The influence of inlet flow asymmetry on the carotid bifurcation hemodynamics

Arterial bifurcations are known to be high-risk areas for the initiation of atherosclerosis. The appearance and growth of atherosclerotic plaques in the bifurcation of the carotid artery can result in severe consequences such as cerebrovascular accidents. The common signs of an atherogenic risk center around the surpassing critical values by certain hemodynamic indices, which are distributed over the artery wall. These indices are related to the effect of blood flow on the arterial wall, and their distribution is influenced by both the bifurcation’s geometric shape and the flow structure at its inlet. The objective of this study is to carry out a comparative analysis of hemodynamic indices in personal-specific models of carotid bifurcation with centrally symmetric and asymmetric input flows. The examined geometric models of bifurcation are based on computed angiography data obtained from the individuals free of apparent pathology. By using computational fluid dynamics within these models, the distribution of hemodynamic indices in a steady periodic flow is calculated and critical zones are determined for them. All the models are divided into two groups – those with symmetric and those with asymmetric input flows. For each model with asymmetric input flow, an alternative geometry is designed to ensure inlet flow symmetry, and comparative numerical calculations of the blood flow are carried out. The results of comparative analysis reveal that the distribution of hemodynamic indices is simpler for the group with symmetric input flow. A comparison of the averages between these two groups with symmetrical and natural asymmetric input flows indicates a 55% better result for the latter group. Furthermore, for almost all models with asymmetric input flow, their alternative models give worse hemodynamic results. Thus, hemodynamic indices in simpler models with symmetrical input flow can serve as an upper estimate for indices in models with natural asymmetric flow. A total of 89 models are included in the study.


Introduction
The carotid bifurcation is a commonly studied area that poses a potential risk for atherogenesis.It is a generally accepted fact that hemodynamic indices based on wall shear stress (WSS) are closely associated with atherogenesis risk [1 -3].These indices reflect the interaction between blood flow and IC-MSQUARE-2023 Journal of Physics: Conference Series 2701 (2024) 012010 IOP Publishing doi:10.1088/1742-6596/2701/1/012010 2 endothelial cells, which can lead to the development and progression of atherosc lerosis.A number of works are devoted to the study of the relationship between bifurcation geometric shape and the risk of developing atherosclerosis [4 -8].Various methods have been proposed for measuring the geometric parameters of the bifurcation, including the adjacent part of the Common Carotid Artery (CCA) [9 -11].However, hemodynamic indices are not only affected by the geometric shape of the bifurcation but also by the symmetry or asymmetry of the flow at its inlet.In particular, if the OCA has a shape close to a circular cylinder with a rectilinear axial line at a sufficiently large distance, then a flow with a centrally symmetric velocity distribution is formed at the inlet section of the bifurcation.In this case, the situation is simplified, and the hemodynamics in the bifurcation is determined only by its own geometry.
The objective of this study is to conduct a comparative analysis of the hemodynamics in the carotid bifurcation based on personal-specific asymmetric and centrally symmetric flows at the bifurcation inlet.The study was based on data sourced from Computed Tomography Angiography (CT A) of the individuals free of apparent pathology, which were used to build geometric models of the carotid artery.Computational fluid dynamics methods were employed to calculate the unsteady blood flow in the built models, with identification of the models characterized by asymmetric flow at the bifurcation entrance.For each identified model, an alternative version was designed, which guarantees symmetric flow at the bifurcation's inlet, and corresponding flow calculations were conducted.Through analysis of the modeling data, hemodynamic index distributions were generated, allowing for a comparative assessment of the impact of inlet flow symmetry-asymmetry on these indices.

Designing the geometric models and numerical calculations
The initial data for designing models was gathered by performing CTAs on 53 carotid arteries of individuals from various age groups who were free of apparent pathology in the bifurcation zone.The 3D geometric models of vessels were created using the following software: SimVascular [12] and Adobe MeshMixer.Models based on the original data are referred to as "Norm".To analyze blood flow in these "Norm" models, the finite element method was employed using SimVascular software making the assumption that blood behaves as a Newtonian liquid with a density of 1060 kg/m 3 and a dynamic viscosity of 4•10 -3 Pa•s.The vessel wall was considered rigid and impermeable.
For all models, the calculations were carried out with identical blood flow parameters: • average inlet flow rate (CCA) is 6.05 ml/s; • ratio of average speeds at outlets is 1.815 ±2%; • the pulse interval length is 0.9 s.At the inlet, the time dependence of the volumetric velocity was set in accordance with the graph in figure 1, which is typical for a healthy individual.Point "A" indicates the moment of time corresponding to the distribution of velocities in orthogonal sections, depicted in figures 2 and 4. By the computational data, a visual analysis was performed to examine the central symmetry of the flow in the bifurcation inlet at a particular moment of time "A" (see figure 1).The study involved creating orthogonal slices using ParaView [13] in the distal section of the CCA of each model and forming a velocity distribution on the slice.According to the results of visual analysis, the designed models were divided into two groups.The first group of 17 models referred to as "Simm" includes models whose velocity distribution is close to being centrally symmetric.The second group includes the remaining 36 models where significant flow asymmetry was evident.For each model within this group, an alternate geometrical variation was designed using MeshMixer to form a centrally symmetric velocity distribution at the bifurcation inlet.The technique involved the construction of an orthogonal section located in front of the bifurcation, with the removal of the proximal portion of the CCA, as shown in figure 3. Additionally, for these models, continuations were constructed in the form of cylinders with generatrices orthogonally placed to the section planes.As a result of this procedure, each of the original "Norm" models belonging to the second group was supplemented with an auxiliary model referred to as "NormC".For every "NormC" model, the bifurcation, Internal Carotid Artery (ICA), and External Carotid Artery (ECA) shapes are identical to the original model.However, the CCA is a cylinder with a rectilinear generatrix.Subsequently, numerical simulations of fluid flow were performed on these "NormC" models, applying the same parameters as to the original models.As expected, the resulting inlet flow appeared as centrally symmetrical.Thus, the "NormC" and the "Symm" groups form a group of 53 models characterized by a centrally symmetric velocity distribution at the bifurcation entrance.

Post-processing and hemodynamic indices calculation
Employing ParaView, the calculations results post-processing were conducted for all 89 designed models to obtain the distributions of hemodynamic indices OSI (Oscillatory Shear Index), TAWSS (Time-Averaged Wall Shear Stress), RRT (Relative Residence Time) [2,14,15] on their walls.Given its reliance on both the shear stress and the oscillation of near-wall flow, an RRT-index was taken as a prime indicator of atherogenesis risks.On the wall of each model, zones were built in which the RRT exceeds the critical value of 6.25 Pa -1 , [15,16] referred to as "critical zones".Thereafter, assessments of integral RRT values (referred to as RRT_int) were provided across the most important in the medical sense parts of these zones.Areas of these parts (denoted as S) were also calculated.A comparative analysis of these indices across different models was conducted.
Figure 4, (a) (b) show critical zones for the Norm_12 and NormC_12 models as an example.Spheres highlighting parts of critical zones for which RRT_int and S-indices are calculated.The ln(1+RRT_int) distribution in the zones corresponds to the scale with an interval of 0 to 6, shown in the figure.The separate insets show the distribution of velocities in the orthogonal section at the bifurcation inlet at time "A" (see figure 1) in the range from 0 to 70 cm/s.Figure 4 (c) shows both models Norm_12 and NormC_12.For various reasons, some models were excluded from the analysis of the calculation results.One model failed to identify the part of the critical zone belonging to the carotid sinus inner wall, thus it was unsuitable for inclusion.Furthermore, six anomalous pairs of the second group models were discounted from the analysis: • one pair has zero values of indices (no critical zones); • three pairs have a specific critical zone configuration, precluding them from being correctly compared with other models.• two pairs have local deformations of the CCA wall near the bifurcation, which prevents their correct comparison.The remaining pairs of the second group models were named the "Main" group.

Results
Table 1 contains the calculation results for the "Symm" group of models.The data in the table is sorted in ascending order of the RRT_int index.The bottom line of the table shows the indices average for the group.

Discussion
As easily seen, table 1 and table 2 illustrate that the RRT_int and S-indices average values for the "Symm" group and the "NormC" models of the "Main" group, exhibit a difference of no more than 6%.It means that the centrally symmetric input flow, along with the hemodynamic index distribution, can occur in real individuals.
The typical critical zone localization for models exhibiting the centrally symmetric flow at the bifurcation inlet (both in the "Symm" and in the "NormC" groups) approximately corresponds to figure 4. At the same time, the localization of the critical zones for the "Norm" group models portrays a greater diversity, influenced not only by the bifurcation's structure but also by the flow's asymmetry originating at some distance from the bifurcation.As a result, the critical zones of the "Norm" models display increased variety, shifting from the inner wall of the bifurcation towards the outer and side walls.In this case, the displacement of the flow core in one direction leads to a corresponding shift of the critical zones in the opposite direction.
An analysis of RRT_int values between model pairs within the "Main" group (see table 2 and fgure 5) reveals that in 27 out of 30 cases, "Norm" models demonstrated RRT_int values that did not exceed the corresponding "NormC" models' values, with the remaining three pairs exhibiting only a slight difference in the opposite direction.This phenomenon probably can be attributed to the fact that actual physiological blood flow deviation from a centrally symmetrical distribution results in the reduction of risk factors for atherogenesis.Intriguingly, the improvement in indices for the four "NormC" models against their corresponding "Norm" models was solely observed in the right-side models.Overall, for the selected dataset, flow asymmetry in the "Norm" models for the overwhelming majority of cases resulted in better hemodynamic indices compared to the corresponding "NormC" mode ls.Therefore, hemodynamic indices for the "NormC" model can be regarded as an "upper estimate" for the corresponding "Norm" model's indices.As easily seen, the geometric and hemodynamic analysis for "NormC" models is simplified in contrast to "Norm" models, as there is no need to take into consideration the input flow's asymmetry in this instance.

Conclusion
Using CT A data from the individuals free of apparent pathology, 53 geometric carotid artery bifurcation models were constructed.Subsequently, numerical calculations of the steady periodic IC-MSQUARE-2023 Journal of Physics: Conference Series 2701 (2024) 012010 blood flow were carried out on these models.According to the results of calculations, a group of models with a centrally symmetric flow at the bifurcation inlet was identified.For each of the remaining models, an alternative variant was built that guaranteed the symmetry of flow at the bifurcation inlet and numerical calculations of the flow were also carried out.A comparison of the indices between second group models and their alternative counterparts unveiled that in almost all cases hemodynamic indices were worse in alternative models.Consequently, the hemodynamic indices obtained on simpler models with symmetric flow at the bifurcation inlet can be considered an upper estimate of the indices of the corresponding models with natural flow.

Figure 1 .
Figure 1.Time dependence of the inlet volume flow rate (ml/s).

Figure 2 (
a) exemplifies a symmetrical velocity distribution in an orthogonal section while figure 2 (b) illustrates instances of asymmetric distributions.The velocity distribution in the sections corresponds to the scale with an interval of 0 to 70 cm/s, shown in the figure.

Figure 2 .
Figure 2. (a) the centrally symmetric flow at the bifurcation inlet, (b) examples of asymmetric flow distributions.

Figure 3 .
Figure 3. Designing a model variant with OCA as a cylinder with a rectilinear generatrix.

Table 1 .
Indices values for the "Symm" group models.

Table 2
comprises the calculation results for pairs of the "Main" group models.The table is sorted by the value of the RRT_int index for the "Norm" models.The bottom line shows the average values