Multiphase Flow Hemodynamic Evaluation of Vertebral Artery Stenosis Lesions and Plaque Stability

Abstract

BACKGROUND:

Atherosclerosis is one of the main causes of vertebral artery stenosis, which reduces blood supply to the posterior circulation, resulting in cerebral infarction or death.

OBJECTIVE:

To investigate stenosis rates and locations on the development of vertebral artery plaques.

METHODS:

Stenosis models with varying degrees and positions of stenosis were established. The stenosis area was comprehensively analyzed using multiphase flow numerical simulation. Wall shear stress (WSS), blood flow velocity, and red blood cell (RBC) volume fraction were calculated.

RESULTS:

Blood flow velocity in 30–70% stenosis of each segment tended to increase significantly higher than normal. Downstream of 50% stenosis exhibited turbulent flow; downstream of 70% displayed reflux. Severe stenosis increases the WSS and distribution area. The mixed area of high and low WSS appeared downstream of the stenosis. The RBC volume fraction at the stenosis increased (maximum value: 0.487 at 70% stenosis in the V4), which was 1.08 times the normal volume fraction. Turbulent and backflow regions exhibited complex RBC volume fraction distributions.

CONCLUSION:

Flow velocity, WSS, and RBC volume fraction at the stenosis increase with stenosis severity, increasing plaque shedding. Narrow downstream spoiler and reflux areas possess low WSS and high erythrocyte volume fractions, accelerating plaque growth.

Keywords

Arterial stenosis computational fluid dynamics multiphase flow red blood cell aggregation plaque

1. Introduction

Vertebral artery (VA) stenosis refers to compression of the vertebral artery by external dynamic or mechanical factors, or vascular stenosis, spasm, or tortuosity of different degrees caused by blood vessel diseases [1]. Stenosis of the vertebrobasilar artery system comprising the vertebral and basilar arteries and their branches can lead to vertebrobasilar insufficiency (VBI) to the posterior circulation of the brain, and subsequently cause recurrent transient ischemic attack (TIA) or cerebral infarction, which can lead to disability or death in severe cases [1–3]. Global statistics reveal that ∼2 million people die of stroke annually, 85% of which are ischemic. More importantly, ∼20% of these strokes occur in the posterior circulation [4]. Atherosclerosis is one of the main causes of arterial narrowing. The vertebral–basilar artery is the second most common site of cerebral plaque accumulation after the carotid bifurcation [5]. However, vertebral artery stenosis is less concerning than symptomatic carotid and basilar stenoses; 25–30% of patients with extracranial cerebral vascular stenosis have stenosis in the extracranial vertebral artery [6]. In particular, vertebral artery origin stenosis (VAOS) can increase stroke risk by 25–35% within 5 years in patients with transient ischemic attack (TIA) symptoms [7].

Computational fluid dynamics (CFD) has been widely applied in the study of vascular diseases [8,9]. Chaichana et al. studied the plaque effect at the left coronary bifurcation on hemodynamics and observed that plaques exert significant changes on vascular hemodynamics [10]. Li et al. compared hemodynamic parameters in patients with normal carotid artery and symptomatic carotid sinus stenosis using CFD, and reported that significantly reduced WSS, dynamic wall pressure, and total pressure gradient are key to carotid sinus atherosclerosis [11]. A study of moderate coronary stenosis by Sezer et al. showed that, for a given stenosis geometry, plaque vulnerability characteristics may affect the hemodynamic correlates of moderate coronary stenosis [12]. However, there are few studies investigating the plaque shedding risk based on the morphology of vertebral artery stenosis.

Most hemodynamic studies treat blood as an incompressible single-term Newtonian fluid, an assumption that holds true for larger vessels, but not for vessels with smaller diameters, tortuous, and complex paths may have certain errors. The difference between multi- and single-phase flows is mainly the volume fraction of each phase, and the exchange of momentum, heat, and mass between the two phases. Jung et al. used a multi-flow method to analyze the blood flow of the right coronary artery and predicted the local hemodynamic changes of early atherosclerosis through red blood cell (RBC) aggregation [13].

We used multiple flow methods to study the effect of vertebral artery stenosis on blood flow, and the hemodynamic differences between vessels exhibiting different degrees of stenosis to explore the mechanism underlying atherosclerosis and plaque shedding. It provides a theoretical basis for the treatment of cardiovascular and cerebrovascular diseases such as cerebral infarction.

2. Methods

2.1. Data sources

This study selected a patient (male, 51 years old) who underwent head and neck computed tomography (CT) angiography at Hongqi Hospital Affiliated to Mudanjiang Medical College on September 3, 2020. No abnormality of vertebral artery was identified in the CT image. We utilized NeuViz 128 (Neusoft Medical System, Shenyang, China) CT equipment with the following scanning parameters: 120 kV, 270 mA, image matrix (512 × 512), and reconstructed slice thickness (1 mm). The patient provided written, informed consent, which was reviewed by the hospital ethics committee.

2.2. Vertebral artery model

The vertebral artery geometric model was extracted using the medical imaging processing software MIMICS (Materialise, Leuven, Belgium) (Fig. 1). The MIMICS segmentation results are output to 3-matic in STL format, and the surface is smoothed.

Fig. 1.

Schematic diagram of the vertebral artery geometry. (A) Segment of the vertebral artery; (B) diameters of mild, moderate and severe stenosis of the V2 segment; (C–F) normal vessel, 30, 50, and 70% stenosis of the V2 segment, respectively.

2.3. Vertebral artery stenosis model

The vertebral arteries, which originate from the proximal subclavian arteries on both sides, pass through the intervertebral foramen and merge into the basilar artery at the lower border of the pons. From the basilar artery to the midbrain, it divides into two posterior cerebral arteries, which supply the posterior 2/5 of the cerebral artery [2]. Figure 1a shows the vertebral artery segments.

According to the measurement method proposed by the North American Symptomatic Carotid Endarterectomy Trial, the vascular stenosis rate = (normal diameter of the distal stenosis - diameter of the most stenosis)/the distal stenosis normal diameter ×100%. Vessel stenosis rate ≤49% was defined as mild, 50% ≤ stenosis rate ≤69% as moderate, and ≥70% was defined as severe [14]. The ideal model of vertebral artery stenosis is artificially constructed using MIMICS software, and vertebral artery stenosis is constructed in the V1, V2, V3, and V4 segments of the left vertebral artery, respectively, representing mild, moderate and severe stenosis. Different from the formula, we chose the stenosis original diameter to replace the distal stenosis diameter, and calculated the diameter of each degree of stenosis using the stenosis rate to simulate normal vertebral artery stenosis. The diameter of the stenosis of each segment is shown in Table 1. Using segment V2 as an example, the original diameter of the stenosis structure point was 3.69 mm, and the diameters of 30–70% were 2.58, 1.85, and 1.11 mm, respectively (Fig. 1B). Figures 1C–F illustrate normal vessels and vessels with 30, 50, and 70% stenosis rates at V2 segment stenosis, respectively.

Table 1
The geometric parameters, mesh parameters and computational fluid dynamics parameters of the models in V1–V4

Vertebral artery segment Stenosis degree Stenosis diameter (mm) Cell count V_max (m/s) WSS_max(Pa) Maximum volume fraction

30% 2.73 1125136 0.33 2.61 0.459

V1 50% 1.95 1024586 0.92 13.93 0.483

70% 1.17 936851 1.74 37.73 0.467

30% 2.59 1223625 0.34 2.19 0.454

V2 50% 1.85 1192069 0.62 7.55 0.459

70% 1.11 1168957 1.29 23.43 0.468

30% 2.62 927693 0.33 1.92 0.463

V3 50% 1.87 898694 0.58 5.39 0.466

70% 1.12 877243 1.47 31.43 0.468

30% 2.04 1113503 0.45 5.00 0.484

V4 50% 1.46 1101403 0.87 16.78 0.485

70% 0.87 1082294 2.38 88.36 0.487

Vertebral artery segment	Stenosis degree	Stenosis diameter (mm)	Cell count	V_max (m/s)	WSS_max(Pa)	Maximum volume fraction
	30%	2.73	1125136	0.33	2.61	0.459
V1	50%	1.95	1024586	0.92	13.93	0.483
	70%	1.17	936851	1.74	37.73	0.467
	30%	2.59	1223625	0.34	2.19	0.454
V2	50%	1.85	1192069	0.62	7.55	0.459
	70%	1.11	1168957	1.29	23.43	0.468
	30%	2.62	927693	0.33	1.92	0.463
V3	50%	1.87	898694	0.58	5.39	0.466
	70%	1.12	877243	1.47	31.43	0.468
	30%	2.04	1113503	0.45	5.00	0.484
V4	50%	1.46	1101403	0.87	16.78	0.485
	70%	0.87	1082294	2.38	88.36	0.487

WSS, Wall shear stress.

2.4. Meshing

All smoothed models were discretized using the ANSYS-Fluent meshing module. The central area of the model adopted hexahedral elements, and the wall was set with 5 boundary layers. We used the Fluent meshing local encryption technology to refine the mesh in the narrow area to ensure that meshes that could achieve computational accuracy. The grid independence test did not produce a significant difference affecting the calculated results. The mesh numbers of all models were distributed between 877,243 and 1,223,625, and the specific mesh numbers are summarized in Table 1.

2.5. Numerical simulation

Considering blood as a two-phase fluid composed of plasma (liquid phase) and RBCs (solid phase), numerical simulation of liquid–solid two-phase flow was conducted. Since RBCs were suspended in plasma, the RBC thermodynamic and kinetic parameters were the same as those of plasma by mathematical definition, and they all exist as continuous distribution functions in space. Therefore, the continuity equation also applies to two-phase flow. Plasma and RBCs satisfy the conservation equations respectively (regardless of gravity), and the mass conservation equations and momentum conservation equations satisfied by plasma are: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \frac{\partial {\alpha}_{{\iota}}{\rho}_{{\iota}}}{\partial _{t}}+{\nabla}\cdot ({\alpha}_{{\iota}}{\rho}_{{\iota}}\vec{{\nu}_{{\iota}}})=0\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \frac{\partial ({\alpha}_{{\iota}}{\rho}_{{\iota}}\vec{{\nu}_{{\iota}}})}{\partial _{t}}+{\nabla}\cdot ({\alpha}_{{\iota}}{\rho}_{{\iota}}\vec{{\nu}_{{\iota}}}\vec{{\nu}_{{\iota}}})=-{\alpha}_{{\iota}}{\nabla}P-{\nabla}P_{t}+{\nabla}\cdot \overline{\overline{{\tau}_{t}}}+m_{s{\iota}}.\end{eqnarray}$ (2)

The mass conservation equation and momentum conservation equation satisfied by RBCs are: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \frac{\partial {\alpha}_{s}{\rho}_{s}}{\partial _{t}}+{\nabla}\cdot ({\alpha}_{s}{\rho}_{s}\vec{{\nu}_{s}})=0\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \frac{\partial ({\alpha}_{s}{\rho}_{s}\vec{{\nu}_{s}})}{\partial _{t}}+{\nabla}\cdot ({\alpha}_{s}{\rho}_{s}\vec{{\nu}_{s}}\vec{{\nu}_{s}})=-{\alpha}_{s}{\nabla}P-{\nabla}P_{s}+{\nabla}\cdot \overline{\overline{{\tau}_{s}}}+m_{{\iota}s}.\end{eqnarray}$ (4)

Among them, 𝛼_𝜄, 𝛼_s are the liquid and solid phase volume fractions, respectively; 𝜌_𝜄, 𝜌_s are the liquid and solid phase densities, respectively; 𝜏_t , 𝜏_s are liquid and solid phase variation tensors, respectively; $\vec{{\nu}_{{\iota}}}$ , $\vec{{\nu}_{s}}$ are the velocity vectors of the liquid and solid phases, respectively; P _t, P _s are the pressures between liquid and solid phases, respectively; m _s𝜄, m _𝜄s are the forces of the liquid-to-solid and solid-to-liquid phases, respectively.

Blood consists of plasma and blood cells. The plasma volume accounts for about 55% of blood [15]. About 91% of plasma is water, and the rest comprises various nutrients such as plasma proteins, lipoproteins, oxygen, enzymes, hormones, inorganic salts, and metabolites. Blood cells are the primary constituents of blood, mainly including RBCs, white blood cells, and platelets. RBCs are the most numerous, accounting for ∼45% of the blood volume. Assuming that plasma is an isotropic, homogeneous. Non-Newtonian viscous fluid with density 𝜌 = 1030 kg⋅m⁻³. The blood viscosity model is the Carreau-Yasuda model [16]. Its module type expression is: $\begin{eqnarray}\displaystyle {\mu}={\mu}_{0}+({\mu}_{0}-{\mu}_{\infty })[1+({\lambda}{\gamma})^{Z}]^{\frac{n-1}{Z}}. & & \displaystyle\end{eqnarray}$ (5)

Among them, 𝜇 is the kinetic viscosity, the low shear viscosity 𝜇₀ and the high shear viscosity 𝜇_∞ are 0.022 Pa⋅s and 0.0022 Pa⋅s, respectively, the time constant 𝜆 is 0.110 s, and the exponents Z and n are 0.644 and 0.392, respectively, 𝛾 is the shear strain rate; RBCs are spherical rigid particles, density 𝜌 = 1090 kg⋅m⁻³, viscosity coefficient 𝜇 = 0.0175 Pa⋅s, diameter d = 8 μm, suspended in plasma [13]. The computational simulations in this paper assume a rigid vessel wall and do not consider the effects of other physiological factors such as elasticity and compliance [17–19] to facilitate clarification of the non-Newtonian properties of blood as a single factor influencing the hemodynamic assessment. To reflect the physiological characteristics of the vertebral artery, the inlet condition of the vertebral artery model was set, accounting for 55% plasma and 45% RBCs [20]. Entrance velocities were obtained using a full cardiac cycle [9]. The distal posterior cerebral artery and superior cerebellar artery were served as outlets and were set as pressure outlet (Fig. 2). The time step is 800; three cycles are calculated, giving the total step of 2400 to ensure accuracy of the calculated results; the final cycle was taken as the analysis result [17].

Fig. 2.

Boundary conditions. (a) Inlet flow rate; (b) outlet boundary.

3. Results

3.1. Comparison of different degrees of stenosis in the V1 segment

It can be observed that the blood flow velocity increased significantly at the stenosis (Figs 3A–C). The maximum velocities of the three stenoses were 0.33, 0.92, and 1.74 m/s, respectively. In the local streamline, we observed that there were more turbulent flow lines downstream of the stenosis vessels in the 50% and 70% stenosis. Vortex lines were observed in 70% of the stenosis. Additionally, the blood flow velocity shown in the profile of the stenotic rear end has a large gradient, and the low flow velocity is located in the streamline disorder or eddy current region. Taking 70% stenosis as an example, the distribution of high-speed blood flow is 1.51–1.74 m/s, while the vortex flow velocity distribution is 0.03–0.20 m/s.

Fig. 3.

V1 and V2 segment 30–70% stenosis blood flow velocity streamline diagram at diastole, local features of streamline and velocity profile at stenosis. (A–C) 30–70% stenosis of V1 segment; (D–F) 30–70% stenosis of V2 segment; a–e: cross-sectional views of each stenosis and before and after the stenosis.

Figures 4A–C show the overall wall shear stress (WSS) of 30–70% stenosis in the V1 segment. The maximum WSSs of the three stenoses shown a gradually increasing trend. The area of high WSS in the stenosis area also increased with the stenosis degree. A low WSS region was in the region between the stenosis and high WSS of different degrees, range from 0.18–0.56, 0.05–0.65, and 0.16–0.71 Pa, respectively. The concentrated high-speed blood flow formed a large velocity gradient with the near-mural area in the middle, resulting in a low WSS area between them. The WSS distribution in other regions was similar.

Fig. 4.

(A–C) Overall WSS and local features of 30–70% stenosis at diastole in the V1 segment; (D–F) overall WSS and local features of 30–70% stenosis at diastole in the V2 segment.

A larger RBC volume fraction appears at 50% and 70% stenosis, of which 50% was the most obvious (Figs 5A–C). There are higher RBC concentrations at the stenosis and the downstream anterior wall, and there is a low fraction area between the two, which is also related to the flow velocity distribution. A higher RBC volume fraction is also observed at the distal basilar artery bifurcation, which is the bifurcation of four branch vessels; the blood flow hits the bifurcation angle on both sides, and RBCs are more likely to accumulate in this area.

Fig. 5.

(A–C) Red blood cell volume fractions with various degrees of stenosis at diastole in the V1 segment; (D–F) red blood cell volume fractions with various degrees of stenosis at diastole in the V2 segment.

3.2. Comparison of different degrees of stenosis in V2 segment

As shown in Fig. 3D–F, the maximum velocity of the three stenoses also shows an increasing trend, which is 0.34, 0.62, and 1.29 m/s, respectively. The flow separation and backflow phenomenon can be seen in the velocity profile of 70% stenosis, that is, the central forward high-speed flow domain and the edge reverse low-speed flow domain occur in the outer near-wall area downstream of the stenosis, and the streamline is swirling. The blood flow velocity distribution in the distal basilar artery of the three stenoses is similar.

The WSS at the stenoses is significantly higher, and it increases with the stenosis degree (Figs 4D–F). There is a low WSS area at the rear of the three stenoses, which forms a large drop with the stenosis, and the distributions are 0.18–0.33, 0.02–0.31, and 0.02–0.63 Pa, respectively. The V2 segment of the vertebral artery runs straighter, and the blood flow is simpler than in other segments. The high-speed blood flow is located in the blood vessel center, forming a large velocity gradient with the proximal wall area. Therefore, the stenosis has little effect on the distribution of WSS on the downstream wall, and both for low WSS.

With the increase of stenosis degree, the RBC volume fraction in the stenosis increased (Fig. 5D–F). The RBC aggregation at 30% stenosis is not obvious, slightly higher than the surrounding wall. The RBC aggregation degree at 50% stenosis is slightly higher than that at 30%, and there is a small area of higher value on the frontal lateral surface of the stenosis posterior segment, and the same area exhibited a higher degree of aggregation at 70% stenosis. Regions with higher RBC volume fractions corresponded to low WSS.

3.3. Comparison of different degrees of stenosis in the V3 segment

The blood flow velocity at the stenosis is greatest, and the maximum values of the three stenoses show an increasing trend (Figs 6A–C). Compared with other stenoses, blood flow velocity of the V3 segment stenosis is relatively small, because the stenosis is located downstream of the vascular transition, and the curved vessels exhibit a deceleration effect. There are reflux areas at 50 and 70% stenosis, and the 70% stenosis shows a larger reflux area. The velocity was the fastest at the center, and the region with a large velocity gradient appeared at 50% and 70% stenosis, which was the reflux region.

Fig. 6.

V3 and V4 segment 30%–70% stenosis blood flow velocity streamline diagram at diastole, local features of streamline and velocity profile at stenosis, (A–C) is 30%–70% stenosis of V3 segment; (D–F) is 30%–70% stenosis of V4 segment Stenosis, a–e are the cross-sectional views of each stenosis and before and after the stenosis.

The stenosis WSSs of the V3 segment reach the maximum at the stenosis, with maximum values of 1.92, 5.39, and 31.43 Pa, respectively (Figs 7A–C show). And there are low WSS distribution areas downstream of the three stenoses, located at the backflow of blood flow. The WSS distribution in the blood reflux area are as follows at 30% (0.01–0.22 Pa), 50% (0.02–0.30 Pa), and 70% (0.09–0.57 Pa) stenoses. The lower flow rate here creates a lower WSS area that is more prone to atherosclerosis.

Fig. 7.

(A–C) The overall WSS and local features of 30%–70% stenosis at diastole in the V3 segment; (D–F) the overall WSS and local features of the 30%–70% stenosis at diastole in the V4 segment.

The RBC volume fractions of V3 stenosis are lower than those of other segment stenoses, with a maximum value at 70% stenosis of 0.462 (Figs 8A–C). The range of higher RBC volume fraction downstream of the three stenoses was similar, but the distribution areas were quite different, particularly in the blood flow backflow area. The 50% stenotic reflux area had scattered areas with higher volume fractions, while in the 70% stenotic reflux area, there were more distributions with lower volume fractions, which may be related to the more complicated blood flow in the 70% stenotic reflux area.

Fig. 8.

(A–C) The red blood cell volume fractions of different degrees of stenosis at diastole in the V3 segment; (D–F) the red blood cell volume fractions of different degrees of stenosis at diastole in the V4 segment.

3.4. Comparison of different degrees of stenosis in V4 segment

Similar to other stenoses, the blood flow velocity is significantly increased at the stenosis in V4 segment, but the maximum value is higher than that of other stenoses (Figs 6D–F). The maximum velocities of the three stenoses are 0.447, 0.87, and 2.38 m/s, respectively. As shown in Fig. 6E and 6F, reverse flow lines appear in the lateral proximal wall downstream of the 50 and 70% stenoses.

Figures 7D–F show the distribution of WSS at the stenosis of the V4 segment. On the whole, the stenosis WSS is significantly higher than that of other parts, and the maximum WSS of each stenosis was 5.00, 16.78, and 88.36 Pa, respectively. The distribution area of the higher WSS increases with the degree of stenosis. A low WSS small area appeared at the proximal end of the three stenoses, with the most obvious at the 50% stenosis. The proximal low WSS areas at the 50 and 70% stenoses also correspond to the low velocity vortex areas in the streamline diagram.

Higher RBC volume fractions were manifested in three stenoses, with RBC aggregation most evident at the 70% stenosis (Fig. 8D–F). There were high volume fraction areas at the stenosis and the downstream part of the stenosis. The 50% and 70% stenosis occupied a larger area, mainly distributed in the inner side of the blood vessel, and the volume fraction was about 0.475–0.481.

4. Discussion

Using computational fluid dynamics, we analyzed the stenotic vertebral artery hemodynamics in different parts and observed the stenosis influence of different degrees on vertebral artery hemodynamics and RBC distribution characteristics in the stenotic vertebral artery. We analyzed WSS, flow velocity distribution, and RBC volume fraction separately.

Blood is a non-Newtonian fluid composed of blood cells and plasma, with non-Newtonian properties such as yield stress, viscoelasticity, thixotropy and shear thinning, and blood viscosity changes with time. When the shear rate is lower than 200 s⁻¹, the blood viscosity decreases with the increase of the shear rate; when the shear rate is higher than 200 s⁻¹, the viscosity tends to remain constant. Studies have shown that large arterial blood flow is characterized by high pulsatility and rapid flow, but it is also affected by the non-Newtonian properties of blood during diastole due to lower flow velocities. The non-Newtonian properties of blood are more pronounced in vessels with smaller diameters or in narrow vessels due to atherosclerosis [21]. The non-Newtonian properties of blood are more pronounced in vessels with smaller diameters or in narrow vessels due to atherosclerosis [22]. The non-Newtonian fluid effect of shear thinning improves the flow turbulence in the high shear gradient zone at the wall compared to the calculated results for Newtonian fluids.

The WSS is the frictional force on the vascular endothelial tissue under the state of blood flow. Stable and normal WSS contributes to the active expression of endothelial cells, the release of beneficial biological factors, and the maintenance of blood vessel normal physiological functions [23]. The WSS distribution trend in each segment of vertebral artery stenosis was similar, as shown in Table 1. With stenosis degree increase, we found: (a) WSS at stenosis was higher than that at non-stenosis; (b) The greater the degree of stenosis, the higher the WSS, and larger area occupied by high WSS; (c) There was a sheet-like high WSS area on the downstream tube wall at the stenosis; (d) There was a low WSS area between the downstream high WSS and the stenosis. A narrowed vessel accelerates blood flow through it, increasing the friction between the blood and the vessel wall. Higher WSS levels are likely to cause damage to vascular endothelial cells. Areas with higher WSS can be observed on the downstream vessel wall at the stenoses of V1, V3, and V4 segments, and the 50 and 70% stenoses are more obvious. When the vascular stenosis caused by atherosclerosis, high WSS will induce the formation of vulnerable plaques and may trigger the molecular mechanism of endothelial cells, leading to plaque rupture [24], the ruptured plaque fragments flow into downstream vessels, causing cerebral infarction. WSS maximum is positively correlated with plaque vulnerability, suggesting that WSS maximum is a potential quantitative parameter for assessing atherosclerosis risk [25]. Additionally, to high WSS, there are also low WSS areas in narrow areas. On the one hand, lower levels of WSS are prone to trigger local vascular wall inflammation, and on the other hand, low WSS is a hemodynamic phenotype that is prone to atherosclerosis [26]. Long-term abnormal WSS acts on the prone sites of atherosclerotic plaques and can promote the up-regulation of endothelial cell pro-atherosclerosis-related genes, including matrix metalloproteinases, calcification genes, inflammatory molecules, pro-angiogenic factors, etc. The expression of angioprotective factors such as nitric oxide is inhibited. Therefore, it promotes endothelial cell dysfunction, accelerates the inflammatory response, oxidative stress response, and apoptosis of the vascular endothelium and other pathological processes, and induces the formation of atherosclerotic plaques [27].

In terms of velocity profile, the blood flow pattern in the stenotic vessel was similar to that of the normal contralateral normal vertebral artery. The velocity at the center of the watershed was fast, and the velocity near the wall was slow. However, the stenosis of the vertebral artery has a smaller diameter, which accelerates the blood flow. The stenosis and downstream of the stenosis show high velocity. The blood flow velocity at the 30%–70% stenosis of each segment of the vertebral artery showed an increasing trend. The high-speed blood flow increased the friction between the blood and the tube wall; therefore, the WSS in the high-velocity region was high. Some studies found that the size of the WSS was positively correlated with the vessel wall thickness increase [28], and this result is in agreement with our findings. As the degree of stenosis increases, the blood flow pattern at the stenosis becomes more complex. There are more turbulent flow lines in the back of stenotic vessels, particularly at 70% stenosis, eddy currents, and flow separation can be observed [29]. These turbulence and eddy currents have low velocities and are prone to particle deposition, especially where flow separation occurs, where LDL concentration polarization can occur [30].

RBC volume fraction is also an important indicator of plaque risk. Among the stenosis of each segment, the V4 segment had the highest RBC volume fraction of the three stenosis degrees, and significant RBC aggregation could be observed. The maximum value of 70% stenosis was 0.487, which was 1.08 times the normal RBC concentration. It is more likely that RBCs accumulate in the anterior segment of the stenosis because they pass through crowded channels more frequently; therefore, RBC accumulation in the downstream vessels after the stenosis is more obvious. In the downstream vessel wall of some stenoses, RBC accumulation areas can be observed. We found an interesting phenomenon that most downstream vascular regions with high RBC volume fractions were also located at lower WSS and had lower flow rates. Under low WSS conditions, RBCs are not easy to be flushed downstream, and it is easy to cause the re-aggregation of particles in the blood, such as high-density lipoprotein and low-density lipoprotein, and the aggregated RBCs bring them more free oxygen. It oxidizes thereby accelerating plaque growth. We found an area with a low RBC volume fraction at 50% stenotic turbulence and 70% reflux in the V3 segment. Although the disturbance and recirculation areas are prone to particle deposition in the previous analysis when the recirculation area has a relatively high flow rate, aggregation is also less likely to occur, and even complex blood flow conditions make the distribution more dispersed.

5. Conclusion

Here, vertebral artery models with different stenosis degrees and positions were used to compare the hemodynamic differences caused by geometric factors. Stenosis exerted a significant impact on blood flow status. The plaque shedding risk increased with the stenosis severity, the flow velocity, WSS and red blood cell volume fraction. Disturbed flow downstream of the stenosis and areas of reflux with low WSS and high red blood cell volume fraction accelerate plaque growth, and severe vertebral artery stenosis may increase the risk of ischemic stroke.

Footnotes

Conflict of interest

None to report.

Funding

This research was supported by the Business Cost of the Basic Scientific Research Project of Heilongjiang Provincial University (No. 2020-KYYWF-0795); Climbing Project of Heilongjiang Provincial Education Department (No. 2018-KYYWFMY-0009); Research Development Plan of Application Technology of Mudanjiang Technology Bureau (HT2020JG052).

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