The results show that the shear rate is low at the bifurcation and in the sinus. 91 Figure 5.4 Time-averaged (I) velocity streamlines and (II) axial velocity contours at different inflow waveforms showing possible regions of recirculation in the patient-specific carotid artery sinus (a) waveform 1 (b) waveform 2 (c) waveform 3 .
Introduction
According to some researchers, cholesterol is synthesized in the arterial walls and diffuses into the lumen (Caro et al., 1971b). A recent study demonstrates the importance of non-Newtonian modeling of blood in the highly constricted vessel (Mendieta et al., 2020).
Objectives
The effect of bifurcation angle variation on flow behavior in general and wall shear stress in particular is investigated for symmetric and asymmetric bifurcations using Computational Fluid Dynamics (CFD) simulations. In Chapter 5, transient CFD simulations were performed in a patient-specific carotid artery bifurcation geometry obtained from the literature.
Flow in Bifurcating Vessels: Effect of Bifurcation Angle
Introduction
In a branch vessel, the flow divides into the two daughter vessels and passes through a curved section present at the branch. In particular, shear is low in the area where the flow is separated from the wall.
Computational methodology
- Computational domain
- Governing equations
- Rheological model
- Boundary conditions
- Numerical schemes
The equations of conservation of mass and momentum can be written as given by Eqs. where 𝜌 is the fluid density, u is the fluid velocity vector, and P is the pressure. 𝝉 is the stress tensor and is represented by Eq. μ represents the viscosity or apparent viscosity of the fluid and D is the shear rate tensor. For a Newtonian fluid, μ is a constant, while for a non-Newtonian fluid, μ is a function of D. The shear rate tensor is represented by Eq. 𝛾̇ is the magnitude of the shear rate tensor D given by Eq.
Results and discussion
- Steady flow
- Pulsatile flow
Due to flow separation, the area available for forward flow is reduced in the daughter vessel near the bifurcation. The pressure drop in the daughter vessel increases with an increase in the bifurcation angle.
Conclusions
Figures 3.37 and 3.38 show respectively the OSI and RRT on the inner and outer walls at the bifurcation plane. For symmetric bifurcations, OSI and RRT are zero everywhere on the inner walls and have non-zero values on the outer wall. The location of peaks in OSI and RRT is different for Newtonian and non-Newtonian fluids on both daughter vessels.
Effect of Sinus Size and Position on Flow Behavior in an Idealized Carotid Artery
Introduction
The hemodynamics study in patient-specific models showed a direct relationship between tortuosity and low WSS or high OSI (Lee et al., 2008). Relative residence time is the time the fluid spends locally near the artery wall (Himburg et al., 2004). Stroke is common in older people due to changes in carotid artery geometry with age, particularly the bifurcation angle and increased curvature (Thomas et al., 2005a).
Computed tomography angiography (CTA) studies show that men are more susceptible to internal carotid artery (ICA) plaque formation (Choi et al., 2015). In contrast, the chances of plaque formation in women are more in the external carotid artery (ECA) (Compagne et al., 2019). The sinus of the internal carotid artery is prone to atherosclerosis, which causes fibromuscular dysplasia, or a carotid tissue caused by ischemic stroke (Choi et al., 2015; Joux et al., 2014).
Computational methodology
- Bifurcation Model
- Rheological models
- Mesh independence study and validation
4.2(a) shows the apparent viscosity as a function of the shear rate obtained from the three rheological models. Experiments have shown that the apparent viscosity of blood is shear dependent at low shear rates but is constant at higher values of shear rate. 4.2(b) shows the apparent viscosity as a function of the shear rate obtained from the three rheological models.
The results obtained from the CFD simulations are compared with the results of Gijsen et al. Validation of the simulations was done with the experimental results of the carotid artery bifurcation model (Rindt et al obtained axial velocity vectors using laser Doppler anemometry (LDA) experiments for steady flow in the midplane of the daughter vessels (radius 8mm & Re =640) at different locations in the sinus (Rindt et al., 1987) In the present work, the carotid geometry is not exactly the same as Rindt et al.
Results and discussion
- Newtonian fluid
- Non-Newtonian fluids
Sinus away from the bifurcation causes more backflow, especially in the middle region of the sinus. The velocity profile in the middle of the sinus shows more recirculation, as shown in Fig. For the minor sinus (w = 2.0), the low TAWSS region is confined to the outer bifurcation wall.
The X -velocity contours and secondary flow streamlines in the sine midplanes are shown in Fig. For larger sine magnitude (w = 3.0), the secondary flow is prominent for the Newtonian case compared to non-Newtonian models. An increase in sinus size shows larger secondary vortices in the center of the sinus.
Conclusions
The Effect of Pulse Rate on Hemodynamics in a Carotid Artery Bifurcation
- Introduction
- Methods and materials
- Geometry
- Governing equations
- Boundary conditions
- Mesh independence study
- Results and discussion
- Conclusions
With the increase in the frequency of the cardiac cycle, the size of the current separation in the sinus region decreases. The knowledge of the RRT distribution in the carotid artery branch for varying pulse needs to be understood. The increase in pulse rate shows a decrease in the size of the higher RRT region, as shown in Fig.
In contrast, the lower pulse rate shows an increase in the size of the higher RRT region (Fig. 5.7c). The secondary flow is present in the cross-sectional plane of the internal and external carotid arteries. As seen in Chapter 4, it is more significant in the sinus region of the internal carotid artery.
Computational Investigations on Bubble Dynamics in Bifurcating Channels
Introduction
Reduction of the lubricating film increases friction and leads to air bubbles (Li et al., 2021). Bubble splitting behavior depends on gravity, surface tension and inertia (Chen et al., 2014; Eshpuniyani et al., 2005). It has recently been shown that tumor growth in mice with hepatocellular carcinoma (liver cancer) can be limited using gas embolotherapy techniques (Harmon et al., 2019).
The magnitude of pressure gradient during reopening is found to be the most important factor for cell damage (Kay et al., 2004). A recent study observed a reduction in hydrodynamic forces by adding a surfactant, reducing lung injury (Muradoglu et al., 2019). In another study, simulations of the 3D non-Newtonian slime fracture found that high surface tension increases the wall shear stress (WSS) and slows down the fracture process (Hu et al., 2020).
Computational methodology
- Governing equations and boundary conditions
- Numerical schemes
- Geometry
- Grid independence study
- Validation
Recently, the effect of symmetric bifurcation angle on bubble fission was analyzed and four fission stages were observed: the first stage of the compression process, the second stage of the compression process, the fast pinch-off stage, and the head-forward process (Du et al., 2020; Ziyi et al., 2019). However, to the best of the author's knowledge, the cleavage dynamics for asymmetric bifurcation are not well understood. The volume fraction of the gas phase is set to zero at the inlet boundary.
However, such a region exists only for the lowest value of Ca in our case, and the bubble thickness changes continuously for higher values of Ca. Film thickness is measured at the center of the bubble. The width and height of the square channel are each 400 μm, and the length is about 5 mm. After the bubble enters the bifurcation, the portion of the bubble at the T-junction begins to thin, and in both cases a neck-like structure develops.
Results and discussion
- Effect of bifurcation angle on bubble splitting
- Effect of flow parameters on bubble propagation in an airway bifurcation
There is a notable difference in the bubble shape for the three values of capillary numbers. The homogeneous cleavage of the bubble occurs even after asymmetry in the bifurcation angle and flow rates in a respective daughter vessel. The pressure is higher in the upper vessel than in the lower one in the area where the bubble is present.
As observed for the baseline scenario, the large pressure gradient changes occur near the bubble. With an increase in the value of the capillary number, the bubble elongates and deviates from the spherical shape. As a result, the length of the bubble in the daughter vessel is more in geometry (b).
Conclusions
Although this study gives a qualitative idea regarding the bubble flow at bifurcations, three-dimensional simulations are required to consider both the main curvatures of the bubble. At a symmetric bifurcation, the bubble divides symmetrically at a higher value of the capillary number (Ca where viscous force dominates over the surface tension force at a symmetric bifurcation. Furthermore, the dynamics of the bubble in a planar, two-dimensional, asymmetric bifurcation becomes studied computationally for different values of Bond and capillary numbers to understand the effect of these parameters on wall shear stress.
For the studied parameters, the bubble does not break up at the bifurcation and goes into the lower daughter vessel. We observe that the stresses, both normal and shear, and their gradients are high in the vicinity of the bubble. It is observed that the apparent viscosity of the shear thinning fluid is higher in the middle region of constant bubble film thickness and is higher at the ends of the bubbles.
Experimental Investigations on the Bubble Dynamics in a Bifurcating Vessel
- Introduction
- Materials and methods
- Fabrication of low-cost bifurcation model
- Experimental setup
- Experimental conditions and material properties
- Results and discussion
- Bubble generation
- Bubble behavior at the bifurcation
- Comparison with CFD
- Conclusions
With the change in liquid flow rate, the length of the bubble in the mother container is observed to vary. At a particular flow rate ratio, the bubble length is observed to increase with a decrease in the viscosity of . As the bubble approaches the carbifurcation, both non-fission and fission regimes are observed in the experiments.
Non-split: As the name suggests, the bubble does not split at the bifurcation and passes into one of the daughter vessels. In the case of partial cleavage, the liquid passes through a film between the bubble and the wall of the daughter container. The curvature of the neck at the bifurcation increases and the bubble leads to the pinch-off stage.
Conclusions
Conclusions
Depending on the bifurcation angle and the capillary number, we observe fissile and non-fissile behavior of the bubble. The bubble splits symmetrically at a symmetrical bifurcation, at a higher value of the capillary number (Ca = 0.0231). For the case of an asymmetric bifurcation angle, with a larger capillary number, the bubble splits almost symmetrically despite the asymmetry in the geometry.
While the bubble at lower capillary number does not split and goes into the lower daughter vessel for all asymmetric cases. Furthermore, the dynamics of the bubble in a planar, two-dimensional, asymmetric bifurcation is studied computationally for different values of Bond and capillary numbers, to understand the effect of these parameters on wall shear stress using air and mucus as gas and liquid . phases, respectively. For all values of Bond and capillary number considered, the bubble does not split at the bifurcation and enters the lower daughter vessel.
Recommendations for future work
Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch. Investigating 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 influence of non-Newtonian properties of blood on flow in large arteries: steady flow in a carotid bifurcation model.
A computational study of the effect of stent design on local hemodynamic factors at the carotid artery bifurcation. Numerical solution of the pulsatile, non-Newtonian and turbulent blood flow in a patient-specific elastic carotid artery. A numerical and experimental analysis of the flow field in a two-dimensional model of the human carotid bifurcation.
