non-Newtonian Rheological Models Research Articles

Selected aspects of blood flow simulations in arteries

This article discusses selected aspects of modelling blood flow in the arteries. The method of reproducing the variable-in-time geometry of coronary arteries is given based on a sequence of medical images of different resolutions. Within the defined shapes of the arteries, a technique of generation of numerical meshes of the same topology is described. The boundary conditions and non-Newtonian rheological models used in blood flow are discussed, as well as the description of blood as a multiphase medium. The work also includes a discussion of tests on the phantom of the carotid artery for the accuracy of measurements made using ultrasonography.

Effects of lubricant rheology and flow turbulence on the dynamic properties of hydrodynamic bearing

The present numerical investigation, which takes into account the coexisted consequence of the turbulence domain and non-Newtonian flow rheology, predicts the dynamic properties of a finite hydrodynamic bearing. Under the proper flow boundary conditions, the turbulence (linear) and non-Newtonian hypotheses have revised the Continuity and Navier–Stokes equation. The finite element approach is acclimated to calculate the clearance extent of the finite hydrodynamic bearing using the Galerkin approach and a sturdy iteration strategy. The cylindrical coordinate's versions of continuity and momentum equations are bestowed for the lubricant field of the finite hydrodynamic bearing, postulating the turbulence domain and non-Newtonian flow rheology. Dynamic properties of a finite hydrodynamic bearing have been enumerated using cross-coupled and direct lubricant-film bearing coefficients, whirl ratio and critical mass at various eccentricity ratios for different ranges of Reynolds numbers and different values of flow behavior index of the non-Newtonian rheological model. In comparison to perfect turbulence and non-Newtonian rheological status, the mixed regime demonstrated improved properties. The direct and cross-coupled lubricant-film bearing coefficients are improved by 12.28% and 20.85% respectively while critical mass is enhanced by 20.55% at selected values of Reynolds number and power-law index. The proposed severe fluid film domain improves the stability of finite hydrodynamic bearings significantly.

THE ANALYSIS OF THE FLOW OF BLOOD IN A STENOSED ARTERY THROUGH SIMULATION: A COMPARISON AMONG VARIOUS NON-NEWTONIAN MODELS

This paper focuses on the dual quality of blood, Newtonian and non-Newtonian, in particular by exploring the energy curves. Careful investigation of the dual property of blood has been made by considering two different geometries to represent a stenosed arterial segment. We present a cautious assessment of non-Newtonian blood rheology impacts in arterial stream simulations by coupling the Newtonian and non-Newtonian models. The flow of energy through the two flow dimensions is meticulously investigated using velocity (kinetic energy), pressure, and wall shear stress (pressure energy). Besides, the proper implementation of an interface boundary condition (IBC) was emphasized to ensure consistency with the flow conditions downstream of a backward-facing step. The integration of the Newtonian and non-Newtonian models adjoins the novelty of the current research. The energy curves are obtained by implementing five different non-Newtonian models to designate a suitable non-Newtonian model for blood flow investigations. The combination of the non-Newtonian models enforced in this research is novel and particular attention is paid to the energy curves obtained. The conclusion was to elect the Carreau model as a suitable non-Newtonian rheological model for the blood flow study. This study was able to finalize the fact that the coupling of Newtonian and non-Newtonian models is necessary to obtain accurate results. For the sinusoidal waveform considered for the velocity, Carreau and the Power law models yield better results, eliminating the other non-Newtonian models from the list. With a better inlet condition imposed in the form of the Fourier series for pressure and velocity, the Carreau model yields the best results.

Investigation of different structures of screw extruders on the flow in direct ink writing SiC slurry based on LBM

Abstract Direct ink writing provides a new method for ceramic material forming. The single-screw extruder is used here to extrude viscous SiC slurry. Because the flow mechanism of ceramic slurry in the slurry direct writing extrusion device is unclear, lattice Boltzmann method (LBM) is used to analyze the flow process of ceramic slurry in the extrusion device. In this study, three different types of special-shaped, single-screw extruders (constant depth variable pitch screw, variable depth constant pitch screw, and variable depth variable pitch screw) are investigated to explore the effects of the shapes on the flow process. Compared with the traditional single-screw extruder, more attention should be paid to the difference in the flow channel. The non-Newtonian rheological model of SiC slurry is built, then the LBM for the non-Newtonian slurry is introduced and used to conduct the simulations based on the aforementioned three different cases. The results show that the effect of constant depth and variable pitch screw on the flow of ceramic slurry is the least and the flow of ceramic slurry in variable depth and variable pitch screw is the most complex.

Assessment of Rheological Models Applied to Blood Flow in Human Thoracic Aorta.

The purpose of this study is to assess the importance of non-Newtonian rheological models on blood flow in the human thoracic aorta. The pulsatile flow in the aorta is simulated using the models of Casson, Quemada and Walburn-Schneck in addition to a case of fixed (Newtonian) viscosity. The impact of the four rheological models (using constant hematocrit) was assessed with respect to (i) magnitude and deviation of the viscosity relative to a reference value (the Newtonian case); (ii) wall shear stress (WSS) and its time derivative; (iii) common WSS-related indicators, OSI, TAWSS and RRT; (iv) relative volume and surface-based retrograde flow; and (v) the impact of rheological models on the transport of small particles in the thoracic aorta. The time-dependent flow in the thoracic aorta implies relatively large variations in the instantaneous WSS, due to variations in the instantaneous viscosity by as much as an order of magnitude. The largest effect was observed for low shear rates (tens s-1). The different viscosity models had a small impact in terms of time- and spaced-averaged quantities. The significance of the rheological models was clearly demonstrated in the instantaneous WSS, for the space-averaged WSS (about 10%) and the corresponding temporal derivative of WSS (up to 20%). The longer-term accumulated effect of the rheological model was observed for the transport of spherical particles of 2 mm and 2 mm in diameter (density of 1200 kg/m3). Large particles' total residence time in the brachiocephalic artery was 60% longer compared to the smaller particles. For the left common carotid artery, the opposite was observed: the smaller particles resided considerably longer than their larger counterparts. The dependence on the non-Newtonian properties of blood is mostly important at low shear regions (near walls, stagnation regions). Time- and space-averaging parameters of interest reduce the impact of the rheological model and may thereby lead to under-estimation of viscous effects. The rheological model affects the local WSS and its temporal derivative. In addition, the transport of small particles includes the accumulated effect of the blood rheological model as the several forces (e.g., drag, added mass and lift) acting on the particles are viscosity dependent. Mass transport is an essential factor for the development of pathologies in the arterial wall, implying that rheological models are important for assessing such risks.

Modelling blood flow in coronary arteries: Newtonian or shear-thinning non-Newtonian rheology?

BackgroundThe combination of medical imaging and computational hemodynamics is a promising technology to diagnose/prognose coronary artery disease (CAD). However, the clinical translation of in silico hemodynamic models is still hampered by assumptions/idealizations that must be introduced in model-based strategies and that necessarily imply uncertainty. This study aims to provide a definite answer to the open question of how to properly model blood rheological properties in computational fluid dynamics (CFD) simulations of coronary hemodynamics. MethodsThe geometry of the right coronary artery (RCA) of 144 hemodynamically stable patients with different stenosis degree were reconstructed from angiography. On them, unsteady-state CFD simulations were carried out. On each reconstructed RCA two different simulation strategies were applied to account for blood rheological properties, implementing (i) a Newtonian (N) and (ii) a shear-thinning non-Newtonian (non-N) rheological model. Their impact was evaluated in terms of wall shear stress (WSS magnitude, multidirectionality, topological skeleton) and helical flow (strength, topology) profiles. Additionally, luminal surface areas (SAs) exposed to shear disturbances were identified and the co-localization of paired N and non-N SAs was quantified in terms of similarity index (SI). ResultsThe comparison between paired N vs. shear-thinning non-N simulations revealed remarkably similar profiles of WSS-based and helicity-based quantities, independent of the adopted blood rheology model and of the degree of stenosis of the vessel. Statistically, for each paired N and non-N hemodynamic quantity emerged negligible bias from Bland-Altman plots, and strong positive linear correlation (r > 0.94 for almost all the WSS-based quantities, r > 0.99 for helicity-based quantities). Moreover, a remarkable co-localization of N vs. non-N luminal SAs exposed to disturbed shear clearly emerged (SI distribution 0.95 [0.93, 0.97]). Helical flow topology resulted to be unaffected by blood rheological properties. ConclusionsThis study, performed on 288 angio-based CFD simulations on 144 RCA models presenting with different degrees of stenosis, suggests that the assumptions on blood rheology have negligible impact both on WSS and helical flow profiles associated with CAD, thus definitively answering to the question “is Newtonian assumption for blood rheology adequate in coronary hemodynamics simulations?”.

Impact of high-speed turbidity currents on offshore spanning pipelines

Pipelines in the deep sea are at risk of damage due to submarine landslides, which can result in the loss of costly infrastructure and pollution stemming from hydrocarbon leaks. Submarine landslides can exhibit a wide range of flow characteristics, which in turn can affect how they interact with pipelines. Researchers have previously focused on pipelines impacted by submarine debris and/or mud flows described by non-Newtonian fluid rheological models and the laminar model. However, the impact of larger-scale and higher-speed submarine turbidity currents described by turbulence models on pipelines has been overlooked. In this study, we address this gap by utilizing a more accurate turbulence simulation method, namely, the large eddy simulation (LES) method, to analyze the effect of submarine turbidity currents on fixed spanning pipelines, and we validate the effectiveness of the proposed method via typical circular cylinder flow experiments and numerical simulations. We find that the lift force on the pipeline impacted by submarine turbidity currents under high-Reynolds number (Re) conditions is particularly significant relative to debris and/or mud flows under low-Re conditions. In parallel, the vortex shedding frequency increases with increasing Re, and the Strouhal number basically remains unchanged and ranges from 0.2–0.25 at 1,112 ≤ Re ≤ 333,559. Furthermore, the vortex structure and its arrangement behind the spanning pipeline become irregular with increasing Re, forming a turbulent vortex street, which reveals the mechanism of pipeline vibration. Finally, a methodology for predicting characteristic drag force and lift force coefficients is established for submarine pipeline design.

Experimental and modeling study on the transient flow and time-dependent yield stress of superfine-tailings cemented paste backfill

The fresh superfine-tailings cemented paste backfill (SCPB) exhibits strong thixotropy, but quantification of the resulting transient flow (non-steady state) and time-dependent yield stress is lacking. In this study, a simple qualitative model was developed to describe the transient flow and time-dependent yield stress of SCPB. The effect of pre-shear time on the rheological behavior of SCPB was investigated. In addition, the adaptability of conventional non-Newtonian rheological models to SCPB was also evaluated. The results showed the Herschel-Bulkley model provides the most stable dynamic yield stress estimation of SCPB compared to the Bingham and modified Bingham models. A longer pre-shear time (within 500 s) led to smaller initial static yield stress and delayed recovery kinetics of static yield stress, but hardly affected the steady state of SCPB and the time required to reach it. The proposed model provides a good quantification of the transient flow at a given shear rate and time-dependent yield stress of SCPB.

Non-Newtonian Endothelial Shear Stress Simulation: Does It Matter?

Patient-specific coronary endothelial shear stress (ESS) calculations using Newtonian and non-Newtonian rheological models were performed to assess whether the common assumption of Newtonian blood behavior offers similar results to a more realistic but computationally expensive non-Newtonian model. 16 coronary arteries (from 16 patients) were reconstructed from optical coherence tomographic (OCT) imaging. Pulsatile CFD simulations using Newtonian and the Quemada non-Newtonian model were performed. Endothelial shear stress (ESS) and other indices were compared. Exploratory indices including local blood viscosity (LBV) were calculated from non-Newtonian simulation data. Compared to the Newtonian results, the non-Newtonian model estimates significantly higher time-averaged ESS (1.69 (IQR 1.36)Pa versus 1.28 (1.16)Pa, p < 0.001) and ESS gradient (0.90 (1.20)Pa/mm versus 0.74 (1.03)Pa/mm, p < 0.001) throughout the cardiac cycle, under-estimating the low ESS (<1Pa) area (37.20 ± 13.57% versus 50.43 ± 14.16%, 95% CI 11.28–15.18, p < 0.001). Similar results were also found in the idealized artery simulations with non-Newtonian median ESS being higher than the Newtonian median ESS (healthy segments: 0.8238Pa versus 0.6618Pa, p < 0.001 proximal; 0.8179Pa versus 0.6610Pa, p < 0.001 distal; stenotic segments: 0.8196Pa versus 0.6611Pa, p < 0.001 proximal; 0.2546Pa versus 0.2245Pa, p < 0.001 distal) On average, the non-Newtonian model has a LBV of 1.45 times above the Newtonian model with an average peak LBV of 40-fold. Non-Newtonian blood model estimates higher quantitative ESS values than the Newtonian model. Incorporation of non-Newtonian blood behavior may improve the accuracy of ESS measurements. The non-Newtonian model also allows calculation of exploratory viscosity-based hemodynamic indices, such as local blood viscosity, which may offer additional information to detect underlying atherosclerosis.

The Influence of Non-Newtonian Model on Properties of Blood Flow Through a Left Coronary Artery with Presence of Different Double Stenosis

Cardiovascular diseases were the main cause for loosing lives in the last decades due to the restricted blood flow states in the blood vessels areas. Numerical investigations have been conducted as the aim of this work to examine the blood flow, and wall shear stresses adjacent to the mono stenosis up to different degrees involved in the main, side and distal main branches as well as observe the pulsatile flow of blood in the left coronary artery through various percentage of stenosis. Both the Carreau non-Newtonian rheological model and the Newtonian model were utilized to model the blood fluid and wall shear stresses of left coronary artery, in a row, all the calculated data were validated with the previously published papers. It was found that the blood flow inside areas of the artery lie within the range of non-Newtonian rheological effects can be present, verifying the need to treat blood as non-Newtonian fluid; especially, with the case of 90% blockage.

Flow and heat transfer analysis of elastoviscoplastic generalized non-Newtonian fluid with hybrid nano structures and dust particles

The Oldroyd-B model, Maxwell and Jeffrey models which are generalized non-Newtonian rheological models are used for the investigation of thermal enhancement in the presence of dust and hybrid nanoparticles. The governing models for fluid and solid phase are solved numerically via shooting method. The convergence and mesh free analysis has been carried out, Nusselt number and shear stress are analyzed for three fluid models (Oldroyd, Maxwell and Jeffrey). It is observed that memory effects in Oldroyd-B hybrid nanofluid are stronger than Maxwell and Jeffrey's hybrid nanofluid. The thickness of momentum boundary layer region can be reduced by increasing Deborah number that characterizes the relaxation time. Viscous dissipation phenomenon has appeared less significant in Jeffrey fluid comparatively. The transport rate of heat energy through Jeffrey hybrid nanofluid is higher than both the Maxwell and Oldroyd model.

Formulation to Calculate Isothermal, Non-Newtonian Elastohydrodynamic Lubrication Problems Using a Pressure Gradient Coordinate System and Its Verification by an Experimental Grease

This paper presents a formulation of point contact elastohydrodynamic lubrication analysis for an isothermal, non-Newtonian flow. A coordinate system of the pressure gradient was employed herein. A Couette flow and a Poiseuille flow were considered along the directions of the zero and non-zero pressure gradients, respectively. The Poiseuille flow velocity was assumed to be represented by a 4th-order polynomial of z along the film thickness direction. The Couette flow velocity was assumed to be represented by a linear function of z. Subsequently, the modified Reynolds equation, which contains an equivalent viscosity, was obtained. Using Bauer’s rheological model, the formulation presented in this study was applied to a grease that has been previously experimented upon. The results of previous studies were compared with those of the present study and a reasonable agreement was noted. The distribution of the equivalent viscosity showed a notable difference from that of Newtonian flow. The formulation can be incorporated easily to the usual elastohydrodynamic lubrication calculation procedure for Newtonian flow. The method can be easily applied to other non-Newtonian rheological models. The equivalent viscosity can be calculated using the one-parameter Newton-Raphson’s method; as a result, the calculation can be performed within a reasonable time.

Impact of leg bending in the patient-specific computational fluid dynamics of popliteal stenting

Endovascular treatment of the femoro-popliteal artery has recently become a valuable therapeutic option for popliteal arterial aneurysms. However, its efficacy remains controversial due to the relatively high rate of complications, such as stent occlusion as result of intra-stent thrombosis. The elucidation of the interplay among vessel geometrical features, local hemodynamics, and leg bending seems crucial to understand onset and progression of popliteal intra-stent thrombosis. To this aim, patient-specific computational fluid dynamic simulations were performed in order to assess the intra-stent hemodynamics of two patients endovascularly treated for popliteal arterial aneurysm by stent-grafts and experiencing intra-stent thrombosis. Both Newtonian and non-Newtonian blood rheological models were considered. Results were presented in terms of tortuosity, luminal area exposed to low (< 0.4 Pa) and high (> 1.5 Pa) time-averaged wall shear stress (TAWSS), area exposed to high (> 0.3) oscillatory shear index (OSI), and flow helicity. Study outcomes demonstrated that leg bending induced significant hemodynamic differences (> 50% increase) in both patients for all the considered variables, except for OSI in one of the two considered patients. In both leg configurations, stent-graft overlapping induced a severe discontinuity of the lumen diameter where the proximal stented zone is characterized by low tortuosity, low velocity, low helicity, low TAWSS, and high OSI; while the distal part has higher tortuosity, velocity, helicity, TAWSS, and lower OSI. Sensitivity study on applied boundary conditions showed that the different inlet velocity profiles for a given inlet waveform affect slightly the numerical solution; conversely, the shape and magnitude of the prescribed inlet waveform is determinant. Focusing on the comparison between the Newtonian and non-Newtonian blood models, the area with low TAWSS is greater in the Newtonian model for both patients, while no significant difference occurs between the surfaces with high TAWSS.GraphicPatient-specific computational fluid dynamic simulations were performed in order to assess the intra-stent hemodynamics of two patients endovascularly treated for popliteal arterial aneurysm and experiencing intra-stent thrombosis. Both Newtonian and non-Newtonian blood rheological models were considered. In both straight and bent leg configurations, stent-graft overlapping induced a severe discontinuity of the lumen diameter where the proximal stented zone is characterized by low tortuosity, low velocity, low helicity, low time-averaged wall shear stress (TAWSS), and high oscillatory index (OSI); while the distal part has higher tortuosity, velocity, helicity, TAWSS, and lower OSI.

LBfoam: An open-source software package for the simulation of foaming using the Lattice Boltzmann Method

This paper presents a 2D/3D Free Surface Lattice Boltzmann Method simulation package called LBfoam for the simulation of foaming processes. The model incorporates the essential physics of foaming phenomena: gas diffusion into nucleated bubbles, bubble dynamics and coalescence, surface tension, the stabilizing disjoining pressure between bubbles, and Newtonian and non-Newtonian rheological models. The software can simulate the growth and interaction of bubbles, and predict final foam structures. The implementation is based on the Palabos library (in C++), which enables large-scale parallel simulations. The software is freely available under the GNU Affero General Public License version 3. Program summaryProgram title:LBfoamCPC Library link to program files:https://doi.org/10.17632/zgxfx6xk4t.1Developer’s repository link:https://github.com/mehdiataei/LBfoamCode Ocean capsule:https://codeocean.com/capsule/8471850Licensing provisions: Affero General Public License (AGPL) v3Programming language: C++Nature of problem: Foaming is a process by which nucleated gas bubbles expand in liquid media such as a molten polymer or a liquid metal to create a cellular structure, which has many applications in industries such as automotive, aerospace, furniture and packaging. This comprehensive simulation model for foaming allows industry to determine optimum foaming conditions more quickly and more accurately, while providing a platform for researchers to study phenomena observed in foaming.Solution method: LBfoam implements a 2D/3D Free Surface Lattice Boltzmann Method (FSLBM) solver that can simulate various foaming phenomena. The model couples the Navier–Stokes and the advection–diffusion equations, and incorporates all essential aspects of foaming such as the growth and interaction of bubbles. All routines are written in C++ and are parallelized using the Message Passing Interface (MPI) library.

State-of-the-Art Computational Models of Circle of Willis With Physiological Applications: A Review

Background: Various computational models of the circle of Willis (CoW) have been developed to non-invasively estimate the blood flow and hemodynamic parameters in intracranial arteries for the assessment of clinical risks such as aneurysms, ischemia, and atherosclerotic plaque growth. This review aims to categorize the latest computational models of CoW and summarize the innovative techniques. Summary of Review: In traditional computational models of CoW, the computational complexity increased from zero-dimensional models to one-dimensional and three-dimensional models. The applications extend from estimating certain hemodynamic parameters to simulating local flow field. The innovative techniques include the combination of models with different dimensions, the extension of vascular structure including heart and veins, as well as the addition of distal fractality, cerebral autoregulation, and intracranial pressure. There are some nontraditional models based on fluid-solid-interaction, control theory, and in-vitro experiments. In all kinds of models, the in-vivo data and non-Newtonian rheological models of blood have been widely applied to improve the accuracy of hemodynamic simulation. Conclusion: Firstly, the selection of model depends on its application scenario. The balance between computational complexity and physiological accuracy deserves further investigation. Secondly, the improvement of CoW models relies on the large-scale validations and the combination of various innovative modeling techniques.

P2433Local blood viscosity and local Reynolds number are associated with coronary plaque calcium and lipid

Abstract Background Despite being a shear-thinning non-Newtonian fluid, most computational fluid dynamic (CFD) simulations assume blood to be a Newtonian fluid with constant viscosity. The use of more realistic assumptions may deepen mechanistic understanding of the relationship between blood flow disturbances and atherosclerosis, and improve the diagnostic accuracy of CFD simulations. Purpose To compare associations between plaque composition and local hemodynamics at a single time point using Newtonian versus non-Newtonian rheological models in patient-specific coronary arteries. To investigate whether viscosity-based local haemodynamic indices correlate with plaque composition. Methods Sixteen patient-specific coronary arteries containing non-culprit plaques were reconstructed from optical coherence tomography imaging. CFD simulations using Newtonian and non-Newtonian models were performed to calculate endothelial shear stress (ESS). Local blood viscosity (LBV) and local Reynolds number (ReL) were calculated from non-Newtonian simulation data. Each haemodynamic index was distributed into quintiles, mapped in 5-degree sectors, and compared to plaque composition using logistic regression. Results In total, 69120 sectors from 960 OCT frames were analysed. The lowest ESS quintiles were associated with underlying lipid (ESS&lt;0.8Pa: odds ratio [OR] 1.26, p&lt;0.001, 95% CI 1.15–1.38; ESS 0.8–1.1Pa: OR 1.71, p&lt;0.001, 95% CI 1.58–1.85), while the highest quintile of ESS (&gt;2.2Pa) had lower odds of underlying lipid (OR 0.89, p=0.015, 95% CI 0.82–0.98) compared to the median ESS quintile. However, in the non-Newtonian results, only the second lowest quintile of ESS (1.1–1.5Pa) was associated with lipid (OR 1.54, p&lt;0.001, 95% CI 1.42–1.67). Low ReL was associated with lipid (ReL&lt;28: OR 1.71, p&lt;0.001, 95% CI 1.55–1.89; ReL 28–38: OR 1.47, p&lt;0.001, 95% CI 1.35–1.58). Conversely, the highest quintile of ReL had decreased odds of lipid (ReL&gt;68: OR 0.69, p&lt;0.001, 95% CI 0.62–0.76) (FIGURE). In both the Newtonian and non-Newtonian results, lower ESS was associated with increased odds of underlying calcium. Whereas the lowest quintile of LBV had a lower odds of calcium (LBV&lt;1.4: OR 0.60, p&lt;0.001, 95% CI 0.52–0.71), the highest quintile had significantly higher odds of underlying calcium (LBV&gt;1.5: OR 1.38, p&lt;0.001, 95% CI 1.18–1.63) Conclusions Using the standard Newtonian assumption, low ESS is associated with underlying lipid. However, using a more realistic non-Newtonian rheological model, there is no strong or consistent relationship between ESS and underlying lipid, highlighting the importance of methodological assumptions and lingering questions in arterial CFD simulation. Non-Newtonian indices LBV and ReL are independently associated with calcium and lipid, respectively, suggesting possible mechanistic effects of local blood viscosity in atherosclerosis and implying their use as novel haemodynamic markers of atherosclerosis.

P858High endothelial shear stress and local Reynolds number are associated with lipid growth of coronary plaques

Abstract Background Local haemodynamic disturbances in coronary blood flow are associated with abnormal endothelial shear stress (ESS) and progressive atherosclerosis. However, standard techniques to estimate ESS lack the diagnostic specificity necessary for future clinical utility. Possible improvements include use of a more realistic non-Newtonian model of blood, which may provide more accurate ESS measurements and is further able to detect local variations in blood viscosity. Purpose To compare accuracy of ESS generated by Newtonian versus non-Newtonian rheological models to detect coronary plaque progression. To investigate local Reynolds number (ReL), a viscosity-based haemodynamic metric calculated by the non-Newtonian model, as an independent marker of plaque progression. Methods Sixteen patients with non-culprit plaques completely visualised in serial optical coherence tomography (OCT) imaging were identified. Plaques were analysed in 0.2mm intervals at each timepoint for lipid and calcium arc. Computational fluid dynamic simulations were performed using Newtonian and non-Newtonian models to calculate ESS, whereas ReL was calculated by the non-Newtonian simulations. Each haemodynamic index was compared to interval changes in lipid and calcium using multivariate regression. Results In total, 894 matched arterial segments from baseline and follow up imaging were analysed. In the Newtonian results, baseline segments exposed to ESS&gt;1.7Pa had a 12.5° increase in lipid arc (95% CI 2.2° to 22.8°, p=0.018) while segments exposed to ESS&lt;1.1Pa had an 8.1° decrease in calcium (95% CI −14.0° to −2.2°, p=0.007). In the non-Newtonian results, baseline regions exposed to ESS&gt;2.2Pa had a 14.4° increase in lipid (95% CI 4.2° to 24.7°, p=0.006) while areas with ESS&lt;1.4Pa had an 8.7° decrease in calcium (95% CI −14.6° to −2.8°, p=0.004). Baseline regions exposed to ReL&lt;34 showed an average 11.9° increase in lipid arc (95% CI 0.6° to 23.2°, p=0.039). Regions exposed to ReL&gt;55 had an average increase in lipid arc of 26.6° (95% CI 14.5° to 38.6°, p&lt;0.001). Conclusions Both Newtonian and non-Newtonian rheological models show that high ESS is associated with increased lipid while low ESS is associated with decreased calcium. ReL is independently associated with interval increases in lipid arc, suggesting a mechanistic role of local blood viscosity in lipid accumulation. ReL may serve as a novel haemodynamic marker of plaque progression.

Blood Flow in Channel Constrictions: A Lattice-Boltzmann Consistent Comparison between Newtonian and Non-Newtonian Models

Lattice Boltzmann simulations have been carried out in order to study the flow of blood in normal and constricted blood channels using Newtonian and non-Newtonian rheological models. Instead of using parameters from previous works as is usually done, we propose a new optimization methodology that provides in a consistent manner the complete set of parameters for the studied models, namely Newtonian, Carreau-Yassuda and Kuang-Luo. The optimization was performed simultaneously using experimental data from several sources. Physical observables such as velocity profiles, shear rate profiles and pressure fields were evaluated. For the normal channel case, it was found that the Newtonian model predicts both the highest velocity and shear rates profiles followed by the Carreau-Yassuda and the Kuang-Luo models. For a constricted channel, important differences were found in the velocity profiles among the studied models. First, the Newtonian model was observed to predict the velocity profile maximum at different channel width positions compared to the non-Newtonian ones. Second, the obtained recirculation region was found to be longer for the Newtonian models. Finally, concerning the constriction shape, the global velocity was found to be lower for a rectangular geometry than for a semi-circular one.

Non-Newtonian numerical modelling of solder paste viscosity measurement

PurposeThe purpose of this paper is to present the establishment of a computational fluid dynamics model for investigating different non-Newtonian rheological models of solder pastes by simulating solder paste viscosity measurement. A combined material model was established which can follow the measured, apparent viscosity values with lower error.Design/methodology/approachThe model included a parallel plate arrangement of rheometers. The diameter of the plate was 50 mm, whereas the gap between the plates was 0.5 mm. Only one quarter of the plate was modelled to enable using fine enough mesh, while keeping the calculation time low. Non-Newtonian properties were set using user defined function in Ansys, based on the Cross and Carreau–Yasuda material models. The viscosity values predicted by the mathematical models were compared to measured viscosity values of different types of solder pastes.FindingsIt was found that the Cross model predicts the apparent viscosity with a relatively high error (even approximately 50 per cent) at lower shear rates, whereas the Carerau–Yasuda model has higher errors at higher shear rates. The application of the proposed, combined model can result in a much lower error in the apparent viscosity between the calculated and measured viscosity values.Originality/valueThe error of Cross and Carreau–Yasuda material models has not been investigated yet in details. The proposed, combined material model can be applied for subsequent simulations via the described UDF, e.g. in the numerical modelling of the stencil printing. This can result in a more accurate modelling of the stencil printing process, which is inevitable considering the printing of solder paste for today fine-pitch, small size components.

Near-Wall Flow in Cerebral Aneurysms

The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, and signalling via mechanotransduction, which are primary functions of the cardiovascular system and abnormalities in these functions are known to affect disease formation and vascular remodelling. This region is denoted by the near-wall region in the present work, and we outline simple yet effective numerical recipes to analyse the near-wall flow field. Computational haemodynamics solutions are presented for six patient specific cerebral aneurysms, at three instances in the cardiac cycle: peak systole, end systole (taken as dicrotic notch) and end diastole. A sensitivity study, based on Newtonian and non-Newtonian rheological models, and different flow rate profiles, is effected for a selection of aneurysm cases. The near-wall flow field is described by the wall shear stress (WSS) and the divergence of wall shear stress (WSSdiv), as descriptors of tangential and normal velocity components, respectively, as well as the wall shear stress critical points. Relations between near-wall and free-stream flow fields are discussed.