Modelling the regulatory system for diabetes mellitus with a threshold window

Jy, Yang; Tang, Sanyi; Cheke, Robert

doi:10.1016/j.cnsns.2014.08.012

Cited by 13 publications

(4 citation statements)

References 38 publications

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“…Up to date, a wide range of mathematical model are investigated, which are categorized into either subcutaneous or intravenous model. Some of it is composed of partial differential equations, 22 ordinary differential equation, 23,24 delayed differential equations and so on. 25 In this work, an intravenous patient model, widely known as Bergman's minimal model, is considered, which is mostly referenced as intravenous glucose tolerance test (IGVTT) model in the literature.…”

Section: Patient Modelmentioning

confidence: 99%

Glucose–insulin stabilization in type-1 diabetic patient: A uniform exact differentiator–based robust integral sliding mode control approach

Alam

Khan

Riaz

et al. 2019

International Journal of Distributed Sensor Networks

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Diabetes mellitus is a persistent metabolic syndrome caused by impaired capability of the body's production and usage of insulin. This impaired capability results in chronic hyperglycaemia, the elevated glucose concentration in the bloodstream, which may lead to many incurable complications. To escape this dire situation, a proper model-based exogenous infusion of insulin bolus is required, which is usually established via different feedback control strategies. In this article, the authors present a mathematical model-based robust integral sliding mode control approach for stabilization of internal glucose-insulin regulatory system in type-1 diabetic patient. Since the state variables of the system are not directly available to the controller, a uniform exact differentiator observer is employed to accomplish the aforementioned task. In the proposed control law, the incorporation of integral term in the switching manifold eliminates the reaching phase, which causes the sliding mode to establish from the very initial point, thus enhances the robustness property of the proposed control scheme. Moreover, the chattering problem is also substantially suppressed to a considerable extent along a defined manifold. To verify the theoretical analysis, the proposed control law is verified via computer simulations which demonstrate the effectiveness of the proposed control law against the external perturbations, that is, unannounced meal intake and physical exercise.

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Section: Patient Modelmentioning

confidence: 99%

Glucose–insulin stabilization in type-1 diabetic patient: A uniform exact differentiator–based robust integral sliding mode control approach

Alam

Khan

Riaz

et al. 2019

International Journal of Distributed Sensor Networks

View full text Add to dashboard Cite

show abstract

“…During the past decades, a variety of mathematical models have been proposed to describe the dynamics of the glucose–insulin interactions including ordinary differential equations [25, 26], partial differential equations [27], and delayed differential equations [28]. In this paper, the following minimal model of the insulin–glucose regulatory system is used to design suboptimal insulin injection rules for T1D patients.…”

Section: Mathematical Model Of Type 1 Diabetesmentioning

confidence: 99%

Blood glucose concentration control for type 1 diabetic patients: a non‐linear suboptimal approach

Batmani

2017

IET syst. biol.

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In this study, a closed-loop treatment strategy is proposed for the control of blood glucose levels in type 1 diabetic patients. Toward this end, a non-linear technique for designing suboptimal tracking controllers, called the state-dependent Riccati equation tracker, is used based on a mathematical model of the glucose-insulin regulatory system. Since two state variables of the utilised model are not available to the controller, a non-linear filter is also designed to estimate these variables using the measured blood glucose concentration. Effects of unannounced meals and regular exercise are investigated for a nominal patient and nine diabetic patients with unknown parameters. Numerical simulations are given to show the effectiveness of the proposed treatment strategy even in the presence of parametric uncertainties and the observation noise.

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“…Moreover, the effect of physical exercise on the dynamics of glucose and insulin has been investigated [30], thus it is interesting to show how does this affects the dynamics if we put this into our proposed models. Recently, non-smooth dynamic systems or Filippov systems have been applied widely in many fields of science [31][32][33], as a result, the dynamical behaviors of the glucose-insulin system could be investigated more clearly once we consider such models. Consequently, to address these with the aim of improving strategies for the treatment of diabetes, such research is planned for the near future and will be reported elsewhere.…”

Section: A C C E P T E D Mmentioning

confidence: 99%

The regulatory system for diabetes mellitus: Modeling rates of glucose infusions and insulin injections

Tang

Cheke

2016

Communications in Nonlinear Science and Numerical Simulation

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Highlights• We develop novel glucose-insulin systems modeling rates of glucose infusions and insulin injections.• The periodic solution for type 1 and permanence for type 2 diabetes of the system have been studied.• The results showed that the period, the frequency and the dose of glucose infusions and insulin injections are crucial.• The blood concentration can be controlled within a normal range using the proposed models. AbstractNovel mathematical models with open and closed-loop control for type 1 or type 2 diabetes mellitus were developed to improve understanding of the glucose-insulin regulatory system. A hybrid impulsive glucose-insulin model with different frequencies of glucose infusions and insulin injections was analyzed, and the existence and uniqueness of the positive periodic solution for type 1 diabetes, which is globally asymptotically stable, was studied analytically. Moreover, permanence of the system for type 2 diabetes was demonstrated which showed that the glucose concentration level is uniformly bounded above and below. To investigate how to prevent hyperinsulinemia and hyperglycaemia being caused by this system, we developed a model involving periodic intakes of glucose with insulin injections applied only when the blood glucose level reached a given critical glucose threshold. In addition, our numerical analysis revealed that the period, the frequency and the dose of glucose infusions and insulin injections are crucial for insulin therapies, and the results provide clinical strategies for insulin-administration practices.

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Modelling the regulatory system for diabetes mellitus with a threshold window

Cited by 13 publications

References 38 publications

Glucose–insulin stabilization in type-1 diabetic patient: A uniform exact differentiator–based robust integral sliding mode control approach

Glucose–insulin stabilization in type-1 diabetic patient: A uniform exact differentiator–based robust integral sliding mode control approach

Blood glucose concentration control for type 1 diabetic patients: a non‐linear suboptimal approach

The regulatory system for diabetes mellitus: Modeling rates of glucose infusions and insulin injections

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