Synergy between shear-induced migration and secondary flows on red blood cells transport in arteries: Considerations on oxygen transport

Journal of the Royal Society Interface

Volumn 11, Issue 97, 2014, Pages

  Biasetti, Jacopo ^a   Spazzini, Pier Giorgio ^b   Hedin, Ulf ^c   Gasser, T Christian ^b  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b ISTITUTO NAZIONALE DI RICERCA METROLOGICA   (Italy)

^c KAROLINSKA UNIVERSITY HOSPITAL   (Sweden)

Author keywords

Artery; Haemoglobin; Oxygen transport; Red blood cells; Secondary flow; Shear induced migration

Indexed keywords

BLOOD; BLOOD VESSELS; CELLS; OXYGEN; PARTIAL PRESSURE; POSITIVE IONS;

ARTERY; HAEMOGLOBINS; OXYGEN TRANSPORT; RED BLOOD CELL; SHEAR-INDUCED MIGRATION;

SECONDARY FLOW;

OXYGEN;

ABDOMINAL AORTA ANEURYSM; ARTERY; ARTICLE; CAROTID ARTERY BIFURCATION; CAROTID SINUS; CELL MIGRATION; CELL TRANSPORT; COMMON CAROTID ARTERY; ERYTHROCYTE; FINITE ELEMENT ANALYSIS; FLOW RATE; GEOMETRY; HUMAN; MATHEMATICAL MODEL; OXYGEN TRANSPORT; PRESSURE; SHEAR FLOW; ANIMAL; BIOLOGICAL MODEL; BLOOD FLOW VELOCITY; CELL MOTION; COMPUTER SIMULATION; MECHANICAL STRESS; METABOLISM; PATHOLOGY; PATHOPHYSIOLOGY; PERIPHERAL OCCLUSIVE ARTERY DISEASE; SHEAR STRENGTH;

ANIMALS; ARTERIAL OCCLUSIVE DISEASES; ARTERIES; BLOOD FLOW VELOCITY; CELL MOVEMENT; COMPUTER SIMULATION; ERYTHROCYTES; HUMANS; MODELS, CARDIOVASCULAR; OXYGEN; SHEAR STRENGTH; STRESS, MECHANICAL;

EID: 84903649926     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2014.0403     Document Type: Article

References (63)

1. Chien S, Usami S, Taylor HM, Lundberg JL, Gregersen MI. 1966 Effects of hematocrit and plasma proteins on human blood rheology at low shear rates. J. Appl. Physiol. 21, 81-87.
2. Chien S. 1970 Shear dependence of effective cell volume as a determinant of blood viscosity. Science 169, 977-979. (doi:10.1126/science.168.3934.977)
3. Abbott JR, Tetlow N, Graham AL, Altobelli SA, Fukushima E, Mondy LA, Stephens TA. 1991 Experimental observations of particle migration in concentrated suspensions: Couette flow. J. Rheol. 35, 773-794. (doi:10.1122/1.550157)
4. Arp PA, Mason SG. 1977 The kinetics of flowing dispersion IX. Doublets of rigid spheres (experimental). J. Colloid Interface Sci. 61, 44-61. (doi:10.1016/0021-9797(77)90414-3)
5. Chow AW, Sinton SW, Iwamiya JH. 1994 Shearinduced particle migration in Couette and parallelplate viscometers: NMR imaging and stress measurements. Phys. Fluids 6, 2561-2576. (doi:10. 1063/1.868147)
6. Gadala-Maria F, Acrivos A. 1980 Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24, 799-811. (doi:10.1122/1. 549584)
7. Hookham PA. 1986 Concentration and velocity measurements in suspensions flowing through a rectangular channel. PhD thesis, California Institute of Technology, Pasadena, CA, USA.
8. Karnis A, Goldsmith HL, Mason SG. 1966 The kinetics of flowing dispersions I. Concentrated suspensions of rigid particles. J. Colloid Interface Sci. 22, 531-553. (doi:10.1016/0021-9797(66)90048-8)
9. Koh CJ, Hookham P, Leal LG. 1993 An experimental investigation of concentrated suspension flows in a rectangular channel. J. Fluid Mech. 266, 1-32. (doi:10.1017/S0022112094000911)
10. Leighton D, Acrivos A. 1987 Measurement of shearinduced self-diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 109-131. (doi:10. 1017/S0022112087000880)
11. Bagchi P. 2007 Mesoscale simulation of blood flow in small vessels. Biophys. J. 92, 1858-1877. (doi:10.1529/biophysj.106.095042)
12. Mansour MH, Bressloff NW, Shearman CP. 2010 Red blood cell migration in microvessels. Biorheology 47, 73-93.
13. Sharan M, Popel AS. 2001 A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall. Biorheology 38, 415-428.
14. van Weert K. Numerical and experimental analysis of shear-induced migration in suspension flow. Report no. WFW 96.062, Eindhoven University of Technology (EUT), Eindhoven, The Netherlands.
15. Aarts PAMM, van den Broek ST, Prins GW, Kuiken GDC, Sixma JJ, Heethaar RM. 1988 Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood. Arterioscler. Thromb. Vasc. Biol. 8, 819-824. (doi:10.1161/01. ATV.8.6.819)
16. Cokelet GR. 1999 Viscometric, in vitro and in vivo blood viscosity relationships: how are they related? Biorheology 36, 343-358.
17. Pries AR, Neuhaus D, Gaehtgens P. 1992 Blood viscosity in tube flow: dependence on diameter. Am. J. Physiol. 263, H1770-H1778.
18. Doddi SK, Bagchi P. 2009 Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79, 046318. (doi:10.1103/ PhysRevE.79.046318)
19. Zhang J, Johnson PC, Popel AS. 2007 An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows. Phys. Biol. 4, 285-295. (doi:10.1088/1478-3975/4/4/ 005)
20. Fedosov DA, Caswell B, Popel AS, Em Karniadakis G. 2010 Blood flow and cell-free layer in microvessels. Microcirculation 17, 615-628. (doi:10.1111/j.1549-8719.2010.00056.x)
21. Phillips RJ, Armstrong RC, Brown RA, Graham AL, Abbott Jr. 1991 A constitutive equation for concentrated suspensions that accounts for shearinduced particle migration. Phys. Fluids A 4, 30-40. (doi:10.1063/1.858498)
22. Liu X, Fan Y, Xu XY, Deng X. 2012 Nitric oxide transport in an axisymmetric stenosis. J. R. Soc. Interface 9, 2468-2478. (doi:10.1098/rsif. 2012.0224)
23. Crawford DW, Back LH, Cole MA. 1980 In vivo oxygen transport in the normal rabbit femoral arterial wall. J. Clin. Invest. 65, 1498-1508. (doi:10. 1172/JCI109815)
24. Crawford DW, Blankenhorn DH. 1991 Arterial wall oxygenation, oxyradicals, and atherosclerosis. Atherosclerosis 89, 97-108. (doi:10.1016/0021-9150(91) 90049-9)
25. Tarbell JM. 2003 Mass transport in arteries and the localization of atherosclerosis. Annu. Rev. Biomed. Eng. 5, 79-118. (doi:10.1146/annurev.bioeng. 5. 040202.121529)
26. Moore JA, Ethier CR. 1997 Oxygen mass transfer calculations in large arteries. J. Biomech. Eng. 119, 469-475. (doi:10.1115/1.2798295)
27. Auer M, Gasser TC. 2010 Reconstruction and finite element mesh generation of abdominal aortic aneurysms from computerized tomography angiography data with minimal user interaction. IEEE Trans. Med. Imaging 29, 1022-1028. (doi:10. 1109/TMI.2009.2039579)
28. Rao R, Mondy L, Sun A, Altobelli S. 2001 A numerical and experimental study of batch sedimentation and viscous resuspension. Int. J. Numer. Methods Fluids 39, 465-483. (doi:10. 1002/fld.246)
29. COMSOL v4.3a. 2012 COMSOL user manual, COMSOL AB. See http://www.comsol.com.
30. Malvern LE. 1969 Introduction to the mechanics of a continuous medium. Englewood Cliffs, NJ: Prentice Hall.
31. Ethier CR, Simmons CA. 2007 Introductory biomechanics: from cells to organisms. Cambridge, UK: Cambridge University Press.
32. Mills C, Gabe I, Gault J, Mason D, Ross J, Braunwald E, Shillingford JP. 1970 Pressure-flow relationships and vascular impedance in man. Cardiovasc. Res. 4, 405-417. (doi:10.1093/cvr/4.4.405)
33. Les AS, Shadden SC, Figueroa CA, Park JM, Tedesco MM, Herfkens RJ, Dalman RL, Taylor CA. 2010 Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics. Ann. Biomed. Eng. 38, 1288-1313. (doi:10.1007/s10439-010-9949-x)
34. Lee S-W, Antiga L, Spence JD, Steinman DA. 2008 Geometry of the carotid bifurcation predicts its exposure to disturbed flow. Stroke 39, 2341-2347. (doi:10.1161/STROKEAHA.107. 510644)
35. Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA. 2006 Outflow boundary conditions for threedimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods. Appl. Mech. Eng. 195, 3776-3796. (doi:10.1016/j.cma. 2005.04.014)
36. McDonald DA. 2004 Blood flow in arteries, 5th edn. London, UK: Edward Arnold.
37. Oka S. 1981 Cardiovascular hemorheology. Cambridge, UK: Cambridge University Press.
38. Biasetti J, Hussain F, Gasser TC. 2011 Blood flow and coherent vortices in the normal and aneurysmatic aortas: a fluid dynamical approach to intra-luminal thrombus formation. J. R. Soc. Interface 8, 1449-1461. (doi:10.1098/rsif.2011.0041)
39. Quemada D. 1981 A rheological model for studying the hematocrit dependence of red cell-red cell and red cell-protein interactions in blood. Biorheology 18, 501-516.
40. Quemada D. 1978 Rheology of concentrated disperse systems II: a model for non-Newtonian shear viscosity in steady flows. Rheol. Acta 17, 632-642. (doi:10.1007/BF01522036)
41. Jansen KE, Whiting CH, Hulbert GM. 2000 A generalized-a method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput. Methods Appl. Mech. Eng. 190, 305-319. (doi:10.1016/S0045-7825(00) 00203-6)
42. Deuflhard P. 1974 A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting. Numer. Math. 22, 289-315. (doi:10.1007/ BF01406969)
43. Subia SR, Ingber MS, Mondy LA, Altobelli SA, Graham AL. 1998 Modelling of concentrated suspensions using a continuum constitutive equation. J. Fluid Mech. 373, 193-219. (doi:10. 1017/S0022112098002651)
44. Krieger IM. 1972 Rheology of monodisperse latices. Adv. Colloid Interface Sci. 3, 111-136. (doi:10.1016/ 0001-8686(72)80001-0)
45. Fang Z, Phan-Thien N. 1995 Numerical simulation of particle migration in concentrated suspensions by a finite volume method. J. Non-Newton. Fluid Mech. 58, 67-81. (doi:10.1016/0377-0257(94)01355-L)
46. Hughes TJR, Franca LP, Hulbert GM. 1989 A new finite element formulation for computational fluid dynamics: VIII. The Galerkin least squares method for advective-diffusive equations. Comp. Methods Appl. Mech. Eng. 73, 173-189. (doi:10.1016/0045-7825(89)90111-4)
47. Humphrey JD. 2002 Cardiovascular solid mechanics: cells, tissues, and organs. New York, NY: Springer.
48. Jeong J, Hussain F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69-94. (doi:10.1017/ S0022112095000462)
49. Ku DN, Giddens DP, Zarins CK, Glagov S. 1985 Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque location and low oscillating shear stress. Arteriosclerosis 5, 293-302. (doi:10.1161/01.ATV.5. 3.293)
50. Zarins CK, Giddens DP, Bharadvaj BK, Sottiurai VS, Mabon RF, Glagov S. 1983 Carotid bifurcation atherosclerosis: quantitative correlation of plaque localization with flow velocity profiles and wall shear stress. Circ. Res. 53, 502-514. (doi:10.1161/ 01.RES.53.4.502)
51. Tada S, Tarbell JM. 2006 Oxygen mass transport in a compliant carotid bifurcation model. Ann. Biomed. Eng. 34, 9,1389-1399. (doi:10.1007/s10439-006- 9155-z)
52. Ma PP, Li XM, Ku DN. 1997 Convective mass transfer at the carotid bifurcation. J. Biomech. 30, 565-571. (doi:10.1016/S0021-9290(97)84506-X)
53. Qiu Y, Tarbell JM. 2000 Numerical simulation of oxygen mass transfer in a compliant curved tube model of a coronary artery. Ann. Biomed. Eng. 28, 26-38. (doi:10.1114/1.251)
54. Parmar KM et al. 2006 Integration of flowdependent endothelial phenotypes by Kruppel-like factor 2. J. Clin. Invest. 116, 49-58. (doi:10.1172/ JCI24787)
55. Peiffer V, Sherwin SJ, Weinberg PD. 2013 Does low and oscillatory wall shear stress correlate spatially with early atherosclerosis? A systematic review. Cardiovasc. Res. 99, 242-250. (doi:10.1093/cvr/ cvt044)
56. Zhang Q, Steinman DA, Friedman MH. 2010 Use of a factor analysis to characterize arterial geometry and predict hemodynamic risk: application to the human carotid bifurcation. J. Biomech. Eng. 132, 114505. (doi:10.1115/1.4002538)
57. Bijari PB, Antiga L, Gallo D, Wasserman BA, Steinman DA. 2012 Improved prediction of disturbed flow via hemodynamically-inspired geometric variables. J. Biomech. 45, 1632-1637. (doi:10.1016/j.jbiomech.2012.03.030)
58. Hoi Y, Wasserman BA, Lakatta EG, Steinman DA. 2010 Carotid bifurcation hemodynamics in older adults: effect of measured versus assumed flow waveform. J. Biomech. Eng. 132, 071006. (doi:10. 1115/1.4001265)
59. Hoi Y, Wasserman BA, Lakatta EG, Steinman DA. 2010 Effect of common carotid artery inlet length on normal carotid bifurcation hemodynamics. J. Biomech. Eng. 132, 121008. (doi:10.1115/1. 4002800)
60. Phan-Thien N, Fang Z. 1996 Entrance length and pulsatile flows of a model concentrated suspension. J. Rheol. 40, 521-529. (doi:10.1122/1.550757)
61. Grinberg L, Yakhot A, Karniadakis GE. 2009 Analyzing transient turbulence in a stenosed carotid artery by proper orthogonal decomposition. Ann. Biomed. Eng. 37, 2200-2217. (doi:10.1007/s10439-009-9769-z)
62. Kefayati S, Holdsworth DW, Poepping TL. 2014 Turbulence intensity measurements using particle image velocimetry in diseased carotid artery models: effect of stenosis severity, plaque eccentricity, and ulceration. J. Biomech. 47, 253-263. (doi:10.1016/j.jbiomech.2013.09.007)
63. Ishii M, Hibiki T. 2010 Thermo-fluid dynamics of two-phase flow. New York, NY: Springer.