A 3D/1D geometrical multiscale model of cerebral vasculature

Journal of Engineering Mathematics

Volumn 64, Issue 4, 2009, Pages 319-330

  Passerini, Tiziano ^a   de Luca, Mariarita ^a,b   Formaggia, Luca ^a   Quarteroni, Alfio ^c   Veneziani, Alessandro ^d  

^a POLITECNICO DI MILANO   (Italy)

^b University of Pittsburgh   (United States)

^c EPFL   (Switzerland)

^d EMORY UNIVERSITY   (United States)

Author keywords

Circle of Willis; Domain splitting; Geometrical multiscale modeling; Matching conditions

Indexed keywords

3-D PROBLEMS; 3D SIMULATIONS; CAROTID ARTERY; CEREBRAL CIRCULATION; CIRCLE OF WILLIS; COMPLEX NETWORKS; COMPUTATIONAL COSTS; COMPUTATIONAL HEMODYNAMICS; DOMAIN SPLITTING; DRIVING MECHANISM; GEOMETRICAL MULTISCALE MODELING; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; MATCHING CONDITION; MATCHING CONDITIONS; MULTI-SCALE MODELING; MULTISCALE MODELS; NUMERICAL MODELS; SPACE SCALE; THREE-DIMENSIONAL (3D); THREE-DIMENSIONAL MODEL; VASCULAR COMPLIANCE; VASCULATURE;

EULER EQUATIONS; HEMODYNAMICS; HYDRODYNAMICS; NAVIER STOKES EQUATIONS; ONE DIMENSIONAL; SURFACE MORPHOLOGY; THREE DIMENSIONAL COMPUTER GRAPHICS;

THREE DIMENSIONAL;

EID: 67649764406     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-009-9281-3     Document Type: Article

References (30)

1. Cebral JR, Castro MA, Soto O, Lohner R, Alperin N (2003) Blood-flow models of the circle of Willis from magnetic resonance data. J Eng Math 47: 369-386
2. Balboni G. Anatomia Umana 1. Ediz. Ermes
3. Mynard JP, Nithiarasu P (2008) A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronoary flow using the locally conservative Galerkin (LCG) method. Commun Numer Methods Eng 24: 367-417
4. Formaggia L, Nobile F, Quarteroni A, Veneziani A (1999) Multiscale modelling of the circulatory system: A preliminary analysis. Comput Visual Sci 2(2/3): 75-83
5. Quarteroni A, Formaggia L, Veneziani A (eds) (2009) Cardiovascular mathematics Springer. http://www.springer.com/math/applications/book/ 978-88-470-1151-9
6. Viedma A, Jimenez Ortiz C, Marco V (1997) Extended Willis circle model to explain clinical observations in periorbital arterial flow. J Biomech 30: 265-272
7. Alastruey J, Moore SM, Parker KH, David T, Peirò J, Sherwin SJ (2008) Reduced modelling of blood flow in the cerebral circulation: coupling 1D, 0-D and cerebral autoregulation models. Int J Num Methods Fl 56: 1061-1067
8. Ferrandez A, David T, Brown MD (2002) Numerical models of auto-regulation and blood flow in the cerebral circulation. Comput Methods Biomech Biomed Eng 5(1): 7-19
9. Vignon I, Figueroa CA, Jansen KC, Taylor CA (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 195: 3776-3796
10. Moura A (2007) The geometrical multiscale modelling of the cardiovascular system: Coupling 3D FSI and 1D models, Mox PhD Thesis, Department of Mathematics, Politecnico di Milano, Italy
11. Quarteroni A, Veneziani A (2003) Analysis of a geometrical multiscale model based on the coupling of PDE's and ODE's for Blood Flow Simulations. Mult Models Sim SIAM 1(2): 173-195
12. Formaggia L, Lamponi D, Quarteroni A (2003) One-dimensional models for blood flow in arteries. J Eng Math 47: 251-276
13. Stergiopulos N, Westerhof BE, Westerhof N (1999) Total arterial inertance as the fourth element of the Windkessel model. Am J Physiol 276: H81-H88
14. Alastruey J, Parker KH, Peirò J, Sherwin SJ (2008) Lumped parameter outflow models for 1D blood flow simulations: Effects on pulse waves and parameter estimation. Commun Comp Phys 4: 317
15. Alastruey J, Parker KH, Peirò J, Byrd SM, Sherwin SJ (2007) Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J Biomech 40: 1794-1805
16. Lippert H, Pabst R (1985) Arterial variations in man: Classification and frequency. JF Bergmann, Munich
17. Hetzel A, von Reuternc G-M, Wernza MG, Drostea DW, Schumacher M (2000) The carotid compression test for therapeutic occlusion of the internal carotid artery. Cerebrovasc Dis 10: 194-199
18. Rogers L (1947) The function of the circulus arteriosus of Willis. Brain 70: 171-178
19. Avman N, Bering EA (1961) A plastic model for the study of pressure changes in the circle of Willis and major cerebral arteries following arterial occlusion. J Neurosurg 18: 361-365
20. Murray KD (1964) Dimensions of circle of Willis and dynamic studies using electrical analogy. J Neurosurg 21: 26
21. Fasano VA, Broggi G (1966) Discussion sur le polygone de Willis. Neurochirurgie 12: 761
22. Clark ME, Himwich WA, Martin JD (1967) Simulation studies of factors influencing cerebral circulation. Acta Neurol Scand 43: 189
23. Hillen B (1986) On the meaning of the variability of the circle of Willis. Acta Morphol Neerlando-Scand 24: 79-80
24. Hillen B, Drinkenburg BAH, Hoogstraten HW, Post L (1988) Analysis of flow and vascular resistance in a model of the circle of Willis. J Biomech 21: 807-814
25. Lyden P, Nelson T (1997) Visualization of the cerebral circulation using three-dimensional transcranial power Doppler ultrasound imaging. J Neuroimag 7: 35-39
26. Macchi C, Catini C, Federico C et al (1996) Magnetic resonance angiographic evaluation of circulus arteriosus cerebri (circle of Willis): A morphology study in 100 human healthy subjects. Ital J Anat Embryol 101: 115-123
27. David T, Brown M, Ferrandez A (2003) Auto-regulation and blood flow in the cerebral circulation. Int J Numer Methods Fluids 43: 701-713
28. Matthys KS, Alastruey J, Peirò J, Khir AW, Segers P, Verdonck PR, Parker KH, Sherwin SJ (2007) Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J Biomech 40: 3476-3486
29. Prosi M, Zunino P, Perktold K, Quarteroni A (2005) Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: A new methodology for the model set up with applications to the study of disturbed lumenal flow. J Biomech 38(4): 903-17
30. Martin V, Clement F, Decoene A, Gerbeau JF (2005) Parameter identification for a one-dimensional blood flow model. Proceedings Cemracs 2004, Esaim, September 2005