Cell Biochemistry and Biophysics

, Volume 61, Issue 1, pp 1–22 | Cite as

Fluid Dynamics of Heart Development

  • Arvind SanthanakrishnanEmail author
  • Laura A. MillerEmail author
Review Paper


The morphology, muscle mechanics, fluid dynamics, conduction properties, and molecular biology of the developing embryonic heart have received much attention in recent years due to the importance of both fluid and elastic forces in shaping the heart as well as the striking relationship between the heart’s evolution and development. Although few studies have directly addressed the connection between fluid dynamics and heart development, a number of studies suggest that fluids may play a key role in morphogenic signaling. For example, fluid shear stress may trigger biochemical cascades within the endothelial cells of the developing heart that regulate chamber and valve morphogenesis. Myocardial activity generates forces on the intracardiac blood, creating pressure gradients across the cardiac wall. These pressures may also serve as epigenetic signals. In this article, the fluid dynamics of the early stages of heart development is reviewed. The relevant work in cardiac morphology, muscle mechanics, regulatory networks, and electrophysiology is also reviewed in the context of intracardial fluid dynamics.


Heart development Hemodynamics Shear stress Mathematical modeling Fluid dynamics 



We would like to thank the University of Utah Mathematical Biology Group and the UNC Fluids and Integrative & Mathematical Physiology Groups for their suggestions and insight. We would also like to thank Dr. Kathy K. Sulik for her excellent SEM images of the mouse embryonic heart used in this review. This work was funded by Miller’s Burroughs Wellcome Fund Career Award at the Scientific Interface.


  1. 1.
    Bartman, T., Walsh, E. C., Wen, K. K., McKane, M., Ren, J., Alexander, J., et al. (2004). Early myocardial function affects endocardial cushion development in zebrafish. PLoS Biology, 2, 673–681.CrossRefGoogle Scholar
  2. 2.
    Bennett, S. (1963). Morphological aspects of extracellular polysaccharides. Journal of Histochemistry and Cytochemistry, 11, 1423.CrossRefGoogle Scholar
  3. 3.
    Biben, C., Weber, R., Kesteven, S., Stanley, E., & McDonald, L. (2000). Cardiac septal and valvular dysmorphogenesis in mice heterozygous for mutations in the homeobox gene nkx2–5. Circulation Research, 87, 888–895.PubMedGoogle Scholar
  4. 4.
    Biechler, S. V., Potts, J. D., Yost, M. J., Junor, L., Goodwin, R. L., & Weidner, J. W. (2010). Mathematical modeling of flow-generated forces in an in vitro system of cardiac valve development. Annals of Biomedical Engineering, 38(1), 109–117.PubMedCrossRefGoogle Scholar
  5. 5.
    Boldt, T., Andersson, S., & Eronen, M. (2002). Outcome of structural heart disease diagnosed in utero. Scandinavian Cardiovascualr Journal, 36(2), 73–79.CrossRefGoogle Scholar
  6. 6.
    Bove, E. L., de Leval, M. R., Migliavacca, F., Guadagni, G., & Dubini, G. (2003). Computational fluid dynamics in the evaluation of hemodynamic performance of cavopulmonary connections after the norwood procedure for hypoplastic left heart syndrome. The Journal of Thoracic and Cardiovascular Surgery, 126(4), 1040–1047.PubMedCrossRefGoogle Scholar
  7. 7.
    Bringley, T. T., Childress, S., Vandenberghe, N., & Zhang, J. (2008). An experimental investigation and a simple model of a valveless pump. Physics of Fluids, 20, 033602-1–033602-15.CrossRefGoogle Scholar
  8. 8.
    Brinkman, H. C. (1947). A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Sciences Research Section A, 1, 27–34.CrossRefGoogle Scholar
  9. 9.
    Broboana, D., Muntean, T., & Balan, C. (2007). Experimental and numerical studies of weakly elastic viscous fluids in a Hele-Shaw geometry. Proceedings of the Romanian Academy, 8, 1–15.Google Scholar
  10. 10.
    Bruneau, B. G., Nemer, G., Schmitt, J. P., Charron, F., & Robitaille, L. (2001). A murine model of holtoram syndrome defines roles of the t-box transcription factor tbx5 in cardiogenesis and disease. Cell, 106, 709–721.PubMedCrossRefGoogle Scholar
  11. 11.
    Burggren, W. W. (2004). What is the purpose of the embryonic heart beat? Or how facts can ultimately prevail over physiological dogma. Physiological and Biochemical Zoology, 77, 333–345.PubMedCrossRefGoogle Scholar
  12. 12.
    Camenisch, T. D., Spicer, A. P., Brehm-Gibson, T., Biesterfeldt, J., & Augustine, M. L. (2000). Disruption of hyaluronan synthase-2 abrogates normal cardiac morphogenesis and hyaluronan-mediated transformation of epithelium to mesenchyme. Journal of Clinical Investigation, 106, 349–360.PubMedCrossRefGoogle Scholar
  13. 13.
    Chapman, W. B. (1918). The effect of the heart-beat upon the development of the vascular system in the chick. The American Journal of Anatomy, 23, 175–203.CrossRefGoogle Scholar
  14. 14.
    Chien, S., Usami, S., Dellenback, R. J., & Gregersen, M. I. (1970). Shear-dependent deformation of erythrocytes in rheology of human blood. American Journal of Physiology, 219, 136–142.PubMedGoogle Scholar
  15. 15.
    Cortez, R. (2001). The method of regularized Stokeslets. SIAM Journal of Scientific Computing, 23(4), 1204–1225.Google Scholar
  16. 16.
    Cokelet, G. R., Merrill, E. W., & Gilliland, E. R. (1963). The rheology of human blood: Measurement near and at zero shear rate. Transactions. Society of Rheology, 7, 303–317.CrossRefGoogle Scholar
  17. 17.
    Crowl, L. M., & Fogelson, A. L. (2009). Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells. Communications in Numerical Methods in Engineering, 26, 471–487.Google Scholar
  18. 18.
    Damiano, E. R., Long, D. S., & Smith, M. L. (2004). Estimation of viscosity profiles using velocimetry data from parallel flows of linearly viscous: Application to microvascular hemodynamics. Journal of Fluid Mechanics, 512, 119.CrossRefGoogle Scholar
  19. 19.
    Davies, P. F. (1995). Flow-mediated endothelial mechanotransduction. Physiological Reviews, 75, 519–560.PubMedGoogle Scholar
  20. 20.
    DeGroff, C. G., Thornburg, B. L., Pentecost, J. O., Thornburg, K. L., Gharib, M., Sahn, D. J., et al. (2003). Flow in the early embryonic human heart. Pediatric Cardiology, 24(4), 375–380.PubMedCrossRefGoogle Scholar
  21. 21.
    Dekker, R. J., Van Soest, S., Fontijn, R. D., Salamanca, S., de Groot, P. G., VanBavel, E., et al. (2002). Prolonged fluid shear stress induces a distinct set of endothelial cell genes, most specifically lung Krüppel-like factor (KLF2). Blood, 100, 1689–1698.PubMedCrossRefGoogle Scholar
  22. 22.
    Dewey, C. F., Jr., Bussolari, S. R., Gimbrone, M. A., Jr., & Davies, P. F. (1991). The dynamic response of vascular endothelial cells to fluid shear stress. Journal of Biomechanical Engineering, 103, 177–185.CrossRefGoogle Scholar
  23. 23.
    Fahraeus, R., & Lindqvist, T. (1931). The viscosity of the blood in narrow capillary tubes. American Journal of Physiology, 96, 562–568.Google Scholar
  24. 24.
    Fishman, M. C., & Chien, K. R. (1997). Fashioning the vertebrate heart: Earliest embryonic decisions. Development, 124, 2099–2117.PubMedGoogle Scholar
  25. 25.
    Forouhar, A. S., Liebling, M., Hickerson, A., Moghaddam, A. N., Tsai, H. J., Hove, J. R., et al. (2006). The embryonic vertebrate heart tube is a dynamic suction pump. Science, 312, 751–753.PubMedCrossRefGoogle Scholar
  26. 26.
    Fung, Y. C. (1996). Biomechanics: Circulation (2nd ed.). New York: Springer-Verlag.Google Scholar
  27. 27.
    Gerould, J. H. (1929). History of the discovery of periodic reversal of heartbeat in insects. Biological Bulletin, 56(3), 215–225.CrossRefGoogle Scholar
  28. 28.
    Gilbert, S. F. (2000). Developmental Biology. Sunderland, MA: Sinauer Associates, Inc.Google Scholar
  29. 29.
    Glickman, N. S., & Yelon, D. (2002). Cardiac development in zebrafish: Coordination of form and function. Seminars in Cell & Developmental Biology, 13, 507–513.CrossRefGoogle Scholar
  30. 30.
    Griffith, B., & Peskin, C. S. (2010). An immersed boundary formulation of the bidomain equations. Unpublished, details available at
  31. 31.
    Groenendijk, B. C. W., Hierck, B. P., Vrolijk, J., Baiker, M., Pourquie, M. J. B. M., Gittenberger-de-Groot, A. C., et al. (2005). Changes in shear stress-related gene expression after experimentally altered venous return in the chicken embryo. Circulation Research, 96, 1291–1298.PubMedCrossRefGoogle Scholar
  32. 32.
    Groenendijk, B. C. W., Van der Heiden, K., Hierck, B. P., & Poelmann, R. E. (2007). The role of shear stress on ET-1, KLF2, and NOS-3 expression in the developing cardiovascular system of chicken embryos in a venous ligation model. Physiology, 22, 380–389.PubMedCrossRefGoogle Scholar
  33. 33.
    Gruber, J., & Epstein, J. A. (2004). Development gone awry–congenital heart disease. Circulation Research, 94, 273–283.PubMedCrossRefGoogle Scholar
  34. 34.
    Hamburger, V., & Hamilton, H. (1951). A series of normal stages in the development of the chick embryo. Journal of Morphology, 88, 49–92.CrossRefGoogle Scholar
  35. 35.
    Henriquez, C. S. (1993). Simulating the electrical behavior of cardiac tissue using the bidomain model. Critical Reviews in Biomedical Engineering, 21, 1–77.PubMedGoogle Scholar
  36. 36.
    Herrmann, C., Wray, J., Travers, F., & Bartman, T. (1992). Effect of 2,3-butanedione monoxime on myosin and myofibrillar atpases: An example of an uncompetitive inhibitor. Biochemistry, 31, 12227–12232.PubMedCrossRefGoogle Scholar
  37. 37.
    Hickerson, A. I., & Gharib, M. (2006). On the resonance of a pliant tube as a mechanism for valveless pumping. Journal of Fluid Mechanics, 555(1), 141–148.CrossRefGoogle Scholar
  38. 38.
    Hickerson, A. I., Rinderknecht, D., & Gharib, M. (2005). Experimental study of the behavior of a valveless impedance pump. Experiments in Fluids, 38, 534–540.CrossRefGoogle Scholar
  39. 39.
    Hierck, B. B. P., Van der Heiden, K. K., Poelma, C., Westerweel, J., & Poelmann, R. E. (2008). Fluid shear stress and inner curvature remodeling of the embryonic heart. Choosing the right lane!. TheScientificWorldJournal, 8, 212–222.PubMedCrossRefGoogle Scholar
  40. 40.
    Hogers, B., DeRuiter, M. C., Baasten, A. M., Gittenberger-de Groot, A. C., & Poelmann, R. E. (1995). Intracardiac blood flow patterns related to the yolk sac circulation of the chick embryo. Circulation Research, 76, 871–877.PubMedGoogle Scholar
  41. 41.
    Hogers, B., DeRuiter, M. C., Gittenberger-de Groot, A. C., & Poelmann, R. E. (1997). Unilateral vitelline vein ligation alters intracardiac blood flow patterns and morphogenesis in the chick embryo. Circulation Research, 80, 473–481.PubMedGoogle Scholar
  42. 42.
    Hove, J. R. (2004). In vivo biofluid imaging in the developing zebrafish. Birth Defects Research, 72, 277–289.PubMedCrossRefGoogle Scholar
  43. 43.
    Hove, J. R. (2006). Quantifying cardiovascular flow dynamics during early development. Pediatric Research, 60, 6–13.PubMedCrossRefGoogle Scholar
  44. 44.
    Hove, J. R., Köster, R. W., Forouhar, A. S., Bolton, G. A., Fraser, S. E., & Gharib, M. (2003). Intracardiac fluid forces are an essential epigenetic factor for embryonic cardiogenesis. Nature, 421, 172–177.PubMedCrossRefGoogle Scholar
  45. 45.
    Hron, J., Malek, J., & Turek, S. (2000). A numerical investigation of flows of shear-thinning fluids with applications to blood rheology. International Journal for Numerical Methods in Fluids, 32, 863–879.CrossRefGoogle Scholar
  46. 46.
    Ichikawa, A., & Hoshino, Z. (1967). On the cell architecture of the heart of Ciona intestinalis. Zoological Magazine, 76, 148–153.Google Scholar
  47. 47.
    Iomini, C., Tejada, K., Mo, W., Vaananen, H., & Piperno, G. (2004). Primary cilia of human endothelial cells disassemble under laminar shear stress. Journal of Cell Biology, 164, 811–817.PubMedCrossRefGoogle Scholar
  48. 48.
    Jones, E. A. V., Baron, M. H., Fraser, S. E., & Dickinson, M. E. (2004). Measuring hemodynamics during development. American Journal of Physiology. Heart and Circulatory Physiology, 287, H1561–H1569.PubMedCrossRefGoogle Scholar
  49. 49.
    Jung, E., & Peskin, C. S. (2001). Two-dimensional simulations of valveless pumping using the immersed boundary method. SIAM Journal on Scientific Computing, 23, 19–45.CrossRefGoogle Scholar
  50. 50.
    Kim, G. B., & Lee, S. J. (2006). X-ray PIV measurements of blood flows without tracer particles. Experiments in Fluids, 41, 195–200.CrossRefGoogle Scholar
  51. 51.
    Lee, P., Griffith, B. E., & Peskin, C. S. (2010). The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement. Journal of Computational Physics, 229(13), 5208–5227.Google Scholar
  52. 52.
    Leiderman, K. M., Miller, L. A., & Fogelson, A. L. (2008). The effects of spatial inhomogeneities on flow through the endothelial surface layer. Journal of Theoretical Biology, 25, 313–325.CrossRefGoogle Scholar
  53. 53.
    Liao, E. C., Zapata, A., Kieran, M., Trede, N. S., Ransom, D., & Zon, L. I. (2002). Non-cell autonomous requirement for the bloodless gene in primitive hematopoiesis of zebrafish. Development, 129, 649–659.PubMedGoogle Scholar
  54. 54.
    Liebau, G. (1954). Ber ein ventilloses pumpprinzip. Naturwissenschaften, 41(14), 327–328.CrossRefGoogle Scholar
  55. 55.
    Liebau, G. (1955). Die strmungsprinzipien des herzens. Zeitschrift für Kreislaufforschung, 44(17–18), 677–684.PubMedGoogle Scholar
  56. 56.
    Liebau, G. (1956). Die bedeutung der trgheitskrfte fr die dynamik des blutkreislaufs. Zeitschrift für Kreislaufforschung, 45(13–14), 481–488.PubMedGoogle Scholar
  57. 57.
    Liu, A., Rugonyi, S., Pentecost, J. O., & Thornburg, K. L. (2007). Finite element modeling of blood flow-induced mechanical forces in the outflow tract of chick embryonic hearts. Computers & Structures, 85(11), 11–14.CrossRefGoogle Scholar
  58. 58.
    Luft, J. H. (1966). Fine structures of capillary and endocapillary layer as revealed by ruthenium red. Federation Proceedings, 25, 1773–1783.PubMedGoogle Scholar
  59. 59.
    Männer, J. (2000). Cardiac looping in the chick embryo: A morphological review with special reference to terminological and biomechanical aspects of the looping process. Anatomical Record, 259, 248–262.PubMedCrossRefGoogle Scholar
  60. 60.
    Manopoulos, C. G., Mathioulakis, D. S., & Tsangaris, S. G. (2006). One-dimensional model of valveless pumping in a closed loop and a numerical solution. Physics of Fluids, 18(1), 017106–017116.CrossRefGoogle Scholar
  61. 61.
    Marshall, W. F., & Nonaka, S. (2006). Cilia: Tuning in to the cell’s antenna. Current Biology, 16, R604–R614.PubMedCrossRefGoogle Scholar
  62. 62.
    McCann, F. V., & Sanger, J. W. (1969). Ultrastructure and function in an insect heart. Experientia. Supplementum, 15, 29–46.Google Scholar
  63. 63.
    McGrath, K. E., Koniski, A. D., Malik, J., & Palis, J. (2003). Circulation is established in a stepwise pattern in the mammalian embryo. Blood, 101, 1669–1676.PubMedCrossRefGoogle Scholar
  64. 64.
    Merrill, E. W., Benis, A. M., Gilliland, E. R., Sherwood, T. K., & Salzman, E. W. (1965). Pressure flow relations of human blood in hollow fibers at low flow rates. Journal of Applied Physiology, 20, 954–967.PubMedGoogle Scholar
  65. 65.
    Miller, L. A. (2011). Fluid dynamics of ventricular filling in the embryonic heart. Cell Biochemistry and Biophysics. doi: 10.1007/s12013-011-9157-9.
  66. 66.
    Mittal, R. (2005). Immersed boundary methods. Annual Review of Fluid Mechanics, 37, 239–261.CrossRefGoogle Scholar
  67. 67.
    Moorman, A. F. M., & Christoffels, V. M. (2003). Cardiac chamber formation: Development, genes, and evolution. Physiological Reviews, 83, 1223–1267.PubMedGoogle Scholar
  68. 68.
    Moorman, A. F. M., Soufan, A. T., Hagoort, J., De Boer, P. A. J., & Christoffels, V. M. (2004). Development of the building plan of the heart. Annals of the New York Academy of Sciences, 1015, 171–181.PubMedCrossRefGoogle Scholar
  69. 69.
    Moorman, A. F. M., Webb, S., Brown, N. A., Lamers, W., & Anderson, R. H. (2003). Development of the heart: (1) Formation of the cardiac chambers and arterial trunks. Heart, 89, 806–814.PubMedCrossRefGoogle Scholar
  70. 70.
    Nauli, S. M., Alenghat, F. J., Luo, Y., Williams, E., Vassilev, P., Lil, X. G., et al. (2003). Polycystins 1 and 2 mediate mechanosensation in the primary cilium of kidney cells. Nature Genetics, 33, 129–137.PubMedCrossRefGoogle Scholar
  71. 71.
    Nauli, S. M., Kawanabe, Y., Kaminski, J. J., Pearce, W. J., Ingber, D. E., & Zhou, J. (2008). Endothelial cilia are fluid-shear sensors that regulate calcium signaling and nitric oxide production through polycystin-1. Circulation, 117, 1161–1171.PubMedCrossRefGoogle Scholar
  72. 72.
    Olesen, S. P., Clapham, D. E., & Davies, P. F. (1988). Hemodynamic shear-stress activates a K+ current in vascular endothelial cells. Nature, 331, 168–170.PubMedCrossRefGoogle Scholar
  73. 73.
    Ottesen, J. T. (2003). Valveless pumping in a fluid-filled closed elastic tube system: One-dimensional theory with experimental validation. Journal of Mathematical Biology, 46(4), 309–332.PubMedCrossRefGoogle Scholar
  74. 74.
    Patterson, C. (2005). Even flow: Shear cues vascular development. Arteriosclerosis, Thrombosis, and Vascular Biology, 25, 1761–1762.PubMedCrossRefGoogle Scholar
  75. 75.
    Peskin, C. S. (2002). The immersed boundary method. Acta Numerica, 11, 479–517.CrossRefGoogle Scholar
  76. 76.
    Peskin, C. S., & McQueen, D. M. (1996). Fluid dynamics of the heart and its valves. In H. G. Othmer, F. R. Adler, M. A. Lewis, & J. C. Dallon (Eds.), Case studies in mathematical modeling: Ecology, physiology, and cell biology (2nd ed.). Upper Saddle River, NJ: Prentice-Hall.Google Scholar
  77. 77.
    Phoon, C. K. L., Aristizábal, O., & Turnbull, D. H. (2002). Spatial velocity profile in mouse embryonic aorta and Doppler-derived volumetric flow: A preliminary model. American Journal of Physiology. Heart and Circulatory Physiology, 283(3), H908–H916.PubMedGoogle Scholar
  78. 78.
    Picart, C., Piau, J. M., & Galliard, H. (1998). Human blood shear yield stress and its hematocrit dependence. Journal of Rheology, 42, 1–12.CrossRefGoogle Scholar
  79. 79.
    Poelma, C., Van der Heiden, K., Hierck, B. P., Poelmann, R. E., & Westerweel, J. (2010). Measurements of the wall shear stress distribution in the outflow tract of an embryonic chicken heart. Journal of the Royal Society Interface, 7(42), 91–103.CrossRefGoogle Scholar
  80. 80.
    Praetorius, H. A., & Spring, K. R. (2001). Bending the MDCK cell primary cilium increases intracellular calcium. Journal of Membrane Biology, 184, 71–79.PubMedCrossRefGoogle Scholar
  81. 81.
    Reckova, M., Rosengarten, C., de Almeida, A., Stanley, C. P., Wessels, A., Gourdie, R. G., et al. (2003). Hemodynamics is a key epigenetic factor in development of the cardiac conduction system. Circulation Research, 93, 77–85.PubMedCrossRefGoogle Scholar
  82. 82.
    Reitsma, S., Slaaf, D. W., Vink, H., van Zandvoort, M. A. M. J., & oude Egbrink, M. G. A. (2007). The endothelial glycocalyx: Composition, functions, and visualization. European Journal of Physiology, 454, 345–359.PubMedCrossRefGoogle Scholar
  83. 83.
    Rychter, Z., Kopecky, M., & Lemez, L. (1955). A micromethod for determination of the circulating blood volume in chick embryos. Nature, 175, 1126–1127.PubMedCrossRefGoogle Scholar
  84. 84.
    Sadler, T. W. (1995). Langman’s medical embryology (7th ed.). Baltimore: Williams & Wilkins.Google Scholar
  85. 85.
    Santhanakrishnan, A., Nguyen, N., Cox, J. G., & Miller, L. A. (2009). Flow within models of the vertebrate embryonic heart. Journal of Theoretical Biology, 259, 449–464.PubMedCrossRefGoogle Scholar
  86. 86.
    Santiago, J. G., Wereley, S. T., Meinhart, C. D., Beebe, D. J., & Adrian, R. J. (1998). A particle image velocimetry system for microfluidics. Experiments in Fluids, 25, 316–319.CrossRefGoogle Scholar
  87. 87.
    Savolainen, S. M., Foley, J. F., & Elmore, S. A. (2009). Histology atlas of the developing mouse heart with emphasis on E11.5 to E18.5. Toxicologic Pathology, 37, 395–414.PubMedCrossRefGoogle Scholar
  88. 88.
    Schlichting, H., & Gersten, K. (2000). Boundary layer theory (8th ed.). New York: Springer-Verlag.Google Scholar
  89. 89.
    Secomb, T., Hsu, R., & Pries, A. (2001). Effect of the endothelial surface layer on transmission of fluid shear stress to endothelial cells. J. Biorheol., 38, 143–150.Google Scholar
  90. 90.
    Sehnert, A. J. (2002). Cardiac troponin t is essential in sarcomere assembly and cardiac contractility. Nature Genetics, 31, 106–110.PubMedCrossRefGoogle Scholar
  91. 91.
    Selamet Tierney, E. S., Wald, R. M., McElhinney, D. B., Marshall, A. C., Benson, C. B., Colan, S. D., et al. (2007). Changes in left heart hemodynamics after technically successful in-utero aortic valvuloplasty. Ultrasound in Obstetrics and Gynecology, 30(5), 715–720.PubMedCrossRefGoogle Scholar
  92. 92.
    Shelley, M., Fauci, L., & Teran, J. (2008). Large amplitude peristaltic pumping of an elastic fluid. Physics of Fluids, 20, 073101.CrossRefGoogle Scholar
  93. 93.
    Singla, V., & Reiter, J. F. (2006). The primary cilium as the cell’s antenna: Signaling at a sensory organelle. Science, 313, 629–633.PubMedCrossRefGoogle Scholar
  94. 94.
    Skalak, R., & Özkaya, N. (1989). Biofluid mechanics. The Annual Review of Fluid Mechanics, 21, 167–204.CrossRefGoogle Scholar
  95. 95.
    Smith, M., Long, D., Damiano, E., & Ley, K. (2003). Near-wall micro-PIV reveals a hydrodynamically relevant endothelial surface layer in venules in vivo. Biophysical Journal, 85, 637–645.PubMedCrossRefGoogle Scholar
  96. 96.
    Taber, L. A., Zhang, J., & Perucchio, R. (2007). Computational model for the transition From peristaltic to pulsatile flow in the embryonic heart tube. Journal of Biomechanical Engineering, 129(3), 441–450.PubMedCrossRefGoogle Scholar
  97. 97.
    Thi, M., Tarbell, J., Weinbaum, S., & Spray, D. (2004). The role of the glycocalyx in reorganization of the actin cytoskeleton under fluid shear stress: A bumper car model. Proceedings of the National Academy of Sciences, 101(47), 16483–16488.CrossRefGoogle Scholar
  98. 98.
    Thisse, C., & Zon, L. I. (2002). Organogenesis-heart and blood formation from the zebrafish point of view. Science, 295(5554), 457–462.PubMedCrossRefGoogle Scholar
  99. 99.
    Thomann, H. (1978). A simple pumping mechanism in a valveless tube. Zeitschrift fr Angewandte Mathematik und Physik (ZAMP), 29(2), 169–177.CrossRefGoogle Scholar
  100. 100.
    Topper, N., & Gimbrone, M. A., Jr. (1999). Blood flow and vascular gene expression: Fluid shear stress as a modulator of endothelial phenotype. Molecuar Medicine Today, 5, 40–46.CrossRefGoogle Scholar
  101. 101.
    Tretheway, D. C., & Meinhart, C. D. (2004). A generating mechanism for apparent fluid slip in hydrophobic microchannels. Physics of Fluids, 16, 1509–1515.CrossRefGoogle Scholar
  102. 102.
    Tucker, D. C., Snider, C., & Woods, W. T. (1988). Pacemaker development in embryonic rat heart cultured in oculo. Pediatric Research, 23, 637–642.PubMedCrossRefGoogle Scholar
  103. 103.
    Ursem, N. T. C., Stekelenburg-de Vos, S., Wladimiroff, J. W., Poelmann, R. E., Gittenberger-de Groot, A. C., Hu, N., et al. (2004). Ventricular diastolic filling characteristics in stage-24 chick embryos after extra-embryonic venous obstruction. Journal of Experimental Biology, 207, 1487–1490.PubMedCrossRefGoogle Scholar
  104. 104.
    Van der Heiden, K., Groenendijk, B. C. W., Hierck, B. P., Hogers, B., Koerten, H. K., Mommaas, A. M., et al. (2006). Monocilia on chicken embryonic endocardium in low shear stress areas. Developmental Dynamics, 235, 19–28.PubMedCrossRefGoogle Scholar
  105. 105.
    Van der Heiden, K., Hierck, B. P., Krams, R., de Crom, R., Cheng, C., Baiker, M., et al. (2007). Endothelial primary cilia in areas of disturbed flow are at the base of atherosclerosis. Atherosclerosis, 196(2), 542–550.PubMedCrossRefGoogle Scholar
  106. 106.
    Vennemann, P., Kiger, K. T., Lindken, R., Groenendijk, B. C. W., Stekelenburg-de Vos, S., ten Hagen, T. L. M., et al. (2006). In vivo micro particle image velocimetry measurements of blood-plasma in the embryonic avian heart. Journal of Biomechanics, 39(7), 1191–1200.PubMedCrossRefGoogle Scholar
  107. 107.
    Vincent, P. E., Sherwin, S. J., & Weinberg, P. D. (2008). Viscous flow over outflow slits covered by an anisotropic Brinkman medium: A model of flow above interendothelial cell clefts. Physics of Fluids, 20(6), 063106–063111.CrossRefGoogle Scholar
  108. 108.
    Wang, Y., Dur, O., Patrick, M. J., Tinney, J. P., Tobita, K., Keller, B. B., et al. (2009). Aortic arch morphogenesis and flow modeling in the chick embryo. Annals of Biomedical Engineering, 37(6), 1069–1081.PubMedCrossRefGoogle Scholar
  109. 109.
    Weinbaum, S., Zhang, X., Han, Y., Vink, H., & Cowin, S. C. (2003). Mechanotransduction and flow across the endothelial glycocalyx. Proceedings of the National Academy of Sciences of the United States of America, 100, 7988–7995.PubMedCrossRefGoogle Scholar
  110. 110.
    Wenning, A., Cymbalyuk, G. S., & Calabrese, R. L. (2004). Heartbeat control in leeches. I. Constriction pattern and neural modulation of blood pressure in intact animals. Journal of Neurophysiology, 91, 382–396.Google Scholar
  111. 111.
    Wilkins-Haug, L. E., Benson, C. B., Tworetzky, W., Marshall, A. C., Jennings, R. W., & Lock, J. E. (2005). In-utero intervention for hypoplastic left heart syndrome—a perinatologist’s perspective. Ultrasound in Obstetrics and Gynecology, 26(5), 481–486.PubMedCrossRefGoogle Scholar
  112. 112.
    Womersley, J. R. (1955). Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. Journal of Physiology, 127, 553–563.PubMedGoogle Scholar
  113. 113.
    Yao, Y., Rabodzey, A., & Dewey, C. F. (2007). Glycocalyx modulates the motility and proliferative response of vascular endothelium to fluid shear stress. American Journal of Physiology. Heart and Circulatory Physiology, 293, H1023–H1030.PubMedCrossRefGoogle Scholar
  114. 114.
    Yoganathan, A. P., Rittgers, S. E., & Chandran, K. B. (2007). Biofluid mechanics: The human circulation (1st ed.). Boca Raton: Taylor and Francis.Google Scholar
  115. 115.
    Yost, H. J. (2003). Left-right asymmetry: Nodal cilia make and catch a wave. Current Biology, 13, R808–R809.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of MathematicsThe University of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations