Koopman theory-based reduced-order modeling for diagnosing obstructive sleep apnea using breathing power diagram

Obstructive sleep apnea (OSA) is a serious medical condition typically diagnosed through polysomnography, consequently incurring economic and time burdens on patients. Although diagnosis based on computational fluid dynamics is available, it is limited owing to high computational costs and reliance on expert knowledge. To address these challenges, we propose a Koopman operator-based reduced-order model (ROM) incorporating nonlinear embeddings via convolutional autoencoders. The developed model is intended to explore the feasibility of supporting OSA-related analysis in computed tomography images of the upper-airway. This model advances dynamics in a latent space through a single Koopman operator layer and leverages techniques—such as the reparameterization trick and β-variational-autoencoder warm-up—as well as novel loss functions and eigenvalue penalty terms to facilitate stable prediction. Comparative evaluations indicate that the proposed model can substantially reduce dimensionality and computational cost while showing improved accuracy relative to conventional data-driven ROMs within the considered experimental setting. Under moderate noise conditions, the model demonstrates increased robustness in the tested scenarios. Furthermore, the proposed method demonstrates the potential to predict novel diagnostic indicators such as breathing diagram and power, which are critical for OSA assessment. Overall, this study establishes a foundation for an accurate and efficient deep learning-based OSA diagnosis.