The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Modeling the glucose–insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays
Abstract
In the glucose-insulin regulatory system, ultradian insulin secretory oscillations are observed to have a period of 50-150 min. After pioneering work traced back to the 1960s, several mathematical models have been proposed during the last decade to model these ultradian oscillations as well as the metabolic system producing them. These currently existing models still lack some of the key physiological aspects of the glucose-insulin system. Applying the mass conservation law, we introduce two explicit time delays and propose a more robust alternative model for better understanding the glucose-insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. We compare the simulation profiles obtained from this two time delay model with those from the other existing models. As a result, we notice many unique features of this two delay model. Based on our intensive simulations, we suspect that one of the possibly many causes of ultradian insulin secretion oscillations is the time delay of the insulin secretion stimulated by the elevated glucose concentration.
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In the citing paper
“Time delays, which are common in modeling the metabolic system (82–85), may induce uncertainty and make machine learning challenging to capture chaotic phenomena (86, 87).”
From The progression of secondary diabetes: A review of modeling studies (2022) · cites this paper as [85]
In the citing paper
“Both Sturis' and Li's models simulated earlier glucose oscillation than insulin oscillation.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
In the citing paper
“For example, Li's model predicted the time difference between glucose and insulin peak levels to be about 20 min, which also depended on the glucose infusion rate.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
In the citing paper
“It was confirmed that the simulated oscillation amplitudes of blood glucose and insulin in the current model were within the amplitude ranges predicted by Li's model.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
In the citing paper
“Li's model demonstrated that both the oscillation amplitude of blood glucose and that of blood insulin depended on the glucose infusion rate.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
In the citing paper
“Such assumption is acceptable in a mathematical approach because the shapes of the functions, instead of their mathematical forms, are more important [8].”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
In the citing paper
“The model simulation results are consistent with those of currently existing theoretical models, such as the models of Sturis et al. and Li et al. [7,8], both of which were developed to mimic experimental findings of ultradian oscillations during constant glucose infusion.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
In the citing paper
“The hypothesis that ultradian insulin secretion represents an instability in peripheral GIG interactions has been the subject of a number of studies, including the mathematical model originally proposed by Sturis et al. and lately modified by Li et al. [7,8], where time-delay is included implicitly or explicitly to produce ultradian oscillation.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
In the citing paper
“The present model has similar characteristics of the models of Sturis et al. and Li et al. [7,8], in simulating ultradian oscillation, without including any time-delay.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
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Sorted by citations
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Metadata
- Authors
- Li, J., Kuang, Y., & Mason, C. C.
- Affiliations
- Arizona State University (US)
- Corresponding author
- Li, Jiaxu
- Venue
- Journal of Theoretical Biology
- Publisher
- Elsevier BV
- Published
- 2006-10
- Volume
- 242
- Issue
- 3
- Pages
- 722-735
- ISSN
- 0022-5193 (ISSN-L)
- OpenAlex
- W2161967671
- Cited by
- 241
- References
- 25
- Citations by year
- 2026: 15 · 2025: 15 · 2024: 11 · 2023: 8 · 2022: 16 · 2021: 12 · 2020: 19 · 2019: 15 · 2018: 9 · 2017: 13 · 2016: 14 · 2015: 14 · 2014: 20 · 2013: 8 · 2012: 10
- FWCI
- 8.50
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Theoretical Biology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Pancreatic function and diabetes
- Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Diabetes Management and Research
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
- Keywords
- glucose-insulin regulatory system, time delay model, insulin secretion, mass conservation, enteral nutrition, glucose infusion
- MeSH terms
- Insulin Secretion, Activity Cycles, Computer Simulation, Diabetes Mellitus, Type 2, Enteral Nutrition, Glucose, Humans, Insulin, Islets of Langerhans, Liver, Models, Biological, Secretory Rate, Time Factors
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