Abstract
The coherent secondary flow structures (i.e., swirling motions) in a curved artery model possess a variety of spatio-temporal morphologies and can be encoded over an infinitely-wide range of wavelet scales. Wavelet analysis was applied to the following vorticity fields: (i) a numerically-generated system of Oseen-type vortices for which the theoretical solution is known, used for bench marking and evaluation of the technique; and (ii) experimental two-dimensional, particle image velocimetry data. The mother wavelet, a two-dimensional Ricker wavelet, can be dilated to infinitely large or infinitesimally small scales. We approached the problem of coherent structure detection by means of continuous wavelet transform (CWT) and decomposition (or Shannon) entropy. The main conclusion of this study is that the encoding of coherent secondary flow structures can be achieved by an optimal number of binary digits (or bits) corresponding to an optimal wavelet scale. The optimal wavelet-scale search was driven by a decomposition entropy-based algorithmic approach and led to a threshold-free coherent structure detection method. The method presented in this paper was successfully utilized in the detection of secondary flow structures in three clinically-relevant blood flow scenarios involving the curved artery model under a carotid artery-inspired, pulsatile inflow condition. These scenarios were: (i) a clean curved artery; (ii) stent-implanted curved artery; and (iii) an idealized Type IV stent fracture within the curved artery.
Highlights
The definition of coherent structure by Robinson [1] states that with reference to a two-dimensional velocity vector field, usually associated with regions of local swirling motion, in a frame of reference moving with the convection velocity, a vortex might be recognized as a region where streamlines describe spiral patterns
This paper addresses the application of wavelet-decomposition methods, the continuous wavelet transform (CWT) approach in coherent structure identification
The particle image velocimetry (PIV) technique was used for secondary flows in a model 180-degree curved artery with and without stent implantations to explore the hemodynamics of post facto clinical scenarios
Summary
The definition of coherent (vortical) structure by Robinson [1] states that with reference to a two-dimensional velocity vector field, usually associated with regions of local swirling motion, in a frame of reference moving with the convection velocity, a vortex might be recognized as a region where streamlines describe spiral patterns. The λci -criterion is a vortex identification method performed by critical-point analysis of the local velocity gradient tensor and its corresponding eigenvalues [5,7,10]. All of these methods find patterns of swirling flow that include vortices with a high circulation and circular morphologies and strain-dominated flows with low circulation and elongated morphologies. For weakly turbulent flows, the typical wavenumber (cut-off frequency or threshold) of coherent structures is not known a priori, and without any a priori assumptions, such thresholds cannot be established [3]
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