A branched one-dimensional model of vessel networks

Journal of Fluid Mechanics

Volumn 621, Issue , 2009, Pages 183-204

  Fullana, Jose Maria ^a   Zaleski, Stéphane ^b,c  

^a Laboratoires Innothera   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c INSTITUT JEAN LE ROND D ALEMBERT   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BLOOD PRESSURE; FREQUENCY RESPONSE; MICROCIRCULATION; MUSCLE;

BRANCHING POINTS; CHARACTERISTIC LENGTH; CLINICAL OBSERVATION; MUSCLE CONTRACTIONS; MUSCULAR ACTIVITIES; NUMERICAL PREDICTIONS; ONE-DIMENSIONAL MODEL; REFLECTION OF WAVES;

BLOOD;

BLOOD; CONFLUENCE; FLOW VELOCITY; MODELING; NUMERICAL METHOD; ONE-DIMENSIONAL MODELING;

EID: 65649107299     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008004771     Document Type: Article

References (53)

1. ALIMI, Y. S., BARTHELEMY, P. & JUHAN, C. 1994 Venous pump of the calf: A stduy of venous and muscular pressures. J. Vascu. Surg. 20 (5), 728-735.
2. ANLIKER, M., ROCKWELL, L. & OGDEN, E. 1971 Nonlinear analysis of flow pulses and shock waves in arteries. ZAMP 22, 217-246.
3. AVOLIO, A. 1980 Multi-branched model of the human arterial system. Med. Biol. Engng Comp. 18, 709-718.
4. BASSEZ, S., CHAUVEAU, M. & FLAUD, P. 2001 Modeling of the deformation of flexible tubes using a single law. application to veins of the lower limb. J. Biomech. Engng 123, 58-65.
5. BERNHARD, S., MOHLENKAMP, S., ERBEL, R. & TILGNER, A. 2005 Oscillatory flow in tube with time-dependent wall deformation and its application to myocardial bridges. In ESAIM: Proceeding (ed. E. Cancés & J-F. Gerbeau), vol. 14, pp. 25-40.
6. BERTRAM, C. D. & PEDLEY, T. J. 1982 A mathematical model of unsteady collapsible tube behaviour. J. Biomech. 15 (1), 39-50.
7. BROOK, BINDI S. 1997 The effect of gravity on the haemodynamics of the giraffe jugular vein. PhD thesis, University of Leeds.
8. CANCELLI, C. & PEDLEY, T. J. 1985 A separated flow model for collapsible tube oscillations. J. Fluid Mech. 157, 375-404.
9. COMOLET, R. 1984 Biomecanique Circulatoire. Masson.
10. CROS, F. 2003 Confluences, remplissage et vidange: Deux aspects singuliers du système veineux jambier. PhD thesis, Université de Paris 7.
11. DAI, G., GERTLER, J. P. & KAMM, R. D. 1999 The effects of external compression on venous blood flow and tissue deformation in the lower leg. J. Biomech. Engng 121 (6), 557-564.
12. ELAD, D., KAMM, R. D. & SHAPIRO, A. H. 1987 Choking phenomena in a lung like model. ASME J. Biomech. Engng 109, 1-9.
13. ELAD, D., KATZ, D., KIMMEL, E. & EINAV, S. 1991 Numerical schemes for unsteady fluid flow through collapsible tubes. J. Biomed. Engng 13, 10-18.
14. FALSON, O. B., HAOND, C., CHASLON, M., MOENNER, M., NAILI, S., PERRAULT, R., FINET, M. & RIBREAU, C. 1998 Endothelial cells in culture: An in vitro model of the wall shear stress gradient effect. J. Biomech. 31 (1001), 173-73.
15. FERNANDEZ, M. A., MILISIC, V. & QUARTERONI, A. 2005 Analysis of a geometrical multiscale blood flow model based on the coupling of ODEs and hyperbolic PDEs. Multiscale Model Simul. 4, 215-236.
16. FORMAGGIA, L., GERBEAU, J.-F., NOBILE, F. & QUARTERONI, A. 2001 On the coupling of 3d and 1d Navier-Stokes equations for flow problems in compliant vessels. Comput. Methods Applied Mech. Engng 191, 561-582.
17. FORMAGGIA, L., NOBILE, F., QUARTERONI, A., VENEZIANI, A. 1999 Multiscale modeling of the circulatory system: A preliminary analysis. Comput. Visual. Science 2, 75-84.
18. FULLANA, J. M., CROS, F., FLAUD, P. & CROS, F. 2003 Filling a collapsible tube. J. Fluid Mech. 494, 285-296.
19. FUNG, Y. C. 1996 Biomechanics:CIrculation. Springer.
20. GRIFFITHS, D. J. 1971 Hydrodynamics of male micturation. I. theory of steady flow through elastic walled tubes. Med. Biol. Engng 9 (6), 581-588.
21. GUYTON, A. C. & JONES, C. E. 1973 Central venous pressure: physiological significance and clinical implications. Am. Heart J. 86 (4), 431-437.
22. HEIL, M. & PEDLEY, T. J. 1996 Large post-buckling deformations of cylindrical shells conveying viscous flow. J. Fluids Struct. 10 565-599.
23. JAN D. L., KAMM, R. D. & SHAPIRO, A. H. 1983 Filling of partially collapsed compliant tube. J. Biomech. Engng 105, 12-18.
24. KAMM R. D. 1982 Bioengineering studies of periodic external compression as prophylaxis against deep vein thrombosis. Part I: numerical studies. J. Biomech. Engng 104 (2), 87-95.
25. KAMM, R. D. & PEDLEY, T. J. 1989 Flow in collapsible tube: A brief review. J. Biomech. Engng 111, 177-179.
26. KAMM, R. D. & SHAPIRO, A. H. 1979 Unsteady flow in a collapsible tube subjected to external pressure of body forces. J. Fluid Mech. 95, 1-78.
27. KIMMEL, E., KAMM, R. D. & SHAPIRO, A. H. 1988 Numerical solutions for steady and unsteady flow in a model of the pulmonary airways. J. Biomech. Engng 110 (4), 292-299.
28. LIGHTHILL, J. M. 1989 Pulse Propagation Theory, chap. 12, pp. 227-252. SIAM.
29. MACCORMACK, R. W. 1969 The effect of viscosity in hypervelocity impact cratering. AIAA Paper No. 69-454.
30. MARZO, A., LUO, X. Y. & BERTRAM, C. D. 2005 Three-dimensional flow through a thick-walled collapsible tube. J. Fluids Struct. 20 817-835.
31. MATON, B., THINEY, G., DANG, S., TRA, S., BASSEZ, S., WICART, P. & OUCHENE, A. 2006a Human muscle fatigue and elastic compressive stockings. Eur. J. Appl. Physiol. 97 (4), 432-442.
32. MATON, B., THINEY, G., OUCHÈNE A., FLAUD, P. & BARTHELEMY, P. 2006b Intramuscular pressure and surface emg in voluntary ankle dorsal flexion: Influence of elastic compressive stockings. J. Electromyogr. Kinesiol. 16 (3), 291-302.
33. MATSUZAKI, Y. & MATSUMOTO, T. 1989 Flow in a two-dimensional collapsible channel with rigid inlet and outlet. ASME J. Biomech. Engng 111, 180-184.
34. MCCLURKEN, M. E., KECECIOGLU, I., KAMM, R. D. & SHAPIRO, A. H. 1981 Steady, supercritical flow in collapsible tubes. Part 2. theoretical studies. J. Fluid. Mech. 109, 391-415.
35. NICOLAIDES, A. N. & ZUKOWSKI, A. J. 1986 The value of dynamic venous pressure measurements. World J. Surg. 10 (6), 919-924.
36. OLUFSEN, M. S. 1999 Structured tree outflow condition for blood flow in larger systemic arteries. Am. J. Physiol. 276 (1 Pt 2), H257-H268.
37. OLUFSEN, M. S. 2000 A one-dimensional fluid dynamic model of the systemic arteries. Stud. Health Technol. Inform. 71, 79-97.
38. OLUFSEN, M. S., PESKIN, C. S., KIM, W. Y., PEDERSEN, E. M., NADIM, A. & LARSEN, J. 2000a Simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann. Biomed. Engng 28 (11), 1281-1299.
39. OLUFSEN, M. S., PESKIN, C. S., KIM, W. Y., PEDERSEN, E.M., NADIM, A. & LARSEN, J. 2000b Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann. Biomed. Engng 28 (11), 1281-1299.
40. OZAWA, E. T., BOTTOM, K. E., XIAO, X. & KAMM, R. D. 2001 Numerical simulation of enhanced external counterpulsation. Ann. Biomed. Engng 29 (4), 284-97.
41. PEYRET, R. & TAYLOR, T. D. 1983 Computational Methods for Fluid Flow. Springer.
42. QUARTERONI, A. & FORMAGGIA, L. 2003 Mathematical Modelling and Numerical Simulation of the Cardiovascular System. In Handbook of Numerical Analysis Series, Vol. XII (special volume): Computational Models for the Human Body, (ed. P. G. Ciarlet & J. L. Lions, guest editor, N. Ayache). Elsevier.
43. RIBREAU, C., NAILI, S. & LANGLET, A. 1994 Head losses in smooth pipes obtained from collapsed tubes. J. Fluids Struct. 8, 183-200.
44. ROSAR, M. E. & PESKIN, C. S. 2001 Fluid flow in collapsible elastic tubes: A three-dimensional numerical model. N.Y. J. Math. 7, 281-302.
45. SHAPIRO, A. H. 1977 Steady flow in collapsible tubes. ASME J. Biomech. Engng 99, 126-147.
46. SHERWIN, S. J., FRANKE, V., PEIRO, J. & PARKER, K. 2003 One-dimensional modelling of vascular network in space-time variables. J. Engng Math. 47, 217-250.
47. STERGIOPULOS, N., YOUNG, D. F. & ROGGE, T. R. 1992 Computer simulation of arterial flow with applications to arterial and aortic stenoses. J. Biomech. 25, 1477-1488.
48. STETTLER, J. C., NIEDERER, P. & ANLIKER, M. 1981 Theoretical analysis of arterial hemodynamics including the influence of bifurcations. Part I: Mathematical models and prediction of normal pulse patterns. Ann. Biomed. Engng 9 (2), 145-164.
49. WAN, JING, STEELE, BROOKE, A., SEAN, STROHBAND, SVEN, G. R. FEIJÓO, HUGHES, THOMAS J. R. & TAYLOR, CHARLES A. 2002 A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease. Comput. Methods Biomech. Biomed. Engng 5 (3), 195-206.
50. WANG, J. J. & PARKER, K. H. 2004 Wave propagation in a model of the arterial circulation. J. Biomech. 37 (4), 457-470.
51. WESTERHOF, N., BOSMAN, F., VRIES, C. & NOORDERGRAAF, A. 1969 Analog studies of the human systemic arterial tree. J. Biomech. 2, 121-143.
52. WILD, R., PEDLEY, T. J. & RILEY, D. S. 1977 Viscous flow in collapsible tubes of slowly-varying elliptical cross-section. J. Fluid Mech. 81, 273-294.
53. YOUNG, D. F. & TSAI, F. Y. 1975 Flow characteristics in models of arterial stenosis. I. steady flow. J. Biomech. 6, 395-410.