# Exploratory application of DMD for particle deposition and fluid field in the respiratory tract

## TL;DR

This paper explores using DMD to efficiently simulate particle deposition and airflow in the respiratory tract, reducing computational costs while maintaining accuracy.

## Contribution

The first demonstration of DMD as a reduced-order model for respiratory tract particle and fluid simulations.

## Key findings

- DMD reconstructed fluid fields with a Mean Relative Error of 12% compared to CFD simulations.
- DMD achieved 85% correlation with ground truth in approximating overall particle distribution.
- Localized discrepancies in DMD reconstructions reached up to 70% relative error.

## Abstract

Simulating particle deposition in the respiratory tract requires high computational effort due to the intricate airway geometry and complex airflow–particle interactions. To address this challenge, this study introduces the first demonstration of Dynamic Mode Decomposition (DMD) as a reduced-order model to infer the trajectories of inhaled particles during a breathing cycle and to evaluate the applicability of DMD as a fluid field interpolator. The periodic nature of respiration and the predominance of sinusoidal boundary conditions make it well-suited for DMD analysis. Three high-fidelity computational fluid dynamics (CFD) simulations were performed under three different inlet volume airflow conditions for the same realistic adult male anthropomorphic phantom respiratory tract model. Reduced-rank DMD reconstructions were compared to the CFD ground truth, yielding a Mean Relative Error (MRE) of 12% in the velocity field. Additionally, a fourth simulation was conducted at an intermediate point to evaluate the interpolation capability of the parametric DMD framework in complex systems. This interpolation resulted in an MRE of 20%, with the reconstructed flow field capturing dominant fluid modes and overall dynamics, though localized discrepancies reached relative errors up to 70%.

While DMD effectively reconstructed fluid fields, preserving mean flow regimes, some deviations were observed in Lagrangian particle tracking, specifically in spatial deposition resolution. However, the method approximated overall particle distribution with an 85% correlation to ground truth and was effective in representing regional deposition patterns across the tracheobronchial tree. These findings support the utility of DMD a computationally efficient approach for fluid field reconstruction and particle transport analysis in respiratory flow simulations.