Fig 2 - uploaded by Maximilian Moser
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The figure demonstrates that at the beginning of the constriction of the elastic tube, the location acts as a low resistance pressure source (p, in the upper part of the figure). As soon as the folds touch, the further compression of the tube leads to the generation of a high resistance flow source, as indicated in the lower part of the figure. This sequence of events is essential for the explanation of the Liebau effect.
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Using simple physical and mathematical models we studied the possible role of asymmetry of the cardiovascular system which evolves in early embryonic life. During this phase of life blood circulates in one direction through the system in spite of the complete lack of valves. In our model we were able to show that asymmetry is a precaution for a val...
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... One option is to use the so-called valveless pumping, the most well-known types of which are peristalsis and the Liebau phenomenon. 1 Valveless pumping based on the Liebau effect 2 works via the periodic pinching of a flexible element (a compliant tube) with an asymmetry in the pincher position, the circuit, or a combination of both. [3][4][5] Unlike peristaltic pumps, the direction of net flow and its magnitude depend nonlinearly on the pinching frequency and duty cycle. ...
Asymmetric pumping can be achieved by periodically compressing a flexible tube in its plane of symmetry using an actuator, as long as the rigid pipes connected to its ends are asymmetric. This mechanism, together with impedance pumping, composes the Liebau effect. While there have been numerous studies on impedance pumping, there is a lack of available research on asymmetric pumping. The aim of this study is to examine the influence of key parameters on the performance of this type of pump. In addition, this study implements an actuator based on soft robotics technology in asymmetric valveless pumping for the first time. The pump developed in this study can be applied in different areas involving the pumping of special fluids, including biomedical applications.
... The pioneering work of Liebau from the mid-1950s was largely forgotten as he did not find many followers in the field of cardiology. Instead several generations of theoretical physicists and mathematicians tried to model this intriguing mechanism using a variety of numerical approaches, often yielding conflicting outcomes [6][7][8][9][10][11][12][13] . Therefore, it became important to test this phenomenon experimentally. ...
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.
... A biological example of micro pumping is human heart that can generate power less than 5 watts, which is not capable to circulate blood alone in the human body [14]. Here, blood vessels comes in to play and contributes to the cardiovascular system for blood circulation [2,13]. Further needs will probably encourage to replicate such natural microflows, thus this was an attempt to make the valveless pumping more efficient as per the need. ...
... Rhythmically pinching stages would generate unidirectional flow across the model. The flow relied fully on the pinching location whether it was clockwise or anti clock wise for the closed loop model [6]. Generally, model of impedance pump consists of elastic tube and a rigid tube filled with fluid as shown in Fig. 1. ...
This present study focused on the performance of net flow rate inside closed loop mechanical circulatory system with single and double pinching impedance pumps which generates a unidirectional flow of fluid around closed loop of soft viscoelastic tubing. The experimental setup consisted of viscoelastic tubing connected between two ends of rigid tube which was compressed rhythmically or squeezed asymmetrically at various frequencies by motorized pinching. Hence, net flow of fluid around the tubing can occur without valves. Experiment was done on two different fluid, namely Newtonian and Non-Newtonian. Result showed that the flow rate inside closed loop system for non-Newtonian fluid and Newtonian fluid were in good agreement with each other. Single pinching showed a lower flow rate compared to double pinching at higher frequency. The results could be used as a model for a new Mechanical Circulatory Support System used by cardiac patients. Factors influencing the performance of valveless impedance pump was also explained.
... Historically, the pumping mechanism in these hearts has been described as peristalsis [27,50]. More recently, DSP has been proposed as a novel cardiac pumping mechanism for the vertebrate embryonic heart by Kenner et al. in [26] and was later declared the main pumping mechanism in vertebrate embryonic hearts by Fourhar et al. in [14]. Debate over which is the actual pumping mechanism of the embryonic heart continues today, with the possibility that the mechanism may vary between species or may be some hybrid of both mechanisms [34,53]. ...
Around the third week after gestation in embryonic development, the human heart consists only of a valveless tube, unlike a fully developed adult heart, which is multi-chambered. At this stage in development, the heart valves have not formed and so net flow of blood through the heart must be driven by a different mechanism. It is hypothesized that there are two possible mechanisms that drive blood flow at this stage—Liebau pumping (dynamic suction pumping (DSP) or valveless pumping) and peristaltic pumping. We implement the immersed boundary method (IBM) with adaptive mesh refinement (IBAMR) to numerically study the effect of hematocrit on the circulation around a valveless tube. Both peristalsis and DSP are considered. In the case of DSP, the heart and circulatory system is simplified as a flexible tube attached to a relatively rigid racetrack. For some Womersley number (Wo) regimes, there is significant net flow around the racetrack. We find that the addition of flexible blood cells does not significantly affect flow rates within the tube forWo ≤ 10, except in the case forWo ≈ 1. 5 where we see a decrease in average flow with increasing volume fraction. On the other hand, peristalsis consistently drives blood around the racetrack for allWo and for all hematocrit considered.
... Similar experiments were conducted by numerous researchers to understand the principles of valveless pumping and to identify the pumping mechanism in the developing heart. Flow rate and direction of the flow were shown to be nonlinearly dependent on the compression frequency and duty cycle (Kenner et al. 2000;Moser et al. 1998;Ottesen 2003;Kilner 2005). An attempt to explain the cause of net flow was provided based on the compliance, wave propagation, and reflection caused by impedance mismatch (Hickerson et al. 2005;Hickerson and Gharib 2006). ...
Biomechanics affect early cardiac development, from looping to the development of chambers and valves. Hemodynamic forces are essential for proper cardiac development, and their disruption leads to congenital heart defects. A wealth of information already exists on early cardiac adaptations to hemodynamic loading, and new technologies, including high-resolution imaging modalities and computational modeling, are enabling a more thorough understanding of relationships between hemodynamics and cardiac development. Imaging and modeling approaches, used in combination with biological data on cell behavior and adaptation, are paving the road for new discoveries on links between biomechanics and biology and their effect on cardiac development and fetal programming.
... This phenomenon is called valveless pumping because forward flow can occur in a closed circulatory system without valves. It is also known as Liebau pumping[7,8]. Valveless pumping is an intriguing phenomenon because the magnitude, and sometimes the direction, of net flow are highly dependent on the frequency of squeezing123. The frequencies at which valveless pumping has been described fall in the range from 0.2 to 20 Hz [2,3,6,91011 with maximal net flows occurring near 3 Hz [2], 5 Hz [3,11], 6 Hz [6], or 15 Hz [10], depending on initial conditions. ...
A valveless pump generates a unidirectional net flow of fluid around a closed loop of soft viscoelastic tubing that is rhythmically compressed at one point. The tubing must have at least two sections with two different stiffnesses. When a short segment of the tube is squeezed asymmetrically at certain frequencies, net flow of fluid around the loop can occur without valves.
Partial differential equations for the pressures, volumes, and flows define a simple one-dimensional model of such a pump, based upon elementary physical principles. Numerical computations on a personal computer can predict measured net flows.
Net flow varies with the frequency and waveform of compression used to excite the pump, as well as with the site of compression and the stiffness and viscosity of the tubing. Net flows on the order of 1 ml/sec are obtained in a water-filled loop including 46 cm of stiffer plastic (Tygon) laboratory tubing and 70 cm of softer latex rubber tubing.
The heretofore mysterious phenomenon of valveless pumping can be described in terms of classical Newtonian physics, in which viscous damping in the walls of the pump is included. Studying valveless pumps in the laboratory and modeling their behavior numerically provides a low-cost, engaging, and instructive exercise for research and teaching in biomedical engineering.
... In fact, in 1985 Takagi and Takahashi proposed a model for rigid pipes and verified the occurrence of valveless pumping in real experiments and numerical simulations. This evidence shows that the application of a periodic force which acts asymmetrically gives rise to net flow [27][28][29][30][31][32]. Hence, the transversal flow asymmetry of the duct channel induced by the Liebau effect would be inferred when the compression chamber flow was driven by a periodic vibration of a piezoelectric buzzer [25]. ...
... Numerous designs for non-moving valves in a pumping system based on changing the flow structure were addressed. Basically, these kinds of valveless pumping systems should originate from the flow asymmetrical features [13][14][15][16][27][28][29][30][31][32]; however, they were rarely noted and addressed. In this study, a duct channel with a piezoelectric buzzer acting as a vibrator was employed to study the effect of flow asymmetry. ...
In this study, a simple pumping system, composed of a piezoelectric buzzer imbedded in a duct channel, was used to study the effect of longitudinal flow asymmetry on pumping performance in view of its importance in the design of valveless pumping systems, in spite of the fact that this has rarely been addressed before. The physical features of flow asymmetry caused by the Liebau effect, during the asymmetrical or asynchronous vibration of a buzzer in the course of space and time, can generate net mass flow and result in a pumping performance that has been confirmed experimentally. The degree of transversal asymmetry of a buzzer in space and time positively correlates with longitudinal asymmetry for pumping performance. This principle should be useful when designing valveless pumping systems, especially for applications for fields like bio-medicine, bio-chemistry, and environmental testing. Since this pumping system uses simple components, no moving valve structure will not damage any biological particles in a transmission process.
... Several experimental works on the pump behaviour have been reported in closed (Liebau 1955Liebau , 1963 Ottesen 2003; Hickerson et al. 2005; Rinderknecht et al. 2005) or open (Liebau 1954; Hickerson et al. 2005; Rinderknecht et al. 2005) systems. Several attempts have been made to explain the physical mechanism that drives a net flow in a specific direction in the impedance pump, using analytical or computational models (Rath & Teipel 1978; Thomann 1978; Moser et al. 1998; Kenner et al. 2000; Jung & Peskin 2001; Borzi & Propst 2003; Ottesen 2003; Auerbach, Moehring & Moser 2004; Manopoulos, Mathioulakis & Tsangaris 2006). To make the problem tractable, these models often included simplifications and limiting assumptions, thus limiting the validity of the explanation. ...
... In their study they presented an example of both pressure and flow waves along the tube, and reported a phase difference between the pressure and flow at the tube edges, with a peak value during compression, and suction during tube release. Yet, relying on previous hypotheses by Kenner et al. (2000), they claimed that the driving mechanism in the pump is mainly attributed to asymmetry in hydraulic losses. This explanation does not clarify the reasons for positive flow, flow in open loops or resonant behavior. ...
... Moreover, in resonance cases, not only is the long passive tube not a resistor (where power is lost), but it is a pump (a power source). These results reinforce the previous experimental observations (Hickerson et al. 2005; ) and are in contrast to the mechanism proposed by previous studies (Thomann 1978; Moser et al. 1998; Kenner et al. 2000; Manopoulos et al. 2006) relying on fluid inertia or asymmetry in energy losses. According to this work, pumping could be achieved with any impedance mismatch at the tube boundary. ...
The valveless impedance pump is a simple design that allows the producion or amplification of a flow without the requirement for valves or impellers. It is based on fluid-filled flexible tubing, connected to tubing of different impedances. Pumping is achieved by a periodic excitation at an off-centre position relative to the tube ends. This paper presents a comprehensive study of the fluid and structural dynamics in an impedance pump model using numerical simulations. An axisymmetric finite-element model of both the fluid and solid domains is used with direct coupling at the interface. By examining a wide range of parameters, the pump's resonance nature is described and the concept of resonance wave pumping is discussed. The main driving mechanism of the flow in the tube is the reflection of waves at the tube boundary and the wave dynamics in the passive tube. This concept is supported by three different analyses: (i) time-dependent pressure and flow wave dynamics along the tube, (ii) calculations of pressure–flow loop areas along the passive tube for a description of energy conversion, and (iii) an integral description of total work done by the pump on the fluid. It is shown that at some frequencies, the energy given to the system by the excitation is converted by the elastic tube to kinetic energy at the tube outlet, resulting in an efficient pumping mechanism and thus significantly higher flow rate. It is also shown that pumping can be achieved with any impedance mismatch at one boundary and that the outlet configuration does not necessarily need to be a tube.
... In the ensuing years, analytical and computational studies have been presented to model possible mechanics responsible for this phenomenon. These models were derived from first principles of solid and fluid mechanics (Thomann 1978; Mahrenholtz 1963; Moser et al. 1998; Kenner et al. 2000; Jung & Peskin 2001; Borzi & Propst 2003; Ottesen 2003; Auerbach, Moehring & Moser 2004). Comprehensive experimental results on the bulk flow behaviours were collected by. ...
... In the ensuing years, analytical and computational studies have been presented to model possible mechanics responsible for this phenomenon. These models were derived from first principles of solid and fluid mechanics (Thomann 1978;Mahrenholtz 1963;Moser et al. 1998;Kenner et al. 2000;Jung & Peskin 2001;Borzi & Propst 2003;Ottesen 2003;Auerbach, Moehring & Moser 2004). Comprehensive experimental results on the bulk flow behaviours were collected by Hickerson, . ...
Valveless pumping can be achieved through the periodic compression of a pliant tube asymmetrically from its interfaces to different tubing or reservoirs. A mismatch of characteristic impedance between the flow channels is necessary for creating wave reflection sites. Previous experimental studies of the behaviour of such a pump were continued in order to demonstrate the wave mechanics necessary for the build-up of pressure and net flow. Specific measurements of the transient and resonant properties were used to relate the bulk responses to the pump mechanics. Ultrasound imaging through the tube wall allowed visualization of the wall motion concurrently with pressure and flow measurements. For analysis, a one-dimensional wave model was constructed which predicted many of the characteristics exhibited by the experiments.
