Delay-Induced Uncertainty in Physiological Systems

Abstract

AbstractMedical practice in the intensive care unit is based on the supposition that physiological systems such as the human glucose-insulin system are reliabile. Reliability of dynamical systems refers to response to perturbation: A dynamical system is reliable if it behaves predictably following a perturbation. Here, we demonstrate that reliability fails for an archetypal physiological model, the Ultradian glucose-insulin model. Reliability failure arises because of the presence of delay. Using the theory of rank one maps from smooth dynamical systems, we precisely explain the nature of the resulting delay-induced uncertainty (DIU). We develop a recipe one may use to diagnose DIU in a general dynamical system. Guided by this recipe, we analyze DIU emergence first in a classical linear shear flow model and then in the Ultradian model. Our results potentially apply to a broad class of physiological systems that involve delay.