# Modeling tissue-scale ciliary transport and mixing in three-dimensional Newtonian flow

## TL;DR

This paper uses 3D simulations to study how cilia movement affects mucus transport and mixing in the respiratory system.

## Contribution

The study introduces 3D simulations of ciliary-driven fluid transport, revealing how cilia density, spacing, and metachrony influence mucociliary clearance.

## Key findings

- Cilia clusters generate flow swirls whose size scales with ciliary density.
- Optimal spacing between ciliary clusters enhances horizontal transport.
- Metachronic waves enhance mixing but may reduce net transport depending on phase lag.

## Abstract

Mucociliary clearance is the primary defense mechanism in our respiratory system against aerosol pathogens and allergens. The rhythmic movement of cilia on airway-lining cells propels mucus flow, driving the movement of trapped particles. However, the impact of cilia density and distribution on mucociliary mixing and transport at the tissue scale remains poorly understood. In the present work, we present three-dimensional (3D) simulations of ciliary-driven mixing and transport of a Newtonian fluid as an approximation of mucus at the tissue scale. We investigate the influence of ciliary density, cilia cluster spacing, and metachrony on fluid mixing and transport. Our findings reveal that: (i) cilia clusters generate flow swirls whose size scales with ciliary density, (ii) a single cilia cluster generates horizontal and upward transport with horizontal mixing, (iii) optimal spacing between ciliary clusters enhances horizontal transport, and (iv) metachronic waves enhances mixing but reduces net transport. These findings provide useful insight into generic principles of cilia-driven transport in viscous fluids and may inform bio-inspired system design, while further work is needed to extend this work to physiologically realistic mucus transport.

The human airway is exposed to foreign particles, including allergens, pathogens, and aerosolized vaccines or medications. The mucus coating the airway surface traps these particles, and the beating cilia extending from the ciliated epithelial cells play a crucial role in propelling the flow of mucus to clear the trapped particles out of the airway. This mucociliary clearance process is critical for the initiation and progression of airway tissue response, such as allergic responses, infections, and treatment effects. Changes in ciliated cell density or mucus production can significantly impact this process. Conversely, achieving a homogeneous distribution of aerosol drug particles within the airway is essential for optimizing treatment outcomes. We simulate cilia-driven mucus flow, using a simplified rod-cilia and Newtonian-fluid model, to examine how the motion of cilia influences the transport and mixing of particles in the mucus. Our key findings suggest an optimal spacing for ciliated cell clusters that enhances directional clearance transport. Intriguingly, while all metachronal waves promotes mixing, its effect on the overall particle clearance depends on the phase lag: some sympletic waves (those travel in the same direction of the forward cilia stroke) enhance transport while majority of the metachronal waves hinder clearance, and can potentially move the particles backwards.