Numerical simulations of pulsatile blood flow using a new constitutive model

Biorheology

Volumn 43, Issue 5, 2006, Pages 637-660

  Fang, Jiannong ^a   Owens, Robert G ^b  

^a EPFL   (Switzerland)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Aggregation; Complex viscosity; Pulsatile flow; Thixotropic; Viscoelastic; Womersley

Indexed keywords

ARTICLE; BLOOD FLOW; BLOOD FLOW VELOCITY; BLOOD RHEOLOGY; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; OSCILLATION; PULSATILE FLOW; SIMULATION; VISCOELASTICITY; VISCOSITY;

BLOOD FLOW VELOCITY; BLOOD VISCOSITY; ERYTHROCYTE AGGREGATION; HEMORHEOLOGY; HUMANS; MODELS, CARDIOVASCULAR; PULSATILE FLOW;

EID: 33750073202     PISSN: 0006355X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (52)

1. M. Anand and K.R. Rajagopal, A shear-thinning viscoelastic fluid model for describing the flow of blood, Int. J. Cardiovascular Medicine and Science 4 (2004), 59-68.
2. H.A. Barnes, The yield stress - a review or "πáß/ ôá pet" - everything flows?, J. Non-Newtonian Fluid Mech. 81 (1999), 133-178.
3. H.A. Barnes, P. Townsend and K. Walters, Flow of non-Newtonian liquids under a varying pressure gradient, Nature 224 (1969), 585-587.
4. H.A. Barnes, P. Townsend and K. Walters, Pulsatile flow of non-Newtonian liquids, Rheol. Acta 10 (1971), 517-527.
5. R.B. Bird, C.F. Curtiss, R.C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids, Vol. 2, Kinetic Theory, John Wiley & Sons, New York, 1987.
6. M. Bureau, J.C. Healy, D. Bourgoin and M. Joly, Rheological hysteresis of blood at low shear rate, Biorheology 17 (1980), 191-203.
7. C.G. Caro, T.J. Pedley, R.C. Schroter and W.A. Seed, The Mechanics of the Circulation, Oxford University Press, Oxford, 1978.
8. N. Casson, A flow equation for pigment-oil suspensions of printing ink type, in: Rheology of Disperse Systems, C.C. Mills, ed., Pergamon, 1959, pp. 84-102.
9. C.F. Chan Man Fong and D. De Kee, Generalized network type constitutive equations, Physica A 218 (1995), 56-68.
10. J. Chen and Z. Huang, Analytical model for effects of shear rate on rouleau size and blood viscosity, Biophysical Chemistry 58 (1996), 273-279.
11. S. Chien, Shear dependence of effective cell volume as determinant of blood viscosity, Science 168 (1970), 977-979.
12. S. Chien, R.G. King, R. Skalak, S. Usami and A.L. Copley, Viscoelastic properties of human blood and red cell suspensions, Biorheology 12 (1975), 341-346.
13. G.R. Cokelet, E.W. Merrill, E.R. Gilliland, H. Shin, A. Britten and R.E. Wells, Jr., The rheology of human blood, Trans. Soc. Rheol. 7 (1963), 303-318.
14. M.M. Cross, Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems, J. Colloid Sci. 20 (1965), 417-437.
15. J.M. Davies, S. Bhumiratana and R.B. Bird, Elastic and inertial effects in pulsatile flow of polymeric liquids in circular tubes, J. Non-Newtonian Fluid Mech. 3 (1978), 237-259.
16. F.H. El-Khatib and E.R. Damiano, Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube, Biorheology 40 (2003), 503-522.
17. W.J. Federspiel and G.R. Cokelet, Blood viscoelasticity for conditions of physiological flow in small arteries, Chem. Eng. Commun. 30 (1984), 275-284.
18. J.C. Healy and M. Joly, Rheological behavior of blood in transient flow, Biorheology 12 (1975), 335-340.
19. D.N. Ku, Blood flow in arteries, Annu. Rev. Fluid Mech. 29 (1997), 399-434.
20. D.W. Liepsch, Flow in tubes and arteries - a comparison, Biorheology 23 (1986), 395-433.
21. X.Y. Luo and Z.B. Kuang, A study on the constitutive equation of blood, J. Biomechanics 25 (1992), 929-934.
22. E.W. Merrill, E.R. Gilliland, G.C. Gokelet, H. Shin, A. Britten and R.E. Wells, Rheology of human blood, near and at zero flow. Effects of temperature and hematocrit level, Biophys. J. 3 (1963), 199-213.
23. E.W. Merrill, A.M. Benis, E.R. Gilliland, T.K. Sherwood and E.W. Salzman, Pressure-flow relations of human blood in hollow fibers at low flow rates, J. Appl. Physiol. 20 (1965), 954-967.
24. T. Murata and T.W. Secomb, Effects of shear rate on rouleau formation in simple shear flow, Biorheology 25 (1988), 113-122.
25. P. Neofytou, Comparison of blood rheological models for physiological flow simulation, Biorheology 41 (2004), 693-714.
26. R.G. Owens, A new microstructure-based constitutive model for human blood, J. Non-Newtonian Fluid Mech. (2006), to appear.
27. N. Phan-Thien, On pulsating flow of polymeric fluids, J. Non-Newtonian Fluid Mech. 4 (1978), 167-176.
28. N. Phan-Thien and J. Dudek, Pulsating flow revisited, J. Non-Newtonian Fluid Mech. 11 (1982), 147-161.
29. C. Picart, J.-M. Piau, H. Galliard and P. Carpentier, Human blood shear yield stress and its hematocrit dependence, J. Rheol. 42 (1998), 1-12.
30. D. Quemada, Rheology of concentrated disperse systems III. General features of the proposed non-Newtonian model. Comparison with experimental data, Rheol. Acta 17 (1978), 643-653.
31. D. Quemada, A rheological model for studying the hematocrit dependence of red cell-red cell and cell-protein interaction in blood, Biorheology 18 (1981), 501-514.
32. D. Quemada, A non-linear Maxwell model of biofluids: application to normal human blood, Biorheology 30 (1993), 253-265.
33. D. Quemada, Rheological modelling of complex fluids. I. The concept of effective volume fraction revisited, Eur. Phys. J. AP 1 (1998), 119-127.
34. D. Quemada, Rheological modelling of complex fluids. IV. Thixotropic and "thixoelastic" behaviour. Start-up and stress relaxation, creep tests and hysteresis cycles, Eur. Phys. J. AP 5 (1999), 191-207.
35. K.R. Rajagopal and A.R. Srinivasa, A thermodynamic framework for rate-type fluid models, J. Non-Newtonian Fluid Mech. 88 (2000), 207-227.
36. C.M. Rodkiewicz, P. Sinha and J.S. Kennedy, On the application of a constitutive equation for whole human blood, Trans. ASME 112 (1990), 198-206.
37. T. Shiga, K. Imaizumi, N. Harada and M. Sekiya, Kinetics of rouleaux formation using TV image analyzer. I. Human erythrocytes, Am. J. Physiol. 245 (1983), H252-H258.
38. D.A. Steinman and C.A. Taylor, Flow imaging and computing: large artery hemodynamics, Ann. Biomed. Eng. 33 (2005), 1704-1709.
39. N. Sun and D. De Kee, Simple shear, hysteresis and yield stress in biofluids, Can. J. Chem. Eng. 79 (2001), 36-41.
40. C.A. Taylor and M.T. Draney, Experimental and computational methods in cardiovascular fluid mechanics, Annu. Rev. Fluid Mech. 36 (2004), 197-231.
41. G.B. Thurston, Theory of oscillation of a viscoelastic fluid in a circular tube, J. Acoust. Soc. Am. 24 (1960), 210-213.
42. G.B. Thurston, Frequency and shear rate dependence of viscoelasticity of human blood, Biorheology 10 (1973), 375-381.
43. G.B. Thurston, Elastic effects in pulsatile blood flow, Microvasc. Res. 9 (1975), 145-157.
44. G.B. Thurston, The viscosity and viscoelasticity of blood in small diameter tubes, Microvasc. Res. 11 (1976), 133-146.
45. G.B. Thurston, Rheological parameters for the viscosity, viscoelasticity and thixotropy of blood, Biorheology 10 (1979), 149-162.
46. G. Vlastos, D. Lerche and B. Koch, The superposition of steady on oscillatory shear and its effect on the viscoelasticity of human blood and a blood-like model fluid, Biorheology 34 (1997), 19-36.
47. F.J. Walburn and D.J. Schneck, A constitutive equation for whole human blood, Biorheology 13 (1976), 201-218.
48. M.C. Williams, J.S. Rosenblatt and D.S. Soane, Theory of blood rheology based on a statistical mechanics treatment of rouleaux, and comparisons with data, Intern. J. Polymeric Mater. 21 (1993), 57-63.
49. J.R. Womersley, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J. Physiol. 127 (1955), 553-563.
50. K.K. Yeleswarapu, Evaluation of Continuum Models for Characterizing the Constitutive Behavior of Blood, PhD thesis, University of Pittsburgh, Pittsburgh, PA, 1996.
51. K.K. Yeleswarapu, M.V. Kameneva, K.R. Rajagopal and J.F. Antaki, The flow of blood in tubes: theory and experiment, Mech. Res. Comm. 25 (1998), 257-262.
52. J.-B. Zhang and Z.-B. Kuang, Study on blood constitutive parameters in different blood constitutive equations, J. Biomechanics 33 (2000), 355-360.