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

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 25 Hz. 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.