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Research Papers

Flow Instability Detected by High-Resolution Computational Fluid Dynamics in Fifty-Six Middle Cerebral Artery Aneurysms

[+] Author and Article Information
Nicole Varble

Department of Mechanical
and Aerospace Engineering,
University at Buffalo,
The State University of New York,
Buffalo, NY 14203;
Toshiba Stroke and Vascular Research Center,
The State University of New York,
Buffalo, NY 14203

Jianping Xiang, Elad Levy

Toshiba Stroke and Vascular Research Center,
The State University of New York,
Buffalo, NY 14203;
Department of Neurosurgery,
University at Buffalo,
The State University of New York,
Buffalo, NY 14203

Ning Lin

Department of Neurosurgery,
University at Buffalo,
The State University of New York,
Buffalo, NY 14203;
Department of Neurosurgery,
Weill Cornell Medical
Center/New York Presbyterian Hospital,
New York, NY 10065

Hui Meng

Department of Mechanical
and Aerospace Engineering,
University at Buffalo,
The State University of New York,
Buffalo, NY 14203;
Toshiba Stroke and Vascular Research Center,
The State University of New York,
Buffalo, NY 14203;
Department of Neurosurgery,
University at Buffalo,
The State University of New York,
Buffalo, NY 14203;
Department of Biomedical Engineering,
University at Buffalo,
The State University of New York,
Buffalo, NY 14203
e-mail: huimeng@buffalo.edu

1Corresponding author.

Manuscript received September 15, 2015; final manuscript received April 5, 2016; published online May 10, 2016. Assoc. Editor: Keefe B. Manning.

J Biomech Eng 138(6), 061009 (May 10, 2016) (11 pages) Paper No: BIO-15-1455; doi: 10.1115/1.4033477 History: Received September 15, 2015; Revised April 05, 2016

Recent high-resolution computational fluid dynamics (CFD) studies have detected persistent flow instability in intracranial aneurysms (IAs) that was not observed in previous in silico studies. These flow fluctuations have shown incidental association with rupture in a small aneurysm dataset. The aims of this study are to explore the capabilities and limitations of a commercial cfd solver in capturing such velocity fluctuations, whether fluctuation kinetic energy (fKE) as a marker to quantify such instability could be a potential parameter to predict aneurysm rupture, and what geometric parameters might be associated with such fluctuations. First, we confirmed that the second-order discretization schemes and high spatial and temporal resolutions are required to capture these aneurysmal flow fluctuations. Next, we analyzed 56 patient-specific middle cerebral artery (MCA) aneurysms (12 ruptured) by transient, high-resolution CFD simulations with a cycle-averaged, constant inflow boundary condition. Finally, to explore the mechanism by which such flow instabilities might arise, we investigated correlations between fKE and several aneurysm geometrical parameters. Our results show that flow instabilities were present in 8 of 56 MCA aneurysms, all of which were unruptured bifurcation aneurysms. Statistical analysis revealed that fKE could not differentiate ruptured from unruptured aneurysms. Thus, our study does not lend support to these flow instabilities (based on a cycle-averaged constant inflow as opposed to peak velocity) being a marker for rupture. We found a positive correlation between fKE and aneurysm size as well as size ratio. This suggests that the intrinsic flow instability may be associated with the breakdown of an inflow jet penetrating the aneurysm space.

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Figures

Grahic Jump Location
Fig. 1

An unruptured MCA case, UR1, using the sensitivity tests is shown with a mesh consisting of 2.2 × 106 elements. A monitoring point at the center of the aneurysm dome, shown by the red dot, was used for illustration of the flow fluctuations and frequency analysis.

Grahic Jump Location
Fig. 2

The results of sensitivity tests on a single unruptured MCA case. (a) The discretization scheme sensitivity tests showing aneurysm-averaged fKE and velocity magnitude for five combinations of first- and second- order discretization schemes. The stable (gray) and unstable regimes which were initially defined by the threshold of aneurysmal fKE of 10−4 m2/s2 (dashed line). Results showed that second-order temporal and spatial discretization schemes are necessary to capture flow fluctuations. (b) Grid-independence study showing convergence of aneurysm-averaged fKE and velocity magnitude between 2.2 × 106 and 4.7 × 106 elements. (c) Time step-independence study showing the aneurysm-averaged fKE and velocity magnitude with successive refinement of the CFL number. For simulations with both 2.2 × 106 and 4.7 × 106 elements, no appreciable change in fluctuation energy and velocity magnitude was found for a CFL number of 1. (d) The results of inflow rate sensitivity tests, where flow rate was varied in the physiologic range. Aneurysmal fKE increased with increasing inflow rates, but the case retained unstable flow characteristics.

Grahic Jump Location
Fig. 3

The distribution of aneurysm-averaged fluctuation energy for all MCA cases in comparison to aneurysm size. The flow instability map where eight cases were found to have unstable flow. The dashed line demarks the verified threshold for unstable flow fKE > 5 × 10−5 m2/s2). All other cases were classified as stable (gray) in terms of velocity fluctuations.

Grahic Jump Location
Fig. 4

Volumetric rendering of fKE in the eight IA cases with unstable flow and eight representative IA cases with stable flow. (a) The eight unstable flow cases (fKE > 5 × 10−5), all of which were unruptured bifurcation aneurysms. (b) Representative stable flow cases including four unruptured (top row) and four ruptured (bottom row) IAs.

Grahic Jump Location
Fig. 5

Streamlines colored by velocity magnitude of the eight unstable flow cases. Each case was a bifurcation aneurysm with a distinct inflow jet. The velocity fluctuations may have arisen from complex interaction of the parent vessel and aneurysms geometry leading to the instability of the inflow jet, which penetrated the aneurysm and subsequently broke down.

Grahic Jump Location
Fig. 6

CFD solutions under second-order discretization schemes of velocity magnitude versus time at a monitoring point in each of the 16 aneurysms in Fig. 4. (a) The eight unstable flow cases, which demonstrated persistent velocity fluctuations, and thus, high aneurysm-averaged fKE in the last three periods. (b) The eight representative stable flow cases, which showed no fluctuations, and thus, low aneurysm-averaged fKE.

Grahic Jump Location
Fig. 7

The frequency analysis results at a monitoring point in the aneurysm dome. (a) The dominant frequencies in the eight cases with unstable flow. (b) Velocity magnitude versus time at a monitoring point in the aneurysm for the final three periods of a representative case (UR1). (c) Power spectral density (note the log-log scale) of the last three periods for one representative case, UR1. The case shows a dominant frequency of 102 Hz.

Grahic Jump Location
Fig. 8

To demonstrate the necessity of second-order discretization schemes, each of the eight cases found to have unstable flow in high-resolution simulations were run using first-order discretization. After three periods, all cases except for one case (UR3, green), were found to have stable flow.

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