Newtonian Analogue Research Articles

An In-Vitro Study On The Carotid Bifurcation And Its Influence On Arterial Haemodynamics With Newtonian And Non-Newtonian Blood Analogs

The carotid artery bifurcation is a region susceptible to atherosclerosis and cardiovascular diseases. The geometry of the bifurcation is individually unique and significant differences have been correlated to both age and gender. Identifying geometric features that produce adverse flow patterns could enable clinicians to make early assessment of an individual’s risk of developing the disease enabling proactive management. Consequently, this study aims to evaluate the influence of the carotid bifurcation angle on arterial haemodynamics using stereoscopic particle image velocimetry. Pulsatile flow conditions were applied to a Newtonian and non-Newtonian blood analog in three compliant, physiologically realistic carotid artery bifurcation phantoms with different bifurcation angles. Results indicate large bifurcation angles can produce adverse flow conditions, increasing size of stagnation regions and promoting plaque development. Additionally, an optimal bifurcation angle could exist that could be considered atheroprotective. Comparison of Newtonian and non-Newtonian blood analogs in one of the geometries show subtle yet significant differences between flow fields, suggesting the shear-thinning behaviour of blood should be carefully considered prior to adopting a Newtonian assumption, even in large vessels.

Experiments and numerical modelling of secondary flows of blood and shear-thinning blood analogue fluids in rotating domains

The transition from concentric primary flow to non-tangential secondary flow of blood was investigated using experimental steady shear rheometry and numerical modelling. The aims were to: assess the difference in secondary flow in a Newtonian versus shear-thinning blood analogue; and measure the secondary flow in the blood. Both experiments and numerical modelling showed that the transition from primary to secondary flow was the same in a Newtonian fluid and a shear-thinning blood analogue. Experiments showed whole blood transitioned to secondary flow at lower modified Reynolds numbers than the Newtonian fluid; and transition was haematocrit dependent with higher RBC concentrations transitioning at lower modified Reynolds numbers. These results indicate that modelling blood as a purely shear-thinning fluid does not predict the correct secondary flow fields in whole blood; non-Newtonian effects beyond shear-thinning behaviour are influential, and incorporating effects such as multiphase contributions and viscoelasticity, yield stress and thixotropy is necessary.

A comprehensive model for viscoplastic flows in channels with a patterned wall: longitudinal, transverse and oblique flows

We develop a comprehensive model for the creeping Poiseuille Bingham flow in channels equipped with a patterned wall, i.e. decorated with grooves or stripes that may represent a superhydrophobic (SH) or a chemically patterned (CP) surface, respectively, with longitudinal, transverse and oblique groove (stripe) orientations with respect to the applied pressure gradient. We rely on the Navier slip law to model the boundary condition on the slippery grooves. We develop semi-analytical, explicit-form and complementary computational fluid dynamics models, with solutions that have reasonable agreement. In contrast to its Newtonian analogue, a distinct solution for the oblique configuration, with an a priori unknown transform matrix, must be developed due to the viscoplastic nonlinear rheology. Our focus is to systematically analyse the effects of the Bingham number ( $B$ ), slip number ( $b$ ), groove periodicity length ( $\ell$ ), slip area fraction ( $\varphi$ ) and groove orientation angle ( $\theta$ ), on the slip velocities, effective slip length ( $\chi$ ), slip angle difference ( $\theta -s$ ), mixing index ( $I_M$ ), flow anisotropy and flow regimes. In particular, we demonstrate that, as $B$ increases, the maximum values of the shear component of $\chi$ , $\theta -s$ and $I_M$ occur progressively at smaller values of $\theta$ , compared with their Newtonian counterparts.

Stationary rotating and axially symmetric dust systems as peculiar General Relativistic objects

We study an exact solution of Einstein's equations describing a self-gravitating system, made of dust, distributed with axial symmetry and in stationary rotation, and we prove that this type of system has no Newtonian analogue. In a low-energy limit, its existence depends on the solution of a Grad-Shafranov equation in vacuum which can be interpreted as a Laplace equation for the toroidal component of the gravitomagnetic potential; in particular, in this system the relativistic rotational effects are of the order of magnitude of Newtonian ones. We therefore argue that this exact solution should contain singularities and discuss the possible consequences of using such a system as simplified model for galactic dynamics.

Tidally-induced nonlinear resonances in EMRIs with an analogue model

One of the important targets for the future space-based gravitational wave observatory Laser Interferometer Space Antenna is extreme mass ratio inspirals (EMRIs), where long and accurate waveform modeling is necessary for detection and characterization. Modeling EMRI dynamics requires accounting for effects such as the ones induced by an external tidal field, which can break integrability at resonances and cause significant dephasing. In this paper, we use a Newtonian analogue of a Kerr black hole to study the effect of an external tidal field on the dynamics and the gravitational waveform. We have developed a numerical framework that takes advantage of the integrability of the background system to evolve it with a symplectic splitting integrator, and compute approximate gravitational waveforms to estimate the timescale over which the perturbation affects the dynamics. Comparing this timescale with the characteristic time under radiation reaction at resonance, we introduce a tool for quantifying the regime in which tidal effects might be included when modeling EMRI gravitational waves. As an application of this framework, we perform a detailed analysis of the dynamics at one resonance to show how different entry points into the resonance in phase-space can produce substantially different dynamics, and how one can estimate bounds for the parameter space where tidal effects may become dominant. Such bounds will scale as , where ɛ measures the strength of the external tidal field, q is the mass ratio, and C is a number which depends on the resonance and the shape of the tide. We demonstrate how to estimate C using our framework for the 2:3 radial to polar frequency resonance in our model system. This framework can serve as a proxy for proper modeling of the tidal perturbation in the fully relativistic case.

Two Spinning Black Holes Balanced by Their Synchronized Scalar Hair.

General relativity minimally coupled to a massive, free, complex scalar field, is shown to allow asymptotically flat solutions, nonsingular on and outside the event horizon, describing two spinning black holes (2sBHs) in equilibrium, with coaxial, aligned angular momenta. The 2sBHs configurations bifurcate from solutions describing dipolar spinning boson stars. The BHs emerge at equilibrium points diagnosed by a test particle analysis and illustrated by a Newtonian analog. The individual BH "charges" are mass and angular momentum only. Equilibrium is due to the scalar environment, acting as a (compact) dipolar field, providing a lift against their mutual attraction, making the 2sBHs (h)airborne. We explore the 2sBHs domain of solutions and its main features.

Non-linear tides and Gauss-Bonnet scalarization

In linear perturbation theory, a static perturber in the vicinity of a Schwarzschild black hole (BH) enhances [suppresses] the Gauss-Bonnet (GB) curvature invariant, RGB, in the high [low] tide regions. By analysing exact solutions of the vacuum Einstein field equations describing one or two BHs immersed in a multipolar gravitational field, which is locally free of pathologies, including conical singularities, we study the corresponding non-linear tides on a fiducial BH, in full General Relativity (GR). We show that the tidal field due to a far away, or close by, static BH creates high/low tides that can deviate not only quantitatively but also qualitatively from the weak field/Newtonian pattern. Remarkably, the suppression in low tide regions never makes RGB negative on the BH, even though the horizon Gaussian curvature may become negative; but RGB can vanish in a measure zero set, a feature qualitatively recovered in a Newtonian analogue model. Thus, purely gravitational, static, tidal interactions in GR, no matter how strong, cannot induce GB− scalarization. We also show that a close by BH produces noticeable asymmetric tides on another (fiducial) BH.

Testing quasi-linear modified Newtonian dynamics theory with Galactic globular clusters in a weak external field

ABSTRACT We developed self-consistent dynamical models of stellar systems in the framework of quasi-linear modified Newtonian dynamics (QUMOND). The models are constructed from the anisotropic distribution function of Gunn and Griffin, combined with the modified Poisson equation defining this gravitation theory and take into account the external field effect. We have used these models, and their Newtonian analogues, to fit the projected density and the velocity dispersion profiles of a sample of 18 Galactic globular clusters, using the most updated data sets of radial velocities and Gaia proper motions. We have thus obtained, for each cluster, estimates of the dynamical mass-to-light ratio (M/L) for each theory of gravity. The selected clusters have accurate proper motions and a well-sampled mass function down to the very low-mass regime. This allows us to constrain the degree of anisotropy and to provide, from comparison with stellar evolution isochrones, a dynamics-independent estimate of the minimum mass-to-light ratio (M/L)min. Comparing the best-fitting dynamical M/L with (M/L)min, we find that for none of the analysed clusters the two gravity theories are significantly incompatible with the observational data, although for one of them (NGC 5024) the dynamical M/L predicted by QUMOND lies at 2.8σ below (M/L)min. Though the proposed approach suffers from some limitations (in particular the lack of a treatment of mass segregation), the obtained results suggest that the kinematics of globular clusters in a relatively weak external field can be a powerful tool to prove alternative theories of gravitation.

Effect of flow rate ratio and positioning on a lighthouse tip ECMO return cannula.

Extracorporeal membrane oxygenation is a life-saving support therapy in the case of cardiopulmonary refractory failure. Its use is associated to complications due to the presence of artificial surfaces and supraphysiological stress conditions. Thus, knowledge of the fluid structures associated to each component can give insight into sources of blood damage. In this study, an experimentally validated numerical study of a conventional lighthouse tip cannula in return configuration was carried out to characterize the flow structures using water or a Newtonian blood analog with different flow rate ratios and cannula positioning and their influence on hemolysis. The results showed that strong shear layers developed where the jets from the side holes met the co-flow. Stationary backflow regions at the vessel wall were also present downstream of the cannula. In the tilted case, the recirculation was much more pronounced on the wide side and almost absent on the narrow side. Small vortical backflow structures developed at the side holes which behaved like obstacles to the co-flow, creating pairs of counter-rotating vortices, which induced locally higher risk of hemolysis. However, global hemolysis index did not show significant deviations. Across the examined flow rate ratios, the holes on the narrow side consistently reinfused a larger fraction of fluid. A radial force developed in the tilted case in a direction so as to recenter the cannula in the vessel.

Coherent propagation of vortex rings at extremely high Reynolds numbers

We take advantage of the extremely small kinematic viscosity of superfluid $^4$ He to investigate the propagation of macroscopic vortex rings at Reynolds numbers between $2 \times 10^4$ and $4 \times 10^6$ . These inhomogeneous flow structures are thermally generated by releasing short power pulses into a small volume of liquid, open to the surrounding bath through a vertical tube $2$ mm in diameter. We study specifically the ring behaviour between $1.30$ and $1.80$ K using the flow visualization and second sound attenuation techniques. From the obtained data sets, containing more than $2600$ realizations, we find that the rings remain well-defined in space and time for distances up to at least $40$ tube diameters, and that their circulation depends significantly on the travelled distance, in a way similar to that observed for turbulent vortex rings propagating in Newtonian fluids. Additionally, the ring velocity and circulation appear to be influenced solely by a single, experimentally accessible parameter, combining the liquid temperature with the magnitude and duration of the power pulse. Overall, our results support the view that macroscopic vortex rings moving in superfluid $^4$ He closely resemble their Newtonian analogues, at least in the absence of significant thermal effects and at sufficiently large flow scales.

Impact of Blood Rheology on Transition to Turbulence and Wall Vibration Downstream of a Stenosis.

Previous experimental flow studies have demonstrated a delay (∼20%) in transition to turbulence for whole blood compared to a Newtonian analog fluid in both a straight pipe and eccentric stenosis model with ridged walls. The impact of wall compliance on the transition to turbulence of blood compared to Newtonian analog and on wall vibration is unknown. The present study employed flexible walls downstream of an eccentric stenosis model and examined the wall vibration during the transition to turbulence with whole blood and a Newtonian analog. Measurements of tube wall vibration velocity (WVV) were used as an indicator of the turbulence level within the flexible tube. WVV was measured at 5, 10, and 15 diameters downstream of the stenosis using a laser Doppler vibrometer at Reynolds numbers 0, 200, 300, 350, 400, 450, 500, 550, 600, 650, 700, and 750. The root mean squares (RMS) of the measured WVV were utilized as an indirect measure of fluid velocity fluctuations present at that location, and hence, an indicator of transition to turbulence. WVV RMS was near-constant until approximately Reynolds number 400. It increased monotonically with Reynolds number for both whole blood and the Newtonian fluid. No differences in the transition to turbulence were observed between whole blood and the Newtonian fluid, as the WVV RMS curves were remarkably similar in shape. This result suggests that rheology had minimal impact on the WVV downstream of a stenosis for transition to turbulence since the fluids had a similar level of vibration.

Extensional Magnetorheology of Viscoelastic Human Blood Analogues Loaded with Magnetic Particles.

This study represents a pioneering work on the extensional magnetorheological properties of human blood analogue fluids loaded with magnetic microparticles. Dynabeads M-270 particles were dispersed in Newtonian and viscoelastic blood analogue fluids at 5% wt. Capillary breakup experiments were performed, with and without the influence of an external magnetic field aligned with the flow direction. The presence of the particles increased the viscosity of the fluid, and that increment was larger when embedded within a polymeric matrix. The application of an external magnetic field led to an even larger increment of the viscosity of the working fluids, as the formation of small aggregates induced an increment in the effective volume fraction of particles. Regarding the liquid bridge stability, the Newtonian blood analogue fluid remained as a Newtonian liquid exhibiting a pinch-off at the breakup time in any circumstance. However, in the case of the viscoelastic blood analogue fluid, the presence of the particles and the simultaneous application of the magnetic field enhanced the formation of the beads-on-a-string structure, as the Ohnesorge number remained basically unaltered, whereas the time of the experiment increased due to its larger viscosity, which resulted in a decrease in the Deborah Number. This result was confirmed with fluids containing larger concentrations of xanthan gum.

Transition to Turbulence Downstream of a Stenosis for Whole Blood and a Newtonian Analog Under Steady Flow Conditions.

Blood, a multiphase fluid comprised of plasma, blood cells, and platelets, is known to exhibit a shear-thinning behavior at low shear rates and near-Newtonian behavior at higher shear rates. However, less is known about the impact of its multiphase nature on the transition to turbulence. In this study, we experimentally determined the critical Reynolds number at which the flow began to transition to turbulence downstream of eccentric stenosis for whole porcine blood and a Newtonian blood analog (water-glycerin mixture). Velocity profiles for both fluids were measured under steady-state flow conditions using an ultrasound Doppler probe placed 12 diameters downstream of eccentric stenosis. Velocity was recorded at 21 locations along the diameter at 11 different flow rates. Normalized turbulent kinetic energy was used to determine the critical Reynolds number for each fluid. Blood rheology was measured before and after each experiment. Tests were conducted on five samples of each fluid inside a temperature-controlled in vitro flow system. The viscosity at a shear rate of 1000 s-1 was used to define the Reynolds number for each fluid. The mean critical Reynolds numbers for blood and water-glycerin were 470 ± 27.5 and 395 ± 10, respectively, indicating a ∼19% delay in transition to turbulence for whole blood compared to the Newtonian fluid. This finding is consistent with a previous report for steady flow in a straight pipe, suggesting some aspect of blood rheology may serve to suppress, or at least delay, the onset of turbulence in vivo.

Deep-MOND polytropes

Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}\rho^\gamma$. As self-consistent structures, such systems can serve as heuristic models for DML, astronomical systems, such as dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, and diffuse galaxy groups. They can also serve as testing ground for various theoretical MOND inferences. In dimensionless form, the equation satisfied by the radial density profile $\zeta(y)$ is (for $\gamma\not=1$) $[\int_0^y \zeta \bar y^2 d\bar y]^{1/2}=-yd(\zeta^{\gamma-1})/dy$. Or, $\theta^n(y)=y^{-2}[(y\theta')^2]'$, where $\theta=\zeta^{\gamma-1}$, and $n\equiv (\gamma-1)^{-1}$. I discuss properties of the solutions, contrasting them with those of their Newtonian analogues -- the Lane-Emden polytropes. Due to the stronger MOND gravity, all DML polytropes have a finite mass, and for $n<\infty$ ($\gamma>1$) all have a finite radius. (Lane-Emden spheres have a finite mass only for $n\le 5$.) I use the DML polytropes to study DML scaling relations. For example, they satisfy a universal relation (for all $\mathcal{K}$ and $\gamma$) between the total mass, $M$, and the mass-average velocity dispersion $\sigma$: $MGa_0=(9/4)\sigma^4$. However, the relation between $M$ and other measures of the velocity dispersion, such as the central, projected one, $\bar\sigma$, does depend on $n$ (but not $\mathcal{K}$), defining a `fundamental surface' in the $[M,~\bar\sigma,~n]$ space. I also describe the generalization to anisotropic polytropes, which also all have a finite radius (for $\gamma>1$), and all satisfy the above universal $M-\sigma$ relation. This more extended class of models exhibits the central-surface-densities relation: a tight relation between the baryonic and the dynamical central surface densities predicted by MOND.

Turning a Newtonian analogy for FLRW cosmology into a relativistic problem

A Newtonian uniform ball expanding in empty space constitutes a common heuristic analogy for FLRW cosmology. We discuss possible implementations of the corresponding general-relativistic problem and a variety of new cosmological analogies arising from them. We highlight essential ingredients of the Newtonian analogy, including that the quasilocal energy is always `Newtonian' in the sense that the magnetic part of the Weyl tensor does not contribute to it. A symmetry of the Einstein-Friedmann equations produces another one in the original Newtonian system.

Technical considerations for medical device manufacturers when designing gastrostomy tubes (G-tubes) using the new ISO 80369-3 connector.

BackgroundGastrostomy tubes (G-tubes) are typically used when people cannot eat food by mouth. The connector section that allows G-tubes to connect to other devices, such as feeding sets or syringes, has been modified on some of the devices to reduce misconnections in hospital settings. The narrow internal diameter of the new connector, standardized under ISO 80369–3, has caused some users to express concern about a reduced flow rate. Previous studies performed on commercial devices determined that it was not conclusive how much the ISO 80369–3 connector contributed towards the reduced flow rate, because when manufacturers designed these new connector-based devices, they often changed other geometric variables (such as distal tube diameter, or length) at the same time. Thus, it became difficult isolating the effect of the connector from other geometric variables.MethodThe key objective of this study was to investigate how different design variables impacted the flow rate through the G-tubes. 3D-printed devices were used to assess the geometric parameters in a systematic manner. Commercial diets and Newtonian analog fluids with matched viscosities were used for testing.ResultsThe flow path length of the “transition section” encompassing the standardized ISO 80369–3 connector in the new devices was found to cause reduced flow. Additionally, results showed that a shortened (≤ 10 mm) transition section, along with a 10% increase in the distal inner diameter of large bore devices (e.g., 24 Fr), can restore flow rates to levels consistent with the previous devices prior to the connector standardization.ConclusionsThe strategy for restoring flow rates to previous levels may help alleviate concerns raised by multiple stakeholders such as health care professionals, patients, caregivers and device manufacturers. In addition, the approach proposed here can be used as a tool for designing future G-tube devices.

Study of the effect of stenosis severity and non-Newtonian viscosity on multidirectional wall shear stress and flow disturbances in the carotid artery using particle image velocimetry

The development of atherosclerosis at the carotid bifurcation is impacted by local variations in wall shear stress (WSS) magnitude and direction, as well as flow complexity within the vessel. In this study, stereoscopic particle image velocimetry (PIV) was used to investigate multidirectional WSS and disturbed flow for idealized models of the carotid bifurcation with varying eccentric stenosis of the internal carotid artery (ICA) and both Newtonian (N-fluid) and non-Newtonian (nN-fluid) blood analogues. Turbulence intensity (TI) was reduced with the nN-fluid compared to N-fluid for mild to moderate stenosis, and comparable for more severely stenosed (70%) models. Differences in maximum TI due to viscosity model ranged from 0.02 m/s to 0.06 m/s compared to much larger differences due to geometry of up to 0.29 m/s between mild and severe stenosis. The level of time-averaged WSS (TAWSS) increased with stenosis severity from 5 Pa to 32 Pa, and nN-fluid led to higher WSS on average than N-fluid counterparts. Regions of elevated oscillatory shear index (OSI) demarcated recirculation regions, and mean OSI in the ICA branch was reduced for nN-fluid models by 9–19% compared to N-fluid. Transverse WSS (transWSS) increased with WSS magnitude and again was higher in nN-fluid models. Surface area exposure to shear metrics indicated that a Newtonian viscosity assumption predicted larger regions of low and oscillatory WSS, while predicting reduced regions of high transWSS, in comparison to the more physiological shear thinning fluid.

Inter-Laboratory Characterization of the Velocity Field in the FDA Blood Pump Model Using Particle Image Velocimetry (PIV).

A credible computational fluid dynamics (CFD) model can play a meaningful role in evaluating the safety and performance of medical devices. A key step towards establishing model credibility is to first validate CFD models with benchmark experimental datasets to minimize model-form errors before applying the credibility assessment process to more complex medical devices. However, validation studies to establish benchmark datasets can be cost prohibitive and difficult to perform. The goal of this initiative sponsored by the U.S. Food and Drug Administration is to generate validation data for a simplified centrifugal pump that mimics blood flow characteristics commonly observed in ventricular assist devices. The centrifugal blood pump model was made from clear acrylic and included an impeller, with four equally spaced, straight blades, supported by mechanical bearings. Particle Image Velocimetry (PIV) measurements were performed at several locations throughout the pump by three independent laboratories. A standard protocol was developed for the experiments to ensure that the flow conditions were comparable and to minimize systematic errors during PIV image acquisition and processing. Velocity fields were extracted at the pump entrance, blade passage area, back gap region, and at the outlet diffuser regions. A Newtonian blood analog fluid composed of sodium iodide, glycerin, and water was used as the working fluid. Velocity measurements were made for six different pump flow conditions, with the blood-equivalent flow rate ranging between 2.5 and 7 L/min for pump speeds of 2500 and 3500rpm. Mean intra- and inter-laboratory variabilities in velocity were ~ 10% at the majority of the measurement locations inside the pump. However, the inter-laboratory variability increased to more than ~ 30% in the exit diffuser region. The variability between the three laboratories for the peak velocity magnitude in the diffuser region ranged from 5 to 25%. The bulk velocity field near the impeller changed proportionally with the rotational speed but was relatively unaffected by the pump flow rate. In contrast, flow in the exit diffuser region was sensitive to both the flow rate and the rotational speed. Specifically, at 3500rpm, the exit jet tilted toward the inner wall of the diffuser at a flow rate of 2.5 L/min, but the jet tilted towards the outer wall when the flow rate was 7 L/min. Inter-laboratory experimental mean velocity data (and the corresponding variance) were obtained for the FDA pump model and are available for download at https://nciphub.org/wiki/FDA_CFD . Experimental datasets from the inter-laboratory characterization of benchmark flow models, including the blood pump model presented herein and our previous nozzle model, can be used for validating future CFD studies and to collaboratively develop guidelines on best practices for verification, validation, uncertainty quantification, and credibility assessment of CFD simulations in the evaluation of medical devices (e.g. ASME V&V 40 standards working group).

A note on a precursor of behavioral momentum.

This is a historical note on a precursor of the concept of behavioral momentum in the late 1950s and early 1960s, in particular, Charles B. description of it in terms of behavioral durability. The note is based largely on two email exchanges we had with John A. (Tony) Nevin, who offered insights on behavioral momentum as a term and a concept that are fit to be public on the occasion of this issue of the Journal of the Experimental Analysis of Behavior in his honor. Nevin addressed graduate work at Columbia University, the Newtonian analogy, the term behavioral momentum, and precursors of his work that are now lost in history. Ferster's description, though, was more compellingly modern than the others and the one first based in research on human operant behavior.

An analysis of the LIGO discovery based on introductory physics

By observing gravitational radiation from a binary black hole merger, the LIGO collaboration has simultaneously opened a new window on the universe and achieved the first direct detection of gravitational waves. Here this discovery is analyzed using concepts from introductory physics. Drawing upon Newtonian mechanics, dimensional considerations, and analogies between gravitational and electromagnetic waves, we are able to explain the principal features of LIGO's data and make order of magnitude estimates of key parameters of the event by inspection of the data. Our estimates of the black hole masses, the distance to the event, the initial separation of the pair, and the stupendous total amount of energy radiated are all in good agreement with the best fit values of these parameters obtained by the LIGO-VIRGO collaboration.