Multimodal Modeling of Ultradian Rhythms Using the Hankel Alternative View of Koopman (HAVOK) Analysis

Abstract

Ultradian rhythms - quasi-rhythmic fluctuations in behavior and physiology with periods shorter than 24 hours - are observed across various organisms, including humans. Despite their role in key biological processes such as sleep architecture and hormone regulation, their underlying mechanisms remain poorly understood. Here, we leveraged wearable sensor technology for continuous monitoring of physiological signals in 16 healthy participants over two weeks. By systematically removing circadian and longer-scale rhythms, we isolated ultradian dynamics and modeled them using the Hankel Alternative View of Koopman (HAVOK) framework,a data-driven approach based on Takens' embedding theorem and Koopman operator theory. This allowed us to characterize ultradian rhythms as an intermittently forced linear system and distinguish between regular oscillatory behavior and more complex dynamics. Across participants, ultradian fluctuations were well-described by the HAVOK model, with intermittent forcing consistently observed. The model demonstrated strong forecasting accuracy, with root mean squared error (RMSE) of $0.0315 \pm 0.02$, $0.0306 \pm 0.02$, and $0.0218 \pm 0.02$ in the leading time-delay coordinates. Notably, a significant sex difference in model rank (z = -2.06, p = 0.0396) suggests that sex hormones may play a key role in ultradian dynamics. These findings provide evidence for intermittently forced linear systems as a useful framework for understanding ultradian rhythms and their regulation.