Bifurcations in valveless pumping techniques from a coupled fluid-structure-electrophysiology model in heart development


  • Nicholas Anthony Battista The College of New Jersey
  • Laura Ann Miller University of North Carolina at Chapel Hill



valveless pumping, heart development, immersed boundary method, fluid-structure interaction, mathematical biology, biomechanics


We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to muscular contraction and hence the overall pumping dynamics. In comparison to previous models, the electro-dynamical model does not use prescribed motion to initiate the pumping motion, but rather the pumping dynamics are fully coupled to an underlying electrophysiology model, governed by the FitzHugh-Nagumo equations. Perturbing the diffusion parameter in the FitzHugh-Nagumo model leads to a bifurcation in dynamics of action potential propagation. This bifurcation is able to capture a spectrum of different pumping regimes, with dynamic suction pumping and peristaltic-like pumping at the extremes. We find that more bulk flow is produced within the realm of peristaltic-like pumping.

Author Biographies

Nicholas Anthony Battista, The College of New Jersey

Assistant Professor of Mathematics

Laura Ann Miller, University of North Carolina at Chapel Hill

Professor of Biology and Mathematics






Original Articles