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TECHNICAL PAPERS: Soft Tissue

Computational Model for the Transition From Peristaltic to Pulsatile Flow in the Embryonic Heart Tube

[+] Author and Article Information
Larry A. Taber1

Department of Biomedical Engineering, Washington University, Campus Box 1097, St. Louis, MO 63130lat@wustl.edu

Jinmei Zhang, Renato Perucchio

Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627

Many authors reserve the term “cushions” for later developmental stages when cells invade the thickenings and begin to mold them into valves composed of connective tissue. Some prefer to call them “mounds” when they consist of acellular extracellular matrix (cardiac jelly) (4). For convenience in this paper, we use the term “cushions” throughout development.

1

Corresponding author.

J Biomech Eng 129(3), 441-449 (Oct 26, 2006) (9 pages) doi:10.1115/1.2721076 History: Received July 06, 2006; Revised October 26, 2006

Early in development, the heart is a single muscle-wrapped tube without formed valves. Yet survival of the embryo depends on the ability of this tube to pump blood at steadily increasing rates and pressures. Developmental biologists historically have speculated that the heart tube pumps via a peristaltic mechanism, with a wave of contraction propagating from the inflow to the outflow end. Physiological measurements, however, have shown that the flow becomes pulsatile in character quite early in development, before the valves form. Here, we use a computational model for flow though the embryonic heart to explore the pumping mechanism. Results from the model show that endocardial cushions, which are valve primordia arising near the ends of the tube, induce a transition from peristaltic to pulsatile flow. Comparison of numerical results with published experimental data shows reasonably good agreement for various pressure and flow parameters. This study illustrates the interrelationship between form and function in the early embryonic heart.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 7

Pumping characteristics of model heart tube. Curves are shown for varied λ with Δ=L fixed (a),(c) and varied Δ with λ=L fixed (b),(d). (a),(b) Volumetric outflow per beat (Vout); and (c),(d) cardiac output.

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Figure 6

Effects of distance between contractile waves (Δ) on pumping behavior of heart tube. With λ=L, temporal results are shown for (a) pressure at center; (b) lumen volume; (c) pressure–volume loops; and (d) outflow rate. The legend applies to all panels.

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Figure 5

Effects of contractile wavelength λ on pumping behavior of heart tube. With Δ=L, temporal results are shown for (a) pressure at center; (b) lumen volume; (c) pressure–volume loops; and (d) outflow rate. The legend applies to all panels. Point 1=end diastole; point 2=begin ejection; point 3=end systole; and point 4=begin filling.

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Figure 4

Pressure and flow wave forms as functions of time (λ=1.6mm; Δ=2mm). Pressure and flow rate are shown for center of tube and outflow end, respectively, for tube without cushions (a),(c), and with cushions (b),(d). The presence of cushions transforms the oscillatory wave forms of peristalsis into patterns more characteristic of pulsatile flow.

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Figure 3

Spatial distributions in model heart tube for representative times during a beat (λ=1.6mm; Δ=2mm). Results are shown for a tube without endocardial cushions (a,a′,a″) and with cushions (b,b′,b″). (a), (b) Outer wall radius and centerline pressure. In tube with cushions, pressure is relatively uniform between the cushions, and peak pressure is an order of magnitude higher relative to the tube without cushions. (a′),(b′) Centerline fluid velocity. Peaks occur near the cushions. (a″),(b″) Fluid shear stress at the wall. Peaks occur near the cushions. Respective times (t¯=t∕T) for curves 1–7 in (a,a′,a″) are 0.22, 0.33, 0.44, 0.56, 0.67, 0.78, 0.89; times for curves 1–6 in (b,b′,b″) are 0.22, 0.28, 0.33, 0.44, 0.56, 0.67.

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Figure 2

Pressure distributions for peristaltic flow through uniform tube (λ=L∕1.8, Δ=0, ϵ=0.8). Wall shape and centerline pressure waves are shown for four representative times. Results given by analytic solution of Li and Brasseur (17) (dashed curves) are practically indistinguishable from those given by the finite element model (solid curves). Nondimensional quantities: time t¯=t∕T; radius a¯=a∕a0; pressure p¯=pa02∕μcλ.

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Figure 1

Geometry for computational model. (a) Model dimensions in passive state. Cross section from cushion region is shown at right. (b) Undeformed model (solid lines) and deformed model (dashed lines) near endocardial cushion as contractile wave passes through outflow region. Note the thickening of the cushion as the wave passes.

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