Simulating and predicting glucose response in lean and obese mice

Brenner, M. Harvey; Kwon, Guim; Lee, H. F.; Johns, Michael; Malik, Nehal

doi:10.1109/nebec.2014.6972740

Cited by 2 publications

(2 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proposed mathematical model to study was presented in [6] and initially introduced in [7]: background values rise through validated in-vivo experiments which eventually demonstrated that the model represents through time adequately changes of plasma glucose and insulin levels. Moreover, the model was used as a reference to evaluate changes in glucose homeostasis in other studies, [8,9]. This work with the following sections is organized.…”

mentioning

confidence: 99%

WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

Gamboa

Coria

Valle

2021

Preprint

View full text Add to dashboard Cite

This work aims to analyze a fifth-order nonlinear ordinary differential equations that describe the glucoregulatory model system based on intravenous injection of glucose via in-vivo experimentation in rats reported previously in the literature. A mathematical analysis shows that existence of an invariant plane condition associated with insulin can determine a type 1 or type 2 diabetes classification. The bounded positive invariant domain (BPID) by applying the Lyapunov direct method establishes a mathematical preamble where maximum cell population is associated to an upper bound set given by a localizing function by applying the LCIS (Localizing Compact Invariant Set) method. Furthermore, an equilibrium point's existing condition is defined if U(t) is an invariant plane and H(G) exists. Also are discussed parameter conditions for renal glucose excretion (k5) and the rate constant of glucose absorption (ka) as a case of study when glycemia function presents existence conditions with or without insulin variable.

show abstract

mentioning

confidence: 99%

WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

Gamboa

Coria

Valle

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The numerical values of parameters were estimated by in vivo experimentation; thus, background values were validated in vivo, showing a good approximation to the time-series of the real measurements of insulin levels and plasma glucose. Although this model was initially introduced in [16], it was used as a reference to evaluate the time series of glucose homeostasis in other kinds of studies [17,18]. Modeling, analysis, and in silico experimentation for diabetes mellitus are valuable tools that allows better understanding of the complicated nature of this disease.…”

Section: Recent Contributions Ode Model Description and Proposed Anal...mentioning

confidence: 99%

Ultimate Bounds for a Diabetes Mathematical Model Considering Glucose Homeostasis

Gamboa

Coria

Valle

2022

Axioms

View full text Add to dashboard Cite

This paper deals with a recently reported mathematical model formulated by five first-order ordinary differential equations that describe glucoregulatory dynamics. As main contributions, we found a localization domain with all compact invariant sets; we settled on sufficient conditions for the existence of a bounded positively-invariant domain. We applied the localization of compact invariant sets and Lyapunov’s direct methods to obtain these results. The localization results establish the maximum cell concentration for each variable. On the other hand, Lyapunov’s direct method provides sufficient conditions for the bounded positively-invariant domain to attract all trajectories with non-negative initial conditions. Further, we illustrate our analytical results with numerical simulations. Overall, our results are valuable information for a better understanding of this disease. Bounds and attractive domains are crucial tools to design practical applications such as insulin controllers or in silico experiments. In addition, the model can be used to understand the long-term dynamics of the system.

show abstract

Simulating and predicting glucose response in lean and obese mice

Cited by 2 publications

References 2 publications

WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

Ultimate Bounds for a Diabetes Mathematical Model Considering Glucose Homeostasis

Contact Info

Product

Resources

About