Predictability failure in glucose-insulin system for ICU patients

Abstract

Modern medicine implicitly assumes that physiological responses to intervention are predictably determined by administered treatments. However, physiological systems containing intrinsic delays between the detection of a stimulus and the biological response may violate this assumption. We investigate the human glucose-insulin system as described by the Ultradian model and mathematically demonstrate that clinically relevant forcing protocols-such as pulsatile insulin delivery and step-wise glucose infusion, both commonly used in intensive care units (ICUs)-can induce sustained temporal chaos that may hamper accurate prediction of the physiological response. If not accounted for, these chaotic dynamics could create difficulties in achieving optimal dosing and timing when administering glucose and insulin in clinical or home care settings. This phenomenon, termed delay-induced uncertainty (DIU), arises from the interaction between physiological delay, intrinsic shear near a limit cycle, and external forcing. Using the Ultradian glucose-insulin model, we compute top Lyapunov exponents to quantify predictability. Across a range of pulsatile and step-wise forcing regimes, including stochastic amplitudes drawn from Markov processes, we observe positive Lyapunov exponents, indicating sustained chaos. Our results suggest that delayed endocrine regulation may fundamentally limit the predictive value of the models used to develop glycemic management strategies, with implications for clinical protocols in the ICU.