Mathematical investigation of diabetically impaired ultradian oscillations in the glucose–insulin regulation

Huard, Benoît; Bridgewater, Adam; Angelova, Maia

doi:10.1016/j.jtbi.2017.01.039

Cited by 12 publications

(11 citation statements)

References 39 publications

(66 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, as in previous studies [11,12,10,13,14] the functions f 1 , f 2 , f 4 are monotonically increasing while f 5 is monotonically decreasing, in line with clinical observations (see [4] and references therein). Under these conditions, it is easily shown that system (1) always possesses a strictly positive steady state (Ḡ,Ī) (see e.g.…”

Section: The Two-delay Modelsupporting

confidence: 90%

“…For a given diabetic state, namely for fixed (α, β), we can look at the recalibration of several parameters to achieve this goal. As was shown in [14] and recalled below, recalibrating γ and d i individually allows us to achieve both goals for a range of diabetic states. We then evaluate the possibility of combining both strategies.…”

Section: Restoring Healthy Regulationmentioning

confidence: 96%

See 1 more Smart Citation

Ultradian rhythms in glucose regulation: A mathematical assessment

Bridgewater

Stringer

Huard

et al. 2019

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

Glucose regulation is an essential function of the human body which enables energy to be effectively utilized by the brain, organs and muscles. This regulation operates in a cyclic manner, in different periodic regimes. Indeed, ultradian rhythms with a period of 70 to 150 minutes have been clinically observed in healthy patients under various glucose stimulation patterns. Various models of these oscillations in plasma glucose and insulin have shown that the presence of two delays in hepatic glycogenesis and pancreatic insulin secretion provide a pathway for explaining these oscillations. The efficacy of this control is typically reduced in the presence of diabetes. In this contribution, we adopt the presence and the accurate tuning of ultradian rhythms as a criterion for healthy glucose regulation. We then investigate a model with two delays of these ultradian rhythms which incorporates parameters accounting for insulin sensitivity and insulin secretion. Additionally, the effect of diabetic deficiencies on this feedback loop is explored by quantifying the joint contribution of delays and diabetic parameters on the limit cycle of this model, which is generated through a Hopf bifurcation. Strategies for restoring an oscillatory regime in a physiologically appropriate range are discussed. Finally, a simple polynomial model of the oscillations is introduced to give further insight into the influence of each physiological subsystem. The approach provides a quantified relationship between diabetic impairments and the plasma glucose-insulin feedback loop.

show abstract

Section: The Two-delay Modelsupporting

confidence: 90%

Section: Restoring Healthy Regulationmentioning

confidence: 96%

Ultradian rhythms in glucose regulation: A mathematical assessment

Bridgewater

Stringer

Huard

et al. 2019

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

show abstract

“…To answer this question, we introduce a perturbative scheme for the periodic solutions of a two-compartment delay differential equation (DDE) model of the ultradian rhythms in the glucose-insulin regulatory system based on the Poincaré-Lindstedt (P-L) method. The model is a polynomial expansion of the system presented in Huard et al (2017), which was originally created in Sturis et al (1991). A large number of authors developed and studied this model to characterise its local and global stability properties and characterise its periodic solutions (Bennett and Gourley 2004;Engelborghs et al 2001;Giang et al 2008;Huard et al 2015;Kissler et al 2014;Li and Kuang 2007;Li et al 2006;Wang et al 2009).…”

Section: What Is the Effect Of Diabetic Parameters On The Amplitude Amentioning

confidence: 99%

“…As in Huard et al (2017), Huard et al (2015) and Li et al (2006), we shall choose an initial value of b 2 = 0.06 for most numerical computations with the reduced model. The value of b 1 is then obtained as b 1 = b 2ĪḠ −n .…”

Section: Value Of Parametersmentioning

confidence: 99%

“…As discussed in O' Meara et al (1993), insulin resistance has been observed to gradually dampen the oscillations, culminating in a loss of synchronisation between glucose and insulin. While insulin resistance may be present in patients without diabetes, it is generally associated with patients with type 2 diabetes (T2DM), and so we take the accurate tuning of the ultradian oscillations to be a sign of healthy regulation (Huard et al 2017). We then propose the following question:…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Amplitude and Frequency Variation in Nonlinear Glucose Dynamics with Multiple Delays via Periodic Perturbation

2020

View full text Add to dashboard Cite

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.

show abstract

Delay-Differential Equations for Glucose-Insulin Regulation

Angelova

Shelyag

2021

2019-20 MATRIX Annals

View full text Add to dashboard Cite

Mathematical investigation of diabetically impaired ultradian oscillations in the glucose–insulin regulation

Cited by 12 publications

References 39 publications

Ultradian rhythms in glucose regulation: A mathematical assessment

Ultradian rhythms in glucose regulation: A mathematical assessment

Amplitude and Frequency Variation in Nonlinear Glucose Dynamics with Multiple Delays via Periodic Perturbation

Delay-Differential Equations for Glucose-Insulin Regulation

Contact Info

Product

Resources

About