Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows

Journal of Biomechanics

Volumn 40, Issue 8, 2007, Pages 1794-1805

  Alastruey, J ^a   Parker, K H ^a   Peiro J ^a   Byrd, S M ^a   Sherwin, S J ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Anatomical variations; Circle of Willis; Collateral flow; One dimensional modelling; Pulse wave propagation

Indexed keywords

BIFURCATION (MATHEMATICS); BLOOD VESSELS; COMPUTER SIMULATION; WAVE PROPAGATION;

ANATOMICAL VARIATIONS; CIRCLE OF WILLIS; COLLATERAL FLOW; ONE-DIMENSIONAL MODELLING; PULSE WAVE PROPAGATION;

BIOMECHANICS;

ANTERIOR CEREBRAL ARTERY; ANTERIOR COMMUNICATING ARTERY; ARTICLE; BRACHIOCEPHALIC TRUNK; BRAIN BLOOD FLOW; BRAIN CIRCULUS ARTERIOSUS; CAROTID ARTERY; CAROTID ARTERY OBSTRUCTION; CONTROLLED STUDY; HUMAN; HUMAN EXPERIMENT; INTERNAL CAROTID ARTERY; INTERNAL CAROTID ARTERY OCCLUSION; MATHEMATICAL COMPUTING; OCCLUSIVE CEREBROVASCULAR DISEASE; POSTERIOR COMMUNICATING ARTERY; PRIORITY JOURNAL; PULSE WAVE; VERTEBRAL ARTERY; VERTEBRAL ARTERY STENOSIS;

ANIMALS; BLOOD FLOW VELOCITY; BLOOD PRESSURE; CEREBROVASCULAR CIRCULATION; CEREBROVASCULAR DISORDERS; CIRCLE OF WILLIS; HUMANS; MODELS, CARDIOVASCULAR;

EID: 34247885810     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jbiomech.2006.07.008     Document Type: Article

References (37)

1. Alastruey, J., 2006. Numerical modelling of pulse wave propagation in the cardiovascular system: development, validation and clinical applications. Ph.D. Thesis, Departments of Bioengineering and Aeronautics, Imperial College London.
2. Burton A.C. Physiology and Biophysics of the Circulation (1965), Year Book Medical Publishers
3. Cassot F., Vergeur V., Bossuet P., Hillen B., Zagzoule M., and Marc-Vergnes J.P. Effects of anterior communicating artery diameter on cerebral hemodynamics in internal carotid artery disease. Circulation 92 (1995) 3122-3131
4. Cassot F., Zagzoule M., and Marc-Vergnes J.P. Hemodynamic role of the circle of Willis in stenoses of internal carotid arteries. An analytical solution of a linear model. Journal of Biomechanics 33 (2000) 395-405
5. Cebral J.R., Castro M.A., Soto O., Löhner R., and Alperin N. Blood-flow models of the circle of Willis from magnetic resonance data. Journal of Engineering Mathematics 47 (2003) 369-386
6. David T., Brown M., and Ferrandez A. Auto-regulation and blood flow in the cerebral circulation. International Journal for Numerical Methods in Fluids 43 (2003) 701-713
7. Dickey P.S., Kailasnath P., Bloomgarden G., Goodrich I., and Chaloupa J. Computer modeling of cerebral blood flow following internal carotid occlusion. Neurological Research 18 (1996) 259-266
8. Fahrig R., Nikolov H., Fox A.J., and Holdsworth D.W. A three-dimensional cerebrovascular flow phantom. Medical Physics 26 (1999) 1589-1599
9. Ferrandez A., David T., and Brown M. Numerical models of auto-regulation and blood flow in the cerebral circulation. Computer Methods in Biomechanics and Biomedical Engineering 5 (2002) 7-20
10. Franke V.E., Parker K.H., Wee L.Y., Fisk N.M., and Sherwin S.J. Time domain computational modelling of 1D arterial networks in monochorionic placentas. Mathematical Modelling and Numerical Analysis 37 (2003) 557-580
11. Hayashi K., Handa H., Nagasawa S., Okumura A., and Moritake K. Stiffness and elastic behavior of human intracranial and extracranial arteries. Journal of Biomechanics 13 (1980) 175-184
12. Henderson R.D., Eliasziw M., Fox A.J., Rothwell P.M., and Barnett H.J.M. Angiographycally defined collateral circulation and risk of stroke in patients with severe carotid artery stenosis. Stroke 31 (2000) 128-132
13. Hillen B., Hoogstraten H., and Post L. A mathematical model of the flow in the circle of Willis. Journal of Biomechanics 19 (1986) 187-194
14. Hillen B., Drinkenburg A.H., Hoogstraten H.W., and Post L. Analysis of flow and vascular resistance in a model of the circle of Willis. Journal of Biomechanics 21 (1988) 807-814
15. Hoksbergen A.W.J., Fülesdi B., Legemate D.A., and Csiba L. Collateral configuration of the circle of Willis. Transcranial color-coded duplex ultrasonography and comparison with postmortem anatomy. Stroke 31 (2000) 1346-1351
16. Hoksbergen A.W.J., Legemate D.A., Ubbink D.T., and Jacobs M.J.H.M. Collateral variations in circle of Willis in atherosclerotic population assessed by means of transcranial color-coded duplex ultrasonography. Stroke 31 (2000) 1656-1660
17. Hoksbergen A.W.J., Majoie C.B.L., Hulsmans F.J.H., and Legemate D.A. Assessment of the collateral function of the circle of Willis: three-dimensional time-of-flight MR angiography compared with transcranial color-coded duplex sonography. American Journal of Neuroradiology 24 (2003) 456-462
18. Karniadakis G.E., and Sherwin S.J. Spectral/hp Element Methods for CFD (2003), Oxford University Press, Oxford
19. Lippert H., and Pabst R. Arterial Variations in Man: Classification and Frequency (1985), J.F. Bergmann, Munich
20. McDonald D.A. Blood Flow in Arteries (1960), Williams and Wilkins, Baltimore
21. Milišić V., and Quarteroni A. Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. Mathematical Modelling and Numerical Analysis 38 (2004) 613-632
22. Moore S.M., Moorhead K.T., Chase J.G., David T., and Fink J. One-dimensional and three-dimensional models of cerebrovascular flow. Journal of Biomechanical Engineering 127 (2005) 440-449
23. Moore, S.M., David, T., Chase, J.G., Arnold, J., Fink, J., 2006. 3D models of blood flow in the cerebral vasculature. Journal of Biomechanics 39, 1454-1463.
24. Moorhead K.T., Doran C.V., Chase J.G., and David T. Lumped parameter and feedback control models of the auto-regulatory response in the circle of Willis. Computer Methods in Biomechanics and Biomedical Engineering 7 (2004) 121-130
25. Oates C. Cardiovascular Haemodynamics and Doppler Waveforms Explained (2001), Greenwich Medical Media LTD
26. Olufsen M.S. Structured tree outflow condition for blood flow in larger systemic arteries. American Journal of Physiology 276 (1999) H257-H268
27. O'Rourke M.F. Pressure and flow waves in systemic arteries and the anatomical design of the arterial system. Journal of Applied Physiology 23 (1967) 139-149
28. Oshima M. A new approach to cerebral hemodynamics. Patient-specific modelling and numerical simulation of blood and arterial wall interaction. IACM Expressions 16 (2004) 4-9
29. Rainest J.K., Jaffrin M.Y., and Shapiro A.H. A computer simulation of arterial dynamics in the human leg. Journal of Biomechanics 7 (1974) 77-91
30. Segers P., Dubois F., DeWachter D., and Verdonck P. Role and relevancy of a cardiovascular simulator. Cardiovascular Engineering 3 (1998) 48-56
31. Sherwin S.J., Formaggia L., Peiró J., and Franke V. Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. International Journal for Numerical Methods in Fluids 43 (2003) 673-700
32. Sherwin S.J., Franke V., Peiró J., and Parker K.H. One-dimensional modelling of a vascular network in space-time variables. Journal of Engineering Mathematics 47 (2003) 217-250
33. Simon A.C., Safar M.E., Levenson J.A., London G.M., Levy B.I., and Chau N.P. An evaluation of large arteries compliance in man. American Journal of Physiology 237 (1979) H550-H554
34. Smith N.P., Pullan A.J., and Hunter P.J. An anatomically based model of transient coronary blood flow in the heart. SIAM Journal on Applied Mathematics 62 (2001) 990-1018
35. Stergiopulos N., Young D.F., and Rogge T.R. Computer simulation of arterial flow with applications to arterial and aortic stenoses. Journal of Biomechanics 25 (1992) 1477-1488
36. Viedma A., Jiménez C., and Marco V. Extended Willis circle model to explain clinical observations in periorbital arterial flow. Journal of Biomechanics 30 (1997) 265-272
37. Wang J.J., and Parker K.H. Wave propagation in a model of the arterial circulation. Journal of Biomechanics 37 (2004) 457-470