Modelling Nasal Airflow using a Fourier Descriptor Representation of Geometry

Procedures capable of providing both compact representations and rational simplifications of complex anatomical flow conduits are essential to explore how form and function are related in the respiratory, cardiovascular and other physiological flow systems. This work focuses on flow in the human nasal cavity. Methods to derive the cavity wall boundary from medical images are first outlined. Anisotropic smoothing of the boundary surface is shown to provide less geometric distortion in regions of high curvature, such as at the ends of the narrow nasal passages. A reversible decomposition of the surface into a stack of planar contours is then effected using an implicit function formulation. Fourier descriptors provide a continuous representation of each contour as a modal expansion, and permit simplification of the geometry by retaining only dominant modes via filtering.

Computations of the steady inspiratory flow field are performed for replica and reduced geometries, where the reduced geometry is derived by retaining only the first fifteen modes in the expansion of each slice contour. The overall pressure drop and integrated wall shear are shown to be virtually unaffected by simplification. More sensitive measures, such as the Lagrangian particle trajectories and residence time distributions show slight changes as discussed.

Comparison of the Fourier descriptor method applied to three different patient data sets indicate the potential of the technique as a means to characterise complex flow conduit geometry, and the scope for further work is outlined.