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Research Papers

# Pulsatile Flow Effects on the Hemodynamics of Intracranial Aneurysms

[+] Author and Article Information
Trung B. Le, Iman Borazjani

Department of Civil Engineering, Saint Anthony Falls Laboratory, University of Minnesota, 2 Third Avenue South East, Minneapolis, MN 55414

Fotis Sotiropoulos1

Department of Civil Engineering, Saint Anthony Falls Laboratory, University of Minnesota, 2 Third Avenue South East, Minneapolis, MN 55414fotis@umn.edu

1

Corresponding author.

J Biomech Eng 132(11), 111009 (Oct 27, 2010) (11 pages) doi:10.1115/1.4002702 History: Received August 14, 2010; Revised September 17, 2010; Posted October 04, 2010; Published October 27, 2010; Online October 27, 2010

## Abstract

High-resolution numerical simulations are carried out to systematically investigate the effect of the incoming flow waveform on the hemodynamics and wall shear stress patterns of an anatomic sidewall intracranial aneurysm model. Various wave forms are constructed by appropriately scaling a typical human waveform such that the waveform maximum and time-averaged Reynolds numbers, the Womersley number $(α)$, and the pulsatility index (PI) are systematically varied within the human physiologic range. We show that the waveform PI is the key parameter that governs the vortex dynamics across the aneurysm neck and the flow patterns within the dome. At low PI, the flow in the dome is similar to a driven cavity flow and is characterized by a quasi-stationary shear layer that delineates the parent artery flow from the recirculating flow within the dome. At high PI, on the other hand, the flow is dominated by vortex ring formation, transport across the neck, and impingement and breakdown at the distal wall of the aneurysm dome. We further show that the spatial and temporal characteristics of the wall shear stress field on the aneurysm dome are strongly correlated with the vortex dynamics across the neck. We finally argue that the ratio between the characteristic time scale of transport by the mean flow across the neck and the time scale of vortex ring formation can be used to predict for a given sidewall aneurysm model the critical value of the waveform PI for which the hemodynamics will transition from the cavity mode to the vortex ring mode.

###### FIGURES IN THIS ARTICLE
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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 1

Aneurysm geometry and computational setup. Ha, Wa, and Da are the depth, neck width, and parent artery diameter at the aneurysm neck, respectively. Ha=6.6 mm, Wa=6.3 mm, and Da=3.6 mm. Aneurysm aspect ratio (depth/neck width) is 1.05. D=3 mm is the diameter of parent artery at the inlet. Note that the proximal part of the parent artery is kept unchanged, while the distal part of parent artery is extruded 15 diameters (15D) further downstream. The curvature (1/R) of proximal parent artery varies between 0.04 mm−1 and 0.44 mm−1 and is 0.22 mm−1 at the proximal neck (R is the radius of curvature).

Figure 2

Flow waveform is plotted in terms of the instantaneous Reynolds number Re during one cardiac cycle. The horizontal lines in the figure mark various characteristic Reynolds numbers: (a) Remax is the peak systolic Reynolds number; (b) Re¯ is the time-averaged Reynolds number; and (c) Remin is the end diastolic Reynolds number. For the various parameters characterizing case 1a (low PI) and case 2a (high PI), see Table 1. The horizontal axis denotes time t over one cardiac cycle T.

Figure 3

Various waveforms used in the simulations plotted throughout one cardiac cycle. (a) Type 1 waveforms were obtained by appropriately scaling the same original waveform-case 1a. Waveform 1a is constructed following a typical waveform in middle cerebral artery. (b) Type 2 (Waveform 2a) is a typical waveform of a healthy subject in internal carotid artery. See Table 1 for the various parameters characterizing the various waveforms shown in this figure. The horizontal axis denotes time t over one cardiac cycle T.

Figure 4

Instantaneous nondimensional vorticity magnitude (|ω| with ω=curl v) and in-plane velocity vector fields for the low PI case 1a (left column) and high PI case 2a (right column) on one representative plane. (a) Early systolic phase, (b) peak systolic phase, (c) early diastolic phase, and (d) late diastolic phase. Straight line in the inflow waveform inset indicates zero flow line.

Figure 5

Instantaneous nondimensional vorticity magnitude (|ω| with ω=curl v) and in-plane velocity vector fields for (a) the cavity mode in case 1c (low PI), (b) the vortex ring mode in case 1d (very high PI), (c) case 1b (high PI), and (d) case 2b (high PI) with shear-layer separation from the proximal neck and vortex-ring formation. Straight line in the inflow waveform inset indicates zero flow line.

Figure 6

Time-averaged (over one cardiac cycle) values of nondimensional wall shear stress magnitude for different types of waveforms. (a) case 1a, cavity mode; (b) case 2a, vortex ring mode; (c) case 1d, vortex ring mode (retrograde flow).

Figure 7

OSI field for different types of waveforms. (a) case 1a, cavity mode; (b) case 2a, vortex ring mode; (c) case 1d, vortex ring mode (retrograde flow).

Figure 8

Temporal distribution of nondimensional shear stress magnitude at the distal dome wall. The location of the point is marked in the inset, which also indicates the average flow direction with a black arrow. The horizontal axis denotes time t over one cardiac cycle T. Point A in the inset is on the distal dome wall. C=cavity mode. V=vortex ring mode.

Figure 9

Instantaneous vortical structures in the dome, showing the inclined vortex ring structures that forms for the waveform 2b. The vortical structure is visualized using the Q-criterion.

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