Effect of differences in proximal neck angles on biomechanics of abdominal aortic aneurysm based on fluid dynamics

Abstract

Background

This study aimed to analyze the effect of proximal neck angulation on the biomechanical indices of abdominal aortic aneurysms (AAA) and to investigate its impact on the risk of AAA rupture.

Methods

CT angiography (CTA) data of patients with AAA from January 2015 to January 2022 were collected. Patients were divided into three groups based on the angle of the proximal neck: Group A (∠β ≤ 30°), Group B (30°<∠β ≤ 60°), and Group C (∠β > 60°). Biomechanical indices related to the rupture risk of AAA were analyzed using computational fluid dynamics modeling (CFD-Post) based on the collected data.

Results

Group A showed slight turbulence in the AAA lumen with a mixed laminar flow pattern. Group B had a regular low-speed eddy line characterized by cross-flow dominated by lumen blood flow and turbulence. In Group C, a few turbulent lines appeared at the proximal neck, accompanied by eddy currents in the lumen expansion area following the AAA shape. Significant differences were found in peak wall stress, shear stress, and the maximum blood flow velocity impact among the three groups. The maximum blood flow velocity at the angle of the proximal neck impact indicated the influence of the proximal neck angle on the blood flow state in the lumen.

Conclusion

As the angle of the proximal neck increased, it caused stronger eddy currents and turbulent blood flow due to a high-speed area near the neck. The region with the largest diameter in the abdominal aortic aneurysm was prone to the highest stress, indicating a higher risk of rupture. The corner of the proximal neck experienced the greatest shear stress, potentially leading to endothelial injury and further enlargement of the aneurysm.

Keywords

Abdominal aortic aneurysms proximal neck angulation finite element analysis computational fluid dynamics

Introduction

Abdominal aortic aneurysm (AAA) is a pathological, localized dilation of the abdominal aorta that can potentially result in rupture. AAAs reportedly occur in 2% of adults, while they occur in approximately 8% of middle-aged and older men.^1,2 Over time, an AAA will typically expand, and without surgical intervention, may rupture with consequent severe bleeding ultimately leading to a fatality rate as high as 90%.³ Clinically, for asymptomatic AAA, surgical repair is typically considered when the maximum diameter exceeds 55 mm or the growth rate surpasses 10 mm per year; even so, intervention carries a mortality risk. However, ruptured aneurysms with a maximum diameter less than 55 mm have accounted for 10%–24% of all cases, while more than 60% of patients with AAA diameters greater than 55 mm never experience rupture.³ This criterion alone is clearly insufficient. Therefore, parameters beyond aneurysmal diameter have been explored, with considerable focus on biomechanical indices, such as the wall stress of diseased blood vessel walls, in an effort to explain and ultimately predict the role of hemodynamics in the occurrence, development, and rupture of AAA.^4–7

Advanced imaging techniques have been widely employed in the cardiovascular system to visualize and display blood flow patterns, revealing the pathophysiology of the circulatory system. Computational fluid dynamics (CFD) has proven to be a rapid and effective research tool in this regard, enabling more comprehensive and complex simulations of systemic hemodynamics.^8,9 Blood flow velocity data, wall shear stress, and wall stress can help identify high-risk sites for rupture through hemodynamic and hydrodynamic parameters.

CFD can display and analyze the blood flow field and stress in blood vessels under various conditions, enabling it to be the primary method for combining medical research with mechanical engineering. There are relatively few studies on the complex morphology of AAA, such as aortic kinking and proximal aneurysm neck angulation, that account for more than 35% of all AAA patients. Risk factors that have often been overlooked in the past, such as the angulation of the proximal neck of AAA and the bifurcation angle of the iliac artery, may increase the risk of AAA rupture.

In previous studies, there have been shortcomings and limitations in the fluid dynamics analysis related to the angulation of the proximal aneurysm neck and the iliac artery bifurcation angle in abdominal aortic aneurysms (AAA).¹⁰ The research focus has primarily addressed smaller proximal aneurysm neck angulations (≤60°), often using simplified, idealized three-dimensional models to validate hypotheses and draw conclusions. However, in actual clinical practice, the angulation of the aneurysm neck in abdominal aortic aneurysms often presents various irregular shapes, not limited to angulations of 60°, and aneurysm diameters and lumen volumes also vary. The idealized models and limited range of research angles may not adequately represent actual data, and the conclusions require further verification.¹¹

Materials and methods

Clinical data

In the present study, both general clinical as well as CTA data were collected from AAA patients treated at our hospital between January 2015 and January 2022. CTA data were stored in DICOM format. Demographic data included age, sex, blood pressure upon admission, and previous medical history. Patients were filtered according to the exclusion criteria, as shown in Figure 1.

Figure 1.

Diagram of participant recruitment. AAA = abdominal aortic aneurysm.

Definitions

The proximal aortic neck diameter was recorded in the minor axis from arterial intima to arterial intima. The lumen length was measured on CT angiography as the distance between the highest point of aneurysmal dilatation and the lowest point of aneurysmal dilatation. The infrarenal angle ∠β was measured, which refers to the spatial angle between the proximal neck and the central axis of the abdominal aortic aneurysm. The maximum diameter was recorded in the major axis from arterial intima to arterial intima (Figure 2).

Figure 2.

Definitions of measurement data. L = lumen length; D = Maximum diameter of abdominal aortic aneurysm; W = proximal neck width;β = proximal neck angle.

Image analysis and data measurement

The Mimics 17.0 workstation was used to assess AAA including measurements of the neck diameter, maximum diameter, lumen length, and infrarenal angle ∠β, which refers to the spatial angle between the proximal neck and the central axis of the abdominal aortic aneurysm.¹² Patients were divided into three groups based on magnitude of neck angle: group A (0°<∠β ≤ 30°), group B (30°<∠β ≤ 60°), and group C (60°<∠β). The measured data were recorded in accordance with international uniform standards.¹³ The geometric indices were calculated and automatically extracted based on the cavity centerline. All patients had infrarenal abdominal aortic aneurysms.

Image acquisition

All scans were obtained using a Philips Brilliance 256-slice spiral CT. The scanning parameters were as follows: tube voltage 100 kV, automatic tube current modulation, pitch 0.914, collimator width 0.625 mm/s × 128 rows, gantry rotation speed 0.4s/r, reconstruction layer thickness 0.9 mm, and reconstruction interval 0.45 mm. The contrast medium used was iodixanol (320gI/L), which was injected through the antecubital vein using a German Ulrich high-pressure syringe at an injection rate of 5.0 mL/s.

Three-dimensional model construction

The CTA DICOM data of the AAAs were processed using Mimics 17.0, with the grayscale threshold range set to 226HU-3071HU. We limited the target area from 2 cm above the infrarenal aortic aneurysm to the origin of the external iliac artery. The plane image extracted through segmentation was converted into the initial three-dimensional (3D) model of the abdominal aortic aneurysm. The contour of the target model was then edited for preliminary smoothing of the 3D model. The centerline of the geometric model of the abdominal aortic aneurysm was constructed. Figure 3(A) illustrates the grayscale threshold range of 226HU-3071HU as a first range mask, expressed as a two-dimensional model without Calculate 3D processing, and displays a complete 3D geometric model of an abdominal aortic aneurysm after Calculate 3D processing, following the removal of the non-target area mask using the Edit Masks tool. Figure 3(B) presents the model of an abdominal aortic aneurysm after preliminary smoothing with the Edit Contours tool, Wrap tool, and Smooth tool. The 3D model of the abdominal aortic aneurysm was exported as an STL file.

Figure 3.

A. The gray threshold obtained by the mask tool ranges from 226HU to 3071HU first range mask, 3D models clear non-target area masks; B. Abdominal aortic aneurysm model was denoised and smooth; C. Tetrahedral meshing of abdominal aortic aneurysm model.

Grid model construction

The 3D model generated was imported into Geomagic 2017, and the mesh was optimized using tools such as removing features, sandpaper, and reducing noise. The surface mesh was generated by redrawing the mesh to decrease the number of meshes and improve mesh quality. The surface patch was constructed through the appropriate surface function, the grid was further developed, surface fitting was completed, and the optimized model was saved as an STP-203 format file. In Solidworks 2017, we created entrance and exit planes perpendicular to the centerline and separated and retained the two ends of the centerline. The volume mesh type was set to tetrahedral mesh, the division method to the octree algorithm, and the mesh cell size to 3 mm. We set the boundary layer grid with an initial height of 1 mm, a layer height growth factor of 1.2, and a total of 3 layers. The volume and boundary layer meshes were generated, mesh quality was checked, the lowest value of mesh quality was set, and the mesh was smoothed as much as possible to improve the quality. Figure 3(C) displays the gridded tetrahedral model.

Finite element analysis

The sequence of analysis was as follows: the Solution interface in Ansys-Workbench 17.0 was opened, the created grid file was imported and the grid unit was defined as mm, the grid was checked and verified the absence of negative volume grids. The pressure-based solver was selected and the SST k-ω model initiated. Assuming that blood is an adiabatic, homogeneous, isotropic, incompressible Newtonian fluid with a steady flow, and setting the blood density at 1050 kg/m³ and the viscosity coefficient at 0.0035 Pa·s. This study conducts a steady-state analysis, referencing the maximum velocity within the cardiac cycle reported in previous studies at the inlet, which is approximately 0.4 m/s. A free outflow boundary condition is applied at the outlet with an outlet pressure of 0. The vessel wall is assumed to be a no-slip rigid tube, and the working pressure is set to the average arterial pressure of 13332.24 Pa (100 mmHg), with the influence of gravity neglected.^14,15 The CFD steady-state simulation of the mass conservation equation was solved, and the Navier–Stokes equation using the SST k-ω turbulence model and the second-order upwind scheme under shear stress transfer convergence. The flow field was initialized by setting the inlet plane velocity, using the 3D coupled solver, applying the SIMPLE algorithm for pressure-velocity coupling, and using the spatial discretization schemes based on the least squares element, standard, and second-order upwind for gradient, pressure, and momentum, respectively. The convergence criterion was set for continuity residual at 10⁻⁵. After several iterations, the calculation converged. The convergence results were Post-processed using Ansys-CFD-Post17.0 software and outputted as the blood flow diagram, flow velocity, wall shear stress, and wall stress distribution.

Statistical analysis

The data were expressed as mean ± standard deviation (variance ± SD). SPSS 25.0 software was used for statistical analysis; the F test was used for the variance homogeneity test, and the one-way analysis of variance (one-way ANOVA) was used to compare the data between groups. The LSD-t method was used for pairwise comparison. The difference was considered statistically significant with a p < .05.

Results

Primary clinical data and measurement data

Initially, data were collected from 42 patients, from which the following were excluded: two patients with lumen diameter less than 30 mm, five with other serious diseases, two who were unable to undergo CTA examination, two with poor or incomplete CTA image quality, one with CTA image layer distance greater than 2 mm, and one on whom a CTA image was unable to obtain. The final study cohort comprised 29 patients, divided into the three previously described groups: A (n = 8), B (n = 14), and C (n = 7). Most of the patients in the three groups were male, and the maximum diameter of the lumen was significantly different. There were no significant differences in age, coronary heart disease, hypertension, diabetes, blood pressure, peripheral arterial disease, proximal neck inflow width, and lumen length among the three groups (Table 1).

Table 1.

Data are mean ± standard deviation or n (%). For continuous variables p values are from analysis of variance and chi square for categorical variables. SBP = systolic blood pressure; DBP = diastolic blood pressure; IHD = ischemic heart disease; PVD = peripheral vascular disease; CVD = cerebrovascular disease. The same letter indicated no statistical significance between the groups (p > .05); Marked with different letters indicated statistically significant differences between groups (p < .05).

Patients	Group A (n = 8)	Group B (n = 14)	Group C (n = 7)	p value
Male sex	7 (87.5)	9 (64.3)	5 (71.4)	0.497
Age-years	69.13±10.91	70.71±7.27	68.00±11.86	0.817
SBP-mmHg	125.88±20.30	151.21±28.28	146.00±11.30	0.062
DBP-mmHg	82.25±10.10	86.43±9.30	93.00±4.20	0.072
CVD	4 (50.0%)	2 (14.3%)	1 (14.3%)	0.203
PVD	5 (62.5%)	10 (71.4%)	4 (57.1%)	0.882
IHD	2 (25.0%)	6 (42.9%)	2 (28.6%)	0.687
Diabetes	1 (12.5%)	6 (42.9%)	3 (42.9%)	0.324
Hypertension	3 (37.5%)	11 (78.6%)	6 (85.7%)	0.110
AAA diameter-mm	38.39±4.54a	46.14±12.81a	59.46±16.37b	0.009
Proximal neck width-mm	19.70±3.7	20.20±4.19	20.81±3.60	0.863
Lumen length-mm	59.11±18.35	78.02±22.80	88.90±29.32	0.058

Flow patterns

The intraluminal blood flow was not complicated when the streamline was small. The blood flow at the neck of the lumen was relatively straight in all three groups, and the blood flow velocity decreased slightly with the increased travel distance. When the blood flow entered the lumen expansion area, the blood flow velocity slowed. The streamline in the lumen cavity of group A was relatively straight and smooth. With the increase of streamline, a few turbulent lines appeared, and the overall flow mode was laminar-based mixed flow, continuing out through the distal outflow channel. The streamline of group B was initially straight, but with the increase of streamline, a relatively regular low-velocity vortex line appeared in the lumen cavity, and the streamline changed into a spiral, showing a mixed blood flow in the lumen, dominated by turbulence. As the streamline continued toward the outflow channel, it gradually reverted into laminar flow. In group C, a small amount of turbulence in the streamline was noted at the proximal neck, and the velocity increased at the corner of the neck then decreased gradually. As it continued into the lumen expansion area, the streamline formed an eddy current along the lumen cavity. The streamline was markedly chaotic and irregular with turbulent flow. As it entered the outflow channel, the streamline gradually became more regular, eventually reverting to laminar flow. The flow velocity in the outflow tract increased in all three groups. Figure 4 shows a chart of blood flow in the three AAA groups in the same state.

Figure 4.

The flow line distribution diagram of a case in group A, B, and C reflects the pattern of blood flow. The straight line indicates laminar flow, while the twisted and chaotic curve indicates eddy current and turbulence.

WS distribution

The wall stress distribution map shows the numerical simulation of the blood flow of the stress component, which was usually perpendicular to the surface section of the abdominal aortic aneurysm. The wall stress distribution map of all three groups as analyzed by CFD, are shown in Figure 5. The results demonstrated that the stress distribution on the AAA wall was uneven. Located at the maximum diameter of the abdominal aortic aneurysm lumen or the posterior wall of the abdominal aortic aneurysm lumen were often the principal areas of maximum stress distribution. The wall stress showed different degrees of gradient change, and most of the wall stress decreased gradually, then increased and declined from the inflow channel to the outflow channel. The range and size of the lumen changed with the structure of the lumen neck. The maximum wall stress of blood flow impact areas were 205.0 ± 84.7 Pa, 327.6 ± 113.2 Pa, and 657.3 ± 141.5 Pa in groups A, B, and C, respectively (Figure 5). The maximum wall stress gradually and significantly increased as the neck angle increased in each of the groups: B > A, and C > B; the peak wall stress appeared to increase in direct correlation to the increase of the proximal angle.

Figure 5.

In the wall stress distribution diagram of a case in group A, B, and C, the closer the color is to red, the higher the stress value is; the closer the color is to blue, the lower the stress value is; the arrow points to the area of high stress concentration.*p < .05 versus group A; **p < .01 versus group A.

WSS distribution

The wall shear stress distribution map shows the numerical simulation of the blood flow of the stress components, which were usually tangent to the surface of the abdominal aortic aneurysm. Comparison of the three groups as analyzed by CFD, are shown in Figure 6. The continuous color-coded spectrum indicates the wall shear stress. The results showed uneven shear stress distribution in the AAA wall; the neck of the aneurysm and the junction with the outflow tract were the main distribution areas of maximum shear stress, while the lumen was often at a relatively low level of shear stress. The wall shear stress showed a somewhat irregular gradient change, and most of the shear stress decreased gradually and then increased from the inflow channel to the outflow channel. The range and size of the lumen changed with the structure of the lumen neck. The maximum wall shear stress of the blood flow impact area increased significantly as the neck angle of each group increased: 4.68 ± 1.8 Pa, 6.85 ± 2.00 Pa, and 9.99 ± 1.34 Pa in groups A, B, and C, respectively. There were significant differences in maximum shear stress between groups as the neck angles increased: B > C, and C > B; the peak wall shear stress appeared to increase in direct correlation with increase of the proximal angle (Figure 6).

Figure 6.

The wall shear stress distribution diagram of one case in group A, B, and C shows that red approaches high stress values and blue approaches low stress values. The arrow points to the area of high stress concentration.*p < .05 versus group A; **p < .01 versus group A.

Velocity of flow

The velocity profile showed the numerical simulation of the blood flow of the stress component, which was usually tangent to the surface section of the abdominal aortic aneurysm. Comparison of the three groups, as analyzed by CFD, is shown in Figure 7. The results showed that the AAA intracavitary blood flow had a velocity distribution initially of fast, then slow, and then fast. Higher velocity values were demonstrated in the lumen’s inflow and outflow channels. Regarding the overall distribution, there was often an acceleration point proximally at the angle of the lumen neck. The larger the angle, the more pronounced the velocity. In contrast, the velocity distribution of the model with a smaller angle was relatively smooth. All three groups showed that flow velocity in the dilated area of the lumen was relatively low.

Figure 7.

The blood flow velocity distribution diagram of a case in group A, B, and C shows a rainbow gradient distribution from high to low in red to blue, and the arrow indicates the area of high blood flow velocity. *p < .05 versus group A; **p < .01 versus group A.

Multivariate analysis

The multiple linear regression analysis (Table 2) elucidated the relationships among wall stress size, wall shear stress, and flow velocity with various factors, yielding R² values of 0.296, 0.387, and 0.729, respectively. These results indicate that the independent variables accounted for 29.6% of the variation in wall stress size, 38.7% in wall shear stress, and 72.9% in flow velocity. ∠β demonstrated a significant positive correlation with wall stress size, wall shear stress, and flow velocity. Furthermore, the proportion of males, diabetes, and proximal neck width all exerted a significant negative correlation with flow velocity. In contrast, other variables, including age, gender, SBP, DBP, CVD, hypertension, PVD, diabetes, IHD, AAA diameter, proximal neck width, and lumen length, did not exhibit a statistically significant impact on either wall stress size or wall shear stress. Similarly, variables such as age, AAA diameter, lumen length, hypertension, CVD, PVD, and DBP failed to display a statistically significant impact on flow velocity.

Table 2.

The multiple linear regression analysis elucidated the relationships among wall stress size, wall shear stress, and flow velocity with various factors.

Model	Wall stress			Wall shear stress			Velocity
Model	Beta	t	p	Beta	t	p	Beta	t	p
Age	0.024	0.090	0.929	−0.149	−0.602	0.556	−0.092	−0.557	0.586
Male sex	−0.051	−0.245	0.810	0.166	0.857	0.405	−0.368	−2.866	<0.05
∠β	0.788	3.578	<0.001	0.642	3.123	<0.001	0.752	5.504	<0.001
AAA diameter	0.020	0.046	0.964	0.601	1.441	0.170	0.590	2.130	0.050
Proximal neck width	−0.008	−0.040	0.969	−0.057	−0.288	0.777	−0.389	−2.982	<0.01
Lumen length	−0.019	−0.046	0.964	−0.709	−1.844	0.085	−0.379	−1.486	0.158
Hypertension	0.081	0.341	0.738	0.025	0.113	0.912	0.174	1.181	0.256
Diabetes	−0.121	−0.574	0.574	0.041	0.209	0.837	−0.299	−2.279	<0.05
CVD	0.111	0.588	0.565	0.186	1.055	0.308	0.038	0.321	0.753
PVD	−0.220	−0.818	0.426	0.024	0.096	0.925	0.082	0.493	0.629
IHD	0.060	0.275	0.787	0.024	0.119	0.907	−0.243	−1.792	0.093
DBP	−0.052	−0.242	0.812	0.092	0.464	0.649	−0.025	−0.190	0.852
SBP	0.062	0.280	0.784	0.050	0.241	0.813	−0.353	−2.556	<0.05
R²	0.296	0.387	0.729

We develop three multiple regression models: model 1 (unadjusted); model 2 (model 1 plus proximal neck width, lumen length, diameter); model 3 (model 2 plus male sex, age,systolic blood pressure, diastolic blood pressure, cerebrovascular disease, ischemic heart disease, peripheral vascular disease, and diabetes, hypertension). Multiple regression models (Table 3) revealed ∠β to be independently predictive of the biomechanical index after adjusting for proximal neck width, lumen length, diameter, male sex, age, systolic blood pressure, diastolic blood pressure, cerebrovascular disease, ischemic heart disease, peripheral vascular disease, and diabetes, hypertension.

Table 3.

The multiple regression analysis for the three models and abdominal aortic aneurysm related factors to predict the biomechanical index.

Model	p value		p value		p value
WS-model 1		WSS-model 1		V-model 1
∠β	<0.001	∠β	<0.001	∠β	<0.001
WS-model 2		WSS-model 2		V-model 2
∠β	<0.001	∠β	<0.001	∠β	<0.001
Proximal neck	0.56	Proximal neck	0.7	Proximal neck	<0.05
lumen length	0.93	lumen length	<0.05	lumen length	0.19
Diameter	0.83	Diameter	0.14	Diameter	0.09
WS-model 3		WSS-model 3		V-model 3
∠β	<0.01	∠β	<0.01	∠β	<0.01
Proximal neck	0.97	Proximal neck	0.78	Proximal neck	<0.01
lumen length	0.96	lumen length	0.09	lumen length	0.16
Diameter	0.96	Diameter	0.17	Diameter	0.05
Male sex	0.81	Male sex	0.41	Male sex	<0.05
Age	0.93	Age	0.56	Age	0.59
SBP	0.78	SBP	0.81	SBP	<0.05
DBP	0.81	DBP	0.65	DBP	0.85
CVD	0.57	CVD	0.31	CVD	0.75
PVD	0.43	PVD	0.93	PVD	0.63
IHD	0.79	IHD	0.91	IHD	0.09
Diabetes	0.57	Diabetes	0.84	Diabetes	<0.05
Hypertension	0.74	Hypertension	0.91	Hypertension	0.26

WS=Wall Stress; WSS=Wall Shear Stress; V=Velocity.

Discussion

In prior research, severe neck angulation (>60°) has been associated with the occurrence, progression, and rupture of abdominal aortic aneurysms (AAA), as well as short-term poor outcomes.¹⁶ However, previous computational fluid dynamics (CFD) studies have had limitations such as limited angle coverage, observation of single fluid mechanics indices, idealized models, and single model analysis.^17–19 Our study aimed to address these limitations by creating precise 3D AAA models using actual patient CTA data, which has been shown to enhance the accuracy of anatomical and hemodynamic assessments in vascular research.²⁰

We categorized cases by increasing neck angles and performed finite element analyses using computational fluid dynamics for each group. This approach allowed us to explore the link between proximal neck angulation and various AAA biomechanical factors, such as wall stress, flow patterns, wall shear stress, and intracavity flow rate in greater detail.²¹ By comparing these factors across AAA models with varying neck angles, we aimed to understand their importance in forming a complete AAA hemodynamic system. This detailed analysis enhances our understanding of the hemodynamic and biomechanical impacts of neck angulation on AAAs, providing new insights that reinforce and extend previous research findings.

Algabri et al. observed eddy currents in an AAA model with a proximal neck angle of 79°, transitioning from laminar to turbulent flow.¹⁸ Kaewchoothong et al. suggested that eddy currents typically did not occur in a straight, healthy aorta, except when the surface was curved.¹⁹ In our study, using patient-specific models, we observed similar phenomena but with greater accuracy and relevance to clinical settings. For instance, in Algabri et al.'s idealized model, reducing proximal cervical lumen angulation resulted in weaker eddy currents and accelerated blood flow in the middle of the aorta.²² Our findings confirmed this but also demonstrated that the patient-specific geometries provided a more nuanced understanding of flow disturbances.

Arzani et al. used various methods to describe flow characteristics and found consistent vortices forming at the proximal end of all aneurysms.^23,24 Our study expanded on this by using more detailed and patient-specific geometries, showing how different neck angulations could affect the formation and intensity of these vortices, thus offering a clearer picture of the hemodynamic environment.²⁵

Overall, our results indicated that AAAs with larger proximal neck angulation generated high-velocity blood flow and turbulence at the neck, leading to higher wall stress and complex circulation patterns. In contrast, smaller proximal neck angulation resulted in less pronounced differences in velocity values, supporting and extending the conclusions of previous studies.

Xenos et al. observed that the peak wall stress increased initially with neck angle from 0° to 20° but slightly decreased at 30° and 40°.¹⁰ By using patient-specific models, our study confirmed these trends and provided more precise quantifications of the stress variations.²⁶ Subramaniam et al. emphasized the role of AAA shape and asymmetry in wall stress, which could be amplified by increasing proximal neck angle.^27,28 Our results reinforced this by showing significant differences in wall stress among groups, with greater angulation leading to higher stress, potentially influencing AAA development and prognosis.

Drewe et al. noted that peak wall shear stress increased with neck angle from 0° to 40°.²⁹ Dolan et al. suggested that high shear stress could cause endothelial injury, while low shear stress could lead to inflammation.³⁰ Our findings aligned with these observations, demonstrating that proximal neck angulation might be associated with AAA endothelial injury and dilation, though further research is needed to confirm this relationship.

In our study, the SST k−ω vortex viscous turbulence model was used to simulate blood flow, and Shek proposed its application in aneurysm treatment.³¹ However, we acknowledge limitations in our research, including the assumption of rigid aortic walls, the neglect of blood deformation effects, the assumption of Newtonian blood behavior, and the omission of factors like calcification, thrombosis, and wall thickness.^32,33 Despite these limitations, our use of patient-specific models represents a significant advancement over previous studies, offering more clinically relevant insights.³⁴ Our sample size was also limited to 29 patients with AAA, and baseline differences in AAA diameter existed among groups, potentially introducing bias.

Conclusions

In the analysis of computational fluid dynamics, the vertical stress and shear stress of the abdominal aortic aneurysm wall increased with the angle of the proximal aneurysm neck. The anterior wall and middle and inferior wall of the abdominal aortic aneurysm are often the areas of maximum vertical stress distribution in the analysis of computational fluid dynamics. In contrast, the angular proximal neck, iliac bifurcation, anterior wall, and inferior wall are often the areas of maximum shear stress distribution.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: 2022JJ40385, Hunan Provincial Natural Science Foundation of Youth Project; 2021SK51713, Hunan Province Clinical Medical Technology Innovation Guidance Project; 20224310NHYCG08, University of South China Clinical Research 4310 Program; 2023SK4041, Hunan Clinical Medical Research Center for thrombotic diseases; 20330046498, Hengyang science and technology innovation Project.

Ethical statement

ORCID iDs

Jie Chen

Guo-shan BI

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