event
Thursday 19 Jan 2023: Amplitude and frequency variation in stimulated glycemic rhythms
Benoit Huard - Northumbria University
Harrison 101 14:30-15:30
The glycemic response to a glucose stimulus is an essential tool for detecting deficiencies in humans such as diabetes. In the presence of constant and periodic glucose infusions 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. These ultradian oscillations are typically modelled using systems of nonlinear equations with two discrete delays and here we give a particular attention to its periodic solutions. 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 impact of periodic (sinusoidal) infusions is characterised through numerical bifurcation analysis. 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.
Joint work with Maia Angelova, Gemma Kirkham and Stefan Ruschel
