanwhile, non-adherence to the therapy due to its sever pain
is prevalent among patients. In this paper, a review of research
efforts towards the development of automatic insulin injection
from control engineering perspective is presented. The reviewed
techniques are basically closed loop approach, which include
PID controllers, Model Predictive Controllers and Adaptive
Controller techniques using machine learning approaches.
Index Terms—Adaptive Controller Technique, Artificial Intel-
ligence, Bergman, Diabetes mellitus, Feedback control, Model
Predictive Controller, Palumbo, PID controller, Reinforcement
Learning.
I. INTRODUCTION
Diabetes is a disorder where the pancreas produces insuffi-
cient insulin to match excess blood sugar in the body. Three
most common diabetes include: Type 1 Diabetes Mellitus
(T1DM), Type 2 Diabetes Mellitus (T2DM) and Hypergly-
caemia in pregnancy. Diabetes mellitus is a disease of the
glucose-insulin regulatory system [1] [2] where the insulin
producing beta-cells has been damaged thereby producing
none to very little insulin leaving the body with no means of
regulating glucose in the blood stream as in the case of T1DM.
T2DM is the condition when body has developed resistance
to insulin.
Diabetes is a threat to health and human development
especially in developing countries such as Nigeria and other
African countries. Available information from International
Diabetes Federation confirms that the prevalence of diabetes is
increasing globally especially in African countries with about
10.4 million adults aged 20-79 years diagnosed of diabetics
in 2007 contributing 3% to global diabetic prevalence [3].
This number grows to 15.5 million in 2017 representing 6%
of global diabetic prevalence and approaching 40.7 million
in 2045. In Nigeria, about 1.7 million adults live with dia-
betics while about 40.33 million diabetic related deaths were
recorded in 2017 [4]. These statistics necessitate the need to
explore various methods of reducing this alarming growth rate
and the need for this research.
The pancreatic endocrine hormones insulin and glucagon
are responsible for regulating the glucose concentration level
in the blood as illustrated in Fig. 1. These hormones - glucagon
and insulin , are secreted in α-cell and β-cell respectively,
which are contained in the Langerhans islets in the pancreas.
When the concentration level of blood glucose (BG) is high,
the β-cells release insulin, which results in lowering the BG
concentration level by inducing the liver and other cells (e.g.
brain) to uptake the excess glucose and by inhibiting hepatic
glucose production. When the BG level is low, the α-cells cells
release glucagon, which results in increasing the BG level by
acting on liver cells and causing them to release glucose into
the blood [5] [6] [7] [8]. If a person’s glucose concentration
level is constantly out of the range (70–110 mg/dl), this person
is considered to have BG problems known as dysglycaemia
(hyperglycaemia or hypoglycaemia).
Fig. 1. Blood Glucose Level regulation [7]
Diabetes Mellitus (DM) has high socioeconomic expendi-
tures because it needs long term monitoring and individual
978-1-7281-5160-1/19/$31.00 © 2019 IEEE
248

care to prevent or decrease complications [9]. Uncontrolled or
poorly controlled diabetes, which cause dysglycaemia (hyper-
glycaemia or hypoglycaemia) lead to evolution or development
of microvascular and macrovascular complications.
Microvascular and macrovascular disease are two forms
of the long-term complications of diabetes. Microvascular
disease includes neuropathy, retinopathy (which results in
reduced vision and finally blindness), nephropathy (which
causes renal failure and finally may require dialysis or kidney
transplantation). Macrovascular disease includes heart disease.
The most important concern in very young children is that hy-
perglycaemia or hypoglycaemia are related to neuro-cognitive
impairments [10] [11]. It has been shown that adequate or even
tight glycaemic control can prevent or delay complications and
finally can reduce them [9]. One of this glycaemic control
is insulin therapy. Insulin therapies have various routes such
as subcutaneous, intramuscular, intravenous, intraperitoneal
injections and inhaled insulin [12] [13]. Oral, gastrointestinal
and transdermal routes are no longer recommended because
the insulin could destroy the digestive tract [14]. Intravenous
route has a little dead time, thus, it is not suitable for some
patients [13].
Insulin therapy is a routine part of daily life for patients with
T1DM and T2DM who are in constant need of insulin injection
[15]. Despite advance in pharmacologic therapy of DM, drugs
are mostly administered by subcutaneous injection. Historical
trend shows that majority of insulin therapy patients are self-
injected using vial, syringe or insulin pen; this trend continues
to rise in many developed and developing countries around
the world [15]. However, non-adherence to insulin therapy is
prevalent among patients with DM. Researches associate this
to factors such as severe pain and fear of using the injection,
complications and difficulty in using injection, lifestyle burden
and restrictive regiments [16].
Furthermore, complications associated with insulin subcu-
taneous injections include the following: bleeding, bruising,
lipohypertrophy, lipoatrophy and idiosyncratic skin pigmen-
tation [15] [17]. Lipohypertrophy is a critical complication
of subcutaneous insulin administration that delays insulin
absorption from the injection site and worsen BG control,
necessitating increasing dose of insulin [15]. Lipohypertrophy
can result in large oscillations in BG level with hypoglycaemic
episodes followed by glucose spikes.
II. IN TRO DU CT IO N TO CO NT ROL ENGINEERING
TECHNIQUES FOR BLOOD GLUCOSE REGULATION
Generally, control techniques for Blood Glucose Regulation
(BGR) systems fall into three categories namely: open and
closed loop [17] [18]. In open-loop control techniques, the
diabetologist injects an amount of insulin dose subcutaneously
to the patient regularly, usually, three to four times a day, while
monitoring the patient’s conditions. This control technique has
been automated and developed to what is known as insulin
injection or insulin pen [17]. While this control technique
is widely used due to its simplicity, it is not efficient, espe-
cially if the patient subjected to various variation in glucose
concentration level [17] [18] [19] [20]. The hidden limitation
placed on open-loop control technique (insulin pen or insulin
injection) is that, unlike the physiological insulin release that
takes place in the pancreas, the level of insulin in the blood is
not dynamically matched to BG concentration in the insulin
injection. Another limitation of open-loop control technique
is that patients are required to live a considerable predictable
lifestyle to allow efficient estimation of concentration level
of insulin/glucose [21]. Thus, a glucose-responsive closed-
loop insulin delivery system, which functions as continuous
subcutaneous insulin infusion system, has been proposed to
remove this limitation [17].
In closed-loop control techniques, the insulin is continu-
ously delivered with online BG sensor that provides feedback
loop to the controller. This closed-loop technique is called
Artificial Pancreas (AP) [17]. AP is a miniaturized automated
insulin delivery system which consists of one or multiple
continuous BG sensor, a mechanical insulin pump (or insulin
injecting device) and a controller (mathematical model of
glucose-insulin regulatory system and the control algorithm
based on the mathematical model) as shown in Fig. 2. The
sensor (or sensors) which continuously measure the value of
BG is fed into the controller; the controller estimates the
optimal insulin injection rate and controls the insulin pump
to supply it to the blood stream of the patient [22].
Fig. 2. Closed-loop Insulin Control Technique [23]
The success of AP depends largely on the accuracy of the
mathematical model used to express BG dynamics in order to
determine the best insulin injection rate to deliver at a time.
Thus, it can be argued that model-based insulin injection has
inherent limitation placed on them by the mathematical model
used. Despite various researches conducted in the field of
control engineering, we still lack efficient AP that can control
the glycaemic levels [18] [22]. Although AP technology has
witness many advancements, nevertheless, due to the mathe-
matical model employed, it may be plagued with challenges of
sensor delays and inaccurate insulin delivery especially when
the patient takes meal which results in erratic BG spikes. A
speedy response to this will cause the system to oscillate,
hence, results in unstable and erratic behaviour of the system
[23]. A slow response controller design allows this disturbance
to wear off before taking action; however, this cannot provide
the required attenuation of postprandial glucose spikes. Thus,
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the design of AP is to find an optimal controller in terms of
speedy time response, which will guarantee stability of the
system against postprandial spikes.
III. REVIEW OF REC EN T LITERATURE
The problem of closed-loop BG level regulation has been a
subject of investigation for decades. Different controllers have
been proposed by various researcher. In this section a review
is presented under controller families such as Proportional
Integral Derivative (PID) and Model Predictive Controllers
(MPC). Following the success of machine learning techniques
in solving engineering problems, a family of controller called
adaptive controllers found in literature is also reviewed.
A. Proportional Integral Derivative (PID) controller
The simplest family of controllers designed for BGR is
PID controllers [24] [25] [26]. The P-controller estimates
the rate of insulin as a difference between measured BG
level and a reference value; the I-controller acts to reduce
the patient’s insulin resistance by enhancing the P-controller
insulin injection rate due to observed errors over a short time-
window; and the D-controller introduces a correction factor to
the P-controller by multiplying the derivative of the actual BG
level with respect to the BG reference value and the derivative
gain factor of the controller [18].
The general form of representing continuous-time PID algo-
rithm uses insulin delivery rate (1) as a function of deviation
of BG level from the desired set-point (2), as follows:
u(t) = u(t0) + Kce(t) + τiZe(t)dt +τd
de(t)
dt (1)
e(t) = r(t)−y(t)(2)
For the patient under Intensive Care Unit (ICU), u(t)is
the manipulated input (i.e. insulin delivery rate), u(t0)is the
basal insulin infusion rate. e(t)is the error, which measures the
deviation of the measured BG level (y(t)) from the set-point
(r(t), the desired BG level). Kc, τiandτdis the proportional
gain, integral gain and derivative gain respectively: these three
parameters are tuned in a typical PID application.
On the other hand, the discretized PID controller algorithm
is represented as:
u[n] = u[0]+ kce[n] + δt
τi
n
X
i=0
e[n]+ τd
δt (e[n]−e[n−1]) (3)
Often time, PID controller algorithm for BGR is desired to
be implemented in what is known as velocity form. This is
obtained by subtracting (3) evaluated at time-step n−1from
(3) evaluated at time-step n to yield:
u[n] = u[n−1] + kc[ζe[n] + ξ e[n−1] + ψe[n−2]] (4)
Where: ζ= (1 + δ t
τi+τd
δt ), ξ = (−1−
2τd
δt )and ψ=τd
δt
In both (3) and (4), u(n)is the current control action, u[0]
is the basal insulin infusion rate, u[n−1] is the control action
taken in the previous time-step. e[n], e[n−1] and e[n−2] is
the error in current time-step, error in previous time-step and
error the previous two time-steps respectively.
Thus, the PID estimates the control of required insulin
delivery based on weighted sum of the PID terms in order to
minimize the error and bring the system to desired BG level.
However, despite the simplicity of design, PID is inherently
a reactive controller which causes the system to oscillate
especially during postprandial period [18] [27] [28]. More
so, [29] observed that trying to control postprandial glucose
level with PID results in life-threatening hyperglycaemia and
hypoglycaemia.
The postprandial glucose spikes was associated with the
use of integral action of the PID controller [30]. Thus [31]
presents a modification to PID controller by considering the
action of Proportional controller only. The resulting algorithm
called Columnar Insulin Dosing (CID) is presented in (5) as
follows:
u[n] = 0.8−0.02(100 −y[n]) (5)
The glucose value used is an average over the past two
samples, also known as two-point moving average filter.
Likewise, [32] presents a computerized control system for
a surgical intensive care unit called Glucose Regulation for
Intensive Care Patient (GRIP). GRIP is a gain-scheduled
PID controller where the proportional gain is a function of
average insulin infusion over the previous 4 hours. A four-
point moving average filter was used to evaluate the glucose
value. However, GRIP associated high derivative gain which
makes the system to be highly unstable. A relatively stable
version is presented in [30] which places a constrain on the
derivative gain.
B. Model Predictive Controller
Another family of controller is called Model Predictive
Controller (MPC), which attempts to model the patient’s
BG regulatory system with mathematical equations based
on assumption of detailed knowledge of the physiology of
the system under consideration. By treating BG regulatory
system as model, the control problem can now be treated
mathematically and optimal control strategy can be easily
determined [29]. The basic approach to MPC is shown in Fig.
3 where the model is used to predict how the future Blood
Glucose Concentration (BGC) level (the output) varies with
perturbations in the current and future insulin infusion rates
(current and future control moves). The objective of optimizer
algorithm is then to find the best set of current and future
insulin infusion rates that maintains the output (BGC level)
within the set-point over the future prediction horizon [33].
Given the patient’s glucose level, insulin delivery rate and
food intake, MPC uses dynamic system model to predict
glucose levels of the patient. It then estimates the appropriate
insulin infusion rate by minimizing the difference between
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Fig. 3. Control Approach of Model Predictive Controller (MPC) [33]
model-predicted BGC level and target BGC level over the
prediction horizon. This prediction horizon is usually chosen
as the time in which the bulk of the effect is seen from the
insulin dose used. By the mathematical model employed in
the design of the MPC, it can incorporates a prediction of
glucose level at different patient’s metabolic conditions such
as postprandial, quasi-steady state (overnight) and exercise; it
can also introduce constraints to insulin delivery rate at the
said conditions to prevent system oscillations as previously
discussed [18] [23] [34]. Thus, the success of MPC depends
on how accurate the physiological system under consideration
is modeled mathematically. The more accurate the model, the
more effective the control law [29].
1) Bergman Model: The most popular mathematical model
is the Bergman’s model proposed in [35] which describes the
dynamic nonlinear interaction of glucose and insulin in an
individual, it gains wide acceptability due to its minimum
number of relevant parameters and capability to represent
different physiological parameters. Equations (6), (7) and (8)
represents the rate of disappearance of BG, the effect of insulin
on remote compartment and the insulin concentration in the
plasma respectively.
dg(t)
dt =p1g(t)−[g(t)−Gb]x(t) + p(t)(6)
dx(t)
dt =−p2x(t) + p3i(t)(7)
di(t)
dt =−η[i(t)−Ib] + ϑu(t)(8)
Where g(t)represents the deviation of BG from its basal
value Gb, similarly, i(t)is the deviation of plasma insulin
concentration from its basal value Ib.X(t)is the proportional
concentration of insulin in a remote compartment. p(t)and
u(t)represent the rate of exogenous glucose and insulin in-
jection respectively, p1, p2, p3are model parameters describing
the physiological dynamics of glucose and insulin interaction
in an individual. Meanwhile, Bergman model is a nonlinear
model, it can be linearized when operated in its equilibrium
position by by setting the equations to zero. The linearized
model is represented in a state space model as follows:



˙
g(t)
˙
x(t)
˙
i(t)


=

−p1−xe−ge−Gb0
0−p2p3
0 0 −η



g(t)
x(t)
i(t)

+

0
0
ϑ


Using Bergman mathematical model, a fuzzy logic based
closed-loop control system for regulation of BG in diabetic
patients was proposed in [6]. The model consists of single-
glucose compartment in which patient’s insulin is assumed to
act through a remote compartment to influence net glucose
uptake. The inflow of glucose and the infused exogenous
insulin are modeled using nonlinear Differential Equations
(DE). Plasma glucose concentration and its rate of change
serve as input to the Fuzzy Logic Controller (FLC) while
insulin infusion rate is the output [6].
Similarly, a fuzzy logic based active insulin infusion closed-
loop controller was developed in [7] based on Bergman math-
ematical model. A Mamdani Fuzzy logic expert system was
used to tune the mathematical model by designing linguistic
rules to set the output of the model. The controller’s ability
to handle multiple meal disturbances was accessed and was
found to perform satisfactorily.
Similar to Bergman model, the model presented in [9] was
motivated by compartmental design diagram where all the
body compartments capable of being affected by diabetes
were modeled using Linear Predictive Model which used
internal parameters based on past inputs to predict future
output values. The numerical estimate of the model was carried
out using Kalman Filtering algorithm. The simulation results
was compared with internal model controller and non-linear
model estimated using first-order DE plus time-delay.
A mathematical model for accurate capturing of the com-
plex dynamics of BG timeseries observed in real world mea-
surement using fractional calculus concepts was presented in
[18]. A time dependent fractional model of BG dynamics was
employed to capture the BG characteristics using a real world
measurement from a public database. The control algorithm
was obtained by formulating an average glycaemic risk index
as cost function. Thus, the controller is tasked with the goal
of finding the best amount of insulin that minimize average
glycaemic risk. To measure the performance of the model, the
distribution of difference of risk index between the predicted
and actual measured data was observed [18].
Although simple to implement, Bergman’s model (and its
variants) failed to account for the rate of insulin delivery to the
blood, it only model glucose delivery. To accurately model BG
regulatory system, both glucose and insulin production has to
be accounted for. A nonlinear mathematical model of diabetes
physiological system based on Delayed Differential Equation
(DDE) was proposed by Palumbo [28]. Unlike Bergman, this
model takes pancreatic insulin delivery rate into consideration,
which makes it suitable for both T1DM and T2DM.
2) Palumbo Model: Palumbo model is a differential equa-
tion representing BG regulation. This model is favorable in the
way it accounts for the interval between the time of BG spike
251

and when insulin injection is applied as time-delay function.
The model is given as follows:
dG(t)
dt =−κxgiI(t)G(t) + Tgh
νg
(9)
dI(t)
dt =−κxiI(t) + TiGmax
νi
f(G(t−τg)) + u(t)(10)
f(G) = G
G∗γ
1 + G
G∗γ(11)
Where G(t)and I(t)denotes the plasma glucose and insulin
respectively. κxgi is the insulin-dependent rate of glucose
uptake by the tissue, κxi is the insulin degradation constant.
Tgh is the net balance between hepatic glucose output and the
insulin independent zero-order glucose tissue uptake, TiGmax
is the maximum insulin secretion in the second phase, Tgh
νgis
the net glucose production (usually a constant). νgand νiis
the glucose and insulin distribution rate. Like Bergman model,
this is also a nonlinear model, given as (11).
A hybrid BG controller based on Palumbo model was
proposed in [10]. The Palumbo delayed model was hybridized
with Fuzzy logic rules for setting the output of the controller.
Genetic algorithm was used to select parameters for the model.
The result shows superiority of the hybridized model over
using pure Palumbo delayed model and Palumbo delayed
model with fuzzy logic [10]. Palumbo nonlinear delay model
serves as the mathematical model employed. The input to the
model are the rate of change of BG and the impaired BG with
reference glucose. A Mamdani Fuzzy logic controller was used
to speed up the setting time of the model. Genetic Algorithm
was used for optimal model parameter selection [10].
Similar to Palumbo, Engelberghs predictive control model is
based on DDE. The model takes the quantity of glucose intake
(from food) as input to model the glucose-dependent insulin
secretion; insulin-independent glucose consumption by the
brain and nerve cells; glucose-dependent insulin consumption
by muscle cells and fat; and glucose production controlled
by insulin concentration. This model was used in [15] to
control the BGL in diabetic patients. To ensure the stability
of the controller, the model was subjected to constraints to
form an objective function which was optimized using Genetic
Algorithm (G.A) [15].
The aforementioned models and their associated controllers
are limited by the accuracy of their mathematical assump-
tions. Furthermore, physiological makeup is different from one
patient to another, thus, to achieve better performance, these
differences must be put into consideration. One will have to
design different MPC controller for each patient in order to
minimize postprandial disturbances in minimum time.
C. Adaptive Controller Techniques
The adaptive controller techniques popularly consider the
use of Artificial Neural Networks (ANN) and Reinforcement
Learning (RL). These two techniques are based on pattern
recognition instead of implication of a predefined hypothesis
as in the case of MPC. Thus, using these techniques, physio-
logical differences of individual patients will be automatically
handled. More so, by learning directly from homeostasis infor-
mation of the patients, this controller can perform regulation
without impeding social activities of the patients.
The ANN considers interactions between variable, uses this
interaction to find a pattern to define input-output relationship
which is static in nature and ignores the glucose control as a
dynamic response. Thus, it greatly over-fit without generaliz-
ing well on unforeseen scenarios.
Reinforcement Learning on the other hand, is based on
the principle of interaction between a decision-making, self-
learning agent (in this case, controller) and its environment (in
this case, glucose homeostasis of the patient). The controller
maps the state of its environment to a certain action (policy)
which defines the response of the agent at each time step (e.g.
increase or decrease insulin infusion rate). During training, the
overall goal of this adaptive controller is to learn an optimal
policy which yield maximum reward over time.
RL does not need a well-represented model (as in MPC) or
labelled training data (as in ANN). After a learning procedure,
the controller develops a strategy from experience to pre-
dict different unseen situations without complex mathematical
specifications of the environment. Thus, RL is uniquely suited
to system with delayed response such as subcutaneous glucose
measurement with insulin injection where feedback can take
up to hours.
For instance, RL was used in [22] to develop an adaptive BG
controller. Palumbo mathematical model was used to define
the controller’s policy, SARSA method which is based on
temporal difference technique was used to solve the model
in a reinforcement learning way. In the end, the authors
were able to control the insulin dosage to control BG level.
Also, [1] solves BG control problems using RL. The agent’s
control policy was defined using H-infinity model which was
minimized using dynamic programming (a RL approach). The
controller has low settling time and high stability to tested
postprandial disturbances.
IV. CONCLUSION
In this paper, a review of developed techniques towards full
realization of automatic insulin injection has been presented.
The review focused mainly on closed-loop techniques which
are desirable due to their feedback path for quick error
minimization. PID controllers due to its simplicity has been
greatly desired by researchers. However, PID is inherently
a reactive controller which causes the system to oscillate
especially during postprandial period; furthermore, trying to
control postprandial glucose level with PID results in life-
threatening hyperglycaemia and hypoglycaemia. To improve
PID performance, several techniques has been developed such
as tuning PID with Fuzzy-Logic controllers, or minimiz-
ing error (postprandial spikes) with optimization techniques,
development of Columnar Insulin Dosing (CID) and the
gain-scheduled PID controller technique called GRIP. MPC
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controllers are found to handle postprandial spikes better
than PID controllers. By modelling patient’s BG regulatory
system with mathematical equations based on assumption of
detailed knowledge of the physiological setup of the patients,
MPC achieves superior performance. Although, the success
of MPC depends largely on the mathematical model used,
two most popular models are Bergman Minimal Model and
Palumbo models. These models have been implemented and
optimized using different methods in the literature with better
and improved performances. Despite the several satisfactory
results reported in literature, automatic insulin injection has not
been fully accepted in clinical settings because of fundamental
physiological differences in diabetic patients which cannot
be fully accounted for in the mathematical models of MPC
controllers. To account for these differences, researchers are
now turning to Adaptive Controllers techniques based on
machine learning methods such as artificial neural networks
and reinforcement learning.
REFERENCES
[1] R. Bergman, D. Finegood, and S. Kahn, “The evolution of β-cell
dysfunction and insulin resistance in type 2 diabetes,” European journal
of clinical investigation, vol. 32, pp. 35–45, 2002.
[2] B. Topp, K. Promislow, G. Devries, R. M. Miura, and D. T FINEGOOD,
“A model of β-cell mass, insulin, and glucose kinetics: pathways to
diabetes,” Journal of theoretical biology, vol. 206, no. 4, pp. 605–619,
2000.
[3] I. D. A. Group, “Idf diabetes atlas,” vol. 3, 2005.
[4] IDF, “Idf dabetes atlas,” British Journal of Diabetes, vol. 8, 2018.
[5] B. Thomas, C. Riverside-Riverside, A. Stephen, and C. Pomona, “A
model of β-cell mass, insulin, glucose, and receptor dynamics with
applications to diabetes,” 2001.
[6] M. Ibbini and M. Masadeh, “A fuzzy logic based closed-loop control
system for blood glucose level regulation in diabetics,” Journal of
medical engineering & technology, vol. 29, no. 2, pp. 64–69, 2005.
[7] S. Yasini, M. B. Naghibi-Sistani, and A. Karimpour, “Active insulin in-
fusion using fuzzy-based closed-loop control,” in 2008 3rd International
Conference on Intelligent System and Knowledge Engineering, vol. 1.
IEEE, 2008, pp. 429–434.
[8] E.-D. E. Zubair AR, Adebayo CO and C. AO, “Development of biomed-
ical devices in africa for africa,” International Journal of Electrical and
Electronics Science, vol. 2, no. 4.
[9] R. S. Parker, F. J. Doyle, and N. A. Peppas, “A model-based algorithm
for blood glucose control in type i diabetic patients,” IEEE Transactions
on biomedical engineering, vol. 46, no. 2, pp. 148–157, 1999.
[10] V. Heydari, A. Karsaz, and R. Heydari, “A new hybrid approach on blood
glucose level control based on palumbo delayed model,” in 2016 IEEE
Intl Conference on Computational Science and Engineering (CSE) and
IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC)
and 15th Intl Symposium on Distributed Computing and Applications
for Business Engineering (DCABES). IEEE, 2016, pp. 361–366.
[11] A. K. Patra and P. K. Rout, “Optimal h insulin injection control for
blood glucose regulation in iddm patient using physiological model,”
International Journal of Automation and Control, vol. 8, no. 4, pp. 309–
322, 2014.
[12] D. B. Muchmore and J. R. Gates, “Inhaled insulin delivery–where are
we now?” Diabetes, Obesity and Metabolism, vol. 8, no. 6, pp. 634–642,
2006.
[13] S. Yasini, M. Naghibi-Sistani, and A. Karimpour, “Agent-based simula-
tion for blood glucose control in diabetic patients,” International Journal
of Applied Science, Engineering and Technology, vol. 5, no. 1, pp. 40–
49, 2009.
[14] D. R. Owens, B. Zinman, and G. Bolli, “Alternative routes of insulin
delivery,” Diabetic Medicine, vol. 20, no. 11, pp. 886–898, 2003.
[15] M. E. Ashari, M. Zekri, and M. Askari, “Control of the blood glucose
level in diabetic patient using predictive controller and delay differential
equation,” in 2015 2nd International Conference on Knowledge-Based
Engineering and Innovation (KBEI). IEEE, 2015, pp. 422–427.
[16] V. Mohan, S. N. Shah, S. R. Joshi, V. Seshiah, B. K. Sahay, S. Banerjee,
S. K. Wangnoo, A. Kumar, S. Kalra, A. Unnikrishnan et al., “Current
status of management, control, complications and psychosocial aspects
of patients with diabetes in india: Results from the diabcare india 2011
study,” Indian journal of endocrinology and metabolism, vol. 18, no. 3,
p. 370, 2014.
[17] X. Guo and W. Wang, “Challenges and recent advances in the subcu-
taneous delivery of insulin,” Expert opinion on drug delivery, vol. 14,
no. 6, pp. 727–734, 2017.
[18] M. Ghorbani and P. Bogdan, “Reducing risk of closed loop control
of blood glucose in artificial pancreas using fractional calculus,” in
2014 36th Annual International Conference of the IEEE Engineering
in Medicine and Biology Society. IEEE, 2014, pp. 4839–4842.
[19] M. Ibbini, M. Masadeh, and M. Bani Amer, “A semiclosed-loop optimal
control system for blood glucose level in diabetics,” Journal of medical
engineering & technology, vol. 28, no. 5, pp. 189–196, 2004.
[20] P. Grant, “A new approach to diabetic control: fuzzy logic and insulin
pump technology,” Medical engineering & physics, vol. 29, no. 7, pp.
824–827, 2007.
[21] M. K. Bothe, L. Dickens, K. Reichel, A. Tellmann, B. Ellger, M. West-
phal, and A. A. Faisal, “The use of reinforcement learning algorithms to
meet the challenges of an artificial pancreas,” Expert review of medical
devices, vol. 10, no. 5, pp. 661–673, 2013.
[22] A. Noori, M. A. Sadrnia et al., “Glucose level control using temporal
difference methods,” in 2017 Iranian Conference on Electrical Engi-
neering (ICEE). IEEE, 2017, pp. 895–900.
[23] C. Cobelli, E. Renard, and B. Kovatchev, “Artificial pancreas: past,
present, future,” Diabetes, vol. 60, no. 11, pp. 2672–2682, 2011.
[24] M. Breton, A. Farret, D. Bruttomesso, S. Anderson, L. Magni, S. Patek,
C. Dalla Man, J. Place, S. Demartini, S. Del Favero et al., “Fully
integrated artificial pancreas in type 1 diabetes: modular closed-loop
glucose control maintains near normoglycemia,” Diabetes, vol. 61, no. 9,
pp. 2230–2237, 2012.
[25] E. M. Watson, M. J. Chappell, F. Ducrozet, S. Poucher, and J. W. Yates,
“A new general glucose homeostatic model using a proportional-integral-
derivative controller,” Computer methods and programs in biomedicine,
vol. 102, no. 2, pp. 119–129, 2011.
[26] G. M. Steil and M. F. Saad, “Automated insulin delivery for type 1
diabetes,” Current Opinion in Endocrinology, Diabetes and Obesity,
vol. 13, no. 2, pp. 205–211, 2006.
[27] R. Sharma, S. Mohanty, and A. Basu, “Improvising tuning techniques of
digital pid controller for blood glucose level of diabetic patient,” in 2016
International Conference on Emerging Trends in Electrical Electronics
& Sustainable Energy Systems (ICETEESES). IEEE, 2016, pp. 159–
163.
[28] E. Renard, J. Place, M. Cantwell, H. Chevassus, and C. C. Palerm,
“Closed-loop insulin delivery using a subcutaneous glucose sensor and
intraperitoneal insulin delivery: feasibility study testing a new model for
the artificial pancreas,” Diabetes care, vol. 33, no. 1, pp. 121–127, 2010.
[29] P. Palumbo, S. Panunzi, and A. De Gaetano, “Qualitative behavior of
a family of delay-differential models of the glucose-insulin system,”
Discrete and Continuous Dynamical Systems Series B, vol. 7, no. 2, p.
399, 2007.
[30] B. W. Bequette, “Analysis of algorithms for intensive care unit blood
glucose control,” 2007.
[31] R. C. Osburne, C. B. Cook, L. Stockton, M. Baird, V. Harmon, A. Keddo,
T. Pounds, L. Lowey, J. Reid, K. A. McGowan et al., “Improving
hyperglycemia management in the intensive care unit,” The Diabetes
Educator, vol. 32, no. 3, pp. 394–403, 2006.
[32] M. Vogelzang, F. Zijlstra, and M. W. Nijsten, “Design and implemen-
tation of grip: a computerized glucose control system at a surgical
intensive care unit,” BMC medical informatics and decision making,
vol. 5, no. 1, p. 38, 2005.
[33] B. W. Bequette, “A critical assessment of algorithms and challenges
in the development of a closed-loop artificial pancreas,” Diabetes
technology & therapeutics, vol. 7, no. 1, pp. 28–47, 2005.
[34] K. Lunze, T. Singh, M. Walter, M. D. Brendel, and S. Leonhardt, “Blood
glucose control algorithms for type 1 diabetic patients: A methodological
review,” Biomedical signal processing and control, vol. 8, no. 2, pp.
107–119, 2013.
[35] R. N. Bergman, Y. Z. Ider, C. R. Bowden, and C. Cobelli, “Quantitative
estimation of insulin sensitivity.” American Journal of Physiology-
Endocrinology And Metabolism, vol. 236, no. 6, p. E667, 1979.
253