A Long-Term Model of the Glucose–Insulin Dynamics of Type 1 Diabetes

Magdelaine, Nicolas; Chaillous, Lucy; Guilhem, Isabelle; Poirier, Jean-Yves; Krempf, Michel; Moog, Claude H.; Carpentier, Éric Le

doi:10.1109/tbme.2015.2394239

Cited by 88 publications

(86 citation statements)

References 17 publications

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“…In this study, a recently appeared glucose-insulin model is investigated, developed in order to increase the efficiency of identification from real patients' samples [23]. The state-space representation of the model is given as follows: [23].…”

Section: Diabetes Modelmentioning

confidence: 99%

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A robust fixed point transformation-based approach for type 1 diabetes control

Kovács

2017

Nonlinear Dyn

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Modeling and control of diabetes mellitus (DM) are difficult due to the highly nonlinear attitude, time-delay effects, the impulse kind input signals and the lack of continuously available blood glucose (BG) level to be regulated. Regarding the mentioned problems, identification of DM model is crucial. Furthermore, due to the lack of information about the internal states (which cannot be measured in everyday life) and because the BG level is not available in every moment over time, adaptive robust control design method regardless exact model dependency would successfully handle these unfavorable effects without simplifications. The recently developed nonlinear robust fixed point transformation (RFPT)-based controller design method requires only a roughly approximate model in order to realize the controller structure. Moreover, parallel simulated approximate models-in order to provide additional internal information-can be used with the method. In this paper, the usability of the novel RFPT-based technique is demonstrated on the physiological problem of diabetes.

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Section: Diabetes Modelmentioning

confidence: 99%

“…The state-space representation of the model is given as follows: [23]. The model has two inputs, namely the external insulin infusion rate u(t) (U/h) and the carbohydrate (CHO) intake r (t) (mg/min 2 ), and one output, the glycemia, G(t) (mg/dL) used as a state of the model as well.…”

Section: Diabetes Modelmentioning

confidence: 99%

A robust fixed point transformation-based approach for type 1 diabetes control

Kovács

2017

Nonlinear Dyn

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“…Our control algorithm is tested and evaluated in silico via a long-term linear time-invariant model, which was recently developed [34]:…”

Section: Virtual Patientmentioning

confidence: 99%

“…Recall some advantage of this modeling with respect to existing ones. It was shown, for instance in [34], that the parameters in [11] cannot be estimated from standard clinical data (CGM, injection and meal intake). Most existing models introduce, however, some apparent equilibria which are not consistent with real life.…”

Section: Virtual Patientmentioning

confidence: 99%

“…See, e.g., [6,9,12,14,33,51] for reviews. Obtaining a suitable mathematical modeling is therefore an essential issue (see, e.g., the previous reviews, and [1,10,34]). Like in many concrete applications, PID control (see, e.g., [12,37,39,49]) and model-based predictive control (see, e.g., [13,25,31,35,41]) are quite often encountered (see, e.g., [24]).…”

Section: Introductionmentioning

confidence: 99%

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A Variable Reference Trajectory for Model-Free Glycemia Regulation

Ridha¹,

Moog²,

Delaleau³

et al. 2015

2015 Proceedings of the Conference on Control and Its Applications

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The control design of an artificial pancreas, a hot research topic in diabetology, is tackled via the newly introduced model-free control and its corresponding "intelligent" proportional controller, which were already quite successful in many concrete and diverse situations. It results in an insulin injection for type 1 diabetes which displays via constant references a good nocturnal/fasting response, but unfortunately a poor postprandial behavior due to long hyperglycemia. When a variable reference is introduced, that switches between a constant one, when glycemia is more or less normal or moderate, and an exponential decay reference path, when a high glycemia rate indicates a meal intake, the results in silico, which employ real clinical data, become excellent. We obtain a bolus-shaped insulin injection rate during postprandial phases. The hyperglycemic peaks are therefore lowered a lot.

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Dynamic modeling of the glucose–insulin system with inhibitors impulsive control

Li,

Liu,

Wang

et al. 2024

Math Methods in App Sciences

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Pulse injection of insulin analogues is an important strategy to control glucose concentrations and can be combined with ‐glucosidase inhibitors to reduce adverse effects to improve glucose control. To elucidate this combination therapy strategy, we assumed dietary intake in the form of pulse glucose injection and proposed a novel mathematical model incorporating pulse injection insulin and ‐glucosidase inhibitors. In type 1 diabetes, the existence and uniqueness of the positive periodic solution is confirmed utilizing the Lambert W function. The global asymptotic stability of the positive periodic solution is achieved through the application of Floquet multiplier theory and the comparison principle. Furthermore, in type 2 diabetes, the permanence of the system is also confirmed through the comparison theorem. Numerical analysis validated the theoretical calculations, highlighting the significance of insulin injection dosage and frequency, as well as ‐glucosidase inhibitor therapy. Additionally, we systematically assessed a rational approach for diabetes treatment combined with ‐glucosidase inhibitors, providing more practical clinical strategies. This facilitates the extension of our model to encompass other drugs that may be utilized in future clinical interventions.

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A Long-Term Model of the Glucose–Insulin Dynamics of Type 1 Diabetes

Cited by 88 publications

References 17 publications

A robust fixed point transformation-based approach for type 1 diabetes control

A robust fixed point transformation-based approach for type 1 diabetes control

A Variable Reference Trajectory for Model-Free Glycemia Regulation

Dynamic modeling of the glucose–insulin system with inhibitors impulsive control

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