Analysis of a model of the glucose-insulin regulatory system with two delays

Jiaxu Li, Yang Kuang

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

We continue a recent attempt to better understand the glucose-insulin regulatory system via a mathematical model of delay differential equations with two discrete time delays. With explicit delays, the model is more realistic in physiology, more accurate in mathematics, and more robust in applications. We study this model analytically and perform carefully designed numerical simulations by allowing two parameters to vary. Our analytical and numerical results confirm most current existing physiological observations and reveal more insightful information. The following factors are critical for ensuring the sustained oscillatory regulation and insulin secretion: (1) the time lag for insulin secretion stimulated by glucose and the newly synthesized insulin becoming "remote insulin" (Theorem 4.2 (b) and Theorem 5.6); (2) the delayed effect of hepatic glucose production (Theorem 4.2 (c) and Theorem 5.6); (3) moderate insulin clearance rate (Theorem 5.6 and simulations in section 6.4); and (4) nonoverwhelming glucose infusion (simulations in section 6.2, 6.3, and 6.4).

Original languageEnglish (US)
Pages (from-to)757-776
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume67
Issue number3
DOIs
StatePublished - 2007

Fingerprint

Insulin
Glucose
Theorem
Secretion
Model
Time Lag
Physiology
Clearance
Delay Differential Equations
Two Parameters
Time delay
Simulation
Discrete-time
Differential equations
Continue
Vary
Mathematical Model
Mathematical models
Numerical Simulation
Numerical Results

Keywords

  • Glucose-insulin regulatory system
  • Insulin secretion
  • Time delay
  • Ultradian oscillation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Analysis of a model of the glucose-insulin regulatory system with two delays. / Li, Jiaxu; Kuang, Yang.

In: SIAM Journal on Applied Mathematics, Vol. 67, No. 3, 2007, p. 757-776.

Research output: Contribution to journalArticle

@article{fcfbc861ebd84843b4fef4418896e134,
title = "Analysis of a model of the glucose-insulin regulatory system with two delays",
abstract = "We continue a recent attempt to better understand the glucose-insulin regulatory system via a mathematical model of delay differential equations with two discrete time delays. With explicit delays, the model is more realistic in physiology, more accurate in mathematics, and more robust in applications. We study this model analytically and perform carefully designed numerical simulations by allowing two parameters to vary. Our analytical and numerical results confirm most current existing physiological observations and reveal more insightful information. The following factors are critical for ensuring the sustained oscillatory regulation and insulin secretion: (1) the time lag for insulin secretion stimulated by glucose and the newly synthesized insulin becoming {"}remote insulin{"} (Theorem 4.2 (b) and Theorem 5.6); (2) the delayed effect of hepatic glucose production (Theorem 4.2 (c) and Theorem 5.6); (3) moderate insulin clearance rate (Theorem 5.6 and simulations in section 6.4); and (4) nonoverwhelming glucose infusion (simulations in section 6.2, 6.3, and 6.4).",
keywords = "Glucose-insulin regulatory system, Insulin secretion, Time delay, Ultradian oscillation",
author = "Jiaxu Li and Yang Kuang",
year = "2007",
doi = "10.1137/050634001",
language = "English (US)",
volume = "67",
pages = "757--776",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",

}

TY - JOUR

T1 - Analysis of a model of the glucose-insulin regulatory system with two delays

AU - Li, Jiaxu

AU - Kuang, Yang

PY - 2007

Y1 - 2007

N2 - We continue a recent attempt to better understand the glucose-insulin regulatory system via a mathematical model of delay differential equations with two discrete time delays. With explicit delays, the model is more realistic in physiology, more accurate in mathematics, and more robust in applications. We study this model analytically and perform carefully designed numerical simulations by allowing two parameters to vary. Our analytical and numerical results confirm most current existing physiological observations and reveal more insightful information. The following factors are critical for ensuring the sustained oscillatory regulation and insulin secretion: (1) the time lag for insulin secretion stimulated by glucose and the newly synthesized insulin becoming "remote insulin" (Theorem 4.2 (b) and Theorem 5.6); (2) the delayed effect of hepatic glucose production (Theorem 4.2 (c) and Theorem 5.6); (3) moderate insulin clearance rate (Theorem 5.6 and simulations in section 6.4); and (4) nonoverwhelming glucose infusion (simulations in section 6.2, 6.3, and 6.4).

AB - We continue a recent attempt to better understand the glucose-insulin regulatory system via a mathematical model of delay differential equations with two discrete time delays. With explicit delays, the model is more realistic in physiology, more accurate in mathematics, and more robust in applications. We study this model analytically and perform carefully designed numerical simulations by allowing two parameters to vary. Our analytical and numerical results confirm most current existing physiological observations and reveal more insightful information. The following factors are critical for ensuring the sustained oscillatory regulation and insulin secretion: (1) the time lag for insulin secretion stimulated by glucose and the newly synthesized insulin becoming "remote insulin" (Theorem 4.2 (b) and Theorem 5.6); (2) the delayed effect of hepatic glucose production (Theorem 4.2 (c) and Theorem 5.6); (3) moderate insulin clearance rate (Theorem 5.6 and simulations in section 6.4); and (4) nonoverwhelming glucose infusion (simulations in section 6.2, 6.3, and 6.4).

KW - Glucose-insulin regulatory system

KW - Insulin secretion

KW - Time delay

KW - Ultradian oscillation

UR - http://www.scopus.com/inward/record.url?scp=34547339786&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547339786&partnerID=8YFLogxK

U2 - 10.1137/050634001

DO - 10.1137/050634001

M3 - Article

AN - SCOPUS:34547339786

VL - 67

SP - 757

EP - 776

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

ER -