Rapid automatic identification of parameters of the Bergman Minimal Model in Sprague-Dawley rats with experimental diabetes for adaptive insulin delivery

Gallardo-Hernández, Ana Gabriela; González-Olvera, Marcos A.; Revilla-Monsalve, Cristina; Escobar, Jésica; Castellanos-Fuentes, Medardo; Leder, Ron S.

doi:10.1016/j.compbiomed.2019.03.028

Cited by 6 publications

(5 citation statements)

References 33 publications

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“…BMM is a well-known nonlinear intravenous model for T1DM that has been extensively studied in the literature. 31,32 Thus, in this article, an observer-based control using the BMM will be designed. Its equations are presented below:…”

Section: Mathematical Model Of T1dm Patientsmentioning

confidence: 99%

Observer‐based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay

Targui,

Castro‐Gomez,

Hernández‐González

et al. 2024

Numer Methods Biomed Eng

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This article introduces an observer‐based control strategy tailored for regulating plasma glucose in type 1 diabetes mellitus patients, addressing challenges like unknown time‐varying delays and meal disturbances. This control strategy is based on an extended Bergman minimal model, a nonlinear glucose‐insulin model to encompass unknown inputs, such as unplanned meals, exercise disturbances, or delays. The primary contribution lies in the design of an observer‐based state feedback control in the presence of unknown long delays, which seeks to support and enhance the performance of the traditional artificial pancreas by considering realistic scenarios. The observer and control gains for the observer‐based control are computed through linear matrix inequalities formulated from Lyapunov conditions that guarantee closed‐loop stability. This design deploys a soft and gentle dynamic response, similar to a natural pancreas, despite meal disturbances and input delays. Numerical tests demonstrate the scheme's effectiveness in glycemic level regulation and hypoglycemic episode avoidance.

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Section: Mathematical Model Of T1dm Patientsmentioning

confidence: 99%

Observer‐based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay

Targui,

Castro‐Gomez,

Hernández‐González

et al. 2024

Numer Methods Biomed Eng

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“…The parameter 𝜃, corresponding to the insulin-independent glucose disappearance rate, is frequently disregarded when dealing with T1DM. 4,12 Still, such a parameter plays an important role in insulin-glucose dynamics. 17 Moreover, the literature suggests that certain glucagon-like hormones impact the efficiency of 𝜃.…”

Section: Problem Statementmentioning

confidence: 99%

“…The parameter

θ

, corresponding to the insulin‐independent glucose disappearance rate, is frequently disregarded when dealing with T1DM 4,12 . Still, such a parameter plays an important role in insulin‐glucose dynamics 17 .…”

Section: Problem Statementmentioning

confidence: 99%

“…In some cases, the patients must follow a straight and exhaustive preparation before and during the trials (see, e.g., Reference 3). Alternatively, 4 proposes a mathematical approach based on Bergman's Minimal Model (BMM). It consists of a genetic algorithm that identifies some parameters of the BMM in diabetic rats.…”

Section: Introductionmentioning

confidence: 99%

“…It consists of a genetic algorithm that identifies some parameters of the BMM in diabetic rats. The method in Reference 4 identifies the parameters on the fly, but the method is heuristic and lacks a formal convergence proof, therefore, it cannot be combined with a model‐based controller. In the absence of reliable parameters, a possible solution is to design model‐based strategies robust to uncertainties.…”

Section: Introductionmentioning

confidence: 99%

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Parameter identification and state estimation for a diabetic glucose‐insulin model via an adaptive observer

Franco

Ríos

Loza

et al. 2022

Intl J Robust & Nonlinear

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In this article, an adaptive observer is designed for patients with Type 1 Diabetes Mellitus. The adaptive observer, synthesized using the so-called Bergman's Minimal Model, simultaneously estimates the states and the parameter corresponding to the insulin-independent glucose disappearance rate. The adaptive observer deals with parameter uncertainties, whereas the food intake is regarded as an external disturbance. The adaptive observer relies on intravenous glucose measurements. The state estimation error converges to a neighborhood of the origin despite the effects of the external disturbances and uncertainties, while the parameter estimation error converges in a fixed time to a neighborhood of the origin. The adaptive observer synthesis is given by a constructive method based on linear matrix inequalities. Simulation results show the feasibility of the proposed scheme. Moreover, the approach is validated in UVA/Padova metabolic simulator for ten in silico adult patients.

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Minimally-Invasive and Efficient Method to Accurately Fit the Bergman Minimal Model to Diabetes Type 2

et al. 2022

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Rapid automatic identification of parameters of the Bergman Minimal Model in Sprague-Dawley rats with experimental diabetes for adaptive insulin delivery

Cited by 6 publications

References 33 publications

Observer‐based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay

Observer‐based control for plasma glucose regulation in type 1 diabetes mellitus patients with unknown input delay

Parameter identification and state estimation for a diabetic glucose‐insulin model via an adaptive observer

Minimally-Invasive and Efficient Method to Accurately Fit the Bergman Minimal Model to Diabetes Type 2

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