Cell Biochemistry and Biophysics

, Volume 61, Issue 1, pp 33–45 | Cite as

Fluid Dynamics of Ventricular Filling in the Embryonic Heart

Original Paper

Abstract

The vertebrate embryonic heart first forms as a valveless tube that pumps blood using waves of contraction. As the heart develops, the atrium and ventricle bulge out from the heart tube, and valves begin to form through the expansion of the endocardial cushions. As a result of changes in geometry, conduction velocities, and material properties of the heart wall, the fluid dynamics and resulting spatial patterns of shear stress and transmural pressure change dramatically. Recent work suggests that these transitions are significant because fluid forces acting on the cardiac walls, as well as the activity of myocardial cells that drive the flow, are necessary for correct chamber and valve morphogenesis. In this article, computational fluid dynamics was used to explore how spatial distributions of the normal forces acting on the heart wall change as the endocardial cushions grow and as the cardiac wall increases in stiffness. The immersed boundary method was used to simulate the fluid-moving boundary problem of the cardiac wall driving the motion of the blood in a simplified model of a two-dimensional heart. The normal forces acting on the heart walls increased during the period of one atrial contraction because inertial forces are negligible and the ventricular walls must be stretched during filling. Furthermore, the force required to fill the ventricle increased as the stiffness of the ventricular wall was increased. Increased endocardial cushion height also drastically increased the force necessary to contract the ventricle. Finally, flow in the moving boundary model was compared to flow through immobile rigid chambers, and the forces acting normal to the walls were substantially different.

Keywords

Biofluids Heart development Shear stress 

Notes

Acknowledgments

The author would like to thank Arvind Santhanakrisnan, Anil Shenoy, and Charles Peskin for meaningful discussions concerning the biofluid mechanics of heart development. The author would also like to thank the Applied Mathematics Fluids Lab Group at the University of North Carolina Chapel Hill for their input and intuition. This work was funded by BWF CASI Award ID # 1005782.01.

References

  1. 1.
    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
  2. 2.
    Hove, J. R. (2004). In vivo biofluid dynamic imaging in the developing zebrafish. Birth Defects Research, 72, 277–289.PubMedCrossRefGoogle Scholar
  3. 3.
    Manasek, F. J. (1981). Determinants of heart shape in early embryos. Federation Proceedings, 40, 2011–2016.PubMedGoogle Scholar
  4. 4.
    Manner, 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
  5. 5.
    Taber, L. A., Lin, I.-E., & Clark, L. A. (2005). Mechanics of cardiac looping. Developmental Dynamics, 1, 42–50.Google Scholar
  6. 6.
    Moorman, A. F. M., & Christoffels, V. M. (2003). Cardiac chamber formation: development, genes, and evolution. Physiological Reviews, 83, 1223–1267.PubMedGoogle Scholar
  7. 7.
    Satou, Y., & Satoh, N. (2006). Gene regulatory networks for the development, evolution of the chordate heart. Genes and Development, 20, 2634–2638.PubMedCrossRefGoogle Scholar
  8. 8.
    Patterson, C. (2005). Even flow: shear cues vascular development. Arteriosclerosis, Thrombosis, and Vascular Biology, 25, 1761–1762.PubMedCrossRefGoogle Scholar
  9. 9.
    Forouhar, A. S., Liebling, M., Hickerson, A., Nasiraei-Moghaddam, A., 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
  10. 10.
    Hove, J. R., Koster, R. W., Forouhar, A. S., Acevedo-Bolton, G., Fraser, S. E., & Gharib, M. (2003). Intracardiac fluid forces are an essential epigenetic factor for embryonic cardiogenesis. Nature, 421, 172–177.PubMedCrossRefGoogle Scholar
  11. 11.
    Misra, S., Fu, A. A., Puggioni, A., Karimi, K. M., Mandrekar, J. N., Glockner, J. F., et al. (2008). Increased shear stress with upregulation of VEGF-A and its receptors and MMP-2, MMP-9, and TIMP-1 in venous stenosis of hemodialysis grafts. American Journal of Physiology: Heart and Circulatory Physiology, 294, 2219–2230.CrossRefGoogle Scholar
  12. 12.
    Thi, M. M., Iacobas, D. A., Iacobas, S., & Spray, D. C. (2007). Fluid shear stress upregulates vascular endothelial growth factor gene expression in osteoblasts. Annals of the New York Academy of Sciences, 1117, 73–81.PubMedCrossRefGoogle Scholar
  13. 13.
    Ohno, M., Cooke, J. P., Dzau, V. J., & Gibbons, G. H. (1995). Fluid shear stress induces endothelial transforming growth factor beta-1 transcription and production. Modulation by potassium channel blockade. Journal of Clinical Investigation, 95, 1363–1369.PubMedCrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    Folkow, B. (1982). Physiological aspects of primary hypertension. Physiological Reviews, 62, 347–504.PubMedGoogle Scholar
  16. 16.
    Mulvany, M. J. (1991). Are vascular abnormalities a primary cause or secondary consequence of hypertension? Hypertension, 18, 52–57.Google Scholar
  17. 17.
    Westerhof, N., Stergiopulos, N., & Noble, M. I. M. (2006). Snapshots of hemodynamics: an aid for clinical research and graduate education. New York: Springer-Verlag.Google Scholar
  18. 18.
    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
  19. 19.
    Herrmann, C., Wray, J., Travers, F., & Barman, 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
  20. 20.
    Mironov, V., Visconti, R. P., & Markwald, R. R. (2005). On the role of shear stress in cardiogenesis. Endothelium, 12, 259–261.PubMedCrossRefGoogle Scholar
  21. 21.
    Thurston, G. B. (1972). Viscoelasticity of human blood. Biophysical Journal, 12, 1205–1217.PubMedCrossRefGoogle Scholar
  22. 22.
    Thurston, G. B. (1979). Rheological parameters for the viscosity viscoelasticity and thixotropy of blood. Biorheology, 16, 149–162.PubMedGoogle Scholar
  23. 23.
    Chien, S., Usami, S., Taylor, H. M., Lundberg, J. L., & Gregersen, M. I. (1966). Effects of hematocrit and plasma proteins on human blood rheology at low shear rates. Journal of Applied Physiology, 21, 81–87.PubMedGoogle Scholar
  24. 24.
    Chmiel, H., & Walitza, E. (1980). On the rheology of blood and synovial. New York: Research Studies Press.Google Scholar
  25. 25.
    Chhabra, R. P., & Richardson, J. F. (2008). Non-Newtonian flow and applied rheology (2nd ed.). Oxford: Butterworth-Heinemann.Google Scholar
  26. 26.
    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
  27. 27.
    Peskin, C. S. (2002). The immersed boundary method. Acta Numerica, 11, 479–517.CrossRefGoogle Scholar
  28. 28.
    Peskin, C. S. (1977). Flow patterns around heart valves: a numerical method. Journal of Computational Physics, 25, 220–252.CrossRefGoogle Scholar
  29. 29.
    Peskin, C. S., & McQueen, D. M. (1996). Fluid dynamics of the heart and its valves. In F. R. Adler, M. A. Lewis, J. C. Dalton, & H. G. Othmer (Eds.), Case studies in mathematical modeling–ecology, physiology, and cell biology (pp. 309–337). New Jersey: Prentice Hall.Google Scholar
  30. 30.
    Jung, E. N., & 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
  31. 31.
    Fogelson, A. L. (1984). A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting. Journal of Computational Physics, 56, 111–134.CrossRefGoogle Scholar
  32. 32.
    Miller, L. A., & Peskin, C. S. (2005). A computational fluid dynamics of `clap and fling’ in the smallest insects. Journal of Experimental Biology, 208, 195–212.PubMedCrossRefGoogle Scholar
  33. 33.
    Miller, L. A., & Peskin, C. S. (2004). When vortices stick: an aerodynamic transition in tiny insect flight. Journal of Experimental Biology, 207, 3073–3088.PubMedCrossRefGoogle Scholar
  34. 34.
    Santhanakrishnan, A., Nguyen, N., Cox, J. G., & Miller, L. A. (2009). Flow within models of the vertebrate embryonic heart. Journal of Theoretical Biology, 259, 449–461.PubMedCrossRefGoogle Scholar
  35. 35.
    Peskin, C. S., & Printz, B. F. (1993). Improved volume conservation in the computation of flows with immersed elastic boundaries. Journal of Computational Physics, 105, 33–46.CrossRefGoogle Scholar
  36. 36.
    Griffith, B. E., Hornung, R. D., McQueen, D. M., & Peskin, C. S. (2009). Parallel and adaptive simulation of cardiac fluid dynamics. In M. Chandra, S. Li, & X. Parashar (Eds.), Advanced computational infrastructures for parallel and distributed adaptive applications (chapter 7, pp. 105–130). New York: John Wiley and Sons.Google Scholar
  37. 37.
    Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical recipes in FORTRAN: the art of scientific computing. Cambridge, UK: Cambridge University Press.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North Carolina Chapel HillChapel HillUSA

Personalised recommendations