Pulsatile Flow Regimes Research Articles

Theoretical and numerical analysis of the flow through a diffuser/nozzle element in pulsatile laminar conditions

Diffuser/nozzle pipes produce a directional flow resistance that is often exploited in microcirculation to generate a pumping action. This work presents an approximate time-dependent theoretical solution based on the mechanical energy conservation equation to predict the laminar flow rate through an ideal diffuser/nozzle pump. The theoretical solution is then used to characterize the dimensionless parameters that control the dynamics of the valveless pump in the pulsatile flow regime. A suitable numerical model is also implemented to solve the flow in a parametrized two-dimensional axial-symmetric domain subjected to an oscillating pressure, and its results are used to assess the theoretical solution. The pump dynamics and the main model parameters, such as the energy-loss coefficients, result in the following dependence on the ratios between the viscous force, the advective inertia, and the temporal inertia, i.e., the Reynolds (Red), Womersley (Wod), and Strouhal (St) numbers referred to throat diameter. In particular, The Womersley number plays an essential role in controlling the global energy loss when Red < 100. The flow transition is also investigated and found when Red exceeds a critical value, which increases with Wod. Finally, the pump efficiency is found to reach its maximum when the convective and temporal inertia become comparable, i.e., St=O(1), consistent with the observed range of St in real-world diffuser/nozzle pumps. This optimum range of functioning of the pump is also observed for cerebrospinal pulsatile flow in the Sylvius aqueduct, suggesting that the modeled mechanism is used to promote or enhance cerebrospinal fluid circulation.

A pneumatically controlled microfluidic rectifier enabling zero backflow under pulsatile flow regime

A pulsatile microfluidic pump transports discrete volume to specific target locations. However, backflow in the pulsatile microfluidic pump often decreases the pumping efficiency and causes unwanted sample mixing due to unsteady boundaries. Employing the concept of a transistor, we developed a pneumatically controlled microfluidic rectifier (PCMR) that prevents backflow in the pulsatile flow regime. This PCMR was interconnected with a microfluidic pulsatile pumping system to characterize the functions of PCMR under continuous pumping sequences (CPS) and discrete pumping sequences (DPS) with various gate pressures on the PCMR. In the passive mode (zero gate pressure), 1.07% backflow for a DPS and 0.12% for a CPS were achieved. However, by adjusting the gate pressure on PCMR actively, we were able to achieve zero backflow for both pumping sequences at the cost of pumping efficiency. Interestingly, when the flow passes through the PCMR under the controlled gate-pressure, a fluidic oscillation was observed due to the force balance between the fluidic pressure and the gate-pressure. This microfluidic system successfully demonstrated half-rectification from various pulsatile flow profiles. By incorporating multiple three-microvalve systems in parallel with frequency modulation, a fully rectified flow pattern can be realized to enable steady laminar flow from pulsatile micropumps.

Impact of coronary bifurcation morphology on wave propagation.

The branching pattern of the coronary vasculature is a key determinant of its function and plays a crucial role in shaping the pressure and velocity wave forms measured for clinical diagnosis. However, although multiple scaling laws have been proposed to characterize the branching pattern, the implications they have on wave propagation remain unassessed to date. To bridge this gap, we have developed a new theoretical framework by combining the mathematical formulation of scaling laws with the wave propagation theory in the pulsatile flow regime. This framework was then validated in multiple species using high-resolution cryomicrotome images of porcine, canine, and human coronary networks. Results demonstrate that the forward well-matchedness (no reflection for pressure/flow waves traveling from the coronary stem toward the microcirculation) is a salient feature in the coronary vasculature, and this result remains robust under many scenarios of the underlying pulse wave speed distribution assumed in the network. This result also implies a significant damping of the backward traveling waves, especially for smaller vessels (radius, <0.3 mm). Furthermore, the theoretical prediction of increasing area ratios (ratio between the area of the mother and daughter vessels) in more symmetric bifurcations found in the distal circulation was confirmed by experimental measurements. No differences were observed by clustering the vessel segments in terms of transmurality (from epicardium to endocardium) or perfusion territories (left anterior descending, left circumflex, and right coronary artery).

Non-dimensional physics of pulsatile cardiovascular networks and energy efficiency.

In Nature, there exist a variety of cardiovascular circulation networks in which the energetic ventricular load has both steady and pulsatile components. Steady load is related to the mean cardiac output (CO) and the haemodynamic resistance of the peripheral vascular system. On the other hand, the pulsatile load is determined by the simultaneous pressure and flow waveforms at the ventricular outlet, which in turn are governed through arterial wave dynamics (transmission) and pulse decay characteristics (windkessel effect). Both the steady and pulsatile contributions of the haemodynamic power load are critical for characterizing/comparing disease states and for predicting the performance of cardiovascular devices. However, haemodynamic performance parameters vary significantly from subject to subject because of body size, heart rate and subject-specific CO. Therefore, a 'normalized' energy dissipation index, as a function of the 'non-dimensional' physical parameters that govern the circulation networks, is needed for comparative/integrative biological studies and clinical decision-making. In this paper, a complete network-independent non-dimensional formulation that incorporates pulsatile flow regimes is developed. Mechanical design variables of cardiovascular flow systems are identified and the Buckingham Pi theorem is formally applied to obtain the corresponding non-dimensional scaling parameter sets. Two scaling approaches are considered to address both the lumped parameter networks and the distributed circulation components. The validity of these non-dimensional number sets is tested extensively through the existing empirical allometric scaling laws of circulation systems. Additional validation studies are performed using a parametric numerical arterial model that represents the transmission and windkessel characteristics, which are adjusted to represent different body sizes and non-dimensional haemodynamic states. Simulations demonstrate that the proposed non-dimensional indices are independent of body size for healthy conditions, but are sensitive to deviations caused by off-design disease states that alter the energetic load. Sensitivity simulations are used to identify the relationship between pulsatile power loss and non-dimensional characteristics, and optimal operational states are computed.

Expansion of bubbles under a pulsatile flow regime in decompressed ovine blood vessels

After decompression of ovine large blood vessels, bubbles nucleate and expand at active hydrophobic spots on their luminal aspect. These bubbles will be in the path of the blood flow within the vessel, which might replenish the supply of gas-supersaturated plasma in their vicinity and thus, in contrast with our previous estimations, enhance their growth. We used the data from our previous study on the effect of pulsatile flow in ovine blood vessels stretched on microscope slides and photographed after decompression from hyperbaric exposure. We measured the diameter of 46 bubbles in 4 samples taken from 3 blood vessels (pulmonary artery, pulmonary vein, and aorta) in which both a “multi-bubble active spot” (MBAS)—which produces several bubbles at a time, and at least one “single-bubble active spot” (SBAS)—which produces a single bubble at a time, were seen together. The linear expansion rate for diameter in SBAS ranged from 0.077 to 0.498mm/min and in MBAS from 0.001 to 0.332mm/min. There was a trend toward a reduced expansion rate for bubbles in MBAS compared with SBAS. The expansion rate for bubbles in an MBAS when it was surrounded by others was very low. Bubble growth is related to gas tension, and under a flow regime, bubbles expand from a diameter of 0.1 to 1mm in 2–24min at a gas supersaturation of 620kPa and lower. There are two phases of bubble development. The slow and disperse initiation of active spots (from nanobubbles to gas micronuclei) continues for more than 1h, whereas the fast increase in size (2–24min) is governed by diffusion. Bubble-based decompression models should not artificially reduce diffusion constants, but rather take both phases of bubble development into consideration.

4D UTE flow: A phase-contrast MRI technique for assessment and visualization of stenotic flows

Inaccuracy of conventional four-dimensional (4D) flow MR imaging in the presence of random unsteady and turbulent blood flow distal to a narrowing has been an important challenge. Previous investigations have revealed that shorter echo times (TE) decrease the errors, leading to more accurate flow assessments. In this study, as part of a 4D flow acquisition, an Ultra-Short TE (UTE) method was adopted. UTE works based on a center-out radial k-space trajectory that inherently has a short TE. By employing free induction decay sampling starting from read-out gradient ramp-up, and by combining the refocusing lobe of the slice select gradient with the bipolar flow encoding gradient, TEs of ≈1 msec may be achieved. Both steady and pulsatile flow regimes, and in each case a range of Reynolds numbers, were studied in an in-vitro model. Flow assessment at low and medium flow rates demonstrated a good agreement between 4D UTE and conventional 4D flow techniques. However, 4D UTE flow significantly outperformed conventional 4D flow, at high flow rates for both steady and pulsatile flow regimes. Feasibility of the method in one patient with Aortic Stenosis was also demonstrated. For both steady and pulsatile high flow rates, the measured flow distal to the stenotic narrowing using conventional 4D flow revealed more than 20% error compared to the ground-truth flow. This error was reduced to less than 5% using the 4D UTE flow technique.

Characterization of an Innovative Implantable Valve-less Pump for Bio or Drug Fluid Delivery − Theory and Experiment

This article describes the design and testing procedures for an innovative implantable pump for medical applications. In contrast to traditional drug delivery methods, this implantable pump delivers drugs or biofluids (blood, plasma, etc.) with better performance. The valve-less feature of the pump reduces the probability of damaged blood cells during pumping, which may be caused by shearing forces on the cell membrane. High accuracy of drug (or biofluid) administration in an implantable pump is beneficial when treating patients. In addition, the pump does not require an external power source since it relies entirely on the body’s own energy from the pulsating character of blood circulation. The theoretical model of the pump elements is built based on nozzle-diffuser elements. The experiment shows that the efficiency ratio decreases when there is an increase in diameter of the nozzle-diffuser element. The efficiency ratio is also affected by the angle and the length of the channel. The maximum flow rate for the designed pump is around 1 ml/min based on a frequency of 1.16 Hz in pulsatile flow regime. The total dimensions (nozzle-diffuser elements and pumping chambers) of our pump are 45 × 6 × 15 mm. However, it is important to note that the dimensions can vary (from micro to macro sizes) depending on the application.

Hemodynamics of the aortic valve and root: implications for surgery.

Hemodynamics of the aortic valve and root: implications for surgery.

Effects of Reynolds number on physiological-type pulsatile flows in a pipe with ring-type constrictions

The effects of Reynolds number on the physiological-type of laminar pulsatile flow fields within the vicinity of mechanical ring-type constriction in small pipes were studied numerically. The parameters considered are: the Reynolds number (Re) in the range of 50–1500; Strouhal number (St) in the range of 0.00156–3.98; Womersley number (Nw) from 0.0 to 50.0. The pulsatile flows considered were physiological-type of simulated flows. Within a pulsating cycle, detailed flow characteristics were studied through the pulsating contours of streamline (ψ), vorticity (Ω), shear stress (τ) and isobar. The relations between the instantaneous flow rate (Q) and instantaneous pressure gradients (dp/dz) are observed to be elliptic. The relations between the instantaneous flow rate (Q) and pressure loss (Ploss) are quadratic. Linear relations were observed between the instantaneous flow rate (Q) and the maximum velocity, maximum vorticity and maximum shear stress. The Reynolds number of the flow in a pulsating cycle was found to have significant effects on the recirculation length and the pressure gradient within the pulsatile flow regime. Copyright © 1999 John Wiley & Sons, Ltd.

The influence of open leaflet geometry on the haemodynamic flow characteristics of polyurethane trileaflet artificial heart valves.

In vitro velocity data were obtained downstream of two versions of the Leeds polyurethane trileaflet heart valve in a simulated pulsatile flow regime using laser Doppler velocimetry. The main difference between the two valves studied was the manufacturing method used to create the valves. The film-fabricated valve was constructed from solvent-cast sheets of polyurethane, thermally formed into the correct leaflet geometry. The dip-cast valve used a stainless steel mould which was dipped into a polyurethane solution to produce the valve leaflets. Significant differences were visible between the fully open leaflet shape of each valve. The distribution of mean axial velocity and Reynolds normal stress (RNS) was shown to be dependent on the shape of the fully open valve orifice. For the film-fabricated valves, flow recirculation and high values of RNS were present downstream of the frame posts. The maximum value of RNS obtained downstream of the film-fabricated valve at peak systole was 147 N/m2. Results for the dip-cast valve showed a more uniform distribution of mean axial velocity and RNS resulting from the more circular central orifice produced by the dip-cast leaflets. The maximum value of RNS obtained downstream of the dip-cast valve at peak systole was 109 N/m2. These results demonstrate the effect of the open valve geometry on the flow characteristics downstream of trileaflet valves and that minor changes to the open leaflet geometry can significantly affect the flow characteristics and the possibility of flow-related blood damage occurring in vivo.