High fidelity computational model of mucocilary flows

Introduction

Inhaled pathogens and particulates are evacuated from the lung through a variety of mechanisms. In the normal healthy state foreign objects are trapped in a mucus layer covering the airway epithelial tissue. Cilia sprout from the epithelial cells and beat in a motion largely confined to a second fluid layer that is found between the mucus layer and the epithelium and called the periciliary liquid (PCL). The mucus exhibits viscoelastic properties. The rheological properties of the PCL are unclear, but it is commonly treated as a Newtonian fluid. The motion of the cilia propel the mucus out of the lung along with the trapped pathogens. The precise nature of the flow induced by the cilia is unclear at present.

I have undertaken a computational study of mucociliary clearance. The highlights of the approach taken here are:

• the internal mechanics of the cilium axoneme are modeled through a finite element method;
• the mucus layer is simulated using newly devised methods for viscoelastic flow;
• the overall model is treated as a fluid-structure interaction problem - the motion of the cilia results from forces exerted by dynein molecules on the axoneme and fluid forces exerted on the cilium membrane.

Methods

• Overlapping (chimera) grid approach for fluid motion
  • A single background Cartesian grid meant to transmit far-field boundary conditions and interactions between cilia
  • Moving. body fitted grids around each individual cilium meant to capture forces imparted by the cilium to the fluid.
• PCL treated as a Newtonian fluid in Stokes regime. Numerical simulation carried out by a second-order projection method

• Mucus treated as a viscoelastic fluid. Numerical simulation carried out by the Double Projection Method.

• Large deflection beam model of the 9+2 microtubules comprising the cilium axoneme
• Spring elements for the nexin links, central spokes
• Elastic membrane model of clium membrane
• Dynein forces obtained from fitting of experimental data or from first-principle model based upon random stepping.

• Parallelized computation capable of simulating 10⁴ - 10⁵ cilia.

Results

• Using experimentally fitted dynein forces, and allowing the phase of the forces to adapt so as to minimize work done on the fluid, initially random-beating cilia exhibit a natural coherence pattern.

• Some numerical data from the simulations: TypicalOutputData

Animations

Publications

Mitran, S.M., “Metachronal wave formation in a model of pulmonary cilia”, Computers & Structures 85(11-14):763-774, 2007. pdf