Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

Spatial velocity profile in mouse embryonic aorta and Doppler-derived volumetric flow: a preliminary model

Characterizing embryonic circulatory physiology requires accurate cardiac output and flow data. Despite recent applications of high-frequency ultrasound Doppler to the study of embryonic circulation, current Doppler analysis of volumetric flow is relatively crude. To improve Doppler derivation of volumetric flow, we sought a preliminary model of the spatial velocity profile in the mouse embryonic dorsal aorta using ultrasound biomicroscopy (UBM)-Doppler data. Embryonic hematocrit is 0.05-0.10 so rheologic properties must be insignificant. Low Reynolds numbers (<500) and Womersley parameters (<0.76) suggest laminar flow. UBM demonstrated a circular dorsal aortic cross section with no significant tapering. Low Dean numbers (<100) suggest the presence of minimal skewing of the spatial velocity profile. The inlet length allows for fully developed flow. There is no apparent aortic wall pulsatility. Extrapolation of prior studies to these vessel diameters (300-350 microm) and flow velocities (~50-200 mm/s) suggests parabolic spatial velocity profiles. Therefore, mouse embryonic dorsal aortic blood flow may correspond to Poiseuille flow in a straight rigid tube with parabolic spatial velocity profiles. As a first approximation, these results are an important step toward precise in utero ultrasound characterization of blood flow within the developing mammalian circulation.     

Flow in a mechanical bileaflet heart valve at laminar and near-peak systole flow rates: CFD simulations and experiments

Time-accurate, fully 3D numerical simulations and particle image velocity laboratory experiments are carried out for flow through a fully open bileaflet mechanical heart valve under steady (nonpulsatile) inflow conditions. Flows at two different Reynolds numbers, one in the laminar regime and the other turbulent (near-peak systole flow rate), are investigated. A direct numerical simulation is carried out for the laminar flow case while the turbulent flow is investigated with two different unsteady statistical turbulence modeling approaches, unsteady Reynolds-averaged Navier-Stokes (URANS) and detached-eddy simulation (DES) approach. For both the laminar and turbulent cases the computed mean velocity profiles are in good overall agreement with the measurements. For the turbulent simulations, however, the comparisons with the measurements demonstrate clearly the superiority of the DES approach and underscore its potential as a powerful modeling tool of cardiovascular flows at physiological conditions. The study reveals numerous previously unknown features of the flow.     

Evaluation of magnetic resonance velocimetry for steady flow

Whole body magnetic resonance (MR) imaging has recently become an important diagnostic tool for cardiovascular diseases. The technique of magnetic resonance phase velocity encoding allows the quantitative measurement of velocity for an arbitrary component direction. A study was initiated to determine the ability and accuracy of MR velocimetry to measure a wide range of flow conditions including flow separation, three-dimensional secondary flow, high velocity gradients, and turbulence. A steady flow system pumped water doped with manganese chloride through a variety of test sections. Images were produced using gradient echo sequences on test sections including a straight tube, a curved tube, a smoothly converging-diverging nozzle, and an orifice. Magnetic resonance measurements of laminar and turbulent flows were depicted as cross-sectional velocity profiles. MR velocity measurements revealed such flow behavior as spatially varying velocity, recirculation and secondary flows over a wide range of conditions. Comparisons made with published experimental laser Doppler anemometry measurements and theoretical calculations for similar flow conditions revealed excellent accuracy and precision levels. The successful measurement of velocity profiles for a variety of flow conditions and geometries indicate that magnetic resonance imaging is an accurate, non-contacting velocimeter.     

Shear-scaling-based approach for irreversible energy loss estimation in stenotic aortic flow – An in vitro study

Today, the functional and risk assessment of stenosed arteries is mostly based on ultrasound Doppler blood flow velocity measurements or catheter pressure measurements, which rely on several assumptions. Alternatively, blood velocity including turbulent kinetic energy (TKE) may be measured using MRI. The aim of the present study is to validate a TKE-based approach that relies on the fact that turbulence production is dominated by the flow’s shear to determine the total irreversible energy loss from MRI scans. Three-dimensional particle tracking velocimetry (3D-PTV) and phase-contrast magnetic resonance imaging (PC-MRI) simulations were performed in an anatomically accurate, compliant, silicon aortic phantom. We found that measuring only the laminar viscous losses does not reflect the true losses of stenotic flows since the contribution of the turbulent losses to the total loss become more dominant for more severe stenosis types (for example, the laminar loss is 0.0094 ± 0.0015 W and the turbulent loss is 0.0361 ± 0.0015 W for the Re_max = 13,800 case, where Re_max is the Reynolds number based on the velocity in the vena-contracta). We show that the commonly used simplified and modified Bernoulli’s approaches overestimate the total loss, while the new TKE-based method proposed here, referred to as “shear scaling” approach, results in a good agreement between 3D-PTV and simulated PC-MRI (mean error is around 10%). In addition, we validated the shear scaling approach on a geometry with post-stenotic dilatation using numerical data by Casas et al. (2016). The shear scaling-based method may hence be an interesting alternative for irreversible energy loss estimation to replace traditional approaches for clinical use. We expect that our results will evoke further research, in particular patient studies for clinical implementation of the new method.     

Turbulence detection in a stenosed artery bifurcation by numerical simulation of pulsatile blood flow using the low-Reynolds number turbulence model

The pulsatile blood flow in a partially blocked artery is significantly altered as the flow regime changes through the cardiac cycle. This paper reports on the application of a low-Reynolds turbulence model for computation of physiological pulsatile flow in a healthy and stenosed carotid artery bifurcation. The human carotid artery was chosen since it has received much attention because atherosclerotic lesions are frequently observed. The Wilcox low-Re k-omega turbulence model was used for the simulation since it has proven to be more accurate in describing transition from laminar to turbulent flow. Using the FIDAP finite element code a validation showed very good agreement between experimental and numerical results for a steady laminar to turbulent flow transition as reported in a previous publication by the same authors. Since no experimental or numerical results were available in the literature for a pulsatile and turbulent flow regime, a comparison between laminar and low-Re turbulent calculations was made to further validate the turbulence model. The results of this study showed a very good agreement for velocity profiles and wall shear stress values for this imposed pulsatile laminar flow regime. To explore further the medical aspect, the calculations showed that even in a healthy or non-stenosed artery, small instabilities could be found at least for a portion of the pulse cycle and in different sections. The 40% and 55% diameter reduction stenoses did not significantly change the turbulence characteristics. Further results showed that the presence of 75% stenoses changed the flow properties from laminar to turbulent flow for a good portion of the cardiac pulse. A full 3D simulation with this low-Re-turbulence model, coupled with Doppler ultrasound, can play a significant role in assessing the degree of stenosis for cardiac patients with mild conditions.     

Orientation and food search behaviour of a deep sea lobster in turbulent versus laminar odour plumes

New Zealand scampi (Metanephrops challengeri) is a commercially important deep-water lobster species that is caught by bottom trawling on areas of muddy seafloor on the continental shelf below 300 m. Efforts are being made to develop lower impact potting methods to harvest scampi, however, they can only be caught when out of their burrows and searching for food. This emergent food searching behaviour appears to be associated with periods of higher tidal flow. Such water flow will increase turbulence along the sea floor, which has been observed to improve the efficiency of chemosensory food searching in some lobster species. Consequently, this study examined the food search behaviour of scampi in response to odours from two types of bait (mackerel and mussel) in both turbulent and laminar flows. Scampi were more efficient at foraging in the turbulent flow than in the laminar flow, using shorter search paths in response to both types of bait. Scampi in the turbulent flow reached the mussel bait 44% faster and with lower mean heading angles than in laminar flow. However, there was no difference between the flow regimes for the mackerel bait. The pattern of orientation behaviour was similar under both flow regimes, suggesting that the scampi were using the same orientation strategy, but it was more accurate in turbulent flows. The results show that the foraging efficiency of scampi improves in turbulent conditions and that this may explain their increased emergent behaviour during periods of higher tidal flows.     

Mammalian cell damage in a novel membrane bioreactor

The experimental study has assessed a novel membrane bioreactor for mammalian cell culture. In the absence of a gas phase, the key features of cell damage associated with laminar and turbulent flow have been identified. The bioreactor employs a dimpled membrane in order to enhance transverse mixing in a narrow channel, but a fall in viable cell density has been observed at Reynolds numbers above Re = 83. In the laminar flow regime wall shear is the critical mechanism and an accurate calculation of shear rate in a complex channel has been achieved using the Reynolds analogy. Flow generating a wall shear rate in excess of 3000 s(-1) has been shown to cause damage. Power dissipation measurements have been used to distinguish between laminar and turbulent flow and also to predict Kolmogorov eddy lengths. An additional turbulent bulk stress damage mechanism at higher Reynolds numbers (Re > 250) results in a very rapid fall in viable cell density.     

Influence of Hydrodynamics and Cell Signaling on the Structure and Behavior of Pseudomonas aeruginosa Biofilms

Biofilms were grown from wild-type (WT) Pseudomonas aeruginosa PAO1 and the cell signaling lasI mutant PAO1-JP1 under laminar and turbulent flows to investigate the relative contributions of hydrodynamics and cell signaling for biofilm formation. Various biofilm morphological parameters were quantified using Image Structure Analyzer software. Multivariate analysis demonstrated that both cell signaling and hydrodynamics significantly (P < 0.000) influenced biofilm structure. In turbulent flow, both biofilms formed streamlined patches, which in some cases developed ripple-like wave structures which flowed downstream along the surface of the flow cell. In laminar flow, both biofilms formed monolayers interspersed with small circular microcolonies. Ripple-like structures also formed in four out of six WT biofilms, although their velocity was approximately 10 times less than that of those that formed in the turbulent flow cells. The movement of biofilm cell clusters over solid surfaces may have important clinical implications for the dissemination of biofilm subject to fluid shear, such as that found in catheters. The ability of the cell signaling mutant to form biofilms in high shear flow demonstrates that signaling mechanisms are not required for the formation of strongly adhered biofilms. Similarity between biofilm morphologies in WT and mutant biofilms suggests that the dilution of signal molecules by mass transfer effects in faster flowing systems mollifies the dramatic influence of signal molecules on biofilm structure reported in previous studies.     

Theory to Predict Shear Stress on Cells in Turbulent Blood Flow

Shear stress on blood cells and platelets transported in a turbulent flow dictates the fate and biological activity of these cells. We present a theoretical link between energy dissipation in turbulent flows to the shear stress that cells experience and show that for the case of physiological turbulent blood flow: (a) the Newtonian assumption is valid, (b) turbulent eddies are universal for the most complex of blood flow problems, and (c) shear stress distribution on turbulent blood flows is possibly universal. Further we resolve a long standing inconsistency in hemolysis between laminar and turbulent flow using the theoretical framework. This work demonstrates that energy dissipation as opposed to bulk shear stress in laminar or turbulent blood flow dictates local mechanical environment of blood cells and platelets universally.     

Optimization of diameters and bifurcation angles in lung and vascular tree structures

An optimization model is described for lung and vascular tree structures. The model extends Murray's model, which is derived from minimal power dissipation due to the frictional resistance of laminar flow and the volume of the duct system. Instead of just laminar flow, it takes into account all types of steady flow, e.g. turbulent and laminar flow, and predicts which structural changes will occur among different parts of trees having different types of flow. The sensitivity of the optimal values is indicated and the model, predictions are compared with literature data.     

Constructal Law of Vascular Trees for Facilitation of Flow

Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures.     

How to perform measurements in a hovering animal's wake: physical modelling of the vortex wake of the hawkmoth, Manduca sexta

The vortex wake structure of the hawkmoth, Manduca sexta, was investigated using a vortex ring generator. Based on existing kinematic and morphological data, a piston and tube apparatus was constructed to produce circular vortex rings with the same size and disc loading as a hovering hawkmoth. Results show that the artificial rings were initially laminar, but developed turbulence owing to azimuthal wave instability. The initial impulse and circulation were accurately estimated for laminar rings using particle image velocimetry; after the transition to turbulence, initial circulation was generally underestimated. The underestimate for turbulent rings can be corrected if the transition time and velocity profile are accurately known, but this correction will not be feasible for experiments on real animals. It is therefore crucial that the circulation and impulse be estimated while the wake vortices are still laminar. The scaling of the ring Reynolds number suggests that flying animals of about the size of hawkmoths may be the largest animals whose wakes stay laminar for long enough to perform such measurements during hovering. Thus, at low advance ratios, they may be the largest animals for which wake circulation and impulse can be accurately measured.     

Effect of flow regimes on the presence of Legionella within the biofilm of a model plumbing system

AIMS: Stagnation is widely believed to predispose water systems to colonization by Legionella. A model plumbing system was constructed to determine the effect of flow regimes on the presence of Legionella within microbial biofilms. METHODS AND RESULTS: The plumbing model contained three parallel pipes where turbulent, laminar and stagnant flow regimes were established. Four sets of experiments were carried out with Reynolds number from 10,000 to 40,000 and from 355 to 2,000 in turbulent and laminar pipes, respectively. Legionella counts recovered from biofilm and planktonic water samples of the three sampling pipes were compared with to determine the effect of flow regime on the presence of Legionella. Significantly higher colony counts of Legionella were recovered from the biofilm of the pipe with turbulent flow compared with the pipe with laminar flow. The lowest counts were in the pipe with stagnant flow. CONCLUSIONS: We were unable to demonstrate that stagnant conditions promoted Legionella colonization. SIGNIFICANCE AND IMPACT OF THE STUDY: Plumbing modifications to remove areas of stagnation including deadlegs are widely recommended, but these modifications are tedious and expensive to perform. Controlled studies in large buildings are needed to validate this unproved hypothesis.     

A mathematical model for the dissolution of non-occlusive blood clots in fast tangential blood flow

Our aim was to study the effect of an axially directed blood plasma flow on the dissolution rate of cylindrical non-occlusive blood clots in an in vitro flow system and to derive a mathematical model for the process. The model was based on the hypothesis that clot dissolution dynamics is proportional not only to the biochemical proteolysis of fibrin but also to the power of the flowing blood plasma dissipated along the clot. The predicted rate of thrombolysis is then proportional to the square of the average blood plasma velocity for laminar flow and to the third power of the average velocity for turbulent flow. To verify the model, the time dependence of the clot cross-sectional area was measured by dynamic magnetic resonance microscopy during fast (turbulent) and slow (laminar) flow of plasma through an axially directed channel along the clot. The flowing plasma contained a magnetic resonance imaging contrast agent (Gd-DTPA) and a thrombolytic agent (recombinant tissue-type plasminogen activator). The experimental data fitted well to the model, and confirmed the predicted increase in the dissolution rate when blood flow changed from a laminar to a turbulent flow regime.     

Shear‐induced diffusion of red blood cells measured with dynamic light scattering‐optical coherence tomography

Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells (RBCs), are fundamental in understanding the blood flow behavior within the microcirculation, and for understanding why diffuse correlation spectroscopy (DCS) measurements of blood flow are dominantly sensitive to the diffusive motion of RBCs. Dynamic light scattering‐optical coherence tomography (DLS‐OCT) takes the advantages of using DLS to measure particle flow and diffusion within an OCT resolution‐constrained three‐dimensional volume, enabling the simultaneous measurements of absolute RBC velocity and diffusion coefficient with high spatial resolution. In this work, we applied DLS‐OCT to measure both RBC velocity and the shear‐induced diffusion coefficient within penetrating venules of the somatosensory cortex of anesthetized mice. Blood flow laminar profile measurements indicate a blunted laminar flow profile and the degree of blunting decreases with increasing vessel diameter. The measured shear‐induced diffusion coefficient was proportional to the flow shear rate with a magnitude of ~0.1 to 0.5 × 10^?6 mm². These results provide important experimental support for the recent theoretical explanation for why DCS is dominantly sensitive to RBC diffusive motion.      

Effect of turbulent models on left ventricle diastolic flow patterns simulation

Abstract

Vortex structures, as one of the most important features of cardiac flow, have a crucial impact on the left ventricle function and pathological conditions. These swirling flows are closely related to the presence of turbulence in left ventricle which is investigated in the current study. Using an extended model of the left heart, including a fluid-structure interaction (FSI) model of the mitral valve with a realistic geometry, the effect of using two numerical turbulent models, k-ε and Spalart-Allmaras (SA), on diastolic flow patterns is studied and compared with results from laminar flow model. As a result of the higher dissipation rate in turbulent models (k-ε and SA), vortices are larger and stronger in the laminar flow model. Comparing E/A ratio in the three models (Laminar, k-ε, and SA) with experimental data from healthy subjects, it is concluded that the results from k-ε model are more accurate.     

Application of multiple forms of mechanical loading to human osteoblasts reveals increased ATP release in response to fluid flow in 3D cultures and differential regulation of immediate early genes

ATP is actively released into the extracellular environment from a variety of cell types in response to mechanical stimuli. This is particularly true in bone where mechanically induced ATP release leads to immediate early gene activation to regulate bone remodelling; however there is no consensus as to which mechanical stimuli stimulate osteoblasts the most. To elucidate which specific type(s) of mechanical stimuli induce ATP release and gene activation in human osteoblasts, we performed an array of experiments using different mechanical stimuli applied to both monolayer and 3D cultures of the same osteoblast cell type, SaOS-2. ATP release from osteoblasts cultured in monolayer significantly increased in response to turbulent fluid flow, laminar fluid flow and substrate strain. No significant change in ATP release could be detected in 3D osteoblast cultures in response to cyclic or static compressive loading of osteoblast-seeded scaffolds, whilst turbulent fluid flow increased ATP release from 3D cultures of osteoblasts to a greater degree than observed in monolayer cultures. Cox-2 expression quantified using real time PCR was significantly lower in cells subjected to turbulent fluid flow whereas c-fos expression was significantly higher in cells subjected to strain. Load-induced signalling via c-fos was further investigated using a SaOS-2 c-fos luciferase reporter cell line and increased in response to substrate strain and turbulent fluid flow in both monolayer and 3D, with no significant change in response to laminar fluid flow or 3D compressive loading. The results of this study demonstrate for the first time strain-induced ATP release from osteoblasts and that turbulent fluid flow in 3D up regulates the signals required for bone remodelling.     

The turbulent boundary layer over a flapping Populus leaf

Abstract The air-flow regime over a Populus leaf was investigated using a constant temperature hot-film sensor which could be glued on the abaxial surface. The leaf was exposed to a laminar or turbulent flow of air in a wind-tunnel, while being free to undergo normal motion. In the laminar air-flow the boundary layer remained laminar, despite the fluttering of the leaf, until a Reynolds number of 2.3 × 10⁴ was reached. When the air incident on the leaf was made turbulent, to resemble natural conditions, the boundary layer became turbulent at a Reynolds number of 0.4 × 10⁴. The experiments suggest that the boundary layers over leaves are always turbulent in the natural wind.     

Direct numerical simulation of transitional flow in a stenosed carotid bifurcation

The blood flow dynamics of a stenosed, subject-specific, carotid bifurcation were numerically simulated using the spectral element method. Pulsatile inlet conditions were based on in vivo color Doppler ultrasound measurements of blood velocity. The results demonstrated the transitional or weakly turbulent state of the blood flow, which featured rapid velocity and pressure fluctuations in the post-stenotic region of the internal carotid artery (ICA) during systole and laminar flow during diastole. High-frequency vortex shedding was greatest downstream of the stenosis during the deceleration phase of systole. Velocity fluctuations had a frequency within the audible range of 100-300Hz. Instantaneous wall shear stress (WSS) within the stenosis was relatively high during systole ( approximately 25-45Pa) compared to that in a healthy carotid. In addition, high spatial gradients of WSS were present due to flow separation on the inner wall. Oscillatory flow reversal and low pressure were observed distal to the stenosis in the ICA. This study predicts the complex flow field, the turbulence levels and the distribution of the biomechanical stresses present in vivo within a stenosed carotid artery.