Kinking and Torsion Can Significantly Improve the Efficiency of Valveless Pumping in Periodically Compressed Tubular Conduits. Implications for Understanding of the Form-Function Relationship of Embryonic Heart Tubes

Abstract

Valveless pumping phenomena (peristalsis, Liebau-effect) can generate unidirectional fluid flow in periodically compressed tubular conduits. Early embryonic hearts are tubular conduits acting as valveless pumps. It is unclear whether such hearts work as peristaltic or Liebau-effect pumps. During the initial phase of its pumping activity, the originally straight embryonic heart is subjected to deforming forces that produce bending, twisting, kinking, and coiling. This deformation process is called cardiac looping. Its function is traditionally seen as generating a configuration needed for establishment of correct alignments of pulmonary and systemic flow pathways in the mature heart of lung-breathing vertebrates. This idea conflicts with the fact that cardiac looping occurs in all vertebrates, including gill-breathing fishes. We speculate that looping morphogenesis may improve the efficiency of valveless pumping. To test the physical plausibility of this hypothesis, we analyzed the pumping performance of a Liebau-effect pump in straight and looped (kinked) configurations. Compared to the straight configuration, the looped configuration significantly improved the pumping performance of our pump. This shows that looping can improve the efficiency of valveless pumping driven by the Liebau-effect. Further studies are needed to clarify whether this finding may have implications for understanding of the form-function relationship of embryonic hearts.

Keywords: Liebau effect; blood vessel kinking; form-function relationship; heart looping; valveless pumping.

Figure 1

Schematic drawing illustrating the similarities between the morphological phenotypes of blood vessel looping in adult human beings and heart tube looping in vertebrate embryos. Pictures are based on arterial phenotypes as classified by Weibel and Fields [40] and on Figure 15 from Tschermak [37].

Figure 2

Schematic drawing illustrating the importance of cardiac looping morphogenesis for correct alignment of the intracardiac flow pathways in the four-chambered heart of lung-breathing vertebrates. The normal situation, presented on the left, shows that the normal displacement of the ventricular bend toward the right body side (d-(dextral)-looping) sets the scene for correct (concordant) alignment between the future atrial and ventricular chambers. The abnormal example, presented on the right, shows that an abnormal displacement of the ventricular bend toward the left body side (l-(levo)-looping) can set the scene for incorrect (discordant) alignment between the future atrial and ventricular chambers. LA, future left atrium; LV, future left ventricle; RA, future right atrium; RV, future right ventricle.

Figure 3

Graphical presentation of the design and dimensions of our experimental apparatus in the straight tube configuration. (A) Pumping system in a frontal view; (B) Pumping system from the upside; (C) Pump (upside view) in a higher magnification. PM, pinching machine; R1, reservoir 1 (upstream reservoir); R2, reservoir 2 (downstream reservoir).

Figure 4

Photographs of our experimental apparatus in the straight tube (A) and looped tube configuration (B). For better visualization, working fluid was stained with blue color. CR, control relay; PM, pinching machine; R1, reservoir 1 (upstream reservoir); R2, reservoir 2 (downstream reservoir).

Figure 5

Graphical presentation of the design and dimensions of our experimental apparatus in the looped tube configuration. The looped tube configuration is characterized by the presence of three kinks (positions marked by labels 1, 2, and 3) and two torsions (positions marked by labels 1 and 3). (A) Pumping system in a frontal view; (B) Pumping system from the upside; (C) Pump (upside view) in a higher magnification. PM, pinching machine; R1, reservoir 1 (upstream reservoir); R2, reservoir 2 (downstream reservoir).

Figure 6

Diagram illustrating the method used for definition of the phase of approximately linear rise of the fluid level in the downstream reservoir. Changes in the fluid levels of one reservoir (∆h/∆t) are shown for two experiments (distilled water, looped tube, compression frequencies 2.5 Hz and 3.0 Hz). The phase of approximately linear rise of the fluid level in the downstream reservoir was defined as lying between the starting point of the experiment (T0) and the time point when half of the maximum fluid level was reached in the downstream reservoir (T0.5hmax).

Figure 7

Diagrams showing the maximum pressure heads (∆pmax) reached in our experiments. (A) Results of low viscous fluid (distilled water) pumping; (B) Results of high viscous fluid (1:1 mixture corn syrup/distilled water) pumping.

Figure 8

Diagrams showing the average flow rates (FR) reached in our experiments. (A) Results of low viscous fluid (distilled water) pumping; (B) Results of high viscous fluid (1:1 mixture corn syrup/distilled water) pumping.

Figure 9

Photographs illustrating the direction of net flow generated in our pump systems and the increase in maximum pressure head (∆pmax) reached by the looped tube (B) as compared to the straight tube (A). For better visualization, working fluid was stained with blue color.