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

TL;DR

This study applies the HAVOK analysis to physiological data from wearable sensors to model and forecast ultradian rhythms, revealing their intermittently forced linear nature and sex differences in dynamics.

Contribution

It introduces a novel application of HAVOK analysis to ultradian rhythms, providing a data-driven framework for understanding their complex dynamics.

Findings

Ultradian rhythms are well-modeled as intermittently forced linear systems.

HAVOK analysis achieves high forecasting accuracy with low RMSE.

Sex differences in model rank suggest hormonal influence on ultradian dynamics.

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.