Skip to main content
SpringerLink
Log in

Cell Distribution and Segregation Phenomena During Blood Flow

  • Chapter
  • First Online:
Complex Fluids in Biological Systems

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Abstract

Blood is the archetype of a biological complex fluid. It is complex in the microstructural and mechanical sense, as a multiphase non-Newtonian viscoelastic fluid, and also in the biological sense, as a tissue that has a wide range of functions from delivery of oxygen and nutrients to response to injury and inflammation. These forms of complexity are interconnected, as the physical nature of blood as a multiphase fluid is intimately related to its biological functions. In the present chapter, we summarize basic features of the structure and biology of blood as well as observations of its dynamics during flow in the body. Emphasis will be put on flow at small scales, where the particulate nature of blood as a suspension of many different types of cells becomes important both physically and functionally. The first part of the chapter describes the nature and biological functions of the various components of blood, as well as the distribution of these components in blood vessels. In particular, it has long been observed that the various cellular components of blood are distributed very nonuniformly, a phenomenon that is physiologically important as well as fascinating from the fluid-dynamical point of flow. The second part of the chapter focuses on computational and theoretical approaches for predicting and understanding the distribution and segregation of blood cells in flow. Various numerical methods are described, with a focus on one of the most widely used for multiphase small-scale flows, the boundary integral method. Computational results for model suspensions are presented that allow careful study of the basic mechanisms underlying segregation phenomena and a model framework is introduced that incorporates these mechanisms in an idealized way. This framework is a stepping stone toward a unified understanding of these segregation phenomena that will hopefully be useful in aiding the development of therapies to modify and exploit blood flow phenomena for disorders as varied as cancer, sickle cell disease, and hemorrhage.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. T. Audesirk, G. Audesirk, Biology: Life on Earth, 4th edn. (Prentice-Hall, Upper Saddle River, NJ, 1996)

    Google Scholar 

  2. Y.C. Fung, B.W. Zweifach, Annu. Rev. Fluid Mech. 3, 189 (1971)

    ADS  Google Scholar 

  3. M. Puig-De-Morales-Marinkovic, K.T. Turner, J.P. Butler, J.J. Fredberg, S. Suresh, Am. J. Physiol. Cell Physiol. 293(2), C597 (2007)

    Google Scholar 

  4. A. Kumar, M.D. Graham, Soft Matter 8, 10536 (2012)

    ADS  Google Scholar 

  5. D. Boal, Mechanics of the Cell, 2nd edn. (Cambridge University Press, Cambridge, 2012)

    Google Scholar 

  6. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter, Molecular Biology of the Cell, 5th edn. (Garland Science, New York, 2007)

    Google Scholar 

  7. M.J. Hickey, P. Kubes, Nat. Rev. Immunol. 9(5), 364 (2009)

    Google Scholar 

  8. S.P. Jackson, Blood 109(12), 5087 (2007)

    Google Scholar 

  9. J.A. Leopold, J. Loscalzo, in Platelets, Thrombosis and the Vessel Wall, ed. by M.C. Berndt (Harwood Academic Publishers, Amsterdam, 2000)

    Google Scholar 

  10. D.M. Wootton, D.N. Ku, Annu. Rev. Biomed. Eng. 1, 299 (1999)

    Google Scholar 

  11. B. Nieswandt, B. Aktas, A. Moers, U.J.H. Sachs, J. Thrombosis Haemostasis 3(8), 1725 (2005)

    Google Scholar 

  12. R. Tran, D.R. Myers, J. Ciciliano, E.L. Trybus Hardy, Y. Sakurai, B. Ahn, Y. Qiu, R.G. Mannino, M.E. Fay, W.A. Lam, J. Cell. Mol. Med. 17(5), 579 (2013)

    Google Scholar 

  13. R.D. Guy, A.L. Fogelson, J.P. Keener, Math. Med. 24(1), 111 (2007)

    MATH  Google Scholar 

  14. J. Cho, D.F. Mosher, J. Thrombosis and Haemostasis 4(7), 1461 (2006)

    Google Scholar 

  15. S.W. Schneider, S. Nuschele, A. Wixforth, C. Gorzelanny, A. Alexander-Katz, R.R. Netz, M.F. Schneider, Proc. Natl. Acad. Sci. USA 104(19), 7899 (2007)

    ADS  Google Scholar 

  16. J.E. Sadler, Annu. Rev. Biochem. 67(1), 395 (1998)

    MathSciNet  Google Scholar 

  17. B. Savage, E. Saldivar, Z. Ruggeri, Cell 84(2), 289 (1996)

    Google Scholar 

  18. T.A. Springer, J. Thrombosis Haemostasis 9, 130 (2011)

    Google Scholar 

  19. C.M. Ward, M.C. Berndt, in Platelets, Thrombosis and the Vessel Wall, ed. by M.C. Berndt (Harwood Academic Publishers, Amsterdam, 2000)

    Google Scholar 

  20. C. Siedlecki, B. Lestini, K. KottkeMarchant, S. Eppell, D. Wilson, R. Marchant, Blood 88(8), 2939 (1996)

    Google Scholar 

  21. Y.C. Fung, Biodynamics: Circulation (Springer, New York, 1996)

    Google Scholar 

  22. H.H. Lipowsky, Biorheology 50, 3 (2013)

    Google Scholar 

  23. E.W. Merrill, Physiol. Rev. 49(4), 863 (1969)

    Google Scholar 

  24. M. Brust, C. Schaefer, R. Doerr, L. Pan, M. Garcia, P.E. Arratia, C. Wagner, Phys. Rev. Lett. 110(7), 078305 (2013)

    ADS  Google Scholar 

  25. S. Chien, Science 168(3934), 977 (1970)

    ADS  Google Scholar 

  26. G.B. Thurston, Biophys. J. 12(9), 1205 (1972)

    ADS  Google Scholar 

  27. W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, 1989)

    Google Scholar 

  28. B. Neu, H.J. Meiselman, J. Biophys. 83(5), 2482 (2002)

    Google Scholar 

  29. M. Rampling, H. Meiselman, B. Neu, O. Baskurt, Biorheology 41(2), 91 (2004)

    Google Scholar 

  30. R. Fåhræus, T. Lindqvist, Am. J. Physiol. 96, 562 (1931)

    Google Scholar 

  31. A. Pries, D. Neuhaus, P. Gaehtgens, Am. J. Physiol. 263(6), H1770 (1992)

    Google Scholar 

  32. J.H. Barbee, G.R. Cokelet, Microvasc. Res. 3(1), 6 (1971)

    Google Scholar 

  33. G.A. Truskey, F. Yuan, D.F. Katz, Transport Phenomena in Biological Systems (Pearson Prentice Hall, 2004)

    Google Scholar 

  34. R. Skalak, N. Ozkaya, T.C. Skalak, Annu. Rev. Fluid Mech. 21, 167 (1989)

    ADS  MathSciNet  Google Scholar 

  35. S. Kim, P.K. Ong, O. Yalcin, M. Intaglietta, P.C. Johnson, Biorheology 46(3), 181 (2009)

    Google Scholar 

  36. A.R. Pries, T.W. Secomb, P. Gaehtgens, Cardiovasc. Res. 32(4), 654 (1996)

    Google Scholar 

  37. K. Svanes, B.W. Zweifach, Microvasc. Res. 1(2), 210 (1968)

    Google Scholar 

  38. Y.C. Fung, Microvasc. Res. 5(1), 34 (1973)

    Google Scholar 

  39. V. Doyeux, T. Podgorski, S. Peponas, M. Ismail, G. Coupier, J. Fluid Mech. 674, 359 (2011)

    MATH  ADS  MathSciNet  Google Scholar 

  40. S.D. Hudson, Phys. Fluids 15(5), 1106 (2003)

    ADS  MathSciNet  Google Scholar 

  41. S.K. Doddi, P. Bagchi, Int. J. Multiphase Flow 34(10), 966 (2008)

    Google Scholar 

  42. L.G. Leal, Annu. Rev. Fluid Mech. 12, 435 (1980)

    ADS  MathSciNet  Google Scholar 

  43. G. Danker, P. Vlahovska, C. Misbah, Phys. Rev. Lett. 102(14), 148102 (2009)

    ADS  Google Scholar 

  44. Y.L. Chen, M.D. Graham, J.J. de Pablo, K. Jo, D.C. Schwartz, Macromolecules 38(15), 6680 (2005)

    ADS  Google Scholar 

  45. J.R. Smart, D.T. Leighton, Phys. Fluids A 3(1), 21 (1991)

    ADS  Google Scholar 

  46. M.D. Graham, Annu. Rev. Fluid Mech. 43(1), 273 (2011)

    ADS  Google Scholar 

  47. R.M. Jendrejack, D.C. Schwartz, J.J. de Pablo, M.D. Graham, J. Chem. Phys. 120(5), 2513 (2004)

    ADS  Google Scholar 

  48. H. Ma, M.D. Graham, Phys. Fluids 17(8), 083103 (2005)

    ADS  Google Scholar 

  49. T. Fischer, C. Haest, M. Stöhr-Liesen, H. Schmid-Schönbein, R. Skalak, Biophys. J. 34(3), 409 (1981)

    Google Scholar 

  50. S. Henon, G. Lenormand, A. Richert, F. Gallet, Biophys. J. 76(2), 1145 (1999)

    Google Scholar 

  51. R. Hochmuth, R. Waugh, Annu. Rev. Physiol. 49(1), 209 (1987)

    Google Scholar 

  52. J. Li, M. Dao, C. Lim, S. Suresh, Biophys. J. 88(5), 3707 (2005)

    Google Scholar 

  53. D. Barthes-Biesel, A. Diaz, E. Dhenin, J Fluid Mech. 460, 211 (2002)

    MATH  ADS  Google Scholar 

  54. P. Pranay, R.G. Henriquez Rivera, M.D. Graham, Phys. Fluids 24(6), 061902 (2012)

    ADS  Google Scholar 

  55. G. Segre, A. Silberberg, J Fluid Mech. 14(1), 136 (2005)

    ADS  Google Scholar 

  56. G. Segre, A. Silberberg, J Fluid Mech. 14(1), 115 (2005)

    ADS  Google Scholar 

  57. B.P. Ho, L.G. Leal, J. Fluid Mech. 65(02), 365 (1974)

    MATH  ADS  Google Scholar 

  58. J.A. Schonberg, E.J. Hinch, J Fluid Mech 203, 517 (1989)

    MATH  ADS  MathSciNet  Google Scholar 

  59. D. Di Carlo, Lab Chip 9(21), 3038 (2009)

    Google Scholar 

  60. E.J. Lim, T.J. Ober, J.F. Edd, G.H. McKinley, M. Toner, Lab Chip 12(12), 2199 (2012)

    Google Scholar 

  61. J.C. Firrell, H.H. Lipowsky, Am. J. Physiol.-Heart C. 256(6), H1667 (1989)

    Google Scholar 

  62. G.J. Tangelder, H.C. Teirlinck, D.W. Slaaf, R.S. Reneman, Am. J. Physiol.-Heart C. 248(3), H318 (1985)

    Google Scholar 

  63. A.S. Popel, P.C. Johnson, Annu. Rev. Fluid Mech. 37, 43 (2005)

    ADS  MathSciNet  Google Scholar 

  64. A.W. Browne, L. Ramasamy, T.P. Cripe, C.H. Ahn, Lab Chip 11(14), 2440 (2011)

    Google Scholar 

  65. A. Jain, L.L. Munn, Lab Chip 11(17), 2941 (2011)

    Google Scholar 

  66. H.W. Hou, A.A.S. Bhagat, A.G.L. Chong, P. Mao, K.S.W. Tan, J. Han, C.T. Lim, Lab Chip 10(19), 2605 (2010)

    Google Scholar 

  67. S.C. Hur, N.K. Henderson-MacLennan, E.R.B. McCabe, D. Di Carlo, Lab Chip 11(5), 912 (2011)

    Google Scholar 

  68. M.J. Pearson, H.H. Lipowsky, Am. J. Physiol.-Heart C. 279(4), H1460 (2000)

    Google Scholar 

  69. H.L. Goldsmith, S. Spain, Microvasc. Res. 27(2), 204 (1984)

    Google Scholar 

  70. K.B. Abbitt, G.B. Nash, Am. J. Physiol.-Heart C. 285(1), H229 (2003)

    Google Scholar 

  71. A. Jain, L.L. Munn, PLoS ONE 4, e7104 (2009)

    ADS  Google Scholar 

  72. D. Fedosov, J. Fornleitner, G. Gompper, Phys. Rev. Lett. 108(2) (2012)

    Google Scholar 

  73. C. Sun, C. Migliorini, L.L. Munn, Biophys. J. 85(1), 208 (2003)

    Google Scholar 

  74. J.B. Freund, Phys. Fluids 19(2), 023301 (2007)

    ADS  Google Scholar 

  75. B. Woldhuis, G.J. Tangelder, D.W. Slaaf, R.S. Reneman, Am. J. Physiol.-Heart C. 262(4), H1217 (1992)

    Google Scholar 

  76. P.A. Aarts, S.A.V.D. Broek, G.W. Prins, G.D. Kuiken, J.J. Sixma, R.M. Heethaar, Arterioscl. Throm. Vas. 8(6), 819 (1988)

    Google Scholar 

  77. W. Tilles, E.C. Eckstein, Microvasc. Res. 33, 211 (1987)

    Google Scholar 

  78. C. Yeh, E.C. Eckstein, J. Biophys. 66(5), 1706 (1994)

    Google Scholar 

  79. L. Crowl, A.L. Fogelson, J. Fluid Mech. 676, 348 (2011)

    MATH  ADS  MathSciNet  Google Scholar 

  80. H. Zhao, E. Shaqfeh, Phys. Rev. E 83(6) (2011)

    Google Scholar 

  81. T. Al Momani, H.S. Udaykumar, J.S. Marshall, K.B. Chandran, Ann. Biomed. Eng. 36(6), 905 (2008)

    Google Scholar 

  82. R.B. Huang, S. Mocherla, M.J. Heslinga, P. Charoenphol, O. Eniola-Adefeso, Mol. Membr. Biol. 27, 312 (2010)

    Google Scholar 

  83. F. Gentile, C. Chiappini, D. Fine, R.C. Bhavane, M.S. Peluccio, M. Cheng, X. Liu, M. Ferrari, P. Decuzzi, J. Biomech. 41(10), 2312 (2008)

    Google Scholar 

  84. K. Loomis, K. McNeeley, R.V. Bellamkonda, Soft Matter 7(3), 839 (2010)

    ADS  Google Scholar 

  85. H. Cabral, Y. Matsumoto, K. Mizuno, Q. Chen, M. Murakami, M. Kimura, Y. Terada, M.R. Kano, K. Miyazono, M. Uesaka, et al., Nat. Nanotechnol. 6(12), 815 (2011)

    ADS  Google Scholar 

  86. R.E. Serda, B. Godin, E. Blanco, C. Chiappini, M. Ferrari, Biochim. Biophys. Acta 1810(3), 317 (2011)

    Google Scholar 

  87. P. Decuzzi, B. Godin, T. Tanaka, S. Lee, C. Chiappini, X. Liu, M. Ferrari, J. Controlled Release 141(3), 320 (2010)

    Google Scholar 

  88. P. Charoenphol, R.B. Huang, O. Eniola-Adefeso, Biomaterials 31(6), 1392 (2010)

    Google Scholar 

  89. J. Tan, A. Thomas, Y. Liu, Soft Matter 8, 1934 (2012)

    ADS  Google Scholar 

  90. F.I. Faruqui, M.D. Otten, P.I. Polimeni, Circulation 75(3), 627 (1987)

    Google Scholar 

  91. C.A. Macias, M.V. Kameneva, J.J. Tenhunen, J.C. Puyana, M.P. Fink, Shock 22(2), 151 (2004)

    Google Scholar 

  92. P.J. Marascalco, H.C. Blair, A. Nieponice, L.J. Robinson, M.V. Kameneva, ASAIO J. 55(5), 503 (2009)

    Google Scholar 

  93. M.V. Kameneva, Z.J.J. Wu, A. Uraysh, B. Repko, K.N. Litwak, T.R. Billiar, M.P. Fink, R.L. Simmons, B. Griffith, H. Borovetz, Biorheology 41(1), 53 (2004)

    Google Scholar 

  94. P.S. Virk, AIChE J. 21(4), 625 (1975)

    Google Scholar 

  95. H.L. Greene, R.F. Mostardi, R.F. Nokes, Polym. Eng. Sci. 20(7), 499 (1980)

    Google Scholar 

  96. N. Antonova, Z. Lazarov, Clin. Hemorheol. Micro. 30(3–4), 381 (2004)

    Google Scholar 

  97. J.J. Pacella, M.V. Kameneva, M. Csikari, E. Lu, F.S. Villanueva, Eur. Heart J. 27(19), 2362 (2006)

    Google Scholar 

  98. T. Sakai, B.M. Repko, B.P. Griffith, J.H. Waters, M.V. Kameneva, Brit. J. Anaesth. 98(1), 23 (2006)

    Google Scholar 

  99. J.J. Pacella, M.V. Kameneva, F.S. Villanueva, Biorheology 46(5), 365 (2009)

    Google Scholar 

  100. X. Chen, D. Zha, J. Xiu, Y. Liao, K. Cui, H. Lin, Z. Jian, F. Hu, X. Huang, B. Zhou, Q. Huang, J. Bin, Y. Liu, Int. J. Cardiol. 147(1), 112 (2011)

    Google Scholar 

  101. A. Cotoia, M.V. Kameneva, P.J. Marascalco, M.P. Fink, R.L. Delude, Shock 31(3), 258 (2009)

    Google Scholar 

  102. M.V. Kameneva, M.S. Polyakova, E.V. Fedoseeva, Fluid Dyn. 25(6), 956 (1991)

    ADS  Google Scholar 

  103. P.C. Sousa, P.M. Coelho, M.S.N. Oliveira, M.A. Alves, J. Non-Newton. Fluid Mech. 166 (17–18), 1033 (2011)

    MATH  Google Scholar 

  104. G. Schettler, H. Schmid-Schonbein, H. Morl, H. Diehm (eds.), Fluid Dynamics as a localizing Factor for Atherosclerosis (Springer, Berlin, 1983)

    Google Scholar 

  105. J.N. Marhefka, R. Zhao, Z.J. Wu, S.S. Velankar, J.F. Antaki, M.V. Kameneva, Biorheology 46(4), 281 (2009)

    Google Scholar 

  106. R. Zhao, J. Marhefka, J. Antaki, M. Kameneva, Biorheology 47(3), 193 (2010)

    Google Scholar 

  107. A.L. Fogelson, R.D. Guy, Comput. Method. Appl. M. 197(25–28), 2087 (2008)

    MATH  MathSciNet  Google Scholar 

  108. H. Zhao, E.S.G. Shaqfeh, V. Narsimhan, Phys. Fluids 24(1), 011902 (2012)

    ADS  Google Scholar 

  109. E.C. Eckstein, F. Belgacem, Biophys. J. 60, 53 (1991)

    Google Scholar 

  110. A. Kumar, M.D. Graham, Phys. Rev. E 84(6), 066316 (2011)

    ADS  MathSciNet  Google Scholar 

  111. A. Kumar, M.D. Graham, Phys. Rev. Lett. 109, 108102 (2012)

    ADS  Google Scholar 

  112. A. Kumar, R.G. Henriquez Rivera, M.D. Graham, J. Fluid Mech. 738, 423 (2014)

    ADS  Google Scholar 

  113. H.S. Lew, Y.C. Fung, Biophys. J. 10(1), 80 (1970)

    ADS  Google Scholar 

  114. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge 1992)

    MATH  Google Scholar 

  115. A. Kumar, M.D. Graham, J. Comput. Phys. 231, 6682 (2012)

    MATH  ADS  MathSciNet  Google Scholar 

  116. M. Loewenberg, E. Hinch, J. Fluid Mech. 321(8), 395 (1996)

    MATH  ADS  Google Scholar 

  117. S. Ramanujan, C. Pozrikidis, J. Fluid Mech. 361, 117 (1998)

    MATH  ADS  MathSciNet  Google Scholar 

  118. A.Z. Zinchenko, R.H. Davis, J. Fluid Mech. 455, 21 (2002)

    MATH  ADS  Google Scholar 

  119. H. Zhao, A.H.G. Isfahani, L.N. Olson, J.B. Freund, J. Comput. Phys. 229, 3726 (2010)

    MATH  ADS  MathSciNet  Google Scholar 

  120. G. Ghigliotti, T. Biben, C. Misbah, J. Fluid Mech. 653(1), 489 (2010)

    MATH  ADS  Google Scholar 

  121. C. Peskin, Acta Numerica 11, 479 (2002)

    MATH  MathSciNet  Google Scholar 

  122. D.M. McQueen, C.S. Peskin, ACM SIGGRAPH Computer Graphics 34(1), 56 (2000)

    Google Scholar 

  123. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, Y.J. Jan, J. Comput. Phys. 169(2), 708 (2001)

    MATH  ADS  Google Scholar 

  124. P. Bagchi, Biophys. J. 92, 1858 (2007)

    ADS  Google Scholar 

  125. P. Pranay, S.G. Anekal, J.P. Hernandez-Ortiz, M.D. Graham, Phys. Fluids 22, 123103 (2010)

    ADS  Google Scholar 

  126. S. Chen, G.D. Doolen, Annu. Rev. Fluid Mech. 30(1), 329 (1998)

    ADS  MathSciNet  Google Scholar 

  127. A. Ladd, R. Verberg, J. Stat. Phys. 104(5–6), 1191 (2001)

    MATH  ADS  MathSciNet  Google Scholar 

  128. P. Hoogerbrugge, J. Koelman, EPL (Europhys. Lett.) 19(3), 155 (1992)

    Google Scholar 

  129. P.B. Warren, Curr. Opin. Colloid Interface Sci. 3(6), 620 (1998)

    Google Scholar 

  130. R.M. MacMeccan, J.R. Clausen, G.P. Neitzel, C.K. Aidun, J. Fluid Mech. 618, 13 (2009)

    MATH  ADS  MathSciNet  Google Scholar 

  131. I.V. Pivkin, G.E. Karniadakis, Phys. Rev. Lett. 101(11), 118105 (2008)

    ADS  Google Scholar 

  132. S. Kim, S.J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover Publicatons, Newyork, 2005)

    Google Scholar 

  133. G. Muldowney, J.J.L. Higdon, J. Fluid Mech. 298, 167 (1995)

    MATH  ADS  Google Scholar 

  134. S.K. Veerapaneni, A. Rahimian, G. Biros, D. Zorin, J. Comput. Phys. 230, 5610 (2011)

    MATH  ADS  MathSciNet  Google Scholar 

  135. M. Deserno, C. Holm, J. Chem. Phys. 109, 7678 (1998)

    ADS  Google Scholar 

  136. L. Greengard, V. Rokhlin, J. Comput. Phys. 73, 325 (1987)

    MATH  ADS  MathSciNet  Google Scholar 

  137. H. Hasimoto, J. Fluid Mech. 5, 317 (1959)

    MATH  ADS  MathSciNet  Google Scholar 

  138. A. Rahimian, S.K. Veerapaneni, G. Biros, J. Comput. Phys. 229, 6466 (2010)

    MATH  ADS  MathSciNet  Google Scholar 

  139. J.P. Hernandez-Ortiz, J.J. de Pablo, M.D. Graham, Phys. Rev. Lett. 98, 140602 (2007)

    ADS  Google Scholar 

  140. N. Mohandas, E. Evans, Annu. Rev. Bioph. Biom. 23(1), 787 (1994)

    Google Scholar 

  141. N. Mohandas, P.G. Gallagher, Blood 112(10), 3939 (2008)

    Google Scholar 

  142. P. Dimitrakopoulos, Phys. Rev. E 85(4), 041917 (2012)

    ADS  Google Scholar 

  143. C. Pozrikidis, J. Comput. Phys. 169(2), 250 (2001)

    MATH  ADS  MathSciNet  Google Scholar 

  144. D.A. Fedosov, B. Caswell, G.E. Karniadakis, Biophys. J. 98(10), 2215 (2010)

    ADS  Google Scholar 

  145. T.W. Secomb, Mechanics of Red Blood Cells and Blood Flow in Narrow Tubes (Chapman and Hall/CRC, London, 2011), pp. 1–19

    Google Scholar 

  146. D. Barthes-Biesel, C. R. Physique 10(8), 764 (2009)

    ADS  Google Scholar 

  147. E. Lac, D. Barthes-Biesel, Phys. Fluids 17(7), 072105 (2005)

    ADS  Google Scholar 

  148. Z. Peng, A. Mashayekh, Q. Zhu, J. Fluid Mech. 742, 96 (2014)

    ADS  Google Scholar 

  149. D. Cordasco, A. Yazdani, P. Bagchi, Phys. Fluids 26(4), 041902 (2014)

    ADS  Google Scholar 

  150. T.M. Fischer, Biophys. J 86(5), 3304 (2004)

    Google Scholar 

  151. A. Viallat, M. Abkarian, Int. Jnl. Lab. Hem. 36(3), 237 (2014)

    Google Scholar 

  152. R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Biophys. J. 13, 245 (1973)

    ADS  Google Scholar 

  153. R. Waugh, E. Evans, Biophys. J. 26(1), 115 (1979)

    ADS  Google Scholar 

  154. M. Zurita-Gotor, J. Blawzdziewicz, E. Wajnryb, Phys. Rev. Lett. 108(6), 68301 (2012)

    ADS  Google Scholar 

  155. V. Narsimhan, H. Zhao, E.S.G. Shaqfeh, Phys. Fluids 25(6), 061901 (2013)

    ADS  Google Scholar 

  156. F.R. Da Cunha, E.J. Hinch, J. Fluid Mech. 309(1), 211 (1996)

    MATH  MathSciNet  Google Scholar 

  157. G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, Oxford, 1994)

    Google Scholar 

  158. M.S. Ivanov, S.F. Gimelshein, Annu. Rev. Fluid Mech. 30(1), 469 (1998)

    ADS  MathSciNet  Google Scholar 

  159. G.A. Bird, Annu. Rev. Fluid Mech. 10(1), 11 (1978)

    ADS  MathSciNet  Google Scholar 

  160. G. Drazer, J. Koplik, B. Khusid, A. Acrivos, J. Fluid Mech. 460, 307 (2002)

    MATH  ADS  MathSciNet  Google Scholar 

  161. K. Koura, Phys. Fluids 29, 3509 (1986)

    ADS  Google Scholar 

  162. R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, vol. 2, Dynamics of Polymeric Liquids (Wiley-Interscience, New York, 1987)

    Google Scholar 

  163. G. D’Avino, P. Maffettone, F. Greco, M. Hulsen, J. Non-Newton. Fluid Mech. 165(9–10), 466 (2010)

    MATH  Google Scholar 

  164. C. Dupont, A.V. Salsac, D. Barthès-Biesel, J. Fluid Mech. 721, 180 (2013)

    MATH  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgment

The authors’ research on issues related to blood flow has been supported by NSF, grants CBET-0852976 (funded under the American Recovery and Reinvestment Act of 2009) and CBET-1132579. The authors are grateful to Prof. Wilbur Lam and to Kushal Sinha, Pratik Pranay, and Rafael Henriquez Rivera for helpful discussions.

Author information

Authors and Affiliations

  1. University of Wisconsin-Madison, Madison, WI, 53706, USA

    Amit Kumar & Michael D. Graham

Authors
  1. Amit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael D. Graham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael D. Graham .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Wisconsin–Madison, Madison, Wisconsin, USA

    Saverio E. Spagnolie

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this chapter

Cite this chapter

Kumar, A., Graham, M.D. (2015). Cell Distribution and Segregation Phenomena During Blood Flow. In: Spagnolie, S. (eds) Complex Fluids in Biological Systems. Biological and Medical Physics, Biomedical Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2065-5_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-2065-5_11

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4939-2064-8

  • Online ISBN: 978-1-4939-2065-5

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation