Mathematical model of glucose–insulin homeostasis in healthy rats

Lombarte, Mercedes; Lupo, Maela; Campetelli, Germán; Basualdo, Marta; Rigalli, Alfredo

doi:10.1016/j.mbs.2013.07.017

Cited by 17 publications

(22 citation statements)

References 12 publications

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“…We used the mathematical model of glucose-insulin homeostasis originally proposed by Lombarte et al [14] to study the extent to which the parameters determine glucose-insulin homeostasis differ between lean and HFD-fed mice. The proposed model consists of three differential equations that describe the changes of blood glucose (G), blood insulin (I), and the amount of glucose (D) in the peritoneal cavity over time.dG/dt = -k 4 (I − I pi ) − k 2 I − k 3 + k 0 D (1)dI/dt = k 1 G − k 6 I (2)dD/dt = -k a D (3)…”

Section: Methodsmentioning

confidence: 99%

“…The term k 4 (I − I pi ), thus, is positive when glucose is taken up into the liver (when I > I pi ) but negative when glucose is released into the circulation from the liver (when I < I pi ). I represents blood insulin concentration, I pi represents blood insulin concentration when the liver changes from the release to the uptake of glucose, and k 4 is the rate constant of uptake or release of glucose by the liver as described in the original paper by Lombarte et al [14]. The k 2 I term represents the insulin-dependent glucose uptake by the tissues including muscle, adipocytes, and liver.…”

Section: Methodsmentioning

confidence: 99%

“…Detailed descriptions of mathematical analysis and parameter estimation are reported in the original paper by Lombarte et al [14]. Since we adopted the same model, mathematical analysis and parameter estimation are identical,…”

Section: Methodsmentioning

confidence: 99%

“…The mathematical model consisting of three differential equations and 9 parameters that describe key components of glucose-insulin homeostasis was first reported and validated in healthy rats by Lomarte et al [14]. Accurate estimation of the rate constants determine glucose-insulin homeostasis in patients may be used for customized drug therapy for patients with T2DM as well as developing individually customized algorithms for the APD systems for patients with T1DM and subpopulations of T2DM.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Estimation of insulin secretion, glucose uptake by tissues, and liver handling of glucose using a mathematical model of glucose-insulin homeostasis in lean and obese mice

Brenner

Abadi

Balouchzadeh

et al. 2017

Heliyon

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Destruction of the insulin-producing β-cells is the key determinant of diabetes mellitus regardless of their types. Due to their anatomical location within the islets of Langerhans scattered throughout the pancreas, it is difficult to monitor β-cell function and mass clinically. To this end, we propose to use a mathematical model of glucose-insulin homeostasis to estimate insulin secretion, glucose uptake by tissues, and hepatic handling of glucose. We applied the mathematical model by Lombarte et al. (2013) to compare various rate constants representing glucose-insulin homeostasis between lean (11% fat)- and high fat diet (HFD; 45% fat)-fed mice. Mice fed HFD (n = 12) for 3 months showed significantly higher body weights (49.97 ± 0.52 g vs. 29.86 ± 0.46 g), fasting blood glucose levels (213.08 ± 10.35 mg/dl vs. 121.91 ± 2.26 mg/dl), and glucose intolerance compared to mice fed lean diet (n = 12). Mice were injected with 1 g/kg glucose intraperitoneally and blood glucose levels were measured at various intervals for 120 min. We performed simulation using Arena™ software based on the mathematical model and estimated the rate constants (9 parameters) for various terms in the differential equations using OptQuest™. The simulated data fit accurately to the observed data for both lean and obese mice, validating the use of the mathematical model in mice at different stages of diabetes progression. Among 9 parameters, 5 parameters including basal insulin, k2 (rate constant for insulin-dependent glucose uptake to tissues), k3 (rate constant for insulin-independent glucose uptake to tissues), k4 (rate constant for liver glucose transfer), and Ipi (rate constant for insulin concentration where liver switches from glucose release to uptake) were significantly different between lean- and HFD-fed mice. Basal blood insulin levels, k3, and Ipi were significantly elevated but k2 and k4 were reduced in mice fed a HFD compared to those fed a lean diet. Non-invasive assessment of the key components of glucose-insulin homeostasis including insulin secretion, glucose uptake by tissues, and hepatic handling of glucose may be helpful for individualized drug therapy and designing a customized control algorithm for the artificial pancreas.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of insulin secretion, glucose uptake by tissues, and liver handling of glucose using a mathematical model of glucose-insulin homeostasis in lean and obese mice

Brenner

Abadi

Balouchzadeh

et al. 2017

Heliyon

View full text Add to dashboard Cite

show abstract

“…In spite -or because-of this, some simplified models have also been developed for blood glucose control. For instance, Lombarte et al [21] proposed a mathematical model given by third-order differential equations with eight identifiable parameters representing inter-and intra-individual properties of glucose-insulin metabolism. For blood glucose control purposes, fairly simplified models that represent the most significant processes of glucose-insulin metabolism are most preferred, and thus more studies in this area are expected in the upcoming years.…”

Section: Mathematical Models Of Glucose-insulin Metabolismmentioning

confidence: 99%

Recent Trends in Blood Glucose Control Studies

2015

Automat Control Physiol State Func

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Diabetes mellitus is a disease of the endocrine system in which blood glucose levels are constantly above the normal range. Since insulin-dependent diabetic patients require insulin administration to maintain blood glucose levels within the normal range, automatic blood glucose control methods to reduce the burden of such open-loop insulin therapy have been studied. In this review, we first introduce some important mathematical models of glucoseinsulin metabolism, followed by some representative blood glucose control systems, where most of them use model predictive control as control algorithm, developed to date and discuss their implications in the near future.

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An adaptive technique based blood glucose control in type‐1 diabetes mellitus patients

Belmon¹,

Auxillia

2020

Numer Methods Biomed Eng

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This study proposes Grasshopper Optimization Algorithm (GOA) based type 1 diabetes mellitus system utilizing the nonlinear Bergman minimal model with proportional integral derivative (PID) controller. GOA is the optimization algorithm, which is utilized for selecting the optimized tuning parameters of the PID controller also solves the nonlinear system parameter identification problem. The novelty of the proposed study is to stabilize the glucose level in blood for type 1 diabetic patients by infusion of insulin in reduced time with optimal quantity. Without any intervention to the normal activities of patients, the supply of insulin injection and glucose monitoring is performed automatically for type 1 diabetic patients using this controller. In between the measured variable and set point, the difference is calculated by the PID controller to evaluate an error values. In realistic patient oriented conditions, the control performance evaluation, control optimization, and advanced patient modelling should be highly concentrated during the research/analysis on blood glucose control. Evaluation is performed to analyze control performances and implementation is done on Simulink/MATLAB environment. The performance analysis of the type 1 diabetes mellitus system with GOA technique is also discussed and to improve the control performance, to optimize the controller parameters. The simulation results have proved the substantial improvement in the performance of proposed algorithm with the better results achieved than the other conventional controllers such as PSO‐PID and EHO‐PID.

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Mathematical model of glucose–insulin homeostasis in healthy rats

Cited by 17 publications

References 12 publications

Estimation of insulin secretion, glucose uptake by tissues, and liver handling of glucose using a mathematical model of glucose-insulin homeostasis in lean and obese mice

Estimation of insulin secretion, glucose uptake by tissues, and liver handling of glucose using a mathematical model of glucose-insulin homeostasis in lean and obese mice

Recent Trends in Blood Glucose Control Studies

An adaptive technique based blood glucose control in type‐1 diabetes mellitus patients

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