Fluid Dynamics of Valveless Pumping in Tubular Hearts

Abstract

The vertebrate embryonic heart first forms as a valveless, tubular pump, and several different pumping mechanisms have been suggested to drive blood flow in these tubular hearts. Previous work has hypothesized net flow in these tiny tubes to be a consequence of either peristalsis, where a traveling contraction wave propels fluid forward, or dynamic suction pumping, where localized contractions interact with compliant boundaries to drive circulation. In reality, the actual pumping mechanism may be a hybrid of both processes. The goal of this thesis is to contribute to our understanding of pumping in tubular hearts using immersed boundary (IB) simulations. The IB method allows one to resolve the fully-coupled fluid-structure interaction of a contracting heart tube that drives the movement of a viscous fluid. Using this in silico model, one can then determine the effects of geometry, actuation, and dimensionless parameters relevant to cardiac morphogenesis on the net flow through the heart. Here, I develop a novel model of two-point dynamic suction pumping that is inspired by the kinematics of the embryonic heart at the stage when the chambers first begin to form and contractions occur at two sites along the tube. This framework also captures the dual pacemaker arrangement characteristic of ascidian hearts, providing a biologically relevant model for comparative study. I also developed a model of three-dimensional peristalsis in a heart tube surrounded by a pericardium, whose constraining effect on wall motion and fluid pressure makes it an essential feature for generating physiologically realistic pumping dynamics. Chapter 3 explores a two-dimensional two-point dynamic suction pumping heart tube model. The heart and circulatory system are modeled as a closed “racetrack” with two actuation points along a section of a straight elastic tube. Using the immersed boundary method, I solve the fully-coupled fluid-structure interaction problem of an elastic, valveless tubular heart immersed in a viscous and incompressible fluid. I analyze flow behavior and wall movement in simulations of the heart tube for a range of Womersley numbers (Wo) and pumping phase differences, as well as for changes in elasticity of the tube, pumping amplitude, and position of the pumps. The results suggest that Wo and pumping phase difference, elasticity, amplitude, and position all play a significant role in the effectiveness of the two-point dynamic suction pumping mechanism when compared to the one-point dynamic suction pump. While the two-dimensional model of two-point DSP has clarified relationships between actuation, compliance, and flow, it cannot capture the fully three-dimensional effects that may strongly influence pumping efficiency. The two-dimensional model also does not allow for a realistic representation of the contraction mechanism. In Chapter 4 of this dissertation, I extend two-point DSP modeling into three dimensions using a hybrid immersed boundary finite element framework (IBFE) with elastic walls to investigate how 3D geometry alters net flow and performance. Comparison with the 2D model reveals fundamental differences and new regimes that highlight the role of DSP in driving flow in valveless embryonic hearts. Lastly, Chapter 5 investigates how heart tube confinement and viscous-inertial scaling regulate fluid transport in a racetrack model of peristaltic pumping in 3D. Using IBFE simulations, I examine the effects of pericardium width and Womersley number on pumping performance. Results show that pericardium width controls flow amplitude without altering waveform, with narrower pericardia enhancing net transport and wider ones reducing it, while net transport increases nearly linearly with Wo, transitioning from viscous damping at low values to inertia-driven flow at higher values. These findings highlight the importance of including pericardial confinement in peristaltic models and demonstrate that both geometric and dynamic factors work in tandem to tune transport efficiency.