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Research Papers

# Time-Resolved DPIV Investigation of Pulsatile Flow in Symmetric Stenotic Arteries—Effects of Phase Angle

[+] Author and Article Information
Satyaprakash Karri

School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA 24061

Pavlos P. Vlachos

Department of Mechanical Engineering, School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA 24061

J Biomech Eng 132(3), 031010 (Feb 17, 2010) (11 pages) doi:10.1115/1.4000934 History: Received April 14, 2009; Revised September 30, 2009; Posted January 04, 2010; Published February 17, 2010; Online February 17, 2010

## Abstract

The effect of phase angle between pressure and flow waveforms on the flow characteristics in stenosed compliant vessels for coronary (phase angle (PA) of approximately $−225 deg$) and peripheral flows (PA of approximately $−45 deg$) is investigated using time resolved digital particle image velocimetry. Synthetic arteries with 50% and 75% stenosis at various physiological conditions with Reynolds numbers (Re) of 250, 350, and 450 and corresponding Womersley parameter $(α)$ of 2.7, 3.2, and 3.7 were studied; wall-shear stresses (WSSs), oscillatory shear index (OSI), and recirculation lengths were determined. Additionally, flow transitional characteristics were examined using power spectral density (PSD), wavenumber spectra, and turbulence statistics of the axial velocity component. It is observed that the coronary flow conditions exhibit lower wall-shear stresses and larger recirculation lengths compared with peripheral flows. Mean peak shear stresses can be as high as $150 dyn/cm2$ and $92 dyn/cm2$ for peripheral and coronary flows, respectively, with 50% stenosis at $Re=450$ and $α=3.7$. These values can be as high as $590 dyn/cm2$ and $490 dyn/cm2$, respectively, for the same conditions with 75% stenosis. The OSI is close to 0.5 near the reattachment point indicating fluctuating WSS over the entire cardiac cycle for both 50% and 75% stenosis. For 50% stenosis, the OSI fluctuated at various locations over the length of the vessel indicating several regions of recirculation in contrast to a distinct recirculation region observed for 75% stenosis. PSD plots across various cross-sections along the length of the vessel and wavenumber spectra along the centerline indicate that turbulence occurs only for 75% stenosis. For coronary flows, the streamwise locations where the flow transitions to turbulence and relaminarizes are approximately one diameter upstream compared with peripheral flows indicating that coronary flows are more susceptible to turbulence.

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## Figures

Figure 1

Schematic of the geometry and the coordinate system with the ROI where data was acquired. The locations where the power spectra (PSD) for axial component of velocity (U) were calculated are shown with dashed lines.

Figure 2

Schematic of the experimental flow loop used for the experiment. Inset shows bypass attachment for the compliant chamber.

Figure 3

Typical flow and pressure waveforms for (a) peripheral flow and (b) coronary flow at Re=250 and α=2.7. Note that for coronary flow, the peak flow occurs when the pressure is near the minimum.

Figure 4

Curved wall given by solid line within the interrogation area, the points indicate discrete points where velocity is estimated using PIV. The arrow is the wall normal vector and its angle from the vertical is measured by θ.

Figure 5

Time average velocity profiles with contours of shear stresses for (a) 50% stenosed peripheral flow and (b) 50% stenosed coronary flow

Figure 6

Time average velocity profiles with contours of shear stresses for (a) 75% stenosed peripheral flow and (b) 75% stenosed coronary flow

Figure 7

Typical contours of reverse coefficient and time-average velocity profiles for Re 450 with 75% stenosis (a) peripheral flow and (b) coronary flow

Figure 8

Average recirculation lengths based on Rc value of 0.9 for peripheral and coronary flows for various degrees of occlusion and Re with corresponding α. The vertical bars show the sensitivity of the results for Rc values of 0.99 and 0.8.

Figure 9

Typical WSS over the cardiac cycle averaged over various cycles for 75% stenosis at Re 350 for (a) peripheral flow and (b) coronary flow

Figure 10

Plot of time-average wall-shear stresses on the bottom wall for (a) 50% stenosis and (b) 75% stenosis at various flow conditions

Figure 11

Plot of OSI along the length of the vessel for (a) 50% stenosis and (b) 75% stenosis for various cases

Figure 12

Contours of power spectral density for normalized axial velocity along various cross-sections along the length of the vessel in logarithmic scale for (a) 50% stenosed peripheral flow, (b) 50% stenosed coronary flow, (c) 75% stenosed peripheral flow, and (d) 75% coronary flow

Figure 13

Wavenumber spectra along the centerline for 50% stenosed arteries at Re 450 for (a) peripheral flow and (b) coronary flow

Figure 14

Wavenumber spectra for 75% stenosed arteries for Re 450 for (a) peripheral flow and (b) coronary flow

Figure 15

Plot of Reynolds normal stresses along the centerline for (a) 50% stenosis and (b) 75% stenosis at all Re and α

Figure 16

Locations of peak ⟨u2⟩, Rc=0.5, Rc=1, peak OSI, and OSI=0 for 75% stenosed at various Re for (a) peripheral flow conditions and (b) coronary flow conditions

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