Delay-induced uncertainty for a paradigmatic glucose-insulin model.

Area of Science:

• Physiology
• Dynamical Systems Theory
• Mathematical Biology

Background:

• Medical practice in intensive care units (ICUs) often assumes predictable physiological systems.
• The human glucose-insulin system is a critical example of such a physiological system.

Purpose of the Study:

• To demonstrate that feedback delays can induce sustained temporal chaos in physiological systems.
• To explain the nature of delay-induced uncertainty (DIU) using dynamical systems theory.
• To develop a general framework for diagnosing DIU in oscillatory systems.

Main Methods:

• Utilized the ultradian glucose-insulin model, a well-validated, finite-dimensional model.
• Applied the theory of rank one maps from smooth dynamical systems.
• Extended the diagnostic framework to infinite-dimensional delay systems, including a linear shear flow.

Main Results:

• Demonstrated that delay within the glucose-insulin system can induce sustained temporal chaos, rendering it unpredictable.
• Precisely explained the nature of delay-induced uncertainty (DIU).
• Showcased the applicability of the DIU framework to infinite-dimensional delay systems, exhibiting chaos in a linear shear flow.

Conclusions:

• Feedback delays are a fundamental source of unpredictability in physiological systems.
• The developed DIU framework provides a method to diagnose and understand temporal chaos in diverse oscillatory dynamical systems.
• The findings have broad implications for mathematical physiology due to the ubiquity of delay.