Modeling Impulsive Injections of Insulin: Towards Artificial Pancreas

Huang, Mingzhan; Li, Jiaxu; Song, Xinyu; Guo, Hongjian

doi:10.1137/110860306

Cited by 111 publications

(101 citation statements)

References 24 publications

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“…In addition, all parameters are positive (for details see [13]), with initial condition G(0) = G 0 > 0, I(0) = I 0 > 0. τ is the period of the impulsive injection of insulin, σ denotes the dose of insulin in each injection applied as an impulse at discrete times t = hτ, h ∈ Z + = {1, 2, 3, ...}.…”

Section: Ag(t)(c + Mi(t)/(n + I(t))mentioning

confidence: 99%

“…The parameter values for models (1.2) and (1.3) (provided in Table 1) used in our simulations were either determined by previous research [3,4,13,34,35], or obtained from models for the intravenous glucose tolerance test (IVGTT) [35][36][37]. We converted units as appropriate and adjusted the values to be within reasonable ranges.…”

Section: Bifurcation Analysis and Biological Implications Of Filippovmentioning

confidence: 99%

“…An artificial pancreas, which is still being developed would function like a real and healthy pancreas allowing diabetic patients to control their blood glucose levels within a normal range automatically [13]. With the help of such an artificial pancreas, patients could improve their life-styles without injecting insulin manually or measuring the glucose infusion rate.…”

Section: Introductionmentioning

confidence: 99%

“…With the help of such an artificial pancreas, patients could improve their life-styles without injecting insulin manually or measuring the glucose infusion rate. However, there are two major impediments to the development of an artificial pancreas including the need for reliable predictive models and the lack of effective and efficient control algorithms [12,13]. To overcome these problems, several reliable mathematical models of delay differential equations which can de-termine the time and the dose of insulin injections for control algorithms have been proposed and investigated [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, pulsatile insulin secretion has been employed to mimic impulsive injections for type 1 or type 2 diabetes mellitus treatment regimes [15,16]. Recently, Huang et al devised a new mathematical model with open-loop control considering impulsive injection of insulin either periodically or by monitoring the plasma glucose concentration level [13]. The model can be described by…”

Section: Introductionmentioning

confidence: 99%

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Modelling the regulatory system for diabetes mellitus with a threshold window

Tang

Cheke

2015

Communications in Nonlinear Science and Numerical Simulation

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Please cite this article as: Yang, J., Tang, S., Cheke, R.A., Modelling the regulatory system for diabetes mellitus with a threshold window, Communications in Nonlinear Science and Numerical Simulation (2014), doi: http:// dx.doi.org/10.1016/j.cnsns. 2014.08.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Modelling the regulatory system for diabetes mellitus with a threshold window AbstractPiecewise (or non-smooth) glucose-insulin models with threshold windows for type 1 and type 2 diabetes mellitus are proposed and analyzed with a view to improving understanding of the glucose-insulin regulatory system. For glucose-insulin models with a single threshold, the existence and stability of regular, virtual, pseudo-equilibria and tangent points are addressed. Then the relations between regular equilibria and a pseudo-equilibrium are studied. Furthermore, the sufficient and necessary conditions for the global stability of regular equilibria and the pseudo-equilibrium are provided by using qualitative analysis techniques of non-smooth Filippov dynamic systems. Sliding bifurcations related to boundary node bifurcations were investigated with theoretical and numerical techniques, and insulin clinical therapies are discussed. For glucose-insulin models with a threshold window, the effects of glucose thresholds or the widths of threshold windows on the durations of insulin therapy and glucose infusion were addressed. The duration of the effects of an insulin injection is sensitive to the variation of thresholds. Our results indicate that blood glucose level can be maintained within a normal range using piecewise glucose-insulin models with a single threshold or a threshold window. Moreover, our findings suggest that it is critical to individualize insulin therapy for each patient separately, based on initial blood glucose levels.

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Section: Ag(t)(c + Mi(t)/(n + I(t))mentioning

confidence: 99%

Section: Bifurcation Analysis and Biological Implications Of Filippovmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modelling the regulatory system for diabetes mellitus with a threshold window

Tang

Cheke

2015

Communications in Nonlinear Science and Numerical Simulation

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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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Sturm‐Picone comparison theorems for nonlinear impulsive differential equations with discontinuous solutions

Kayar

Masiha

2017

Math Methods in App Sciences

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The nonlinear versions of Sturm-Picone comparison theorem as well asLeighton's variational lemma and Leighton's theorem for regular and singular nonlinear impulsive differential equations with discontinuous solutions having fixed moments of impulse actions are established. Although discontinuity of the solutions causes some difficulties, these new comparison theorems cover the old ones where impulse effects are dropped.

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Modeling Impulsive Injections of Insulin: Towards Artificial Pancreas

Cited by 111 publications

References 24 publications

Modelling the regulatory system for diabetes mellitus with a threshold window

Modelling the regulatory system for diabetes mellitus with a threshold window

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

Sturm‐Picone comparison theorems for nonlinear impulsive differential equations with discontinuous solutions

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