Abstract

The objective of this research is to analyze the hemodynamic differences in five configurations of left subclavian artery (LSA) stent grafts after LSA endovascular reconstruction in thoracic endovascular aortic repair (TEVAR). For numerical simulation, one three-dimensional thoracic aortic geometry model with an LSA stent graft retrograde curved orientation was reconstructed from post-TEVAR computed tomography angiography (CTA) images, and four potential LSA graft configurations were modified and reconstructed: three straight (0, 2, and 10 mm aortic extension) and one anterograde configuration. The blood perfusion of the LSA, flow field, and hemodynamic wall parameters were analyzed. The vortex evolution process was visualized by the Liutex method which enables accurate extraction of the pure rigid rotational motion of fluid and is highly suitable for identifying the vortex structure of blood flow near the vessel wall. The average flow in the retrograde configuration decreased by 11.2% compared to that in the basic configuration. When the LSA stent graft extends in the aortic lumen, flow separation is observed, and vortex structures begin to form at the proximal inferior arterial geometry and the wall of the extension in late systole. A greater extension length and inflow angle upstream resulted in a greater oscillatory shear index (OSI) and relative residence time (RRT) on the nearby wall of the posterior flow field of the extension. Shorter intra-aortic extension length (<10 mm) and smaller LSA stent graft inflow angle (<120 deg) may be recommended in TEVAR, considering LSA perfusion and minimized flow field disturbance.

1 Introduction

Thoracic endovascular aortic repair (TEVAR) has become a standard method for treating thoracic aortic disease, including aortic aneurysms, dissection, penetrating aortic ulcers, and intramural hematoma [13]. For the aortic arch branches, reconstruction of the left subclavian artery (LSA) is more common than other branches. Endovascular LSA reconstruction provides minimal invasion and quick recovery, and recent data suggest that endovascular LSA reconstruction has similar perioperative outcomes to open reconstruction [4]. According to recent guidelines, LSA recanalization is strongly recommended for preserving blood perfusion in the central nervous system. Moreover, in patients with significant curves in the aortic arch, it is recommended that the aortic graft crossover the curve and land on a proximal straight section [5]. This helps avoid the bird beak phenomenon, which is closely associated with endoleak and retrograde dissection.

Endovascular LSA reconstruction techniques include the parallel graft technique and the fenestrated and branched TEVAR technique (F/B TEVAR). As an endoleak cannot be avoided in the parallel graft technique due to its construction, it is only used for emergency surgery or bail-out treatment and is not recommended as the first choice. Therefore, F/B TEVAR is assumed to be a potentially promising technique for endovascular arch repair [6]. Commercially available customized devices, physician-modified endografts, and commercial off-the-shelf devices are now widely used in F/B TEVAR. Among these techniques, LSA bridge stent grafting and aortic inner branch grafting are needed to reduce endoleaks and stabilize aortic grafts. In F/B TEVAR, when an inner branch exists, an original structure in company-designed devices or modified on the graft wall by physicians, the branched graft in the aortic lumen generally moves in two directions (antegrade or retrograde) to the blood flow while being parallel to the longitudinal axis of the main graft. For example, the Zenith arch branched device (COOK Medical, Bloomington, IN) and Relay branch thoracic stent-graft system (Terumo Aortic, Tokyo, Japan) are designed with antegrade inner branches, while the GORE TAG thoracic branch endoprosthesis is designed with an antegrade inner branch (W. L. Gore & Associates, Flagstaff, AZ). When there is no inner branch, the directions of bridging grafts are more complicated, which might be affected by the morphology of the branch artery, the type of aortic arch, the relative position of the origin of the branch artery, and the fenestration location of the main graft. Previous clinical research on TEVAR has focused only on serious complications, such as stroke, spinal cord ischemia, and endoleak [7]. Hemodynamic changes in the reconstructed LSA have seldom been studied. Some clinical statistical research has demonstrated the possibility of mural thrombus formation in stent grafts [8]. With the help of computational fluid dynamics, the effect of different LSA grafts on blood flow can be revealed, and the risk of thrombosis can be evaluated.

In this study, different LSA stent graft geometries were designed and reconstructed based on postoperative thoracic aortic geometry. Through numerical simulation, LSA perfusion differences and the hemodynamic characteristics of different LSA stent graft configurations were revealed, and wall parameter conditions and their distribution mechanisms were elucidated through vortex structure evolution. The results could help clinicians evaluate LSA perfusion and thrombotic risk associated with different LSA stent graft configurations in TEVAR.

2 Methods

2.1 Geometry.

This study was conducted in accordance with the principles of the Declaration of Helsinki and met the requirements of medical ethics. The ethical review committee of the center approved this research, and our study was purely observational and retrospective in nature and used anonymous data.

The patient involved in this study was a 68-yr-old male patient with a Stanford type B aortic dissection who was sent for emergency surgery with a chief complaint of sudden back pain with a tearing sensation for 6 h. Pre-operative computed tomography angiography (CTA) revealed proximal dissection close to the LSA, and perfusion of the distal visceral branches was not significantly affected. A preloaded fenestration thoracic aorta stent graft system with an embedded inner branch (diameter, 36–28 mm; length, 240 mm; WeFlow-Tbranch Stent Graft System, Hangzhou Endonom Medtech, China) was adopted, and a bridging graft (12×110 mm) was implanted from the LSA to the inner branch after the aorta stent graft was released. CTA was performed one week after TEVAR with a Toshiba Aquilion 64 CT scanner (0.78×0.78 mm imaging resolution; 1 mm slice thickness). The operation was successful, with no major adverse events occurring within the hospital or during the one-year follow-up.

The establishment of the vascular model could not be achieved according to a mathematical model due to individual variations among patients. We preserved the primary surface details of the blood vessels while smoothing out areas with calcification and secondary vascular resection, all under the supervision of a vascular surgeon. The original blood flow area in each CTA slice was accurately segmented by professional vascular surgeons. During this process, the calcification of the vessel wall and the secondary branch vessels were excluded from segmentation. The target fluid domain (Fig. 1) was reconstructed with high precision using mimics (Materialize, Leuven, Belgium), which included the ascending aorta (AA), descending aorta (DA), brachiocephalic trunk (BT), left common carotid artery (LCCA), and LSA. The low smoothness area of the preliminary model underwent preliminary smoothing using 3-matics (Materialize, Leuven, Belgium) and was reconstructed with triangular surfaces based on the trend and curvature of the blood vessels to ensure smoothness with respect to the surrounding vessel wall. Subsequently, non-uniform rational B-splines (NURBS) surfaces were reconstructed according to triangular surfaces, while both vessel inlet and outlets were set perpendicular to the axial blood flow in geomagicstudio (3D Systems, Morrisville, NC). Manual adjustments were made to address high degree of intersection positions between vascular branches on the aortic arch in order to prevent undesirable angles. Additionally, to ensure minimal stent intervention in the aortic geometry during surface and mesh editing, while avoiding self-intersecting surfaces, the graft wall of the intra-aortic extension was modified to consist of two layers with a distance of 1.0 mm. The inner wall is connected to the LSA stent graft wall, while the outer wall is connected to the aortic arc wall.

Fig. 1
Thoracic aortic geometry model and five LSA stent graft configurations. (a) Digital subtraction angiography showing the configuration of the aortic and LSA grafts after endovascular repair. (b) The model was reconstructed from post-thoracic endovascular aortic repair CTA images. Case E was directly reconstructed with CTA, and the other four configurations of LSA stent grafts were created based on patient E. The details are described in Table 1. AA, ascending aorta; BT, brachiocephalic trunk; LCCA, left common carotid artery; LSA, left subclavian artery.
Fig. 1
Thoracic aortic geometry model and five LSA stent graft configurations. (a) Digital subtraction angiography showing the configuration of the aortic and LSA grafts after endovascular repair. (b) The model was reconstructed from post-thoracic endovascular aortic repair CTA images. Case E was directly reconstructed with CTA, and the other four configurations of LSA stent grafts were created based on patient E. The details are described in Table 1. AA, ascending aorta; BT, brachiocephalic trunk; LCCA, left common carotid artery; LSA, left subclavian artery.
Close modal

Left subclavian artery branched stent grafts, which are adopted or potentially used in clinical practice and have the same geometry as the aortic arch, were created in four categories. Basic (case A), straight (cases B and C), anterograde (case D), and retrograde (case E) configurations were used for a total of five configurations obtained by varying the length, orientation, and curvature of the intra-aortic extension of the LSA branched stent graft (Fig. 1 and Table 1). Case E was directly reconstructed with CTA, and the other four configurations of LSA stent grafts were created based on the configuration of case E. Case A had no intra-aortic extension and was similar to the pre-operative geometry. As we mainly focused on the parallel comparison of the postoperative effects of different LSA stents rather than the pre-operative effects, we chose case A as the baseline configuration. All five configurations have identical inlets and outlets, and the boundaries were trimmed to a flat plane along the inner normal direction of the wall.

Table 1

Geometry details of five left subclavian artery stent graft configurations

Stent nameDescriptionInternal diameter (mm)Intra-aortic length (mm)Stent graft inflow angle (deg)
ABasic configuration120120
BStraight configuration type 1122120
CStraight configuration type 21210120
DAnterograde orientation (upstream facing orifice)12200
ERetrograde orientation (downstream facing orifice)1220180
Stent nameDescriptionInternal diameter (mm)Intra-aortic length (mm)Stent graft inflow angle (deg)
ABasic configuration120120
BStraight configuration type 1122120
CStraight configuration type 21210120
DAnterograde orientation (upstream facing orifice)12200
ERetrograde orientation (downstream facing orifice)1220180

Stent graft inflow angle refers to the angle between the centerline of the stent graft and the axial flow velocity direction.

2.2 Computational Mesh and Mesh Sensitivity.

The fluid domains of five different LSA branched stent grafts were unstructured and tetrahedral meshed with a maximum size of 1.1 mm using icem (ANSYS, Canonsburg, PA). The flow field near the aortic wall was captured by ten prism layers, where the first layer thickness was approximately 0.08 mm, and subsequent layers grew exponentially with a height ratio of 1.05 until the thickness of the last layer matched the core mesh size. The five computational domains of cases A, B, C, D, and E have 3,825,024, 3,826,897, 3,834,782, 3,839,402, and 3,808,681 elements, respectively. Based on evaluating the peak systolic wall shear stress (WSS) on the aortic arch and at a specific location on the descending aorta, refined meshes of case E with 6,803,263 elements were created to verify the mesh independence (Fig. 2). Additionally, we have ensured time independence of the current mesh by reducing the computational time-step to 0.00005 s.

Fig. 2
Mesh and time independence validation
Fig. 2
Mesh and time independence validation
Close modal

2.3 Boundary Conditions.

Due to the lack of patient-specific velocity and pressure profiles, the boundary conditions used in this study were set according to in vivo measurements (slightly modified from a previous study [9]). Time-varying mass flow rate profiles at the AA inlet and DA outlet and time-varying pressure profiles at the BT, LCCA, and LSA outlets are shown in Fig. 3. The outlets of the right subclavian artery and right common carotid artery (branches of the BT) were assumed to experience the same pressure conditions [10]. The velocity and pressure profiles were composed by a Fourier series using eight harmonics. The inlets were subjected to a uniform flat inflow profile, while the pressure distribution was set perpendicular to the boundary of all configurations. A flat or plug pulsatile velocity profile applied at the aortic inlet has been confirmed by various in vivo measurements of different animal models distal to the aortic valve, and mild helical flow in the AA has been neglected [10]. The no-slip boundary condition at the wall, assumed to be rigid, was applied. The heart rate was set to approximately 67 beats/min (T = 0.89 s). The same boundary conditions were imposed on all five LSA branched stent graft configurations for comparison purposes. The turbulence degree of all the inlets and outlets is set to 5% [11]. Due to the twisting and squeezing of blood flow into the ascending aorta [12], there is a slight spiral flow at the inlet of the ascending aorta. Hence, we opt for a turbulence intensity that is relatively higher, specifically 5%. The hydraulic diameter of reverse flow is set at each inlet and outlet (Table 2). Four key time points (t1–t4) were set at the acceleration, peak, deceleration, and end of systole, and two key time points (t5 and t6) were set at the peak and end of diastole in sequence. The corresponding calculated data were analyzed for instantaneous results.

Fig. 3
Boundary conditions of the model. Time-varying mass flow rate profiles at the AA inlet and DA outlet and time-varying pressure profiles at the BT, LCCA, and LSA outlets. AA, ascending aorta; DA, descending aorta; BT, brachiocephalic trunk; LCCA, left common carotid artery; LSA, left subclavian artery.
Fig. 3
Boundary conditions of the model. Time-varying mass flow rate profiles at the AA inlet and DA outlet and time-varying pressure profiles at the BT, LCCA, and LSA outlets. AA, ascending aorta; DA, descending aorta; BT, brachiocephalic trunk; LCCA, left common carotid artery; LSA, left subclavian artery.
Close modal
Table 2

Hydraulic diameter settings of outlets

Boundary nameAABT-1BT-2LCCALSADA
Hydraulic diameter (mm)41.04.729.786.348.7924.0
Boundary nameAABT-1BT-2LCCALSADA
Hydraulic diameter (mm)41.04.729.786.348.7924.0

2.4 Calculation Settings.

Blood is considered an incompressible, homogeneous, and Newtonian fluid with a viscosity of 3.5 × 10−3 Pa·s and a density of 1050 kg/m3 [13]. Shear rates in large arteries are predominantly high, and the viscosity of blood can reach the high shear rate limit of 3.5 × 10−3 Pa·s [14]. The maximum Reynolds number (Remax) of the five cases at the LSA outlet is approximately 6702 at peak systole, and the Womersley number (α) based on the average cross-sectional area is 6.4. For unsteady pulsatile flow, turbulence occurs at a Reynolds number much larger than expected for steady flow. A previous experimental study showed that the critical Reynolds number Rec for unsteady flow takes the form of Rec = k·α, with k ranging from 250 to 1000 [15]. When the maximum Reynolds number is greater than the critical Reynolds number threshold range, the flow is assumed to be turbulent.

Numerical solutions were obtained using ansysfluent (v15.0, ANSYS, Canonsburg, PA), and a scale-adaptive simulation turbulence model was applied for simulation, which exhibits both steady solutions and scale resolving characteristics depending on the flow situation [16]. The calculation of the scale-adaptive simulation method in the unstable flow region is similar to that of large eddy simulation, and the calculation in the steady-state region is similar to that of the Reynolds-averaged Navier–Stokes equations, which can ensure the calculation accuracy and reduce the calculation time. The pressure implicit with splitting of operators scheme was used to solve the pressure–velocity coupling field, the second-order central difference was used for space integration, and the second-order Euler method was used for time integration with a fixed time-step of 10−4 s. The maximum root-mean-square residual was set to 10−3 as a convergence criterion. To avoid the influence of initial conditions on the calculation results and to achieve a periodically stable state of the flow field, each simulation continued until a converged cyclic solution was reached, and a total of ten cycles were calculated for each model. The tenth cycle calculation results were used for instantaneous analysis, and only the sixth to tenth cycle calculation results were counted for time-averaged analysis.

2.5 Hemodynamic Parameters.

Computational fluid dynamics results were analyzed using cfdpost (v15.0, ANSYS, Canonsburg, PA) and tecplot 360 (Tecplot Inc., Bellevue, WA). A number of WSS-based parameters are widely accepted as indicators of abnormal flow and are analyzed to identify potentially thrombogenic areas. The time-averaged WSS (TAWSS) is a parameter that represents the mean value of the WSS over a period of time; low TAWSS values (<0.4 Pa) are known to stimulate a proatherogenic endothelial phenotype, and high TAWSS values (>18 Pa) have been identified as an indicator of an area at risk of platelet activation [17]. The TAWSS was defined as

where ti and tf denote the initial and final times of a statistical period, respectively, and τw denotes the value of the WSS vector.

The oscillatory shear index (OSI) is a parameter that describes the cyclic departure of the WSS vector from its predominant axial alignment. A high OSI (>0.25) induces perturbed endothelial alignment and ultimately results in intimal hyperplasia [18], defined as
The relative residence time (RRT) is a combination of OSI and TAWSS and is related to the low-velocity flow recirculation zone, particle near-wall residence time, and in vivo endothelial permeability [19] and is defined as
A vortex is intuitively recognized as the rotational/swirling motion of a fluid. Several vortex identification criteria have been developed for visualizing vortex structures and their evolution in turbulence, including the Q-criterion [20], λ2-criterion [21], and λci-criterion [22]. In this research, we use the new vortex visualization method, Liutex, to visualize the vortex evolution process, which is more accurate than the traditional method for capturing the evolution process of vortex structures near walls. The Liutex method systematically solved the problem of how to derive pure rigid rotating parts from fluid motion [23], which could eliminate shear deformation and represent local rotation [24]; thus, the analysis of the vortex structure near the vessel wall can provide an in-depth and clear interpretation of the reason for the formation of the wall parameter distribution. The evolution of the vortex structure in the vasculature may be closely related to the formation of intracavitary thrombi. Liutex decomposes the fluid velocity gradient as

where R represents the local rigid rotation, and NR represents the nonrotational rotation. We display the blood flow vortex evolution process by Liutex through user-defined functions implementation.

3 Results

3.1 Left Subclavian Artery Blood Perfusion Comparison.

Figure 4 shows a comparison of the instantaneous, average, and peak LSA outlet flow rates among the five configurations. The instantaneous flow rates of the five configurations had almost the same variation trend during the cardiac cycle (Fig. 4(a)), but the average and peak flow rates were quite different (Fig. 4(b)). The average LSA outlet flow rate of case A was approximately 1.85 L/min, and the peak flow rate was approximately 6.80 L/min. Compared with those of the basic configuration, the average flow rates of configurations B, C, and E decreased the most significantly, that of case E decreased by 11.2%, and that of case D, the only configuration, increased by 3.19%. Similarly, the peak flow rate of all the other configurations decreased, and that of case E decreased the most significantly, by 9.28%. In addition, the average flow rate of case C was lower than that of case B. The flow rate results indicated that LSA perfusion may decrease as the intra-aortic extension length and angle of the LSA stent graft to the upstream increased.

Fig. 4
Comparison of the left subclavian artery outlet flow rate among the five configurations. The instantaneous flow rate of the five configurations had similar variation trends during the cardiac cycle (a). However, compared with those in case A, the peak flow rates (b, dots) and average flow rates (b, bars) change in the other four configurations. In particular, case E suffers a significant decrease in both the peak flow rate and average flow rate.
Fig. 4
Comparison of the left subclavian artery outlet flow rate among the five configurations. The instantaneous flow rate of the five configurations had similar variation trends during the cardiac cycle (a). However, compared with those in case A, the peak flow rates (b, dots) and average flow rates (b, bars) change in the other four configurations. In particular, case E suffers a significant decrease in both the peak flow rate and average flow rate.
Close modal

3.2 Flow Field Comparison and Analysis.

Figure 5 shows the streamlines at t2 for the five-stent graft configuration. Since the same boundary conditions were imposed on all five configurations and to highlight the differences between different configurations, cases B, C, D, and E are shown locally. This way of analyzing the results will be used in the following results. In general, due to the decrease in vascular diameter, blood flow accelerates after entering the BT, LCCA, and LSA, and part of the flow field becomes disrupted. Blood flow decreased significantly after these branches passed through the aortic arch. For cases B, C, D, and E, due to the influence of the intra-aortic extension, the streamline was disrupted at the posterior flow field of the aortic arch. In particular, since E is downstream of the orifice and the intra-aortic extension of the graft reduces the flow area in the aortic arch, blood flow is obviously accelerated under the stent graft. Although the peak velocity of blood flow in systole is relatively high and the flow field is relatively uniform, flow field disorder could still be observed inside and in the rear of the LSA stent graft, which indicates that intra-aortic extension will have a certain impact on the flow field inside the aortic arch and LSA. An in-depth investigation of the characteristics of the flow field is illustrated by vortex structure evolution throughout the whole cardiac cycle.

Fig. 5
Streamlines in the thoracic aorta model
Fig. 5
Streamlines in the thoracic aorta model
Close modal

Figure 6 shows the vortex structure evolution in five LSA branched stent graft configurations at different time points (Liutex = 50). In the early systole (t1), the vortex structures in the last period in the aortic arch gradually dissipated and moved downstream. Vortex structures begin to form at the proximal inferior arterial geometry, and the wall of the LSA branched stent graft undergoes intra-aortic extension in late systole (t3). These vortex structures twisted, merged, moved downstream (t4), gradually fragmented, and dissipated at the distal end of the aortic arch at late diastole (t6).

Fig. 6
Vortex evolution of five left subclavian artery stent graft configurations in a cardiac cycle (Liutex = 50), vortices are shaded in small rainbow as velocity magnitude
Fig. 6
Vortex evolution of five left subclavian artery stent graft configurations in a cardiac cycle (Liutex = 50), vortices are shaded in small rainbow as velocity magnitude
Close modal

Groups of vortex structures that formed from intra-aortic extension evolved and fragmented in the posterior flow field of the LSA stent graft. The strength and influence range of vortex structures generated by five stent graft configurations differ from one another. Few vortex structures are generated in case A throughout the cardiac cycle. The increase in graft intra-aortic extension length is directly proportional to the augmentation of vortex formation, with case E exhibiting the most pronounced effect. Due to the retrograde-oriented configuration, intra-aortic extension severely impedes blood flow in the aortic arch, and large groups of small vortex structures continue to interact with the arterial wall.

3.3 Hemodynamic Markers of Thrombosis.

The results of our simulations demonstrate that when the stent graft extension length ranges from 0 to 10 mm (cases A, B, and C) and the inflow angle is less than 120 deg (cases C and D), there is a slight impact on the LSA perfusion(<4.26%) and downstream wall parameters. However, the most remarkable changes of the effect occurred in case E (length > 10 mm, inflow angle = 180 deg).

Due to the reduction in blood flow area in the aortic arch caused by intra-aortic extension of the LSA branched stent graft, there was a slight increase in TAWSS on the adjacent wall of the intra-aortic extension of the graft, specifically in zones a (≈0.6 Pa), b (≈0.75 Pa), and c (≈1 Pa). Notably, zone d exhibited the most significant increase (≈2.5 Pa) compared to case A (≈0.5 Pa).

Compared to the corresponding regions (OSI ≈ 0.25) in case A, there was a significant increase in OSI observed in zones a′, b′, c′, and e′ (>0.4), while interestingly, zone d′ exhibited consistently low values below 0.2 throughout the entire region. Based on Fig. 6, zones a′, b′, c′, and e′ were continuously influenced by small vortex structures present in the nearby flow field during the entire cardiac cycle. These vortices induced frequent alterations in both velocity and direction of blood flow, causing deviation of the WSS vector from its predominant axial orientation and ultimately resulting in an elevation of OSI. The OSI at the proximal end of the LSA exhibited a notable and significant increase, approximately reaching 0.4.

The RRT distributions of the five configurations exhibited a significant increase in zones of e″ (>30) and c″ (≈20), while experiencing a slight increase in a″ and b″ (≈12), and a decrease in d″, as compared to the corresponding regions (≈2) of case A. The OSI and RRT generally exhibit an increase with the extension length of intra-aortic segment and the upstream inflow angle.

4 Discussion

This study showed that different LSA stent graft configurations after TEVAR have different intra-aortic hemodynamics, influencing both LSA blood flow and the risk of postoperative thrombosis.

In F/B TEVAR, when an inner branch exists, an original structure in company-designed devices or modified on the graft wall by physicians, the branched graft in the aortic lumen generally moves in two directions (antegrade or retrograde) to the blood flow while being parallel to the longitudinal axis of the main graft. For example, the Zenith arch branched device (COOK Medical) and relay branch thoracic stent-graft system (Terumo Aortic) are designed with antegrade inner branches, while the GORE TAG thoracic branch endoprosthesis is designed with an antegrade inner branch (W. L. Gore & Associates). When there is no inner branch, the directions of bridging grafts are more complicated, which might be affected by the morphology of the branch artery, the type of aortic arch, the relative position of the origin of the branch artery, and the fenestration location of the main graft. Previous clinical research on TEVAR has focused only on serious complications, such as stroke, spinal cord ischemia, and endoleak [7]. Hemodynamic changes in the reconstructed LSA have seldom been studied.

To ensure that the simulation results were reliable and reasonable, the flow rates of the ascending aorta and descending aorta were derived from a previous magnetic resonance imaging study in vivo, and the deduced pressure was applied at the branch vessel outlets of the aortic arch [9,10]. The mass flow inlet and pressure outlet boundary conditions have been widely used in modeling the aortic arch [9,25,26]. Moreover, the reliability of the vascular geometry reconstruction, mesh generation, and analysis methods adopted in this paper were verified in our previous study.

In early clinical practice, the LSA usually underwent embolization and was covered by an aortic graft when the aortic lesions reached zone 2. However, according to recent guidelines, LSA recanalization is strongly recommended for preventing spinal cord injury, potentially reducing stroke risk and preventing other ischemic complications [3]. Continuous blood flow to the LSA is generally regarded as a technical success in LSA recanalization, but blood flow or pressure in the LSA is seldom measured. In fact, reversed flow in the left vertebral artery could still be identified in some fenestrated and branched patients. According to the simulation results in this study, there are perceptible differences in the perfusion of the five LSA stent graft configurations, especially for case E. The anterograde configuration (case D) exhibited increased perfusion, while the retrograde configuration (case E) showed the smallest perfusion. Straight configurations (cases B and C, Fig. 3) fell somewhere in between.

Studies on LSA perfusion are limited; therefore, the clinical significance of the 11.2% decrease in blood flow in case E is difficult to evaluate. Generally, revascularization is not needed when the decrease in subclavian artery flow caused by subclavian artery stenosis is asymptomatic [27]. However, when the internal mammary artery is used for coronary bypass, a subclavian artery stenosis >75% is recommended for revascularization [28]. This criterion is made mainly according to the critical stenosis theory, which indicates that blood flow decreases sharply when stenosis reaches a certain level. An 11.2% decrease in blood flow requires more than 80% stenosis [29]. In this manner, case E may exert a subtle influence on the general population. However, in situations where the blood supply of the LSA plays a crucial role in downstream perfusion, such as via the dominant left vertebral artery, preservation of pre-existing left internal mammary artery coronary bypass grafts or left upper extremity dialysis access, it may be necessary to avoid constructing case E.

Aortic graft thrombosis is more commonly reported after endovascular abdominal aneurysm repair, with a morbidity of approximately 10–20% [30]. Compared to the specific configuration of main aortic endograft-iliac endografts in endovascular abdominal aneurysm repair, the configuration of the main aortic endograft was straight, which may be related to fewer thrombotic events. However, when a thrombus is formed in a thoracic aortic endograft, it can develop rapidly and become catastrophic [31,32]. Moreover, when the LSA was reconstructed, the inner branch or bridging grafts markedly disturbed the original flow (Fig. 4). Due to the use of the same boundary conditions and similar LSA stent grafts, the differences in the hemodynamic parameters (Fig. 7) among the five configurations were qualitatively small for the ascending and descending aorta. However, the flow field of the aortic arch is greatly affected. The simulation results showed that the TAWSS only obviously differed near the intra-aortic extension region of the LSA stent graft. The presence of the stent graft in the aortic arch reduces the blood flow area, resulting in an increased velocity gradient and subsequently leading to a remarkable elevation in TAWSS. In the posterior flow field of the LSA stent graft intra-aortic extension, large vortex structures twisted, merged, gradually fragmented, and dissipated. During almost the whole cardiac cycle, groups of small vortex structures continuously affect the magnitude and direction of the force on the nearby wall, which inevitably leads to low TAWSS and high OSI and further creates a high RRT, indicating that the blood flow is not well transported here, and the possibility of blood substance deposition is increased, leading to an increase in thrombosis risk [33]. For the five configurations, this process is inconspicuous in A, B, and C but prominent in D and E (Fig. 6), which indicates that the intra-aortic extension configuration always has a certain impact on the posterior flow field of the LSA stent graft intra-aortic extension and a higher RRT level on the nearby vascular wall, which increases the risk of thrombosis. In terms of subsequent thrombosis risk after TEVAR, case E suffers the most, followed by D, and the straight configuration is better with a smaller intra-aortic extension length.

Fig. 7
TAWSS, OSI, and RRT distributions on the anterior (right) and posterior (left) walls of the thoracic aorta and branches. The TAWSS increased on the nearby wall of the graft intra-aortic extension zone, including zones a, b, c, and d and zone d. The OSIs of zones a′, b′, c′, and e′ increased, and those of zone d′ decreased. The RRT of zones e″ and c″ in cases E and D significantly increased, a″ and b″ in cases B and C slightly increased, and d″ in case E decreased. TAWSS, time-averaged wall shear stress; OSI, oscillatory shear index; RRT, relative residence time.
Fig. 7
TAWSS, OSI, and RRT distributions on the anterior (right) and posterior (left) walls of the thoracic aorta and branches. The TAWSS increased on the nearby wall of the graft intra-aortic extension zone, including zones a, b, c, and d and zone d. The OSIs of zones a′, b′, c′, and e′ increased, and those of zone d′ decreased. The RRT of zones e″ and c″ in cases E and D significantly increased, a″ and b″ in cases B and C slightly increased, and d″ in case E decreased. TAWSS, time-averaged wall shear stress; OSI, oscillatory shear index; RRT, relative residence time.
Close modal

5 Limitation

The current study had several limitations. The Windkessel models have not been employed for the outlet boundary conditions, and thus the presented results for each case do not accurately reflect physiological aspects but rather a more engineering-oriented approach. The utilization of the rigid wall assumption in numerical simulations of the aortic arch is less likely to accurately predict the Windkessel effect and has been observed to overestimate WSS by 29% when compared to fluid–structure interaction models; however, it does not appear to remarkably impact the distribution of WSS. Moreover, most of the reconstructed aortic arch and LSA areas are covered by rigid stents, which makes the assumption of rigid walls more reasonable. Due to the lack of in vivo measurement data, the blood flow and vessel wall parameter results obtained by numerical simulation cannot be compared with those of patients without pre-operative data; the sample size of LSA stent grafts is small, and the conclusions of this paper will be verified by more samples and experiments in subsequent studies. The simulation results obtained in this paper may exhibit quantitative discrepancies from those of individual patients, but a qualitative comparison of five configurations remains relatively accurate. In future studies, the in vivo measurement data of patients will be integrated for further investigation.

6 Conclusions

Among the five configurations of LSA stents, the retrograde configuration (case E) remarkably reduces perfusion in the LSA and affects wall parameters near the intra-aortic extension to a greater extent. The recommendation for enhancing LSA perfusion and minimizing flow disturbance on the adjacent wall of the posterior flow field is to consider a shorter length (<10 mm) for the intra-aortic extension and a smaller inflow angle (<120 deg) for the LSA stent graft.

Author Contribution Statement

All the authors listed contributed to the study.

Funding Data

  • National Key Research and Development Program of China (2022YFC3006203; Funder ID: 10.13039/501100002855).

  • Shanghai Sailing Program (Grant No. 22YF1422700; Funder ID: 10.13039/501100003399).

  • National Natural Science Foundation of China (62073309; Funder ID: 10.13039/501100001809).

  • Guangdong Basic and Applied Basic Research Foundation (2022B1515020042; Funder ID: 10.13039/501100021171).

  • Shenzhen Engineering Laboratory for Diagnosis & Treatment Key Technologies of Interventional Surgical Robots (XMHT20220104009).

Conflict of Interest

The authors declare that they do not have anything to disclose regarding any conflicts of interest related to this manuscript.

Ethics Approval

This study was conducted in accordance with the principles of the Declaration of Helsinki and met the requirements of medical ethics.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

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