On the quantification and visualization of transient periodic instabilities in pulsatile flows

Muhammad Owais Khan; Christophe Chnafa; Diego Gallo; Filippo Molinari; Umberto Morbiducci; David A Steinman; Kristian Valen-Sendstad

doi:10.1016/j.jbiomech.2016.12.037

On the quantification and visualization of transient periodic instabilities in pulsatile flows

J Biomech. 2017 Feb 8:52:179-182. doi: 10.1016/j.jbiomech.2016.12.037. Epub 2016 Dec 31.

Authors

Muhammad Owais Khan¹, Christophe Chnafa², Diego Gallo³, Filippo Molinari⁴, Umberto Morbiducci³, David A Steinman², Kristian Valen-Sendstad⁵

Affiliations

¹ Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada; Computational Cardiac Modeling Department, Simula Research Laboratory, Lysaker, Norway.
² Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada.
³ Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy.
⁴ Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy.
⁵ Computational Cardiac Modeling Department, Simula Research Laboratory, Lysaker, Norway. Electronic address: kvs@simula.no.

PMID: 28069165
DOI: 10.1016/j.jbiomech.2016.12.037

Abstract

Turbulent-like flows without cycle-to-cycle variations are more frequently being reported in studies of cardiovascular flows. The associated stimuli might be of mechanobiological relevance, but how to quantify them objectively is not obvious. Classical Reynolds decomposition, where the flow is separated into mean and fluctuating velocity components, is not applicable as the phase-average is zero. We therefore expanded on established techniques and present the idea, analogous to Reynolds decomposition, to decompose a flow with transient instabilities into low- versus high frequency components, respectively, to discriminate flow instabilities from the underlying cardiac pulsatility. Transient wall shear stress and velocity signals derived from computational fluid dynamic simulations were transferred to the frequency domain. A high-pass filter was applied to subtract the 99% most-energy-containing frequencies, which gave a cut-off frequency of 25Hz. We introduce here the spectral power index, and compute the fluctuating kinetic energy, based on the high-pass filtered velocity components, both being frequency-based operators. The efficacy was evaluated in an aneurysm model for multiple flow rates demonstrating transition to turbulent-like flows. The frequency-based operators were found to better correlate with the qualitatively observed flow instabilities compared to conventional descriptors, like time-averaged wall shear stress or oscillatory shear index. We demonstrate how the high frequencies beyond the physiological range could be analyzed and/or transferred back to the time domain for quantification and visualization purposes. We have introduced general frequency-based operators, easily extendable to other cardiovascular territories based on a posteriori heuristic filtering that allows for separation, isolation, and quantification of cycle-invariant turbulent-like flows.

Keywords: Cycle-invariant turbulent-like flows; Fluctuating kinetic energy; Hemodynamics; Spectral power index; Visualization.

MeSH terms

Computer Simulation
Hydrodynamics
Models, Cardiovascular
Pulsatile Flow*
Stress, Mechanical
Time Factors