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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Levick, J. R., 2010, An Introduction to Cardiovascular Physiology, 5th ed., Hodder Arnold, London.
Tan, F. P. P., Torii, R., Borghi, A., Mohiaddin, R. H., Wood, N. B., and Xu, X. Y., 2009, “Fluid-Structure Interaction Analysis of Wall Stress and Flow Patterns in a Thoracic Aortic Aneurysm,” Int. J. App. Mech., 1, pp. 179–199. [CrossRef]
Ahmed, S. A., and Giddens, D. P., 1984, “Pulsatile Poststenotic Flow Studies With Laser Doppler Anemometry,” J. Biomech., 17, pp. 695–705. [CrossRef] [PubMed]
Ahmed, S. A., 1998, “An Experimental Investigation of Pulsatile Flow Through a Smooth Constriction,” Exp. Therm. Fluid Sci., 17, pp. 309–318. [CrossRef]
Tan, F. P. P., Soloperto, G., Bashford, S., Wood, N. B., Thom, S., Hughes, A., and Xu, X. Y., 2008, “Analysis of Flow Disturbance in a Stenosed Carotid Artery Bifurcation Using Two-Equation Transitional and Turbulence Models,” ASME J. Biomech. Eng., 130, p. 061008. [CrossRef]
Stein, P. D., and Sabbah, H. N., 1976, “Turbulent Blood Flow in the Ascending Aorta of Humans With Normal and Diseased Aortic Valves,” Circ. Res., 39(1), pp. 58–65. [CrossRef] [PubMed]
Giddens, D. P., Mabon, R. F., and Cassanova, R. A., 1976, “Measurements of Disordered Flows Distal to Subtotal Vascular Stenoses in the Thoracic Aortas of Dogs,” Circ. Res., 39, pp. 112–119. [CrossRef] [PubMed]
Seed, W. A., and Wood, N. B., 1971, “Velocity Patterns in the Aorta,” Cardiovasc. Res., 971(5), pp. 319–330. [CrossRef]
Nerem, R. M., Seed, W. A., and Wood, N. B., 1972, “Experimental Study of the Velocity Distribution and Transition to Turbulence in Aorta,” J. Fluid. Mech., 52, pp. 137–160. [CrossRef]
Parker, K. H., 1977, “Instability in Arterial Blood Flow,” Cardiovascular Flow Dynamics and Measurements, N. H. C.Hwang and N. A.Normann, eds., University Park, Baltimore, pp. 633–663.
Leuprecht, A., Kozerke, S., Boesiger, P., and Perktold, K., 2003, “Blood Flow in the Human Ascending Aorta: A Combined MRI and CFD Study,” J. Eng. Math., 47, pp. 387–404. [CrossRef]
Jin, S., Oshinski, J., and Giddens, D. P., 2003, “Effects of Wall Motion and Compliance on Flow Patterns in the Ascending Aorta,” J. Biomech. Eng., 125, pp. 347–354. [CrossRef] [PubMed]
Svensson, S., Gårdhagen, R., Heiberg, E., Ebbers, T., Loyd, D., Länne, T., and Karlsson, M., 2006, “Feasibility of Patient Specific Aortic Blood Flow CFD Simulation,” Lect. Notes Comput. Sci., 4190, pp. 257–263. [CrossRef]
Khanafer, K., and Berguer, R., 2009, “Fluid–Structure Interaction Analysis of Turbulent Pulsatile Flow Within a Layered Aortic Wall as Related to Aortic Dissection,” J. Biomech., 42, pp. 2642–2648. [CrossRef] [PubMed]
Benim, A. C., Nahavandi, A., Assmann, A., Schubert, D., Feindt, P., and Suh, S. H., 2011, “Simulation of Blood Flow in Human Aorta With Emphasis on Outlet Boundary Conditions,” Appl. Math. Model., 35, pp. 3175–3188. [CrossRef]
Menter, F., Langtry, R., and Volker, S., 2006, “Transition Modelling for General Purpose CFD Codes,” Flow, Turbul. Combust., 77, pp. 277–303. [CrossRef]
Wood, N. B., and Xu, X. Y., 2006, “Modelling of Haemodynamics in the Cardiovascular System by Integrating Medical Imaging Techniques and Computer Modelling Tool,” Multidisciplinary Approaches to Theory in Medicine, R.Paton and L.McNamara, eds., Elsevier, New York, pp. 325–351.
Barth, P. J., and Jesperson, D. C., 1989, “The Design and Application of Upwind Schemes on Unstructured Meshes,” AIAA Paper No. AIAA-89-0366.
Ferzinger, J. H., and Peric, M., 1999, Computational Methods for Fluid Dynamics, 3rd ed., Springer, Berlin.
Hutchinson, B. R., and Raithby, G. D., 1986, “A Multigrid Method Based on the Additive Correction Strategy,” Numer. Heat Transfer, 9, pp. 511–537. [CrossRef]
Womersley, J. R., 1955, “Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries When the Pressure Gradient Is Known,” J. Physiol., 127, pp. 553–563. [PubMed]
Martini, F. H., 1995, Fundamentals of Anatomy and Physiology, 3rd ed., Prentice Hall, Englewood Cliffs, NJ.
Wood, N. B., 1975, “A Method for the Determination and Control of the Frequency Response of the Constant-Temperature Hot-Wire Anemometer,” J. Fluid Mech., 67, pp. 769–786. [CrossRef]
Bellhouse, B. J., and Rasmussen, C. G., 1968, “Low-Frequency Characteristics of Hot-Film Anemometers,” DISA Inf., 6, pp. 3–10.
Brison, J. F., Charnay, G., and Compte-Bellot, G., 1979, “Calcul des Transferts Thermiques Entre Film Chaud et Substrat par un Modėle a Deux Dimensions: Prévision de la Réponse Dynamique de Sondes Usuelles,” Int. J. Heat Mass Transfer, 22, pp. 111–119. [CrossRef]
Seed, W. A., and Wood, N. B., 1970, “Development and Evaluation of a Hot-Film Velocity Probe for Cardiovascular Studies,” Cardiovasc. Res., 4, pp. 253–263. [CrossRef] [PubMed]
Wood, N. B., 1999, “Aspects of Fluid Dynamics Applied to the Larger Arteries,” J. Theor. Biol., 199, pp. 137–161. [CrossRef] [PubMed]
Arzani, A., Dyverfeldt, P., Ebbers, T., Shadden, S. C., 2011, “In Vivo Validation of Numerical Prediction for Turbulence Intensity in an Aortic Coarctation,” Ann. Biomed. Eng., 40, pp. 860–870. [CrossRef] [PubMed]
Akhavan, R., Kamm, R. D., and Shapiro, A. H., 1991, “An Investigation of Transition to Turbulence in Bounded Oscillatory Stokes Flows—Part I: Experiments,” J. Fluid Mech., 225, pp. 395–422. [CrossRef]
Tan, F. P. P., Wood, N. B., Tabor, G., and Xu, X. Y., 2011, “Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model,” ASME J. Biomech. Eng., 133, p. 051001. [CrossRef]
Bogren, H. G., and Buonocore, M. H., 1999, “4D Magnetic Resonance Velocity Mapping of Blood Flow Patterns in the Aorta in Young vs. Elderly Normal Subjects,” J. Magn. Reson. Imaging, 10, pp. 861–869. [CrossRef] [PubMed]
Frydrychowicz, A., Berger, A., Munoz Del Rio, A., Russe, M. F., Bock, J., Harloff, A., and Markl, M., 2011, “Interdependencies of Aortic Arch Secondary Flow Patterns, Geometry, and Age Analysed by 4-Dimensional Phase Contrast Magnetic Resonance Imaging at 3 Tesla,” Eur. Radiol., 22, pp. 1122–1130. [CrossRef] [PubMed]
Morbiducci, U., Ponzini, R., Rizzo, G., Cadioli, M., Esposito, A., De Cobelli, F., Del Maschio, A., Montevecchi, F. M., and Redaelli, A., 2009, “In Vivo Quantification of Helical Blood Flow in Human Aorta by Time-Resolved Three-Dimensional Cine Phase Contrast Magnetic Resonance Imaging,” Ann. Biomed. Eng., 37, pp. 516–531. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In