CoChat
Sign Up
Cited by 35Diabetes Management and ResearchNonlinear Differential Equations AnalysisPancreatic function and diabetes

Modeling impulsive insulin delivery in insulin pump with time delays

Song, Xinyu, Huang, Mingzhan, Li, Jiaxu·2014·SIAM Journal on Applied Mathematics
DOI 10.1137/130933137
Open this paper in CoChat — free account

Abstract

We continue our attempt of modeling the open-loop control of glucose level by impulsive insulin injections. Several time delays exist in the system. The delays include the time needed for insulin from injection depot to transport to the interstitial compartment, the time for the slow inhibition of the hepatic glucose production (HGP), and the time for insulin secretion caused by the elevated glucose concentration level from remaining functional pancreatic $\beta$-cells. None of them are negligible. The model proposed in this paper incorporates these time delays. Our analytical studies show that all solutions are permanent, a periodic solution exists, and for the case of type 1 diabetes mellitus the periodic solution is unique and globally asymptotically stable. Numerically it has been shown that moderate time delays in the system are beneficial in lowering blood sugar level rather than harmful. In contrast, these time delays cause that the open-loop control takes a longer time to lower glucose concentration level. Our studies also elucidate the noticeable inhibitory effect on HGP by the remaining functional $\beta$-cells. Similarly to our previous work, we demonstrated that a smaller dose with higher delivery frequency has a better effect on continuous subcutaneous insulin injection administration. We expect that our findings are helpful for clinical therapies.

Integrity signals

Registry

Crossref · 10.1137/130933137

Cites

57 of 57 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Time delays are common in modeling the metabolic system.

    “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 [83]

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Related

Authors
Song, X., Huang, M., & Li, J.
ORCID
Venue
SIAM Journal on Applied Mathematics
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2014-01
Volume
74
Issue
6
Pages
1763-1785
ISSN
  • 0036-1399 (ISSN-L)
  • 1095-712X
DOI
10.1137/130933137
OpenAlex
W2059261651
Cited by
35
References
57
Citations by year
2026: 3 · 2025: 3 · 2024: 4 · 2023: 5 · 2022: 4 · 2021: 3 · 2020: 4 · 2019: 3 · 2018: 3 · 2017: 1 · 2016: 2
FWCI
0.80
Type
journal article
Language
en
Open access
closed
Locations
SIAM Journal on Applied Mathematics (publishedVersion)
Topics
  • Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Diabetes Management and Research
  • Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
  • Health Sciences › Medicine › Surgery › Pancreatic function and diabetes
Keywords
insulin pump, time delay, glucose-insulin dynamics, type 1 diabetes, hepatic glucose production, pancreatic beta-cell insulin secretion, periodic solutions, global asymptotic stability, insulin pump therapy, blood glucose regulation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review