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.

Net flow generation in closed-loop valveless pumping

Net flow generation in valveless pumping, met in many physiological applications and recently in micropumping devices, constitutes an open fluid dynamics issue due to the complex interaction between the fluid medium and the flexible walls of the pump. In the context of the present experimental work, the conditions of the net flow generation are examined in a closed-loop horizontal valveless pump, which consists of a rigid and an elastic tube of equal diameters and lengths, and a pincher that forces the liquid within the tube to oscillate at Reynolds and Womersley numbers up to 7800 and 48, respectively. Pinching off as well as at the mid-length of the pump flexible tube, net flow is generated at certain pinching frequencies for which details are presented based on simultaneous recording of the pressure at the two tube junctions, the flow rate and the displacement of the pincher. Pinching off the mid-length of the pump at low pinching frequencies, net flow rate is practically null due to the almost identical pressure waveforms at the tube junctions, which vary in phase with the pincher motion. However, close to the first natural frequency of the hydraulic loop, the reflection of the pressure waves at the tube junctions combined with their increased phase difference cause high axial pressure gradients, which when they increase simultaneously with the squeezing of the tube, net flow rate maximization occurs. Pinching at the flexible tube mid-length area, nonzero net flow rates can also be generated, the sign of which changes when the pincher mid-point crosses the tube mid-length without being nullified.

Valveless Fluid Pumping via Zero-Net-Momentum Injection

A novel mechanical method to valvelessly pump fluid has been developed using zero-net-momentum injection via a syringe and a tilted canister that function together as a periodic mass source and sink. Unlike previously discovered valveless pumping methods, this method does not require any elastic tubing and can be achieved by simple manual actuation, making it a simpler and less expensive valveless alternative. The flow rate is highly dependent on the frequency at which momentum is injected and retracted from the system. The direction of the flow can be changed by switching the location of the syringes. This pumping paradigm has potential applications in microfluidics where elastic channels are difficult to fabricate and valveless fluid actuation methods are preferred.

Functional Morphology of the Cardiac Jelly in the Tubular Heart of Vertebrate Embryos

The early embryonic heart is a multi-layered tube consisting of (1) an outer myocardial tube; (2) an inner endocardial tube; and (3) an extracellular matrix layer interposed between the myocardium and endocardium, called “cardiac jelly” (CJ). During the past decades, research on CJ has mainly focused on its molecular and cellular biological aspects. This review focuses on the morphological and biomechanical aspects of CJ. Special attention is given to (1) the spatial distribution and fiber architecture of CJ; (2) the morphological dynamics of CJ during the cardiac cycle; and (3) the removal/remodeling of CJ during advanced heart looping stages, which leads to the formation of ventricular trabeculations and endocardial cushions. CJ acts as a hydraulic skeleton, displaying striking structural and functional similarities with the mesoglea of jellyfish. CJ not only represents a filler substance, facilitating end-systolic occlusion of the embryonic heart lumen. Its elastic components antagonize the systolic deformations of the heart wall and thereby power the refilling phase of the ventricular tube. Non-uniform spatial distribution of CJ generates non-circular cross sections of the opened endocardial tube (initially elliptic, later deltoid), which seem to be advantageous for valveless pumping. Endocardial cushions/ridges are cellularized remnants of non-removed CJ.

Functional Morphology of the Cardiac Jelly in the Tubular Heart of Vertebrate Embryos

The early embryonic heart is a multi-layered tube consisting of (1) an outer myocardial tube; (2) an inner endocardial tube; and (3) an extracellular matrix layer interposed between myocardium and endocardium, called “cardiac jelly” (CJ). During the past decades, research on CJ has mainly focused on its molecular and cell biological aspects. This review focuses on the morphological and biomechanical aspects of CJ. Special attention is given to (1) the spatial distribution and fiber architecture of CJ; (2) the morphological dynamics of CJ during the cardiac cycle; and (3) the removal/remodeling of CJ during advanced heart looping stages, which leads to the formation of ventricular trabeculations and endocardial cushions. CJ acts as a hydraulic skeleton displaying striking structural and functional similarities with the mesoglea of jellyfish. CJ not only represents a filler substance, facilitating end-systolic occlusion of the embryonic heart lumen. Its elastic components antagonize the systolic deformations of the heart wall and thereby power the refilling phase of the ventricular tube. Non-uniform spatial distribution of CJ generates non-circular cross sections of the opened endocardial tube (initially elliptic, later deltoid), which seem to be advantageous for valveless pumping. Endocardial cushions arise from non-removed remnants of the original CJ.

Existence and Stability of Periodic Solution Related to Valveless Pumping

Valveless pumping, also known as Liebau effect, can be described as the unidirectional flow of liquid in a system without valves that is caused by the asymmetry of placing of the periodically working pump. Recently, the research in this field has been reevoked, partially due to its possible application in nanotechnologies. In this paper, a configuration of one pipe and one tank is considered from the mathematical point of view. Qualitative properties of a class of nonlinear differential equations that model the assumed system configuration are investigated. New sufficient conditions for the existence of positive T-periodic solutions are given. Correspondingly, exponential stability of periodic solution is treated. Presented results are new. They extend and complement earlier ones in the literature.

Bifurcations in valveless pumping techniques from a coupled fluid-structure-electrophysiology model in heart development

We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to muscular contraction and hence the overall pumping dynamics. In comparison to previous models, the electro-dynamical model does not use prescribed motion to initiate the pumping motion, but rather the pumping dynamics are fully coupled to an underlying electrophysiology model, governed by the FitzHugh-Nagumo equations. Perturbing the diffusion parameter in the FitzHugh-Nagumo model leads to a bifurcation in dynamics of action potential propagation. This bifurcation is able to capture a spectrum of different pumping regimes, with dynamic suction pumping and peristaltic-like pumping at the extremes. We find that more bulk flow is produced within the realm of peristaltic-like pumping.