Clinical data and images were acquired from a patient with a large aneurysm arising from the inferior wall of the aortic arch. The patient underwent TEVAR with a single-branched Nexus™ device. Figure 2 outlines the timeline of the case being studied, with reconstructions from clinical images showing the progression of the case. Ethical approval was obtained from the local Ethics Committee, and written consent was given by the patient.

The aneurysm, measuring 9.6 × 6.0 × 5.9 cm in the aneurysmatic sac, led to compressions in the distal pulmonary vessels but there were no morphometric changes to the innominate artery (IA), left common carotid (LCC) artery and left subclavian artery (LSA). Pre-intervention CT images with measurements of diameters and distances at three different locations are shown in Figure 3.

The patient was treated with TEVAR using the Nexus™ device; the intervention was carried out following a debranching procedure to set up a bypass between the right common carotid (RCC) and LCC, as well as the LCC and LSA. The procedure was successful and restored flow in the arch whilst successfully excluding the aneurysm, with a suitable proximal sealing length of 3.5 cm from the IA, greater than the minimum recommended length of 3.0 cm. The measured landing diameter of the ascending aorta was 38 mm, and that of the device was 43 mm, thereby producing an oversize ratio of 13.2%. The aneurysmal sac was successfully sealed, both LCC-RCC bypass and LCC-LSA bypass were patent. However, follow-up scans indicated the LCC-RCC bypass remained patent whilst the LCC-LSA bypass was compromised with a thrombus in the bypass near the LCC vascular stroma. A final follow-up of the patient 10 months after the intervention revealed the formation of an aneurysmal sac in the ascending aorta with migration of the ascending module of the device and a suspected leak or tear in the ascending aorta.

The patient had other comorbidities which needed to be taken into consideration during the treatment planning stages. Prior to intervention, the patient was on alendronate 10 mg OD, atorvastatin 20 mg OD, folic acid 5 mg BD, methotrexate 20 mg weekly, omeprazole 20 mg OD, prednisolone 5 mg BD. Following the intervention, the medication was adjusted to alendronate 70 mg OD, aspirin 75 mg OD (for 3 months), atorvastatin 20 mg OD, bisoprolol 1.25 mg OD, clopidogrel 75 mg OD (for 3 months), folic acid 10 mg weekly, methotrexate 15 mg weekly, omeprazole 20 mg OD, prednisolone 10 mg OD.

Anatomically accurate 3D geometries were reconstructed based on CT scans acquired using an ECG-gated spiral CT scanner (Siemens Somatom) at various stages as described in Figure 2. Image segmentation and 3D reconstruction of the aorta were performed using an image processing software, Mimics (v20, Materialise, Leuven, Belgium). A thresholding technique was adopted to isolate the regions of interest (ROI). User-defined lower and upper limits of grayscale intensity were set for thresholding, with a typical lower limit of 270–280 HU and an upper limit of 2,000 HU or above depending on the image resolution. This produced initial 2D masks on all the available slices. A split mask function was then used to separate the ROI from unwanted neighboring tissues that might have been included in the initial masks. The separated masks were manually inspected and modified if necessary to ensure all pixels in the targeted vessels were selected. Finally, the reconstructed geometries were smoothed using the Discrete Gaussian filter based on a linear smoothing enhancement algorithm. The smoothing function requires a smoothing factor (within range 0–1) and the number of iterations (within range 1–500) to be specified. A specific “compensate shrinkage” feature was enabled to preserve the shape of the geometry, thereby preventing the lumen of the aorta and its branches from shrinking. This was ensured by comparing vessel diameters extracted from the reconstructed 3D surface with those measured in the CT images at multiple locations of interest. Sensitivity tests indicated that setting a smoothing factor of 0.1 and 50 iterations for each stage of smoothing produced reliable reconstructions used in this study. Figure 4 shows the pre-TEVAR geometry which featured a large aortic arch aneurysm in the inferior radius of the arch and three supra-aortic branches emerging from the arch. The model also included the right brachiocephalic artery and RCC which bifurcate from the IA, resulting in four model outlets in the arch. The post-TEVAR geometry (Figure 3) incorporated the implanted device where the two modules were considered as one body and connected with the unstented portions of the aorta. The IA branch and its bifurcation were included while the LCC and LSA were excluded as they were covered by the main module. As a result, the post-TEVAR geometry had two outlets in the arch.

Mesh generation was carried out using ANSYS ICEM CFD (v15.0, ANSYS Inc., Canonsburg, PA, USA). For haemodynamic analysis, unstructured meshes consisting of 10 prismatic boundary layers at the wall were generated with approximately 6.8 and 5 million elements in the post-TEVAR and pre-TEVAR geometries respectively. For biomechanical structural analysis, a constant wall thickness of 1.4 mm was applied to the reconstructed 3D luminal surface, creating a solid volume representing the aortic wall. Figure 5 shows the solid domain geometry consisting of 6.8 million elements and the delineation of the stented and unstented regions.

Flow in the aorta was described by the transient, three-dimensional equations for conservation of mass and momentum. Blood was modelled as a Newtonian fluid with a constant density of 1,060 kgm⁻³ and dynamic viscosity of 0.004 Pa s. Based on the measured peak flowrate of 2.34 × 10⁻⁴m³/s and inlet area of 993.13 mm², the peak Reynolds number was 2,182.3 and the corresponding Womersley number was 19.2. This combination indicated that flow in the ascending aorta was likely to be disturbed (20), hence the need to employ the SST-Tran (shear stress transport—transitional) model, which has been shown to be more suitable for physiological flows involving potential transition from laminar to turbulent flow (21, 22).

In order to solve the flow governing equations numerically, suitable boundary conditions at the inlet and outlets are required. These should, as much as possible, represent the flow conditions specific to the patient and the stage of treatment being considered. The inflow waveform was adapted from a previous study (22) and then adjusted to represent the recorded cardiac output of the patient and further tuned to the dimensions of the model inlet (23, 24). The lack of patient-specific inflow data, such as 4D Flow MRI specific to the patient, necessitated the implementation of a novel method for generating realistic 3D inlet velocity profiles (IVPs). A synthetic dataset of virtual aortic velocity profiles was generated by employing statistical shape modelling (SSM) to a clinical dataset consisting of 31 thoracic aortic aneurysm (TAA) cases; this produced representative 3D IVPs comparable to that of the velocity distributions observed whilst using specific 4D Flow MRI data (25). The velocity profile producing peak systolic velocity closest to that of the clinical measurement was chosen and interpolated in time to match the length of the cardiac cycle. Figure 6 shows the generated IVPs prescribed at the model inlet. The length of the cycle was adjusted according to the heart rate (HR) of the patient (Pre-TEVAR HR: 74 beats/minute, Post-TEVAR HR: 84 beats/min).

A 3-element Windkessel model (3-EWM) was prescribed at the outlets and tuned according to blood pressure measurements made throughout the observation and treatment phases (pre-TEVAR aortic pressure: 119/72 mmHg, post-TEVAR brachial pressure: 133/62 mmHg) using an established method (26). Since the 3-EWM requires mean arterial pressure (MAP) values for the necessary parameters to be set, MAP was calculated from the measured systolic and diastolic pressures (SP and DP respectively) (27).MAP=DP+13(SP−DP)Since the measured post-TEVAR pressure corresponded to the brachial (brach) pressure, which cannot be directly utilised for the 3-EWM, the measured brachial pressure was converted to central (cent) pressure using the following expression (28), with DPcent=DPbrach,SPbrach≈0.83SPcent+0.15DPcentAll the model parameters used in the 3-EWM are given in Table 1. In addition, the employment of SST-Tran model required a turbulence intensity (Tu) to be prescribed at the inlet. A low Tu of 1% was set based on previous experience (21, 22). The wall was assumed to be rigid with a no-slip boundary condition. CFD simulations were carried out using ANSYS CFX v15.0 (ANSYS, Canonsburg, PA, United States) with a fixed time-step of 0.001 s and a convergence criterion of 10⁻⁵. All simulations were run for at least 3 cycles until a periodic solution was reached.

For finite element analysis (FEA) of wall deformation and stress in the post-TEVAR model, the native aorta was assumed to be an isotropic, homogeneous and linear elastic material with a Young's modulus (E) of 0.8 MPa and Poisson's ratio (ν) of 0.49 (29). The stented region was also modelled as a linear elastic material with a Young's modulus of 15 MPa and Poisson's ratio of 0.3 (30, 31). The material densities were 1,100 kg.m⁻³ and 2,140 kg.m⁻³ for the native aorta and stented region respectively (30) (Molony et al., 2009). Since the aortic wall model was reconstructed from CT images obtained at diastole, it was necessary to account for prestress in the aorta under diastolic pressure conditions. Prestress was estimated using an iterative approach proposed and evaluated in previous studies (32, 33). The iterative process was carried out until the maximum total deformation in the stressed configuration was less than 0.5 mm under a diastolic pressure, allowing for the structural domain to achieve equilibrium with the internal blood pressure (34). The obtained prestress tensor was then applied in the FEA simulation where the geometry was tethered at the inlet and branch outlets and peak systolic pressure distribution from the flow simulations were applied as the load at the internal surface of the wall model. All FEA simulations were carried out using ANSYS Static Structural v19.2 (ANSYS, Canonsburg, PA, United States).

This investigation explores the haemodynamic response to the implanted device, focusing on localised flow patterns, WSS-related metrics and flow disturbances. A list of the indices used here are defined in Table 2. A detailed description of the relevant haemodynamic metrics for the investigation can be found in our previous work (14).

Figure 7 shows instantaneous streamlines at peak systole for all the simulated scenarios (PRE, POST, and FU1). Flow in the ascending aorta was helical with high velocities skewed towards the outer curvature in all models. The presence of the aneurysm in the arch (PRE) caused a large recirculation zone in the aneurysm sac. Excluding the aneurysm via TEVAR restored a more desirable flow pattern in the arch, as can be seen in POST. This not only led to more uniform flow into the supra-aortic branches, but also virtually eliminated any undesirable recirculating flow in the arch. Aside from small differences in the supra-aortic branches, there seem to be no qualitative differences in flow patterns between POST and FU1.

Comparison of the time-varying outflow through the RCC outlet is given in Figure 8 for the three simulated scenarios. The large recirculation zone in the aneurysm sac affected perfusion of the arch branches in PRE where flow through the RCC outlet was retrograde for approximately 64% of the cardiac cycle. PRE also had a lower peak flowrate and significantly lower flow throughout the cycle, providing a mean outflow of 3.48 × 10⁻⁶m³s⁻¹ (0.21 L/min) through the RCC. Other arch branches also experienced large periods of retrograde flow ranging between 64%–69% of the cardiac cycle. Post-TEVAR flow through the RCC was mostly antegrade with a mean outflow of 9.59 × 10⁻⁶m³s⁻¹ (0.57 L/min). The difference in outflow between POST and FU1 was due to the altered boundary conditions in FU1 to represent the break in the carotid-subclavian bypass further downstream of the RCC. As a result, FU1 had a lower flow rate of 5.55 × 10⁻⁶m³s⁻¹ (0.33 L/min) through the RCC.

The vortical flow structure throughout the modelled aorta is visualised using the λ₂ criterion as shown in Figure 9. A threshold value of −100 s⁻² was chosen in order to isolate the relevant vortex cores formed in the aorta and to make suitable qualitative comparisons. Pre-TEVAR aneurysmatic flow understandably presented with a greater degree of disturbance as flow entered the arch branches compared to the post-TEVAR model which presented with vortical flow that can be often seen in and attributed to the curved nature of the vessel giving rise to counter-rotating vortices.

Wall shear stress and its associated indices are important near wall haemodynamic parameters which can affect endothelial cell proliferation and play a role in thrombus formation (35, 36). Figure 10 demonstrates the difference in time-averaged WSS (TAWSS) patterns between PRE and POST. Both present with a large area of high TAWSS along the outer curvature of the ascending aorta, which is due to the skewed inlet velocity profile and the curvature of the aorta. The large recirculation zone in the aneurysmal sac, as seen in Figure 7, led to extremely low TAWSS in this area (PRE), with elevated TAWSS along the outer curvature of the arch and in the emerging branches. In the PRE model, a patch of elevated (>2.5 Pa) TAWSS can be seen in the inner curvature of the arch, immediately downstream of the aneurysm.

Comparisons of WSS-related indices between POST and FU1 are shown in Figure 11, displaying high degree of similarities. TAWSS and transverse WSS (transWSS) are useful metrics which serve as indicators for thrombus formation and plaque development, and there appears to be no extremes of magnitudes or abnormal spatial distribution of either. Endothelial cell activation potential (ECAP) identifies regions of high oscillatory shear index (OSI) and low TAWSS and regions of ECAP higher than 5.0 can pose a risk of thrombus formation (37, 38). However, in these cases there appears to be no abnormally high values of ECAP.

The implanted SG experiences a displacement force (DF) resulting from the change in net momentum owing to pressure and WSS generated by the aortic blood flow. Since pressure is the dominant component, the time-varying nature of displacement force is expected to closely resemble the pressure waveform (39). Figure 12 shows the displacement force acting on the ascending module of the endograft in POST, decomposed into three orthogonal components as defined in the figure. The displacement force was primarily in the z-direction but with a significant component in the y-direction due to the non-planar curvature of the aorta, thus along the coronal plane for the individual.

Figure 13 demonstrates the difference in displacement force between POST and FU1, with the endograft experiencing a consistently higher force in FU1 than in POST throughout the cycle. The maximum displacement force in FU1 was 15% higher than in POST.

Since the ascending module of the device is of particular interest in this case, it was further divided into separate segments, and the magnitude of displacement force was calculated for each of these segments. As shown in Figure 14, the distribution of displacement force was non-uniform with larger values in the distal portion of the ascending module. Segment 3 experienced the largest displacement force, followed by segment 2 and 1, which are closer to the overlapping region between the ascending module and the main endograft.

Figure 15 presents the spatial distribution of wall displacement and von Mises stress (equivalent stress) obtained with the FE analysis. The structural analysis was carried out at peak systole to represent the worst-case scenario when the aorta was subjected to the maximum pressure load. The highest von Mises stresses were observed in the distal ascending aorta, immediately upstream of the emerging branch. This coincides with the previously highlighted overlapping region between the two modules. The maximum displacement of up to 2.41 mm was observed at the distal end of the arch and could be attributed to the region not being anchored by the LCC and LSA.

As shown in Figure 7, the presence of a large aneurysm in the arch caused a significant reduction in flow velocity and recirculating flow in this region, which adversely influenced the flow leading into the arch vessels as reported by others (13). This was evidenced through a prolonged period of retrograde flow through the RCC (Figure 8), which could impair blood perfusion further downstream. Multidirectional flow can also lead to extreme WSS, which may increase the risk for thrombus formation and/or atherosclerotic lesion development in the supra-aortic arteries (40).

The TEVAR procedure using a single branched endograft successfully excluded the aneurysm and restored more organised flow in the arch. A smoother lumen, in the absence of the aneurysm, allowed for sufficient flow leading into the IA, which in turn perfused the LCC and LSA through the bypass performed pre-TEVAR. Nevertheless, the non-planar and tortuous geometry of the arch was exacerbated after the endograft was deployed as can be seen from the post-TEVAR geometry (Figure 4). The procedure also resulted in increased flow into the IA, which was the only supra-aortic branch directly perfused through the arch and it had to carry additional flow to supply the LCC and LSA. The choice of device was made based on the complex nature of the region being treated and to ensure sufficient perfusion to the supra-aortic branches. Branched and fenestrated endografts would both serve the purpose of aortic branch perfusion, but the local haemodynamics will be influenced by the endograft design. Using a branched stent-graft allows for flow to be smoothly guided into the emerging arch branch. Additionally, the ability of the main module of the single branched device to be securely anchored in the deployed region made it the more suitable choice in this case.

Flow patterns in the POST and FU1 were largely similar throughout the aorta, with a small difference in the IA due to the different outflow through the RCC branch. Close examination of WSS-related indices also revealed no significant alteration between POST and FU1 as shown in Figure 11, suggesting that the minor change in outflow conditions through the RCC in FU1 had not affected the global flow patterns and near wall haemodynamics.

It was clear from the final follow-up (FU2) CT scan (Figure 2) that further complications occurred between FU1 and FU2. The scan revealed the formation of a large aneurysm alongside the ascending module of the device, which extended along the outer curvature of the arch. Flow through this bulge perfused the native ostia of the LSA and LCC which were initially occluded prior to the TEVAR procedure. It was suspected that a leak or tear occurred in the ascending aorta, but the origin of the leak was undetermined, and a suspected source of the leak could be migration of the device or dehiscence due to improper fixation. This necessitated a closer examination of the biomechanical environment of the ascending aorta in searching for a plausible cause for the suspected leak.

Firstly, the possibility of device migration was assessed. The main module of the device was unlikely to move as it was anchored securely by the branch leading into the IA, but the ascending module was connected to the main module through a self-protecting sleeve and relied on a radial force interlocking mechanism to hold it in place. Migration of the ascending module could occur if the displacement force (DF) acting on it was sufficient to move it upward or pull it away from the main module, which would lead to type I or type III endoleak respectively (41). Previous studies suggested that DF exerted on the endograft can have a considerable effect on its spatial stability (42), and that the magnitude and direction of DF are influenced by the endograft geometry, the haemodynamic state of the patient, and the local geometry of the vessel (39, 43–45). Therefore, it was necessary to evaluate the DF experienced by the ascending module in both POST and FU1.

Our results showed that despite overall flow patterns being largely similar between POST and FU1, the DF increased by approximately 15% in FU1. The only difference between the POST and FU1 models was the outflow conditions imposed at the outlets. As has already been mentioned, the boundary conditions were altered to reflect the compromised LCC-LSA bypass, with excess flow being diverted to the descending aorta. This redirected flow resulted in changes in the normal pressure forces on the vessel wall, leading to an increase in DF. Nevertheless, the maximum DF of 11.33 N in FU1 was well below the reported threshold of 32 N to dislocate a non-planar stent-graft in the thoracic aorta (46). While threshold values have been reported for the abdominal and thoracic aorta (47, 48), there is little information in the literature on the magnitude of DF needed to cause device migration in the ascending aorta. It was also interesting to note the direction of DF as illustrated in Figure 12 which shows clearly that the total DF experienced by the ascending module deviates from its local longitudinal direction. This was attributed to the curvature and non-planarity of the aorta, especially in the region of interest here, giving rise to increased anterio-posterior and lateral components (43). The direction of DF vector indicated that it would pull the ascending module laterally away from the outer curvature, which could compromise the stability in the proximal landing zone or lead to misalignment in the device (18, 19). Further analysis of the distribution of DF along the ascending module showed that the region close to the connection between the two modules experienced relatively high DF (Figure 14).

The spatial distribution of von Mises stress obtained with the finite element analysis showed high stresses in the region where the two parts of the device connect (Figure 15), owing to the highly tortuous local geometry and the emergence of the IA branch. The maximum von Mises stress was approximately 1.3 MPa, which exceeded the yield stress for dilated ascending aorta of 1.2 ± 0.1 MPa referenced in other studies (49, 50). Although the maximum stress occurred in the wall protected by the endograft, and the graft is much stiffer and can withstand higher stresses compared to the native aorta, the extremely high level of stress in this region could compromise the device locking mechanism, thereby increasing the risk of disconnection between the two modules. Moreover, high stress concentrations were also observed in the proximal and distal ends of the device, resulting from local geometric discontinuity and compliance mismatch between the graft and the native aorta. Such focal high stress regions have been found to correlate strongly with the locations of stent-graft induced new entry in type B aortic dissections (51, 52). Based on these findings, it is plausible to speculate that a proximal tear might have occurred which then led to the formation of the observed aneurysm.

In the CFD simulations presented in this investigation, the aortic wall was assumed to be rigid and the supra-aortic vessels bypass was not included in the post-TEVAR model. The rigid wall assumption is expected to have a minor influence on the predicted flow patterns, especially in the post-TEVAR and follow-up models where a large part of the aorta was supported by the endograft. Excluding the supra-aortic vessels bypass is also likely to have an insignificant effect on the predicted haemodynamics and wall stress, even though its inclusion would have provided the opportunity to investigate potential causes for the failed carotid-subclavian bypass observed at FU1. In the finite element stress analysis, the aortic wall was modelled as a linear elastic material; this assumption was made because within the region of interest, the post-TEVAR aortic wall was largely integrated with the endograft with a relatively small section of the native aorta at the proximal and distal end of the device. In addition, the periodic motion of the aortic root and its influence on the ascending aorta were ignore, which could have influenced the predicted wall stress (53). Finally, the results presented here were confined to a single patient. However, the number of patients undergoing TEVAR of the entire aortic arch with a single-branched device is very limited and this paper focused on presenting a longitudinal analysis at multiple stages of the treatment.