Amplitude and frequency variation in nonlinear glucose dynamics with multiple delays via periodic perturbation

Bridgewater, Adam, Huard, Benoit and Angelova, Maia (2020) Amplitude and frequency variation in nonlinear glucose dynamics with multiple delays via periodic perturbation. Journal of Nonlinear Science, 30 (3). pp. 737-766. ISSN 0938-8974

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Official URL: https://doi.org/10.1007/s00332-020-09612-1

Abstract

Characterising the glycemic response to a glucose stimulus is an essential tool for detecting deficiencies in humans such as diabetes. In the presence of a constant glucose infusion in healthy individuals, it is known that this control leads to slow oscillations as a result of feedback mechanisms at the organ and tissue level. In this paper, we provide a novel quantitative description of the dependence of this oscillatory response on the physiological functions. This is achieved through the study of a model of the ultradian oscillations in glucose-insulin regulation which takes the form of a nonlinear system of equations with two discrete delays. While studying the behaviour of solutions in such systems can be mathematically challenging due to their nonlinear structure and non-local nature, a particular attention is given to the periodic solutions of the model. These arise from a Hopf bifurcation which is induced by an external glucose stimulus and the joint contributions of delays in pancreatic insulin release and hepatic glycogenesis. The effect of each physiological subsystem on the amplitude and period of the oscillations is exhibited by performing a perturbative analysis of its periodic solutions. It is shown that assuming the commensurateness of delays enables the Hopf bifurcation curve to be characterised by studying roots of linear combinations of Chebyshev polynomials. The resulting expressions provide an invaluable tool for studying the interplay between physiological functions and delays in producing an oscillatory regime, as well as relevant information for glycemic control strategies.

Item Type: Article
Uncontrolled Keywords: Delay differential equations, Periodic solutions, Perturbationmethod, Glucose regulation, Diabetes.
Subjects: C900 Others in Biological Sciences
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Elena Carlaw
Date Deposited: 09 Oct 2019 13:10
Last Modified: 14 Oct 2020 15:45
URI: http://nrl.northumbria.ac.uk/id/eprint/41057

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