Dimensionless analysis of valveless pumping in a thick-wall elastic tube: Application to the tubular embryonic heart

Following the Beat: Imaging the Valveless Pumping Function in the Early Embryonic Heart

In vertebrates, the coordinated beat of the early heart tube drives cardiogenesis and supports embryonic growth. How the heart pumps at this valveless stage marks a fascinating problem that is of vital significance for understanding cardiac development and defects. The developing heart achieves its function at the same time as continuous and dramatic morphological changes, which in turn modify its pumping dynamics. The beauty of this muti-time-scale process also highlights its complexity that requires interdisciplinary approaches to study. High-resolution optical imaging, particularly fast, four-dimensional (4D) imaging, plays a critical role in revealing the process of pumping, instructing numerical modeling, and enabling biomechanical analyses. In this review, we aim to connect the investigation of valveless pumping mechanisms with the recent advancements in embryonic cardiodynamic imaging, facilitating interactions between these two areas of study, in hopes of encouraging and motivating innovative work to further understand the early heartbeat.

Dilatation of the bridging cerebral cortical veins in childhood hydrocephalus suggests a malfunction of venous impedance pumping

Dogs with a naturally occurring form of hydrocephalus have an elevated transmural venous pressure leading to cortical vein dilatation. The purpose of this study is to discover if there is vein dilatation in childhood hydrocephalus and to estimate the pressure required to maintain any enlargement found. Children with hydrocephalus between the ages of 4 and 15 years were compared with a control group. Magnetic resonance venography (MRV) and flow quantification were performed. The arterial inflow, sagittal sinus and straight sinus venous outflow were measured and the outflow percentages compared to the inflow were calculated. The cross-sectional area of the veins were measured. There were a total of 18 children with hydrocephalus, compared to 72 age and sex matched control MRV’s and 22 control flow quantification studies. In hydrocephalus, the sagittal sinus venous return was reduced by 12.9%, but the straight sinus flow was not significantly different. The superficial territory veins were 22% larger than the controls but the vein of Galen was unchanged. There is evidence of a significant increase in the superficial vein transmural pressure in childhood hydrocephalus estimated to be approximately 4 mmHg. An impedance pump model is suggested to explain these findings.

Building Valveless Impedance Pumps From Biological Components: Progress and Challenges

Valveless pumping based on Liebau mechanism entails asymmetrical positioning of the compression site relative to the attachment sites of the pump's elastic segment to the rest of the circuit. Liebau pumping is believed to play a key role during heart development and be involved in several other physiological processes. Until now studies of Liebau pump have been limited to numerical analyses, in silico modeling, experiments using non-biological elements, and a few indirect in vivo measurements. This review aims to stimulate experimental efforts to build Liebau pumps using biologically compatible materials in order to encourage further exploration of the fundamental mechanisms behind valveless pumping and its role in organ physiology. The covered topics include the biological occurrence of Liebau pumps, the main differences between them and the peristaltic flow, and the potential uses and body sites that can benefit from implantable valveless pumps based on Liebau principle. We then provide an overview of currently available tools to build such pumps and touch upon limitations imposed by the use of biological components. We also talk about the many variables that can impact Liebau pump performance, including the concept of resonant frequencies, the shape of the flowrate-frequency relationship, the flow velocity profiles, and the Womersley numbers. Lastly, the choices of materials to build valveless impedance pumps and possible modifications to increase their flow output are briefly discussed.

Output of a valveless Liebau pump with biologically relevant vessel properties and compression frequencies

Liebau pump is a tubular, non-peristaltic, pulsatile pump capable of creating unidirectional flow in the absence of valves. It requires asymmetrical positioning of the pincher relative to the attachment sites of its elastic segment to the rest of the circuit. Biological feasibility of such valveless pumps remains a hotly debated topic. To test the feasibility of the Liebau-based pumping in vessels with biologically relevant properties we quantified the output of Liebau pumps with their  compliant segments made of a silicone rubber that mimicked the Young modulus of soft tissues. The lengths, the inner diameters, thicknesses of the tested compliant segments ranged from 1 to 5 cm, 3 to 8 mm and 0.3 to 1 mm, respectively. The compliant segment of the setup was compressed at 0.5–2.5 Hz frequencies using a 3.5-mm-wide rectangular piston. A nearest-neighbor tracking algorithm was used to track movements of 0.5-mm carbon particles within the system. The viscosity of the aqueous solution was varied by increased percentage of glycerin. Measurements yielded quantitative relationships between viscosity, frequency of compression and the net flowrate. The use of the Liebau principle of valveless pumping in conjunction with physiologically sized vessel and contraction frequencies yields flowrates comparable to peristaltic pumps of the same dimensions. We conclude that the data confirm physiological feasibility of Liebau-based pumping and warrant further testing of its mechanism using excised biological conduits or tissue engineered components. Such biomimetic pumps can serve as energy-efficient flow generators in microdevices or to study the function of embryonic heart during its normal development or in diseased states.

Impedance Pumping and Resonance in a Multi-Vessel System

Impedance pumping is a mechanism that generates flow in a compliant vessel by repeatedly actuating the vessel asymmetrically, without employing any internal valves, blades, or other mechanisms. The net flow is obtained by establishing a constructive wave pattern. Elaborate studies of impedance pumping in a single vessel have shown that the flow rate strongly depends on the actuation frequency, as well as on other parameters, such as actuator location and amplitude, and that it operates best in the resonance mode. The present study extends these principles to a network of multiple compliant vessels, representing a cardiovascular system. The flow is modeled numerically by the one-dimensional approximation of the Navier-Stokes equations. Two configurations were examined, systems consisting of three and five compliant vessels. First, the natural frequencies of these configurations were identified. Then, the dependence of the net flow rate (NFR) on the actuating frequency was explored, showing that impedance pumping operates best in the resonance mode in the case of a network of vessels as well. The impact of other parameters were studied as well, such as the location of one or two actuators, actuation amplitude, actuator width, the duty cycle, and the phase lag between the actuators. The results show that impedance pumps can generate significant NFR and the obtained NFR can be manipulated by properly setting up one or more of the governing parameters. These findings indicate that impedance pumping principles may be applied to flow control of the cardiovascular system.

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

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.

2D and 3D Mechanobiology in Human and Nonhuman Systems

Mechanobiology involves the investigation of mechanical forces and their effect on the development, physiology, and pathology of biological systems. The human body has garnered much attention from many groups in the field, as mechanical forces have been shown to influence almost all aspects of human life ranging from breathing to cancer metastasis. Beyond being influential in human systems, mechanical forces have also been shown to impact nonhuman systems such as algae and zebrafish. Studies of nonhuman and human systems at the cellular level have primarily been done in two-dimensional (2D) environments, but most of these systems reside in three-dimensional (3D) environments. Furthermore, outcomes obtained from 3D studies are often quite different than those from 2D studies. We present here an overview of a select group of human and nonhuman systems in 2D and 3D environments. We also highlight mechanobiological approaches and their respective implications for human and nonhuman physiology.