Discrete cilia modelling with singularity distributions: application to the embryonic node and the airway surface...

Area of Science:

• Fluid dynamics
• Biophysics
• Computational biology

Background:

• Accurate modeling of fluid flow generated by cilia is crucial for understanding various biological processes.
• Existing models often struggle with accuracy in both near-field and far-field predictions.
• Cilia play vital roles in embryonic development, mucociliary clearance, and reproductive functions.

Purpose of the Study:

• To develop and validate an efficient singularity-based technique for modeling cilia-driven flows.
• To investigate the fluid dynamics of embryonic nodal cilia and their role in leftward flow generation.
• To analyze flow patterns within the periciliary layer of airway surfaces.

Main Methods:

• Cilia are modeled as curved, slender ellipsoidal bodies using distributed Stokeslet and potential source dipole singularities.
• An integral equation is formulated and solved using efficient discretization.
• Particle tracking and flow analysis are performed for simulated cilia arrays and airway models.

Main Results:

• The singularity model accurately predicts near-field and far-field velocities, validating against boundary conditions.
• Embryonic nodal cilia generate leftward flow via a 'posterior tilt,' with mean transport of ~1 µm/s, and no negative fluid transport layer.
• Airway periciliary layer models show significant periciliary liquid movement driven by mucus shear flow, even during ciliary recovery strokes.

Conclusions:

• The singularity technique offers an accurate and efficient method for modeling cilia-driven fluid dynamics.
• The study elucidates the mechanism of leftward flow in embryonic development and confirms periciliary layer dynamics.
• Future applications include understanding morphogen gradients, mechanosensing, and reproductive system fluidics.