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We investigate the consequences of periodic, on-off glucose infusion on theglucose-insulin regulatory system on the basis of a system-level mathematicalmodel with two explicit time delays. Studying the effects of such infusionprotocols is mathematically challenging yet a promising direction for probingthe system response to infusion. We pay special attention to the interplay ofthe infusion with intermediate-time-scale, ultradian oscillations that arise asa results of the physiological response of glucose uptake and back-release intothe bloodstream. By using numerical solvers and numerical continuationsoftware, we investigate the response of the model to different infusionpatterns, and explore how these patterns affect the overall levels of glucoseand insulin, and can lead to entrainment. By doing so, we provide a road-map ofsystem responses that can potentially help identify new test strategies fordetecting abnormal responses to glucose uptake.

Sounding the metabolic orchestra: A delay dynamical systems perspective on the glucose-insulin regulatory response to on-off glucose infusion