ArticlePDF Available


  • The University of mustansiriya, College of Engineering


The type1 of diabetes is a chronic situation characterized by abnormally high glucose levels in the blood. Persons with diabetes characterized by no insulin secretion in the pancreas (ß-cell) which also known as insulin-dependent diabetic Mellitus (IDDM). In order to keep the levels of glucose in blood near the normal ranges (70-110mg/dl), the diabetic patients needed to inject by external insulin from time to time. In this paper, a Modified Second Order Sliding Mode Controller (MSOSMC) has been developed to control the concentration of blood glucose levels under a disturbing meal. The parameters of the suggested design controller are optimized by using chaotic particle swarm optimization (CPSO) technique, the model which is used to represent the artificial pancreas is a minimal model for Bergman. The simulation was performed on a MATLAB/SIMULINK to verify the performance of the suggested controller. The results showed the effectiveness of the proposed MSOSMC in controlling the behavior of glucose deviation to a sudden rise in blood glucose.
Applied Computer Science, vol. 16, no. 2, pp. 1831
Submitted: 2020-05-10
Revised: 2020-05-19
Accepted: 2020-06-20
Type I Diabetes, Second Order Sliding Mode Control, Chaotic Particle Swarm Optimization, BEM model
Ekhlas H. KARAM*, Eman H. JADOO
The type1 of diabetes is a chronic situation characterized by abnormally
high glucose levels in the blood.
Persons with diabetes characterized by
no insulin secretion in the pancreas -cell) which also known as insulin-
dependent diabetic Mellitus (IDDM). In order to keep the levels of glucose
in blood near the normal ranges (70110mg/dl), the diabetic patients
needed to inject by external insulin from time to time. In this paper,
a Modified Second Order Sliding Mode Controller (MSOSMC) has been
developed to control the concentration of blood glucose levels under a dis-
turbing meal. The parameters of the suggested design controller are
optimized by using chaotic particle swarm optimization (CPSO) technique,
the model which is used to represent the artificial pancreas is a minimal
model for Bergman. The simulation was performed on a MATLAB/SIMULINK
to verify the performance of the suggested controller. The results showed the
effectiveness of the proposed MSOSMC in controlling the behavior of glu-
cose deviation to a sudden rise in blood glucose.
Mustansiriyah University, College of Engineering, Computer Engineering Department,
Palestine Street, 14022, Baghdad, Iraq,,
Diabetes mellitus is one of the most important chronic diseases which results
from a high blood sugar for a long time due to insufficient insulin generation in
the blood (Bergman, Phillips & Cobelli, 1981). The concentration of glucose in the
bloodstream is naturally regulated by two hormones: insulin and glucagon. Both of
these hormones are secreted by β-cells and α cells in the Langerhans islands of the
pancreas, respectively. The concentration of glucose ranges from 70 to 110 (mg/dL).
Accordingly, there are two states, hyperglycemia (glucose concentration is above the
normal ranges) and hypoglycemia (low glucose concentration than the normal
ranges) (Basher, 2017).
Diabetes is broken down into two major types. The type 1 diabetes mellitus
(T1DM) and Type 2 diabetes mellitus (T2DM) in the first type the patient's body
can’t produce enough insulin and doses of insulin need to be injected into the
human body to control blood glucose levels, while the second type starts with
insulin resistance, a condition in which cells do not respond properly to insulin.
This type of diabetes is a common type and known as noninsulin-dependent
diabetes (Sylvester & Munie, 2017).
In order to prevent the effects of high blood glucose levels the best approach
is to administer insulin during a moment when blood glucose is supposed to rise.
With the Advance of technology, the so-called artificial pancreas emerged its
consists of three main components, glucose sensor, insulin pump and control
techniques to generate the necessary insulin dose based on glucose measurements
(Kaveh & Shtessel, 2006). The block diagram of the closed loop system for
glucose level control shown in Figure 1.
Fig. 1. Block diagram of closed-loop insulin delivery system
There are several studies that use a closed-loop controller to keep blood glucose
(BG) diabetic concentration within the appropriate range, such as: (Kaveh and
Shtessel, 2006) used higher order sliding mode controller (HOSMC) to regulate
the levels of blood glucose. (Garcia-Gabin, et al., 2009) suggested a sliding mode
predictive control (SMPC) which is the combining sliding mode control technology
with model predictive control (MPC). In a (Abu-Rmileh & Garcia-Gabin, 2011)
used a combination of the robust sliding mode control (SMC) and the Smith predic-
tor (SP) structures. Nasrin et al. suggest a Sliding Mode Control (SMC) based on
Backstepping technique (Parsa, Vali & Ghasemi, 2014). Waqar et al. suggest
a non-linear super twisting control algorithm based on SMC approach has been
addressed for regulation of glucose concentration in blood plasma of type 1 diabetes
patients (Alam, et al., 2018).
In this paper, the MSOSMC is suggested to regulate the levels of blood glu-
cose, the CPSO algorithm was used for tuning the parameters of the controller.
To accomplish these objectives Bergman Minimal (BEM) mathematical model
which considered here. The outliner of this paper as follows: The BEM math-
ematical model of blood glucose system presented in section 2. The details of
the SOSMC described in section 3, while the design of the MSOSMC explained
in section 4. And the CPSO algorithm illustrated in section 5. The proposed
controller's analysis and simulation results will be discussed in section 6, while
the final conclusions listed in the last section.
Specific mathematical models have been suggested to explain the complexi-
ties of diabetes and to compare the interaction between models of glucose and
the delivery of insulin that helps design a diabetes model. Among these models,
the minimal Bergman model, a common reference model in the literature,
approaches the dynamic response of blood glucose concentration in a diabetic to
insulin injections. Bergman model consists of three differential equations as
follows (Sylvester, 2017), (Abu-Rmileh & Garcia-Gabin, 2011):
     
    (1)
      
where: is the plasma glucose concentration in [mg/dL], proportional
to the insulin concentration in the remote compartment [1/min], is the plasma
insulin concentration in [mU/dL], and is injected insulin rate in [mU/min],
 are parameters of the model. The term,  in the
third equation of this model, serves as an internal regulatory function that formu-
lates insulin secretion in the body, which does not exist in diabetics, the 
represent the rate of exogenous insulin. The value of will be significantly
reduced; therefore it can be approximated as zero (Parsa, Vali & Ghasemi,
2014). Which is disturbance signal (meal disturbance) can be modeled by
a decaying exponential function of the following form (Fisher, 1991):
    (2)
where: represents the absorption rate of the meal, is meal size and 
represents the beginning time of meal digestion.
SMC is a robust and simple procedure for synthesizing controllers for linear
and nonlinear processes based on the Variable Structure Control (VSC)
The discrete control has high switching frequency, which causes a "chattering-
phenomenon", it considered undesired property that appear in SMC's control
action (Djouima, et al., 2018). There are different methods that have been used
to overcome the chattering phenomena such as replacing the sign(s) by boundary
function like sat(s), using terminal SMC, integral SMC, and other different methods.
One of the most efficient methods to overcome this problem by using Second
Order Sliding Mode Control. There are different SOSMC algorithms, such as
Sub-Optimal (SO), Twisting (TW) and Super-Twisting (ST) algorithm. ST-SMC
does not require the information of in its formulation and application which is
simpler and preferable (Matraji, Al-Durra & Errouissi, 2018).
The ST-SMC utilized similar design steps as standard SMC. The same
sliding surface as in Eq. (3) is applied and the control laws are stated in Eq. (8).
The sliding surface can be introduced as:
   (3)
where  and  is error and derivative of the error respectively,  is given
   (4)
where is the reference input (Basal Value) and  is the output signal
(measured glucose).
The constant is chosen to be positive. The choice of decides the conver-
gence rate of the tracking error.
The ST algorithm is dened by the following control law (Matraji, Al-Durra
& Errouissi, 2018; Levant, 2013):
   , (5)
  (6)
  (7)
where and are positive bounded constants. The control law of the super
twisting SOSMC is given by:
    (8)
In this paper, a Modified SOSMC based on super twisting is suggested as
shown in fig. 2, which considered as improvement to the SOSMC, the control
law of the super twisting SOSMC (Eq. (8)) is modified to:
     (9)
where  is nonlinear auxiliary part given by:
  
 (10)
where are small positive numbers that will be tuning by (PSO and CPSO)
Fig. 2. Modified SOSMC block diagram
The Particle Swarm Optimization algorithms (PSO) is the common evolutionary
techniques. Which is adopt a random sequence for their parameter. The PSO algo-
rithm is initialized with a population of candidate solutions which is called
a particle. N particles are moving around in a D-dimensional search space of the
problem (Amet, Ghanes & Barbot, 2012).
The position of the  particle at the  iteration is represented by
 . The velocity for the  particle can be written as
 . The best position that has so far been visited by the 
particle is represented as  = ( ) which is also called pbest.
The global best position attained by the whole swarm is called the global best
(gbest) and represented as () = ( ). The velocity vector at the
 iteration is represented as () = (). At the next iteration,
the velocity and position of the particle are calculated according to (11, 12):
        (11)
     (12)
where are called acceleration coefficients. is called inertia weight, and
are random value in the range [0, 1]. The parameters   and is the
key factors that effected the convergence behavior (Wang, Tan & Liu, 2018).
In the Chaotic Particle Swarm Optimization algorithms (CPSO) the parameters
and are modified by using logistic map based on the following equation:
            (13)
where is s a control parameter with a real number from  and     .
Then introduce a new velocity update as in equations (14).
            (14)
  
Important advantages of the chaotic optimization algorithm (COA) are sum-
marized as: easy implementation, short execution time and speed-up of the search.
Observations, however, reveal that the COA also has some problems including:
(i) COA is effective only for small decision spaces; (ii) COA easily converges in
the early stages of the search process. Therefore, hybrid methods have attracted
attention by the researchers (Hadi, 2019) The flowchart that represented this
algorithm illustrated below.
Fig. 3. General flowchart of the CPSO algorithm
The results of simulations for BEM model addressed in Eq. (1), parameters of
BEM model are available on table (1), and the suggested controller based on the
CPSO algorithm are offered in this section for a BG levels of 70 mg/dl. The BEM
model response without controller is showen in figure (4). In this paper, the sim-
ulations are carried out dynamically for three patients with the initial conditions
220, 200 and 180mg/dl for patients 1, 2 and 3, respectively. In the simulation,
the meal glucose disturbance that given in Eq. (2) the value of its parameters are
  , b , and  
Fig. 4. Glucose output of three patients with disturbance
(open-loop glucose regulatory system)
You can note that the glucose value of the normal person is stabilized at the
basal level in the presence of the disturbance (meal), while the patient's glucose
level remains dangerous outside the range. The simulation second part is the pro-
posed controller is applied to the system and the response of a patients in the
presence of the disturbance is tested. To examine the robustness of the control
algorithm to the parameter change, three sets of parameters for three different
patients have been used. The parameters of CPSO algorithm are considered here
as in Table 2.
Tab. 1. Bergman Minimal Model Parameters (Garcia-Gabin, et al.,
2009; Abu-Rmileh & Garcia-Gabin, 2011).
Tab. 2. The parameters of CPSO algorithm
CPSO Parameters
Maximum number of iterations
Number of particles
Acceleration constant
Inertia weight factor
Random values
Control parameter
Chaotic initial value
Table 3 illustrate the optimal parameters for SOSMC and MSOSMC controllers
gotten from the CPSO algorithm.
Tab. 3. Optimal controller parameters
Figures (5 to 10) shows the response of BEM model for three patients after
applying the suggested controllers to regulated the BG level according to Table 3
It can be noticed from simulation results (Figures (5 to 10) and Tables (4 to 6))
of the suggested controllers that the glucose output with these controllers tracks
the desired BG level with small settling time (), study state error (), and the
Mean Absolute Percentage Error () between the glucose value under the
control system and that under the normal model according to the following
 
 (15)
where is the duration of simulation,  is the glucose value returned by
the reference model, and  represents the actual output of the system
under the controller.
Fig. 5. Blood glucose concentration for patient 1 based on the suggested controllers
and CPSO algorithm
Fig. 6. Insulin infusion rate for patient1 based on the suggested controllers and CPSO
Fig. 7. Blood glucose concentration for patient 2 based on the suggested controllers
and CPSO algorithm
Fig. 8. Insulin infusion rate for patient2 based on the suggested controllers
and CPSO algorithm
Fig. 9. Blood glucose concentration for patient 3 based on the suggested controllers
and CPSO algorithm
Fig. 10. Insulin infusion rate for patient3 based on the suggested controllers
and CPSO algorithm
Tab. 4. The simulation result’s evaluation parameters for patient 1
The controller used
Tab. 5. The simulation result’s evaluation parameters for patient 2
The controller used
Tab. 6. The simulation result’s evaluation parameters for patient 3
The controller used
The comparison between controllers is shown in Tables (4 to 6). This tables
illustrates the performance of controllers. The MSOSMC has the best average
performance which satisfies the design requirement.
In this paper, a simple modified second order sliding mode controller has been
suggested based on ST algorithm and CPSO algorithm. The performance analysis
of the suggested control strategy concerning plasma glucose-insulin stabilization
is comprehensively demonstrated by computer simulations. To validate the ro-
bustness of the suggested controller, the diabetic patient is exposed to external
disturbance, that is, a meal. The closed-loop system has been simulated for different
patients with different parameters, in the presence of the food intake disturbance
and it has been shown that the glucose level is stabilized at its basal value (reference
input) in a reasonable amount of time. The effectiveness of the suggested controller
compared with the classical SOSMC are verified by simulation results for three
Abu-Rmileh, A., & Garcia-Gabin, W. (2011). Smith predictor sliding mode closed-loop glucose
controller in type 1 diabetes. IFAC Proc. Vol., 18(PART 1), 17331738.
Alam, W., Ali, N., Ahmad, S., & Iqbal, J. (2018). Super twisting control algorithm for blood
glucose regulation in type 1 diabetes patients. In 2018 15th International Bhurban
Conference on Applied Sciences and Technology (IBCAST) (pp. 298303). IEEE.
Amet, L., Ghanes, M., & Barbot, J-P. (2012). HOSM control under quantization and saturation
constraints: Zig-Zag design solutions. In 2012 IEEE 51st IEEE Conference on Decision and
Control (CDC) (pp. 54945498). Maui, HI.
Basher, A.S. (2017). Design fuzzy control system for blood glucose level for type-1 diabetes
melitus patients using ga a simulation study (Msc. Thesis). The Islamic University (Gaza).
Bergman, R.N., Phillips, L.S., & Cobelli, C. (1981). Physiologic evaluation of factors controlling
glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose
sensitivity from the response to intravenous glucose. The Journal of clinical investigation.
68(6), 14561467.
Djouima, M., Azar, A.T., Drid, S., & Mehdi, D. (2018). Higher Order Sliding Mode Control for
Blood Glucose Regulation of Type 1 Diabetic Patients. International Journal of System
Dynamics Applications (IJSDA), 7(1), 6584.
Fisher, M.E. (1991). A semiclosed-loop algorithm for the control of blood glucose levels in
diabetics. IEEE Trans Biomed Eng, 38(1), 5761.
Garcia-Gabin, W., Zambrano, D., Bondia, J., & Vehí, J. (2009). A sliding mode predictive control
approach to closed-loop glucose control for type1 diabetes. IFAC Proceedings Volumes,
42(12), 8590.
Hadi, E.A. (2019). Multi Objective Decision Maker for Single and Multi Robot Path Planning
(MSc. thesis). University of Technology (Iraq).
Kaveh, P., & Shtessel, Y.B. (2006). Blood Glucose Regulation in Diabetics Using Sliding Mode
Control Techniques. In 2006 Proceeding of the Thirty-Eighth Southeastern Symposium on
System Theory (pp. 171175). Cookeville, TN.
Levant, A. (1993). Sliding order and sliding accuracy in sliding mode control. Int J Control, 58(6),
Matraji, I., Al-Durra, A., & Errouissi, R. (2018). Design and experimental validation of enhanced
adaptive second-order SMC for PMSG-based wind energy conversion system.
International Journal of Electrical Power & Energy Systems, 103, 2130.
Parsa, N.T., Vali, A., & Ghasemi, R. (2014). Back Stepping Sliding Mode Control of Blood
Glucose for Type I Diabetes. World Academy of Science, Engineering and Technology,
International Journal of Medical, Health, Biomedical, Bioengineering and Pharmaceutical
Engineering, 8(11), 779783.
Sylvester, D.D., & Munje, R.K. (2017). Back stepping SMC for blood glucose control of type-1
diabetes mellitus patients. International Journal of Engineering Technology Science and
Research, 4(5), 17.
Wang, D., Tan, D., & Liu, L. (2018). Particle swarm optimization algorithm: an overview. Soft
Computing, 22(2), 387408.
... In the Ref. [11], the output feedback SMC was designed to retain the glucose value in a desired level, and its performance was compared with the open-loop approaches. In the Ref. [12], the particle-swarm optimization scheme was used to tune a SMC scheme, and it was shown that the glucose level was kept near to the desired range. The terminal SMC was developed in the Ref. [13], and the effect of mathematical uncertainties was analyzed. ...
Full-text available
The insulin injection rate in type-I diabetic patients is a complex control problem. The mathematical dynamics for the insulin/glucose metabolism can be different for various patients who undertake different activities, have different lifestyles, and have other illnesses. In this study, a robust regulation system on the basis of generalized type-2 (GT2) fuzzy-logic systems (FLSs) is designed for the regulation of the blood glucose level. Unlike previous studies, the dynamics of glucose–insulin are unknown under high levels of uncertainty. The insulin-glucose metabolism has been identified online by GT2-FLSs, considering the stability criteria. The learning scheme was designed based on the Lyapunov approach. In other words, the GT2-FLSs are learned using adaptation rules that are concluded from the stability theorem. The effect of the dynamic estimation error and other perturbations, such as patient activeness, were eliminated through the designed adaptive fuzzy compensator. The adaptation laws for control parameters, GT2-FLS rule parameters, and the designed compensator were obtained by using the Lyapunov stability theorem. The feasibility and accuracy of the designed control scheme was examined on a modified Bergman model of some patients under different conditions. The simulation results confirm that the suggested controller has excellent performance under various conditions.
Conference Paper
Full-text available
This is an increasing belief that consequences due to hyperglycemia can be mitigated using a close loop control system. This paper investigates a robust non-linear control approach based on sliding mode control (SMC) algorithm for type 1 diabetes patients. Bergman’s minimal model have been used to analyse the behaviour of glucose and insulin dynamics in blood plasma inside human body. Control law based on super twisting SMC algorithm is formulated and simulated. Results demonstrated the performance and effectiveness of the proposed control scheme. Also the proposed control scheme is compared with traditional SMC on the basis of performance parameters in the presence of external disturbances. Results dictate that the proposed control law exhibits robustness and overperforms by demonstrating accurate trajectory tracking with relatively less control efforts and alleviating chattering.
Full-text available
Type 1 diabetes mellitus (T1DM) treatment depends on the delivery of exogenous insulin to obtain near normal glucose levels. This article proposes a method for blood glucose level regulation in type 1 diabetics. The control strategy is based on comparing the first order sliding mode control (FOSMC) with a higher order SMC based on the super twisting control algorithm. The higher order sliding mode is used to overcome chattering, which can induce some undesirable and harmful phenomena for human health. In order to test the controller in silico experiments, Bergman's minimal model is used for studying the dynamic behavior of the glucose and insulin inside human body. Simulation results are presented to validate the effectiveness and the good performance of this control technique. The obtained results clearly reveal improved performance of the proposed higher order SMC in regulating the blood glucose level within the normal glycemic range in terms of accuracy and robustness.
Full-text available
Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. Since presented in 1995, it has experienced a multitude of enhancements. As researchers have learned about the technique, they derived new versions aiming to different demands, developed new applications in a host of areas, published theoretical studies of the effects of the various parameters and proposed many variants of the algorithm. This paper introduces its origin and background and carries out the theory analysis of the PSO. Then, we analyze its present situation of research and application in algorithm structure, parameter selection, topology structure, discrete PSO algorithm and parallel PSO algorithm, multi-objective optimization PSO and its engineering applications. Finally, the existing problems are analyzed and future research directions are presented.
Conference Paper
Full-text available
In many experimental systems, discrete and bounded actuators implement control laws with sampling, quantization and saturation problems. This paper is dedicated to only the last two in the context of the implementation of a Super-Twisting sliding mode control. A new control design, called “Zig-Zag sliding mode control”, is proposed. Issues of quantization and saturation problems are respectively investigated directly and implicitly by the proposed control. The main contribution of the proposed method consists in having a faster convergence and well performances even when the saturation of the actuators is decreased up to a certain limit in which other methods fail to converge. Simulation results of the proposed method compared to the results of traditional implementations highlight the well founded Zig-Zag design.
Full-text available
The synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay.
This paper presents Adaptive Second-Order Sliding Mode Control (SOSMC) for power control of Permanent Magnet Synchronous Generator (PMSG). The control objective is to force the PMSG to generate the desired power through regulating the winding current. Specifically, Super Twisting (ST) algorithm SOSMC is adopted in this paper to derive a robust and fast current control for PMSG-based Wind Energy Conversion System (WECS). ST algorithm is renowned for its robustness against parametric uncertainty and external disturbance, but it suffers from the chattering problem. The existing Adaptive Super Twisting (AST) algorithm can reduce the chattering effect, but often at the expense of degraded transient response. In this work, an alternative way is proposed to implement AST algorithm in order to achieve fast transient response, while at the same time attenuate the chattering problem. The controller performance is validated through an experimental setup consisting of a wind turbine emulator and a PMSG which is connected to the grid via back-to-back converter. The experimental results show better performance of the closed-loop system in terms of response time, steady-state error, and chattering despite the presence of parametric uncertainty.
Conference Paper
The development of robust and efficient glucose control algorithms is key to making the artificial pancreas a reality. In this paper a sliding mode predictive control (SMPC) is obtained by combining the design technique of a sliding mode control with a model based predictive control (MPC). The SMPC combines the main advantages of the two control methods: the robust features of SMC and the good performance of MPC, including the handling of constraints on manipulated and controlled variables. Control action is composed by three parts: a predictive one from an optimization problem, a discontinuous one given by the switching term and finally, a feed-forward action given by an insulin bolus that is injected when a meal is ingested. The prediction model is linear and it is represented by a second order model with time delay. In order to test the controller in silico experiments, the Hovorka model has been considered. The proposed control algorithm shows considerable robustness for intra-patient variability, as well as an enhanced ability to handle measurement uncertainties and disturbance rejection, especially focusing on postprandial behaviour.
In this paper, a theoretical analysis of the control of plasma glucose levels in diabetic individuals is undertaken using a simple mathematical model of the dynamics of glucose and insulin interaction in the blood system. Mathematical optimization techniques are applied to the mathematical model to derive insulin infusion programs for the control of blood levels in diabetic individuals. Based on the results of the mathematical optimization, a semiclosed-loop algorithm is proposed for continuous insulin delivery to diabetic patients. The algorithm is based on three hourly plasma glucose samples. A theoretical evaluation of the effectiveness of this algorithm shows that it is superior to two existing algorithms in controlling hyperglycemia. A glucose infusion term representing the effect of glucose intake resulting from a meal is then introduced into the model equations. Various insulin infusion programs for the control of plasma glucose levels following a meal are then assessed. The theoretical results suggest that the most effective short-term control is achieved by an insulin infusion program which incorporates an injection to coincide with the meal.
The quantitative contributions of pancreatic responsiveness and insulin sensitivity to glucose tolerance were measured using the 'minimal modeling technique' in 18 lean and obese subjects (88-206% ideal body wt). The individual contributions of insulin secretion and action were measured by interpreting the dynamics of plasma glucose and insulin during the intravenous glucose tolerance test in terms of two mathematical models. One, the insulin kinetics model, yields parameters of first-phase (Φ1) and second-phase (Φ2) responsivity of the β-cells to glucose. The other glucose kinetics model yields the insulin sensitivity parameter, S(I). Lean and obese subjects were subdivided into good (K(G) > 1.5) and lower (K(G) < 1.5) glucose tolerance groups. The etiology of lower glucose tolerance was entirely different in lean and obese subjects. Lean, lower tolerance was related to pancreatic insufficiency (Φ2 77% lower than in good tolerance controls [P <0.03]), but insulin sensitivity was normal (P >0.5). In contrast, obese lower tolerance was entirely due to insulin resistance (S(I) diminished 60% [P < 0.01]); pancreatic responsiveness was not different from lean, good tolerance controls (Φ(I): P >0.06; Φ2: P >0.40). Subjects (regardless of weight) could be segregated into good and lower tolerance by the product of second-phase β-cell responsivity and insulin sensitivity (Φ2.S(I)). Thus, these two factors were primarily responsible for overall determination of glucose tolerance. The effect of Φ1 was to modulate the K(G) value within those groups whose overall tolerance was determined by Φ2.S(I). This Φ1 modulating influence was more pronounced among insulin sensitive (Φ1 vs. K(G), r = 0.79) than insulin resistant (obese, low tolerance; Φ1 vs. K(G), r = 0.91) subjects. This study demonstrate the feasibility of the minimal model technique to determine the etiology of impaired glucose tolerance.