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Research Papers

A Numerical Study of Aortic Flow Stability and Comparison With In Vivo Flow Measurements

[+] Author and Article Information
N. B. Wood, R. Torii

Department of Chemical Engineering,
Imperial College London,
South Kensington Campus,
London SW7 2AZ, UK

W. A. Seed

Faculty of Medicine (Emeritus),
Imperial College London,
Charing Cross Campus,
London W6 8RP, UK

D. O'Regan

Institute of Clinical Science,
Imperial College London,
Hammersmith Campus,
London W12 0NN, UK

X. Y. Xu

Department of Chemical Engineering,
Imperial College London,
South Kensington Campus,
London SW7 2AZ, UK
e-mail: yun.xu@imperial.ac.uk

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received January 17, 2012; final manuscript received October 9, 2012; accepted manuscript posted December 8, 2012; published online December 27, 2012. Assoc. Editor: Hai-Chao Han.

J Biomech Eng 135(1), 011003 (Dec 27, 2012) (9 pages) Paper No: BIO-12-1016; doi: 10.1115/1.4023132 History: Received January 17, 2012; Revised October 09, 2012; Accepted December 08, 2012

The development of an engineering transitional turbulence model and its subsequent evaluation and validation for some diseased cardiovascular flows have been suggestive of its likely utility in normal aortas. The existence of experimental data from human aortas, acquired in the early 1970s with catheter-mounted hot film velocimeters, provided the opportunity to compare the performance of the model on such flows. A generic human aorta, derived from magnetic resonance anatomical and velocity images of a young volunteer, was used as the basis for varying both Reynolds number (Re) and Womersley parameter (α) to match four experimental data points from human ascending aortas, comprising two with disturbed flow and two with apparently undisturbed flow. Trials were made with three different levels of inflow turbulence intensity (Tu) to find if a single level could represent the four different cases with 4000 < Re < 10,000 and 17 < α < 26. A necessary boundary condition includes the inflow “turbulence” level, and convincing results were obtained for all four cases with inflow Tu = 1.0%, providing additional confidence in the application of the transitional model in flows in larger arteries. The Reynolds-averaged Navier–Stokes (RANS)-based shear stress transport (SST) transitional model is capable of capturing the correct flow state in the human aorta when low inflow turbulence intensity (1.0%) is specified.

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Figures

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Fig. 1

Oblique sagittal MR angiography reconstruction (left) and the final 3D aorta geometry reconstructed from the angiogram (right)

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Fig. 4

Case 1 inflow Tu 1%. (a) Turbulence intensity surfaces. Left: peak systole, predominant level 1% (light colored); maximum level 2% (dark colored). Right: midretardation, predominant level 7% (light colored); maximum level 12% (dark colored); (b) instantaneous streamlines: left: peak systole; right: midretardation.

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Fig. 5

Case 2 inflow Tu 1%. (a) Turbulence intensity surfaces. Left: peak systole, predominant level 1% (light colored); maximum level 2% (dark colored). Right: midretardation, predominant level 1% (light colored); maximum level 3% (dark colored); (b) instantaneous streamlines: left: peak systole; right: midretardation.

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Fig. 6

Case 3 inflow Tu 1%. (a) Turbulence intensity surfaces. Left peak systole, predominant level 1% (light colored); maximum level 2% (dark colored). Right: midretardation predominant level 2% (light colored); maximum level 2.5% (dark colored); (b) instantaneous streamlines: left: peak systole; right: midretardation.

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Fig. 7

Case 4 inflow Tu 1%. (a) Turbulence intensity surfaces. Left: peak systole, predominant level 1.5% (light colored); maximum level 2.5% (dark colored). Right: midretardation predominant level 4% (light colored); maximum level 12% (dark colored); (b) instantaneous streamlines: left: peak systole; right: midretardation.

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Fig. 8

Case 1: Top row. Velocity magnitude contours in AA just above midheight with secondary flow vectors (peak systole: left; midretardation: right), showing principal vortex with intense shear layer, lower left. Outer wall (right-posterior) is towards upper left. Bottom row. Tu showing effect of intense vortex at lower right during midretardation.

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Fig. 9

Progression of turbulence kinetic energy (TKE or k) through the pulse cycle

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Fig. 3

Flow rate waveforms derived from the subject-specific waveform (Case 0) to match the data values of Rê and α of the four cases shown in the stability diagram in Fig. 2

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Fig. 2

Stability diagram showing in vivo disturbed and undisturbed flow data. The upper straight line represents Rê = 250 α derived for canine descending aortas (DA), while the lower line represents Rê = 150 α, derived for canine ascending aortas (AA). Canine data ranges are shown by the dashed boxes. Circular symbols are human AA data. (The ordinate, marked Rê, is the peak systolic Reynolds number, Rê, of the flow and α is the Womersley parameter). The numbers 1–4 represent our four test cases, while the larger gray disc represents the reference case (Case 0), which provided the generic human aorta anatomy and flow wave.

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