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Merging flows in an arterial confluence: the vertebro-basilar junction

Published online by Cambridge University Press:  26 April 2006

J. Ravensbergen ,
J. K. B. Krijger ,
B. Hillen  and
H. W. Hoogstraten
J. Ravensbergen
Affiliation:
Department of Functional Anatomy, Utrecht University, The Netherlands
J. K. B. Krijger
Affiliation:
Department of Functional Anatomy, Utrecht University, The Netherlands
B. Hillen
Affiliation:
Department of Functional Anatomy, Utrecht University, The Netherlands
H. W. Hoogstraten
Affiliation:
Department of Mathematics, University of Groningen, The Netherlands
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Abstract

The basilar artery is one of the three vessels providing the blood supply to the human brain. It arises from the confluence of the two vertebral arteries. In fact, it is the only artery of this size in the human body arising from a confluence instead of a bifurcation. Earlier work, concerning flow computations in simplified models of the basilar artery, has demonstrated that a junction causes distinctive flow phenomena. This paper presents three-dimensional finite-element computations of steady viscous flow in a rigid symmetrical junction geometry representing the anatomical situation in a more realistic way. The geometry consists of two round tubes merging into a single round outlet tube. The Reynolds number for the basilar artery ranges from 200 to 600, and both symmetrical and asymmetrical inflow from the two inlet tubes has been considered.

Just downstream of the confluence a ‘double hump’ axial velocity profile is found. In the transition zone the flow pattern appears to have a complicated structure. In the symmetrical case the axial velocity profile shows a sharp central ridge, whereas in the asymmetrical case the highest ‘hump’ crosses the centreline of the tube. The flow has a highly three-dimensional character with secondary velocities easily exceeding 25% of the mean axial flow velocity. The secondary flow pattern consists of four vortices. Under all simulated flow conditions, the inlet length turns out to be much larger than the average length of the human basilar artery.

To validate the computational model, a comparison is made between numerical and experimental results for a junction geometry consisting of tubes with a rectangular cross-section. The experiments have been performed in a Perspex model with laser Doppler velocimetry and dye injection techniques. Good agreement between experimental and computational results is found. Moreover, all essential flow phenomena turn out to be quite similar to those obtained for the circular tube geometry.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 304 , 10 December 1995 , pp. 119 - 141
Copyright
© 1995 Cambridge University Press

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References

Berger, S. A., Talbot, L. & Yao, L. S. 1983 Flow in curved pipes. Ann. Rev. Fluid Mech. 15, 461–512.Google Scholar
Caro, C. G., Pedley, T. J., Schroter, R. C. & Seed, W. A. 1978 The Mechanics of the Circulation. Oxford University Press.
Cuvelier, C., Segal, A. & Van Stef.Nhoven, A. A. 1986 Finite Element Methods and Navier-Stokes Equations. Dordrecht: D. Reidel.
Friedmann, M., Gillis, J. & Liron, N. 1968 Laminar flow in a pipe at low and moderate Reynolds numbers. Appl. Sci. Res. 19, 426–438.Google Scholar
Hayashi, K., Nunomora, M., Naiki, T. & Abe, H. 1992 LDA studies of flow characteristics in a vertebrobasilar arterial junction model. In Proc. 7th Intl Conf. on Biomedical Engineering, Singapore. December 1992, pp. 61–64.
Kjearnes, M., Svindland, A., Walloe, L. & Wille, O. 1981 Localization of early atherosclerotic lesions in an arterial bifurcation in humans. Acta Path. Microbiol. Scand. A 89, 35–40.Google Scholar
Krijger, J. K. B., Heethaar, R. M., Hillen, B., Hoogstraten, H. W. & Ravensbergen, J. 1992 Computation of steady three-dimensional flow in a model of the basilar artery. J. Biomech. 25, 1451–1465.Google Scholar
Krijger, J. K. B., Hillen, B. & Hoogstraten, H. W. 1989 Mathematical models of the flow in the basilar artery. J. Biomech. 22, 1193–1202.Google Scholar
Krijger, J. K. B., Hillen, B. & Hoogstraten, H. W. 1991 A two-dimensional model of pulsating flow in the basilar artery. Z. Angew. Math. Phys. 42, 649–662.Google Scholar
Krijger, J. K. B., Hillen, B., Hoogstraten, H. W. & Van Den Raadt, M. P. M. G. 1990 Steady two-dimensional merging flow from two channels into a single channel. Appl. Sci. Res. 47, 233–246.Google Scholar
Ku, D. N., Giddens, D. P., Zarins, C. K. & Glagov, S. 1985 Pulsatile flow and atherosclerosis in the human carotid bifurcation. Arteriosclerosis 5, 293–302.Google Scholar
Ku, D. N. & Liepsch, D. W. 1986 The effects of non-Newtonian viscoelasticity and wall elasticity on flow at 90 degrees bifurcation. Biorheology 23, 359–370.Google Scholar
Mcdonald, D. A. 1974 Blood Flow in Arteries. London, Arnold.
Mcdonald, D. A. & Potter, J. M. 1951 The distribution of blood to the brain. J. Physiol. 114, 356–371.Google Scholar
Nijhof, E. J., Uijttewaal, W. S. J. & Heethaar, R. M. 1994 A laser Doppler system for measuring distributions of blood particles in narrow flow channels. IEEE Trans. Instrum. Meas. 43, 430–435.Google Scholar
Pedley, T. J. 1977 Pulmonary fluid dynamics. Ann. Rev. Fluid Mech. 9, 229–274.Google Scholar
Pedley, T. J. 1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.
Ravensbergen, J., Tarnawski, M., Vriens, E. M., Hillen, B., Caro, C. G. & Van HUFFELEN, A. C. 1995 New facilities to perform in vivo flow velocity measurements in the basilar artery. Neuroradiology (to appear)
Schroter, R. C. & Sudlow, M. F. 1969 Flow patterns in models of the human bronchial airways. Respiration Physiol. 7, 341–355.Google Scholar
Segal, A. 1993 Sepran User Manual. Leidschendam, The Netherlands: Ingenieursburo SEPRA.
Van De Vosse, F. N., Van Steenhoven, A. A., Segal, A. & Janssen, J. D. 1989 A finite element analysis of the steady laminar entrance flow in a 90° curved tube. Intl J. Numer. Meth. Fluids 9, 275–287.Google Scholar
Xu, X. Y., Collins, M. W. & Jones, C. J. H. 1992 Flow studies in canine artery bifurcations using a numerical simulation method. ASME J. Biomech. Engng Trans. 114, 504–511.Google Scholar
Zarins, C. K., Giddens D. P., Bharadvaj, B. K., Sottiurai, V. S., Mabon, R. F. & Glagov, S. 1983 Carotid bifurcation: quantitative correlation of plaque localisation with flow velocity profiles and wall shear stress. Circulation Res. 53, 502–514.Google Scholar