Finite-time control of plasma glucose in insulin therapies for diabetes

Liu, Shouzong; Huang, Mingzhan; Song, Xinyu; Shi, Xiangyun

doi:10.1186/s13662-018-1532-z

Cited by 3 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we formulated a novel switched impulsive dynamical system and used optimal control theory to study therapy protocols for diabetics with insulin pump in a limited time. Compared with model proposed in [20], our new model considers not only the endpoint control of plasma glucose level but also the fluctuations during the control process, which is in more accordance with the actual situation. Taking into account both the fluctuations of plasma glucose level and the amount of insulin injected, we investigated three therapy strategies for two different objective functions.…”

Section: Resultsmentioning

confidence: 95%

“…To the best of our knowledge, very few works on the limited time control of glucose concentration have been done. The work [20] studied a finite-time control of the plasma glucose level, which focuses on the glucose level at the terminate time of control but ignores the fluctuation during the control process. It is worth pointing out that the ignorance of extreme fluctuations of glucose concentration during control process may have undesirable consequences in the clinic.…”

Section: Model Formulationmentioning

confidence: 99%

“…and according to equation (10), we have Then equations (17) and (20) can be transformed respectively into…”

Section: Optimal Injection Strategies and Numerical Simulationsmentioning

confidence: 99%

See 2 more Smart Citations

Optimal selection of injection doses and injection timings for insulin therapy in a limited time

Liu

Huang

et al. 2020

Adv Differ Equ

Self Cite

View full text Add to dashboard Cite

In this paper, we study the injection strategies of insulin for the impulsive therapy of diabetes in a limited time. According to whether we consider the risk of hypoglycemia or not, we develop two different control objectives and investigate three different injection strategies for each control objective. We apply a time-rescaling method to overcome technical obstacles in optimal impulsive control and compute the gradient formulas of cost functions with respect to injection doses and injection timings. By means of numerical simulations we get the optimal injection doses and injection timings for each injection strategy. Our study indicates that for the control objective without considering the risk of hypoglycemia, the optimal injection timing control is more effective than the optimal injection dose control, whereas the mixed control achieves almost the same effect as the optimal injection timing control. For the other control objective considering the risk of hypoglycemia, the optimal injection timing control performs better than the optimal injection dose control in avoiding emergence of hypoglycemia, and the mixed control provides the best strategy in preventing hyperglycemia from occurrence.

show abstract

Section: Resultsmentioning

confidence: 95%

Section: Model Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Optimal selection of injection doses and injection timings for insulin therapy in a limited time

Liu

Huang

et al. 2020

Adv Differ Equ

Self Cite

View full text Add to dashboard Cite

show abstract

A Caputo Fabrizio fractional order model for control of glucose in insulin therapies for diabetes

Saleem

Farman

Ahmad

et al. 2020

Ain Shams Engineering Journal

View full text Add to dashboard Cite

On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense

Yao

Rashid

İnç

et al. 2022

MATH

View full text Add to dashboard Cite

<abstract><p>Very recently, several novel conceptions of fractional derivatives have been proposed and employed to develop numerical simulations for a wide range of real-world configurations with memory, background, or non-local effects via an uncertainty parameter $ [0, 1] $ as a confidence degree of belief. Under the complexities of the uncertainty parameter, the major goal of this paper is to develop and examine the Atangana-Baleanu derivative in the Caputo sense for a convoluted glucose-insulin regulating mechanism that possesses a memory and enables one to recall all foreknowledge. However, as compared to other existing derivatives, this is a vitally important point, and the convenience of employing this derivative lessens the intricacy of numerical findings. The Atangana-Baleanu derivative in the Caputo sense of fuzzy valued functions (FVF) in parameterized interval representation is established initially in this study. Then, it is leveraged to demonstrate that the existence and uniqueness of solutions were verified using the theorem suggesting the Banach fixed point and Lipschitz conditions under generalized Hukuhara differentiability. In order to explore the regulation of plasma glucose in diabetic patients with impulsive insulin injections and by monitoring the glucose level that returns to normal in a finite amount of time, we propose an impulsive differential equation model. It is a deterministic mathematical framework that is connected to diabetes mellitus and fractional derivatives. The framework for this research and simulations was numerically solved using a numerical approach based on the Adams-Bashforth-Moulton technique. The findings of this case study indicate that the fractional-order model's plasma glucose management is a suitable choice.</p></abstract>

show abstract

Finite-time control of plasma glucose in insulin therapies for diabetes

Cited by 3 publications

References 25 publications

Optimal selection of injection doses and injection timings for insulin therapy in a limited time

Optimal selection of injection doses and injection timings for insulin therapy in a limited time

A Caputo Fabrizio fractional order model for control of glucose in insulin therapies for diabetes

On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense

Contact Info

Product

Resources

About