Neuromechanical pumping: boundary flexibility and traveling depolarization waves drive flow within valveless, tubular hearts

  • Austin Baird
  • Lindsay Waldrop
  • Laura Miller
Original Paper Area 3


In this paper, we develop a neuromechanical model of pumping in a valveless, tubular heart inspired by the tunicate, Ciona savignyi. Valveless, tubular hearts are common throughout the animal kingdom. The vertebrate embryonic heart first forms as a valveless, tubular pump. The embryonic, juvenile, and adult hearts of many invertebrates are also valveless, tubular pumps. Several different pumping mechanisms have been propsed for tubular hearts, and it is not clear if all animals employ the same mechanism. We compare the flows generated by this pumping mechanisms to those produced by peristalsis using a prescribed contraction wave and to those produced by impedance pumping across a parameter space relevant to Ciona savignyi. The immersed boundary method is used to solve the fully-coupled fluid-structure interaction problem of an elastic tubular heart immersed in a viscous fluid. The FitzHugh–Nagumo equations are used to model the propagation of the action potential which initiates the contraction. We find that for the scales relevant to Ciona, both the neuromechanical pumping mechanism and peristalsis produce the strong flows observed in the tunicate heart. Only the neuromechanical model produces flow patterns with all of the characteristics reported for valveless, tubular hearts. Namely, the neuromechanical pump generates a bidirectional wave of contraction and peristalsis does not.


Tubular hearts Peristalsis Liebau pumping Immersed boundary method FitzHugh–Nagumo Embryonic hearts  Tunicates 

Mathematics Subject Classification




The authors would like to thank the Japanese Society for Mathematical Biology and the Society of Mathematical Biology for their support to attend the conference. This work was funded by NSF DMS CAREER # 1151478 awarded to L. A. M. and NSF DMS RTG # 0943851 to R. McLaughlin.


  1. 1.
    Anderson, M.: Electrophysiological studies on initiation and reversal of the heart beat in Ciona intestinalis. J. Exp. Biol. 49, 363–385 (1968)Google Scholar
  2. 2.
    Baird, A., King, T., Miller, L.A.: Numerical study of scaling effects in peristalsis and dynamic suction pumping. In: Proceedings of the AMS, Special Session on Biological Fluid Dynamics: Modeling, Computations, and Applications, vol. 628, pp. 129–148 (2014)Google Scholar
  3. 3.
    Bringley, T., Childress, S., Vandenberghe, N., Zhang, J.: An experimental investigation and a simple model of a valveless pump. Phys. Fluids 20(033), 602 (2008)Google Scholar
  4. 4.
    Davidson, B.: Ciona intestinalis as a model for cardiac development. Semin. Cell Dev. Biol. 18, 16–26 (2007)CrossRefGoogle Scholar
  5. 5.
    FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445–466 (1961)CrossRefGoogle Scholar
  6. 6.
    Forouhar, A.S., Liebling, M., Hickerson, A., Nasiraei-Moghaddam, A., Tsai, H., Hove, J.R., Fraser, S.E., Dickinson, M.E., Gharib, M.: The embryonic vertebrate heart tube is a dynamic suction pump. Science 312(5774), 751–753 (2006). doi: 10.1126/science.1123775.
  7. 7.
    Harrison, J., Waters, J., Cease, A., Cease, A., VandenBrooks, J., Callier, V., Klok, C., Shaffer, K., Socha, J.: How locusts breathe. Physiology 28, 18–27 (2013)CrossRefGoogle Scholar
  8. 8.
    Hickerson, A.I., Rinderknecht, D., Gharib, M.: Experimental study of the behavior of a valveless impedance pump. Exp. Fluids 38(4), 534–540 (2005)CrossRefGoogle Scholar
  9. 9.
    Hodgkin, A.L., Huxley, A.F.: Propagation of electrical signals along giant nerve fibres. In: Proceedings of the Royal Society of London Series B, Biological Sciences, pp. 177–183 (1952)Google Scholar
  10. 10.
    Jung, E., Peskin, C.: Two-dimensional simulations of valveless pumping using the immersed boundary method. SIAM J. Sci. Comput. 23(1), 19–45 (2001). doi: 10.1137/S1064827500366094.
  11. 11.
    Kalk, M.: The organization of a tunicate heart. Tissue Cell 2, 99–118 (1970)CrossRefGoogle Scholar
  12. 12.
    Keener, J.P.: Wave propagation in Myocardium. In: Glass, L., Hunter, P., McCulloch, A. (eds.) Theory of Heart –Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function, pp. 405–436. Springer, New York (1991)Google Scholar
  13. 13.
    Kriebel, M.E.: Conduction velocity and intracellular action potentials of the tunicate heart. J. Gen. Physiol. 50(8), 2097–2107 (1967)CrossRefGoogle Scholar
  14. 14.
    Lemaire, P.: Evolutionary crossroads in developmental biology: the tunicates. Development 138, 2143–2152 (2011)CrossRefGoogle Scholar
  15. 15.
    Liebau, G.: Über ein ventilloses pumpprinzip. Naturwissenschaften 41, 327–327 (1954). doi: 10.1007/BF00644490 CrossRefGoogle Scholar
  16. 16.
    Liebau, G.: Die stromungsprinzipien des herzens. Z Kreislaufforsch 44, 677 (1955)Google Scholar
  17. 17.
    Männer, J., Wessel, A., Yelbuz, T.: How does the tubular embryonic heart work? looking for the physical mechanism generating unidirectional blood flow in the valveless embryonic heart tube. Dev. Dyn. 239, 1035–1046 (2010)CrossRefGoogle Scholar
  18. 18.
    McMahon, B., Wilkens, J., Smith, P.: Invertebrate circulatory systems. Compr. Physiol. Suppl. 30, 931–1008 (2011)Google Scholar
  19. 19.
    Miller, L.A., Peskin, C.S.: Flexible clap and fling in tiny insect flight. J. Exp. Biol. 212(19), 3076–3090 (2009)CrossRefGoogle Scholar
  20. 20.
    Mittal, R.: Locomotion with flexible propulsors: Ii. Computational modeling of pectoral fin swimming in sunfish. Bioinspir. Biomim. 1, S35–S41 (2006)CrossRefGoogle Scholar
  21. 21.
    Nichols, D.: The water-vascular system in living and fossil echinoderms. Palaeontology 15(4), 519–538 (1972)Google Scholar
  22. 22.
    Pendar, H., Kenny, M.C., Socha, J.J.: Tracheal compression in pupae of the beetle zophobas morio. Biol. Lett. 11(6), 20150,259 (2015)CrossRefGoogle Scholar
  23. 23.
    Peskin, C.S.: The immersed boundary method. Acta Numer. 11, 479–517 (2002). doi: 10.1017/S0962492902000077.
  24. 24.
    Peskin, C.S., McQueen, D.M.: Fluid dynamics of the heart and its valves. In: Othmer, H.G., Adler, F.R., Lewis, M.A., Dallon, J.C. (eds.) Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology, 2nd edn. Prentice-Hall, New Jersey (1996)Google Scholar
  25. 25.
    Pozrikidis, C.: A study of peristaltic flow. J. Fluid Mech. 180, 515–527 (1987)CrossRefGoogle Scholar
  26. 26.
    Socha, J.J., Lee, W.K., Harrison, J.F., Waters, J.S., Fezzaa, K., Westneat, M.W.: Correlated patterns of tracheal compression and convective gas exchange in a carabid beetle. J. Exp. Biol. 211(21), 3409–3420 (2008)CrossRefGoogle Scholar
  27. 27.
    Teran, J., Fauci, L., Shelley, M.: Viscoelastic fluid response can increase the speed and efficiency of a free swimmer. Phys. Rev. Lett. 104(3), 38,101 (2010)CrossRefGoogle Scholar
  28. 28.
    Tytell, E.D., Hsu, C., Williams, T.L., Cohen, A.H., Fauci, L.J.: Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming. Proc. Natl. Acad. Sci. 107(46), 19,832–19,837 (2010)CrossRefGoogle Scholar
  29. 29.
    Waldrop, L., Miller, L.: The role of the pericardium in the valveless, tubular heart of the tunicate, ciona savignyi. J. Exp. Biol. 218, 2753–2763 (2015a). doi: 10.1242/jeb.116863
  30. 30.
    Waldrop, L., Miller, L.A.: Large-amplitude, short-wave peristalsis and its implications for transport. Biomech. Model. Mechanobiol. (2015b). doi: 10.1007/s10237-015-0713
  31. 31.
    Xavier-Neto, J., Castro, R., Sampaio, A., Azambuja, A., Castillo, H., Cravo, R., Simoes-Costa, M.: Parallel avenues in the evolution of hearts and pumping organs. Cell. Mol. Life Sci. 64, 719–734 (2007)CrossRefGoogle Scholar
  32. 32.
    Xavier-Neto, J., Davidson, B., Simoes-Costa, M., Castillo, H., Sampaio, A., Azambuja, A.: Evolutionary origins of the heart. In: Rosenthal, N., Harvey, R. (eds.) Heart Development and Regeneration, vol. 1, 1st edn, pp. 3–38. Elsevier Science and Technology, London (2010)CrossRefGoogle Scholar

Copyright information

© The JJIAM Publishing Committee and Springer Japan 2015

Authors and Affiliations

  1. 1.DurhamUSA
  2. 2.School of Natural SciencesMercedUSA
  3. 3.Chapel HillUSA

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