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

Abstract

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.

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Acknowledgments

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.

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Correspondence to Laura Miller.

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Baird, A., Waldrop, L. & Miller, L. Neuromechanical pumping: boundary flexibility and traveling depolarization waves drive flow within valveless, tubular hearts. Japan J. Indust. Appl. Math. 32, 829–846 (2015). https://doi.org/10.1007/s13160-015-0195-3

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Keywords

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

Mathematics Subject Classification

  • 92C35