# Influence of breathing-induced motion on hemodynamics following fEVAR with renal stenting

Alessandra Corvo, Stéphane Avril, Stéphan Haulon, Alberto Aliseda, Fanette Chassagne

► To cite this version:

Alessandra Corvo, Stéphane Avril, Stéphan Haulon, Alberto Aliseda, Fanette Chassagne. Influence of breathing-induced motion on hemodynamics following fEVAR with renal stenting. Annals of Biomedical Engineering, In press. hal-05514882

HAL Id: hal-05514882

https://hal.science/hal-05514882v1

Submitted on 21 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Influence of breathing-induced motion on
hemodynamics following fEVAR with renal
stenting

Alessandra Corvo¹, Stéphane Avril¹*, Alberto Aliseda²,
Stéphan Haulon³, Fanette Chassagne¹

¹Mines Saint-Etienne, INSERM, U 1059 Sainbiose, Saint-Etienne, 42023, France.

²Department of Mechanical Engineering, University of Washington, Seattle, 98105, WA, USA.

³Aortic Center, Marie Lannelongue Hospital, Groupe Hospitalier Paris Saint Joseph, Paris Saclay University, Le Plessis-Robinson, Paris, 92350, France.

*Corresponding author(s). E-mail(s): avril@emse.fr;

Contributing authors: alessandra.corvo@emse.fr; aaliseda@uw.edu;

s.haulon@ghpsj.fr; fanette.chassagne@emse.fr;

**Abstract**

**Purpose** Fenestrated EndoVascular Aneurysm Repair (fEVAR) has been demonstrated to be an excellent treatment for complex abdominal aortic aneurysms. In addition to the aortic endograft, bridging stent-grafts (SG) are deployed within the renal arteries, resulting in rare but serious renal complications. This study aims to assess renal artery hemodynamic changes post-fEVAR, including the effect of respiration-induced renal deformation.

**Methods** Pre-fEVAR models were segmented from CT scans (patients involved in clinical trial NCT04724863), while post-fEVAR models were created from structural simulations that included respiratory-induced deformation. Computational Fluid Dynamics (CFD) simulations applied inflow velocity waveforms at the supraceliac aorta and Windkessel boundary conditions at the outlets. A dynamic mesh was implemented to reproduce renal deformation during breathing, and inspiration and expiration static configurations were analyzed.

**Results** Post-fEVAR reduction in renal artery flow was detected, together with recirculation regions near the SG protrusions into the aorta. Higher time-averaged wall shear stress was observed in the unstented section of the renal arteries. The comparison between static and dynamic mesh simulations reveals that renal artery motion has negligible effect on
the flow. Finally, velocity fields were compared to metrics used clinically to assess renal
stenosis, to build a model for the prediction of renal complications in silico.

**Conclusion** This study evaluates the impact of renal stenting on flow, accounting for respiratory-induced deformation. It shows a minimal influence on overall hemodynamics, but significant reduction of renal flow post-fEVAR. Future studies should evaluate a patient cohort who experienced renal complications to correlate CFD metrics with post-operative clinical outcomes.

**Keywords:** EVAR, Breathing, CFD, Peripheral SG

# 1 Introduction

EndoVascular Aortic Repair (EVAR) has become the most common surgical technique for patients with unruptured Abdominal Aortic Aneurysm (AAA), thanks to its low invasiveness. It accounts for 83% of intact AAA repairs in the United States in 2015, with a reduced mortality of 0.8% compared to 6% after open surgical repair [1]. Especially in patients aged ≥ 80 years, EVAR is considered the treatment of choice with lower immediate postoperative mortality than open repair (2.3% against 8.6%, respectively) [2]. In complex AAA, i.e. AAA with non infra-renal neck that precludes the use of conventional EVAR, fenestrated EVAR (fEVAR), which includes fenestrations in the main stent-graft through which the blood can flow to branch arteries [3], has proven to be an excellent treatment, with early low morbidity [4]. FEVAR is performed with custom-made devices, personalized to patient geometry [5]. Renal artery stenting is performed after the insertion of the aortic endograft, and is associated with additional risks, mainly adverse renal outcomes, including postoperative acute renal failure (ARF) [6].

Notably, a single-center retrospective study reported renal complications in 12.3% of patients undergoing fEVAR, with the majority of cases attributed to stent stenosis, followed by stent occlusions [7]. Renal artery stenosis (RAS) is a significant restriction of the renal lumen [8], leading to blood flow reduction through one or both of the renal arteries [9]. This process may cause renal ischemia and hypertension, and ultimately evolve to arterial occlusion [8, 10]. Renal artery occlusion is the total obstruction of the blood flow, and its risk in the presence of renal bridging stent-grafts reached up to 9% in the first 4 years after fEVAR and/or branched EVAR (bEVAR). [11].

Post-operative renal ischemia may also result from arterial thrombosis [12], which is the formation of a blood clot within the arterial lumen, obstructing blood flow [13]. In a stenting procedure, stent thrombosis is an acute vessel occlusion that requires an emergency procedure to restore patency [14]. Three factors are considered responsible for thrombus formation: haemostasis, endothelial dysfunction, and hypercoagulability, according to Virchow's triad [15]. This concept can also be applied to medical devices, developing a new type of Virchow's triad related to device thrombosis, in which blood properties (coagulation, platelet activation, endothelial disruption), surface properties (protein adhesion, roughness), and flow (extreme high/low shear rate) are all involved [16].

Post-operative CT imaging is typically performed after EVAR, as the gold standard to assess
the patient's condition and identify any potential complications, with the first scan usually conducted within 30 days post-procedure [17, 18]. Postoperative surveillance with color duplex ultrasound (US) can also be performed as a complementary method to CT, detecting potential complications that may be missed on CT scans [19, 20]. Ultrasound imaging may be used as a clinical screening examination to detect the presence of RAS [21]. More specifically, the values of peak systolic velocity (PSV) for the renal arteries and the aorta are extracted from Doppler ultrasound [22]. By computing the ratio between these velocities, the renal-aortic systolic ratio (RAR), one of the most reliable US metrics, is obtained [21]. A RAR ≥ 3.5 predicts at least 60% of RAS with a sensitivity of 84% to 93%, according to several studies [23–26]. When for other studies, a RAR ≥ 5.1 is predictive for 70% renal artery in-stent restenosis [27].

Another commonly measured parameter that may indicate the development of RAS is PSV: an in-stent PSV threshold of 226 cm/s has been identified as predictive of RAS, with a sensitivity of 100% [28]. By combining the two metrics (PSV ≥ 200 cm/s with RAR of ≥ 3.5), an overall accuracy of 78% in detecting ≥ 60% stenosis was found [21].

Since the early detection of the aforementioned complications is quite complex, hemodynamics in the peripheral arteries needs to be monitored, with a particular focus on the renal arteries, to detect possible thrombogenic flow patterns. This will provide a complete perspective of the occurrence of possible complications, even long after surgery. Computational Fluid Dynamics (CFD) studies can help assess hemodynamic changes both post-operatively and over the respiratory cycle.

Previous CFD studies have demonstrated changes in renal artery flow post-operatively, with a focus on fEVAR, to evaluate the specific impact of the renal coverage [29–35]. However, only the last four studies included patient-specific geometries in their simulation workflow [32–35]. According to Wen et al. and Lin et al., renal stenting led to peak renal flow reduction, compared to the pre-operative configuration [29, 35]. For Van de Velde et al., partial renal coverage caused low and marked oscillations in wall shear stress, potentially inducing atherosclerosis and subsequent RAS [36].

However, these studies have not modeled the actual post-operative peripheral stent-graft geometry, and did not account for the effect of breathing motion. Although Tran et al. investigated hemodynamics across different clinical conditions, their analysis was based on static, patient-specific geometries and did not include respiratory simulation [32]. In particular, breathing was never modeled through a dynamic mesh approach.

It is well known that the renal arteries bend during respiration, undergoing conformational changes, particularly in their branching angle and curvature [37]. Previous studies have modeled the hemodynamic changes resulting from different renal configurations using idealized geometries [29, 30]. Nevertheless, they have not actually modeled the respiration-induced hemodynamic changes. Consequently, the primary aim of this study is to combine the outcomes of peripheral SG deployment simulations with the CFD analysis of hemodynamic changes in the renal arteries, pre- and post-EVAR, at the inspiratory and expiratory phases. Furthermore, to understand the dynamical effect of respiration-induced deformations in CFD studies, mesh motion is incorporated throughout the respiratory cycle.
# 2 Materials and Methods

## 2.1 Geometries and mesh generation

### 2.1.1 Data acquisition and image segmentation

Arterial anatomies of two patients who underwent fEVAR at Marie Lannelongue Hospital (Aortic Center, Groupe Hospitalier Paris Saint Joseph, Paris Saclay University, Le Plessis-Robinson, France) were included in this study. Patients signed an informed consent and were enrolled in a clinical trial (NCT04724863) between April 2020 and January 2021. The two patients have an average age of 74 years and present a clinical history characterized by hyper-tension, respiratory comorbidities, and previous surgical interventions. CT scans, pre- and post-EVAR, were performed during breath-hold conditions. Four CT image sets per patient were then acquired: pre-operative inspiration and expiration, post-operative inspiration and expiration.

Geometrical models of the pre-EVAR configuration were generated via a semi-automatic segmentation using 3D Slicer. Each model included the abdominal aorta, the celiac and superior mesenteric artery (SMA), the right (RRA) and left renal artery (LRA), both at inspiration and expiration configurations of the two patients [38].

### 2.1.2 Generation of geometries pre- and post-EVAR

The breathing effect was numerically simulated in the pre-operative geometry by applying a displacement at the distal end of the renal arteries, equal to the kidney movement measured from the CT scans [38]. Main body and peripheral renal SG deployment was numerically simulated via structural Finite Element (FE) simulations, in a workflow validated in our published work [38]. The geometries extracted from these simulations were used as the post-EVAR geometries, as extracting renal arteries and bridging stent-grafts geometries from the post-op CT scans presented significant challenges due to low image resolution compared to the size of the stent structure, leading to high uncertainty.

For each patient, four distinct geometries were obtained from segmentation:

* pre-fEVAR inspiration configuration

* pre-fEVAR expiration configuration

from numerical simulation:

* post-fEVAR inspiration configuration

* post-fEVAR expiration configuration

In addition, to study the dynamic effect of the deformation resulting from respiration, structural FE simulations of breathing were used to reconstruct the deformation of the aorta and the renal arteries, in both pre-EVAR and post-EVAR configurations, at various time intervals during the respiratory cycle, via the implementation of the dynamic mesh.

**PRE-fEVAR geometries** were obtained by segmenting CT images acquired at two different respiratory phases (inspiration and expiration). To reduce computational cost, the models were truncated above the celiac artery and just below the abdominal aortic aneurysm, thereby excluding the iliac arteries. This allowed the models to focus on the abdominal section of
the aorta containing the aneurysm, along with the celiac artery, SMA, both RRA and LRA. Minimal smoothing was applied to the segmented geometries. To ensure the velocity is perpendicular to the inlet and outlet surfaces, the models were cut orthogonally to the centerline at these boundaries. These steps were performed using STAR-CCM+ (Siemens Digital Industries Software, Texas, USA). When needed, flow extensions were added at the outlets, using Vascular Modeling ToolKit (VMTK). Pre-EVAR geometries for inspiration and expiration of Patient 1 are shown in Figure 1a.

**Post-fEVAR geometries** were extracted from structural FE simulations of SG deployment (described in previous work [38]), as post-op imaging does not provide sufficient resolution and contains artifacts. The stent wire structure (modeled as beam elements) was neglected, based on the assumption that its thickness does not play a crucial role in the simulation outcomes (stent thickness is approximately half that of the graft and one-fifth that of the arterial wall). Extracting post-operative geometries from structural FE simulations rather than from post-operative CT scans allowed us to account for the actual deformation of the SG for CFD simulations. As a result of structural FE simulations of SG deployment [38], the post-fEVAR models included the aorta with its stent-graft, the renal arteries with their stents-grafts. The post-fEVAR geometries were modified (smoothing, flow-extension addition, capping, and remeshing) and adapted for CFD simulations. The internal aortic lumen was entirely removed and replaced with the lumen of the aortic graft, which becomes the effective lumen post-surgery. Similarly, the internal lumen of the renal arteries was replaced by the peripheral graft lumen obtained from the simulations (Figure 1b). For the protrusion of the peripheral graft into the aorta, a thickness of 0.2 mm was prescribed, consistent with the actual thickness of the commercially available peripheral graft. A detailed view of this graft protrusion is shown in Figure 1c. Subsequently, the geometries were truncated just below the aortic aneurysm, smoothed, and cut perpendicularly, with the addition of flow extensions, following the same procedure applied to the pre-EVAR geometries. All these steps were carried out using ANSYS SpaceClaim (ANSYS Inc., Canonsburg, PA, USA), Onshape (PTC Inc., Boston, MA, USA), and STAR-CCM+ (Siemens Digital Industries Software, Texas, USA).

### 2.1.3 Mesh generation pre- and post-EVAR

The three-dimensional models were then meshed with tetrahedral elements using STAR-CCM+. A mesh element size of 0.5 mm was chosen for the regions of interest (renal arteries and the ostia of the renal arteries at the aorta), following previous studies [32]. Mesh refinement was performed for the renal stent-graft protrusion in the aorta, with a cell size of 0.2 mm. Areas not included in these regions were meshed with cell size of 1 mm [32]. Simulations in which the grid remains fixed in space, cells do not deform, are referred to as static mesh simulations (rigid walls).

## 2.2 Implementation of the dynamic mesh

Deformation of the renal arteries induced by respiration was simulated to study its effect on the renal arteries hemodynamics. A 5-second respiratory cycle (12 breaths per minute) was simulated [39], and mesh motion was applied on the renal artery walls.

For the pre-fEVAR configurations, displacements of the renal arteries and aortic branches
<figure><img src="image_2.png" /><figcaption>**Fig. 1:** (a) Pre-EVAR three-dimensional geometry of Patient 1, at inspiration (light grey) and expiration (dark grey). (b) Post-EVAR three-dimensional geometry of Patient 1, at inspiration (light grey) and expiration (dark grey); the arrows show the distal end of the renal stent-graft. (c) Detail of the flared protrusion of the left renal artery for Patient 1.</figcaption></figure>

obtained from structural Finite Element Method (FEM) simulations with breathing displacements of the renal arteries ends were applied. Specifically, a User Defined Function (UDF) implemented in ANSYS Fluent (ANSYS Inc., Canonsburg, PA, USA) and made open source [40], assigns unique IDs to the boundary nodes and prescribes their motion based on the previously computed displacements, updating the mesh node coordinates at each time step. Using Fluent's dynamic mesh feature, the surfaces involved in the motion (the inlet, the five outlets, and the surfaces of renal arteries and the aortic segment) can be selected, and their positions over time updated based on input text files containing the coordinates to achieve continuous movement. However, since Fluent requires displacement inputs for each time step (1/1000 s), temporal interpolation was applied to node displacements to generate 5000 input text files for the dynamic mesh.

Spatial interpolation was required, in addition to temporal interpolation, as we could not run structural FEM simulations of breathing directly using CFD geometries (substantially modified through the suppression of the renal artery wall in the stented region, as only the lumen was considered), as meshes were not exactly the same. Node displacements for the stents, the grafts, and the renal arteries during breathing were computed from the structural FE simulations (obtained from our validated workflow [38]) and interpolated to match the CFD volumetric mesh and time step. Subsequently, Fluent's smoothing was used to ensure internal mesh quality.

To simulate the mesh motion during a 5-second respiratory cycle, we assumed 60% expiration (3 seconds) and the remaining 40% inspiration (2 seconds), typical of the adult respiratory cycle. This translates into the adoption of the 5000 input files containing the node coordinates for temporal interpolation, of which 3000 (60%) are needed for the expiratory phase, in which the renal arteries move upward, and another 2000 input files (40%) correspond to the inspiratory phase (downward movement of the renal arteries).
## 2.3 Boundary conditions for flow simulation

**Inlet boundary condition.** A physiological pulsatile velocity profile was imposed at the inlet of the model (supra-celiac aorta), obtained from Phase-Contrast Magnetic Resonance Imaging (PC-MRI) of AAA patients under resting conditions [41].

**Outlet boundary conditions.** 2-element Windkessel boundary conditions were applied at the outlets to mimic the compliance C and the resistance R of the distal aorta and peripheral arteries (celiac artery, SMA, RRA, LRA). These parameter values were adjusted to replicate physiological flow splits observed in vivo: 20% for the celiac artery, 15% for the SMA, RRA, and LRA, and 35% for the distal aorta [42]. Identical boundary conditions were applied for both the models, pre- and post-op, as well as for the inspiration and expiration geometries.

**Flow simulation.** Blood was modeled as a Newtonian fluid with a viscosity of 0.0035 Pa·s and a density of 1.06 g/cm³. The simulations were run on Ansys Fluent by fully resolving the Navier-Stokes equations with high spatial and temporal resolution (time step of 0.001 s), for this relatively low Reynolds number flow ($Re_{peak} \sim 1000$), during two full respiratory cycles encompassing 10 cardiac cycles (10s) for the dynamic mesh. For the static mesh, simulations were run for five cardiac cycles (5s). Maximum residuals requirement was set to $1 \cdot 10^{-6}$. The results were saved for analysis every 0.02 s from the last cardiac cycle (static mesh) and from the last respiratory cycle (dynamic mesh).

## 2.4 Simulation setup

The entire simulation plan consists of six simulations per patient: 1a and 2a, 1b and 2b, 1c and 2c. Two different breathing conditions were considered for each patient: inspiratory (1a, 2a) and expiratory phase (1b, 2b), in which the vessel walls were modeled as rigid. To simulate a complete breathing cycle and account for vessel wall deformation during breathing, two additional simulations, including moving mesh, were performed (1c, 2c).

Three simulations were run in the pre-EVAR configuration (1a, 1b, 1c), and three in the post-EVAR configuration (2a, 2b, 2c). The outline of the entire simulation plan is summarized in Figure 2.

## 2.5 Patients clinical condition from clinical data

## 2.6 Analysis Tools and Comparison with Clinical Metrics

Hemodynamics metrics were extracted to compare the different configurations and analyze the impact of fEVAR and vessel wall deformations. Flow rates and peak systolic velocities (PSV) were exported from the simulation results.

Time-averaged wall shear stress (TAWSS) was computed with equation 1, at the renal arteries for all the models, dividing them into stented and unstented regions. Through an appropriate MATLAB (The MathWorks Inc., Natick, Massachusetts) code, an angle $\theta$ was defined for each renal artery, starting from an initial point $P_0$ on the renal artery walls, then varying from $-\pi$ to $+\pi$ around its centerline. The reference point $P_0$ is identified on the cranial proximal region of the renal artery.

TAWSS contour maps were generated by plotting the TAWSS values at the sampled points along each renal artery centerline while varying $\theta$, to obtain a complete TAWSS distribution around the renal artery walls, as if the arterial surfaces were cut open.
<figure><img src="image_3.png" /><figcaption>Fig. 2: Simulation plan</figcaption></figure>

$$ TAWSS = \frac{1}{T} \int_{0}^{T} |\tau_{w}| dt \qquad (1) $$

To quantitatively compare the velocity fields resulting from simulations with static and dynamic meshes, three cross-sections were selected from the post-EVAR model (2 for the pre-EVAR model), corresponding to three specific regions: SG protrusion into the aorta (absent for the pre-EVAR model), renal ostium, and 5-mm downstream the stent-graft.

Velocity contours were extracted for these three cross-sections, both for velocity magnitude in the static model ($v_{static}$) and in the moving mesh model ($v_{dynamic}$), together with the computation of the corresponding normalized velocity differences (excluding the values of velocity at the arterial wall) derived from the velocity values, computed as follows (Eq. 2):

$$ \hat{\Delta}v = \frac{v_{\text{dynamic}} - v_{\text{static}}}{v_{\text{static}}} \qquad (2) $$

Finally, to compare the simulation results with the clinical metrics normally used to detect RAS and mentioned in the Introduction section, the renal-aortic systolic ratio (RAR) was computed, based on Eq. 3 [21]. Renal PSV was extracted along the full length of the renal artery, whereas the aortic velocity was defined as the maximum velocity in the abdominal aorta at the level of the renal arteries [43].

$$ RAR = \frac{\text{Peak Systolic Velocity}_{\text{renal}}}{\text{Peak Systolic Velocity}_{\text{aorta}}} \qquad (3) $$

The images and plots for the post-processing were created using ParaView Visualization ToolKit (Los Alamos National Laboratory, Santa Fe), CFD-Post (ANSYS Inc., Canonsburg, PA, USA), MATLAB, and Python.

# 3 Results

## 3.1 Flow: impact of breathing pre-EVAR

The differences in flow rate for both arteries and patients are shown in Figure 3. Mean and peak flow rate values for both arteries and patients are summarized in Table 1, for all of the
analyzed conditions.

The comparison of the flow rates at the outlets of the two renal arteries during pre-EVAR inspiration and expiration, shown in Figure 3 (a, b, c, d), highlights the expiratory phase characterized by higher branching angles and curvature changes (Figure 3.a-purple).

As shown in Table 1, variations of the flow rate exist at expiration (mean flow variations ranging from -2.8% to 0.5%) in the pre-EVAR configuration (Table 1). The right renal artery of Patient 2 had the most pronounced reduction in mean flow (Figure 3.c), while the left renal artery of Patient 2 showed a slight increase (Figure 3.d). In three out of the four renal arteries analyzed, the peak flow rate decreased at expiration in the pre-EVAR configuration (Table 1).

## 3.2 Flow: impact of renal artery stenting

Investigating the renal flow rate pre- and post-fEVAR, Figure 3 (e, f, g, h) clearly shows that the presence of the stent-graft leads predominantly to a reduction in renal artery flow. This effect is particularly evident in the left renal artery of Patient 1, where reduction was 35% post-operatively (Figure 3.f). The exception can be found in the left renal artery of Patient 2, with a 2% increase in mean renal flow rate post-EVAR, although flow was still reduced at systolic peak (Figure 3.h).

Overall, a decrease in the post-EVAR peak flow rate was observed in all of the analyzed renal arteries, for both inspiration and expiration configurations (Table 1).

<table><caption>**Table 1:** Renal mean flow rate $\bar{Q}$ and peak flow rate $Q_{max}$ (in brackets) in the left and right renal arteries, at inspiration and expiration, pre- and post-fEVAR, along with their corresponding percentage variations.</caption><thead><tr><th>Patient</th><th>Clinical condition</th><th>Artery</th><th>Q&#773; (Q<sub>max</sub>)<br>Inspiration<br>[ml/s]</th><th>Q&#773; (Q<sub>max</sub>)<br>Expiration<br>[ml/s]</th><th>Variation in Q&#773;<br>(Exp.-Insp.)<br>[%]</th><th>Variation in Q&#773;<br>(post-op.-pre-op.)<br>[%]</th></tr></thead><tbody><tr><td rowspan="4">Pat. 1</td><td rowspan="2">pre-EVAR</td><td>LRA</td><td>7.31 (25.96)</td><td>7.18 (25.56)</td><td>-1.8%</td><td>-</td></tr><tr><td>RRA</td><td>7.50 (35.56)</td><td>7.44 (35.11)</td><td>-0.8%</td><td>-</td></tr><tr><td rowspan="2">post-EVAR</td><td>LRA</td><td>4.74 (16.30)</td><td>4.74 (16.32)</td><td>0%</td><td>-35.1%</td></tr><tr><td>RRA</td><td>7.46 (32.17)</td><td>7.19 (30.97)</td><td>-3.6%</td><td>-0.5%</td></tr><tr><td rowspan="4">Pat. 2</td><td rowspan="2">pre-EVAR</td><td>LRA</td><td>8.23 (23.64)</td><td>8.27 (23.88)</td><td>+0.5%</td><td>-</td></tr><tr><td>RRA</td><td>8.35 (28.12)</td><td>8.12 (27.19)</td><td>-2.8%</td><td>-</td></tr><tr><td rowspan="2">post-EVAR</td><td>LRA</td><td>8.39 (22.99)</td><td>8.64 (23.65)</td><td>+3.1%</td><td>+1.9%</td></tr><tr><td>RRA</td><td>7.69 (26.64)</td><td>6.45 (21.04)</td><td>-16.1%</td><td>-7.9%</td></tr></tbody></table>

## 3.3 Impact of SG protrusion on the flow

Velocity fields in the renal arteries were analyzed to further investigate the impact of the stent-graft deployment. In particular, velocity streamlines at the level of the branching of the renal arteries and, more specifically, at the stent-graft protrusion into the aortic lumen are shown in
<figure><img src="image_4.png" /><figcaption>**Fig. 3:** Renal flow at inspiration (green/blue) and expiration (purple/red) for Patient 1 and Patient 2, pre-fEVAR (dashed lines) and post-fEVAR (continuous lines).</figcaption></figure>
Figure 4, both pre- and post-fEVAR.

The presence of the stent-graft protrusion into the aorta led to the formation of recirculation zones around the protrusion, both superiorly and inferiorly, which did not exist pre-EVAR (Figure 4.a). This effect of the protrusion on flow patterns was observed in both patients, and is shown for Patient 1 in Figure 4.

<figure><img src="image_5.png" /><figcaption>**Fig. 4:** Velocity streamlines showing recirculation areas upstream and downstream the SG aortic protrusion for RRA and LRA in Patient 1, including the moving mesh, pre-fEVAR (a) and post-fEVAR (b). Velocity streamlines showing recirculation areas at the SG protrusion into the aorta for Patient 1 for RRA and LRA pre-fEVAR (c) and post-fEVAR (d). The model has been vertically cut by a plane to show the velocity streamlines.</figcaption></figure>

## 3.4 Comparison between static and dynamic mesh

First, to qualitatively compare the flow fields resulting from the static and dynamic meshes, velocity streamlines were compared at inspiration, for both pre- and post-fEVAR models, as shown in Figure 4.c-d. Similar to what was observed with the static mesh (Figure 4c-d), recirculation areas were found superior and inferior to the SG protrusions (Figure 4a-b) when considering the moving mesh (at the time step corresponding to inspiration).

Focusing on the right renal artery, a detailed view of the post-EVAR outflow from the artery,
resulting from the stenting, is shown in Figure 4.b).

As described in the Materials and Methods section, for quantitative comparison, velocity contours are analyzed for two sections in the pre-op model and three different cross-sections in the post-op model (Figure 5). For better visualization, the results are shown only for the post-op model of Patient 1, but the same conclusions were drawn for Patient 2. The values of mean and maximum velocities have been added to the plot (Figure 5), and mean $\Delta v$ is shown in Table 2 for all the models.

As can be observed in Figure 5, velocity contours showed minor differences between the static and dynamic meshes. The differences in velocity were found to be minimal for the three post-op sections (2.2% largest mean difference for any artery in Patient 1).

The same trend also applies to the pre-op model and to the other patient (8.4% largest mean difference for any artery in Patient 2).

<table><caption>**Table 2:** Mean normalized velocity differences between static and dynamic meshes for Patient 1 and Patient 2, and cross-sections A0, A1, A2 for RRA, B0, B1, B2 for LRA.</caption><thead><tr><th rowspan="2">Patient</th><th>Section</th><th>Δv (mean)</th></tr><tr><th>RRA / LRA</th><th>RRA / LRA</th></tr></thead><tbody><tr><td rowspan="2">Patient 1 pre-fEVAR</td><td>A1 / B1</td><td>1.0% / 0.8%</td></tr><tr><td>A2 / B2</td><td>0.9% / 0.6%</td></tr><tr><td rowspan="2">Patient 1 post-fEVAR</td><td>A0 / B0</td><td>2.2% / 1.6%</td></tr><tr><td>A1 / B1</td><td>1.2% / 0.5%</td></tr><tr><td rowspan="2">Patient 2 pre-fEVAR</td><td>A1 / B1</td><td>0.2% / 0.2%</td></tr><tr><td>A2 / B2</td><td>0.5% / 8.4%</td></tr><tr><td rowspan="2">Patient 2 post-fEVAR</td><td>A2 / B2</td><td>0.3% / 0.3%</td></tr><tr><td>A0 / B0</td><td>2.3% / 1.3%</td></tr><tr><td rowspan="2"></td><td>A1 / B1</td><td>0.9% / 2.4%</td></tr><tr><td>A2 / B2</td><td>3.9% / 0.3%</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>**Fig. 5:** Comparison between velocity contours for three different cross sections for each artery (A0, A1, A2, B0, B1, B2) in Patient 1 and for inspiration at the systolic peak of the post-op model. Velocity contours for the static and dynamic meshes are shown, together with the corresponding computed normalized differences.</figcaption></figure>
## 3.5 TAWSS: comparison pre- and post-fEVAR

Time-Averaged Wall Shear Stress was calculated in the renal arteries, for both patients, pre- and post-fEVAR, and at the two different phases of the respiratory cycle.

Maps of TAWSS (Figure 6) show TAWSS distributions along and around the renal artery centerline, as described in the Materials and Methods section. Areas of low TAWSS are visible at the renal bifurcation, in the stented zone post-fEVAR at the inlet of the renal arteries (Figure 6b, d). Specifically, even lower TAWSS was detected in the same zones pre-fEVAR (Figure 6a, c).

While, in the unstented zone, a local increase in TAWSS was observed at expiration, especially for Patient 2, post-fEVAR (Figure 6d). Overall, a general increase in post-op TAWSS, compared to pre-op, is observed.

<figure><img src="image_7.png" /><figcaption>**Fig. 6:** TAWSS distribution for Patients 1 and 2, before and after intervention, averaged over 1 second during inspiration and expiration. Dashed lines indicate the separation between the stented and unstented region (distal section)</figcaption></figure>
The results obtained were then compared with previous numerical work [33] that previ-
ously reported significant differences in TAWSS between stented and unstented regions of the
renal arteries.

As shown in Figure 7, an overall increase in TAWSS was observed in the post-fEVAR config-
uration, although a local reduction in TAWSS can be observed at the branching of the renal
arteries. Additionally, when comparing TAWSS between stented and unstented regions, our
models showed the same decrease in TAWSS in the stented regions reported by Tran et al.,
confirming the trend (Figure 7).

Nevertheless, TAWSS values in our simulations were generally higher than those reported in Tran et al., although with the same tendencies.

<figure><img src="image_8.png" /><figcaption>**Fig. 7:** TAWSS computed for stented and unstented regions for both patients, pre- and post-fEVAR, with comparison with results from Tran et al. [32]. An asterisk (*) is used to denote the results from the present study.</figcaption></figure>

**3.6 Evaluation of clinical parameters: RAR and PSV**

Renal-Aortic Ratio and Peak Systolic Velocity in the renal arteries were computed for both patients in the post-op model. It has been demonstrated that the PSV cutoff value that provides an overall accuracy of 81% for ≥ 60% stenosis is 285 cm/s [21], although different values for this parameter can be found in the literature (Table 3). The RAR cutoff value providing a sensitivity of 93% for ≥ 60% stenosis is 3.5 (Table 3) [23, 24, 26]. Consequently, these two metrics can be adopted as indicators to detect ≥ 60% stenosis.

Nodes where RAR exceeded 3.5 and renal PSV exceeded 285 cm/s were identified and their
location shown in Figure 8. The distribution of RAR and PSV in the renal arteries for Patient
1 and 2 highlights the areas where values are higher than the cutoff.

As shown in Figure 8, regions with RAR > 3.5 were not found in either the right or left renal
arteries, but some areas in Patient 2 exhibited PSV > 285 cm/s. Although RAR is designed to diagnose existing significant renal artery stenosis or monitor its progression [25], no metrics exist to predict future stenosis. In our study, we analyze the association between RAR values and the presence of post-operative complications. The absence of regions where RAR > 3.5 suggests that no immediate significant stenosis or occlusion is present, which is consistent with clinical observations, but it does not allow for predictions of long-term complications.

<figure><img src="image_9.png" /><figcaption>**Fig. 8:** RAR map (post-fEVAR) highlighting areas where RAR > 3.5 for Patient 1 (a) and Patient 2 (c). PSV map (post-fEVAR) highlighting areas where PSV > 285 cm/s for Patient 1 (b) and Patient 2 (d).</figcaption></figure>

# 4 Discussion

**Impact of breathing on flow.** This is the first study that analyzes hemodynamics changes induced by respiration in patients treated with fEVAR, associated with both breathing-induced renal artery deformations and renal artery fenestrated stenting. A slight decrease in mean flow < 5% was observed for three out of four renal arteries during expiration, pre-op (Table 1), which can be associated to an increase in branching angle. The variation in mean flow rate between respiratory phases was more pronounced in arteries with branching angles and curvatures that vary widely during breathing. Conversely, in the left renal artery of Patient 2 that remained straight during respiration, a slight increase in peak flow was detected, as it is not subjected to bending during breathing.
<table><caption>**Table 3:** Values of clinical parameters to evaluate RAS from clinical literature [21, 23, 24, 26, 27, 44].</caption><thead><tr><td>Stenosis [%]</td><td>RAR</td><td>Renal PSV [cm/s]</td><td>References</td></tr></thead><tbody><tr><td>&gt; 60</td><td>≥ 3</td><td>&gt; 180</td><td>House et al. [44]</td></tr><tr><td>&gt; 60</td><td>≥ 3.5</td><td>&gt; 180</td><td>Zierlet et al. [24]</td></tr><tr><td>&gt; 60</td><td>≥ 3.5</td><td>-</td><td>Kohler et al. [23]</td></tr><tr><td>≥ 60</td><td>≥ 3.5</td><td>≥ 200</td><td>Fernandez et al. [26]</td></tr><tr><td>≥ 60</td><td>≥ 3.7</td><td>≥ 285</td><td>AbuRhama et al. [21]</td></tr><tr><td>≥ 70</td><td>≥ 5.1</td><td>≥ 395</td><td>Chi et al. [21]</td></tr></tbody></table>

These minimal flow differences are considered physiologically plausible, as hemodynamics is not expected to vary substantially within the respiratory cycle. Our findings are consistent with previous work that investigated the effect of branching angle on renal blood flow [29, 30, 45]. In Wen et al., a renal artery with an upward orientation exhibited relatively low blood perfusion, considering both 0% and 30% renal stenosis [29]. This upward configuration of the renal artery closely resembles the expiration phase in our models.

Similarly, Kandail et al. investigated the effect of branching angle (angle between the aortic and renal artery centerlines). From 30° to 90° branching angle, an increase in mean renal flow rate of 5% was observed. But, as in the present study, a 3% decrease in mean renal flow was observed when the angle increased from 90° to 120° [30]. Mortazavinia et al. also reported that branching angle increase led to renal mass flow reduction, potentially resulting in severe hypertension [45]. This confirms that, as in our study, breathing-induced variations can lead to variations of no more than 5% in mean renal flow pre-op, suggesting that the overall impact of renal deformations on renal perfusion is minor.

**Impact of RA stenting on the flow.** By comparing pre- and post-op mean renal flow, the change was found to be negative in three out of four arteries, with variations ranging from +2% to -35%. This confirms findings by Tran et al., who reported a reduction in renal flow of 35% in arteries affected by fEVAR [33]. Furthermore, Lin et al. performed CFD simulations in a patient-specific model and observed similar renal perfusion pre and post-op, with a more evident reduction (3.9%) in peak flow rate in the left renal artery [35]. Our results confirm this trend: peak flow reduction in the two left renal arteries. This reduction in renal perfusion is the consequence of the increased vascular resistance following renal stent-graft insertion.

**Impact of SG protrusion on the flow.** An important role is hypothesized for the presence of peripheral stent-graft protrusion into the aorta which, naturally, does not exist pre-operatively. This protrusion locally alters flow patterns, leading to flow recirculation at the entrance to the renal arteries (Figure 4). At the systolic peak, this was observed also by Kandail et al. for all of their flared geometries [31]. They suggested that this recirculation area, exhibiting lower velocities, could promote thrombogenicity at the renal ostium. In contrast, they reported no such flow patterns for unflared configurations [31]. The importance of SG protrusion is also highlighted by the studies of Ben-Ahmed et al. and Tran et al., where SG protrusion into the aorta after fEVAR was observed to induce flow reductions and lower velocities [32, 34].
**Comparison between static and dynamic renal deformation.** By comparing the velocity contours across various cross-sections, the discrepancies between the statically deformed renal artery and the dynamic deformation of the renal artery throughout the respiratory cycle are shown in Table 2. The spatially-averaged differences ranged from 0.2% to 8.4%, indicating that the simplification introduced by taking a static deformation of the renal artery at one point of the cardiac cycle, rather than simulating the dynamically deforming artery across the entire cycle, are all below a threshold of 10%, with the highest values observed in sections near the stent-graft protrusions (Figure 5). These results suggest that assuming static deformation at the two limits of the respiratory cycle (highest renal position in inspiration and lowest position in expiration) is a reasonable assumption to investigate the effects of breathing motion on renal artery hemodynamics.

The dynamic effect of breathing during an entire respiratory cycle may be neglected, as the inertia associated with wall motion is negligible compared to the inertia in the flow.

**TAWSS Comparison.** WSS maps show minor differences between inspiration and expiration (Figure 6). Similarly, changes in renal perfusion between the two breathing phases are limited. The largest differences for the stented case occurred in the RRA of Patient 1, where a reduction in TAWSS from inspiration to expiration was detected (-6.7%) in the proximal 20 mm of the artery (Figure 6b).

Across all TAWSS maps, the tendency is to increase at expiration within the distal ≈ 15 mm of the renal arteries, typically corresponding to the region of maximum vessel curvature (Figure 6).

As shown in Figure 6, TAWSS was found to be higher post-op (Figure 6, 7), in agreement with the findings of Ben-Ahmed et al. for fEVAR patients [34]. This increase is particularly evident for Patient 2 (Figure 6c-d), especially in the stented region of the two renal arteries (first 10 mm).

This difference may be related to the imposed boundary conditions and the specific geometry of the renal arteries of Patient 2, characterized by a small caliber. Arteries with smaller diameters are more susceptible to higher wall shear stress, even in the pre-EVAR model (Figure 6 c-d). TAWSS values are higher on average than in previous studies [32], mainly due to the morphological differences mentioned above.

Notably, stented regions exhibited lower TAWSS, consistent with Tran et al. (Figure 7). This difference is attributed to the presence of recirculation areas in the stented regions, particularly at the entrance of the renal arteries. Regions characterized by lower TAWSS appear in flow recirculation zones found post-op, confirming what was previously described in [30]. These flow patterns exist in the first 5 mm of the renal arteries' centerlines and, particularly, along $\theta = 0$ (Figure 6), matching the recirculation zones in Figure 4.

It is worth mentioning that areas of particularly low TAWSS post-op were associated with higher risk of thrombosis in previous studies [46].

**Evaluation of clinical metrics.** Renal-Aortic Ratio and Peak Systolic Velocity are computed within the renal arteries post-op with no regions where RAR was higher than 3.5 (Figure 8 a-c), but some zones with $PSV > 285$ cm/s are detected in the right renal artery of Patient 2 (Figure 8d).

However, as shown in Table 3, most studies set RAR the threshold value to 3.5 or 3.7, indicative of a 60% stenosis. Conversely, previous studies do not conform to the cutoff
values of peak systolic velocity in the renal arteries, which range from 180 to 395 cm/s [21, 24, 26, 27, 44]. This wide variability makes it challenging to draw conclusions based on this metric from our CFD simulations.

For this reason, we focused exclusively on RAR as a metric to detect complications. No regions with RAR > 3.5 (Figure 8) were found, suggesting that no clinically relevant complications are expected to develop in these two patients.

The absence of clinical complications in the renal arteries of both patients supports the validity of our simulation workflow: clinical follow-up did not report the development of either post-operative renal artery stenosis or occlusions, and no such complications were detected by physicians.

The comparison between the results of numerical simulations and clinical follow-up provides a preliminary validation of our simulation workflow. This supports the potential of numerical simulations as a useful tool to assess the risk of renal artery complications occurring in patients undergoing renal artery stenting.

However, some limitations can be identified in this study:

* a larger cohort of patients would be necessary to further validate the workflow;

* the absence of vessel wall deformation responding to blood pressure fluctuations;

* same inlet waveforms applied to all models, not derived from patient-specific measurements;

* personalized boundary conditions, taking into account post-fEVAR hemodynamics changes.

An important limitation of this work is the small sample size (two patients), hence limiting its generalizability. However, this work should be considered a novel, exploratory study aimed at introducing a new methodological framework, which can serve as a foundation for further investigations on larger cohorts. Enlarging the cohort of patients, especially including patients who developed renal artery complications, would enhance the predictive performance of the model and refine the post-processing of the clinical metrics, taking into account the different types of renal artery complications that may occur.

Another simplification in this simulation workflow is the absence of arterial wall response deformation due to blood flow. Wall motion was externally imposed by applying respiration-induced deformations derived from FEM simulations, but the prescribed renal artery motion did not include the pressure fluctuations with the cardiac cycle. According to previous studies, cardiac pulsatility did not show a significant influence on renal artery morphological changes, compared to respiration [47].

Finally, as a final consideration, boundary conditions at the various outlets were tuned based on the individual characteristics of each patient. However, the same inlet waveform was applied to the aortic inlet of all models. This choice, consistent with the need to maintain identical boundary conditions in order to assess the impact of stent-graft implantation on renal hemodynamics, represents a necessary modeling simplification. The waveform was not derived from patient-specific measurements of velocity, but was based on previously published studies, due to the unavailability of patient-specific flow data for these cases. Such an approach does not consider the decrease in flow rate after the fEVAR implantation, due to the increased resistance induced by the stent grafts (main body and peripheral stent grafts).

In future works, personalized boundary conditions could be applied to the models, taking into
account the differences in flow split that occur after fEVAR, tuning once again resistance and
compliance to reflect these hemodynamics changes

This study represents the first to assess hemodynamics changes induced by breathing in patient-specific fEVAR models, showing only minimal impact of breathing-induced deformations. The novelty of this work lies in its innovative approach for investigating, for the first time, the impact of respiratory-induced deformations on renal hemodynamics, a new contribution not present in previous studies. In contrast to Tran et al. [32], thanks to this workflow, based on FEM simulations, the actual post-fEVAR geometry of bridging stent-grafts could be reconstructed, including the specific flaring of each SG, and implemented in CFD simulations.

The results of our study revealed that neglecting dynamic breathing motion is a reasonable approximation for renal flow simulations. Furthermore, the study showed that renal artery stenting led to a reduction in renal perfusion with localized flow recirculation around the SG protrusions, at the renal artery ostia, confirming observations from previous studies.

Finally, future research will aim to expand the patient cohort to improve the effectiveness of the proposed workflow. In particular, CFD analysis on additional clinical cases with more detailed clinical follow-up data is planned, especially patients for which renal artery complications have been clinically reported. This will lead to a potential correlation between metrics derived from CFD and clinical metrics, advancing the case for the effectiveness of numerical simulation as a predictive surgical planning and follow-up tool.

## Acknowledgements

This project benefits from a public grant managed by the French National Research Agency, under the 3rd PIA, and integrated into the France 2030 plan, with the following reference: ANR-21-RHUS-0011.

## Author Contributions

All authors (AC, SA, AA, SH, FC) contributed to the conception and design of the study. SH provided and acquired the clinical data. AC developed the simulation and computations with the support of SA, AA, SH, FC. AC analyzed and interpreted the data with the support of SA, AA, FC. AC wrote the manuscript with the support of SA, AA, FC. All the authors (AC, SA, AA, SH, FC) critically revised the manuscript and approved the final version.

## Declarations

### Conflict of interest

The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: Stephan Haulon is a consultant and has IP with Cook Medical, GE Healthcare, and Bentley. Stéphane Avril is cofounder of Predisurge, France.
## Ethical approval

Patients were enrolled in a study between April 2020 and January 2021 (Aortic Center, Marie Lannelongue Hospital, Paris, France). This study was registered in [ClinicalTrials.gov (registry)](https://ClinicalTrials.gov) with the identifier NCT04724863 on January 26, 2021.

The clinical trial NCT04724863 was approved by the ethical review boards, as required by law, following the Declaration of Helsinki, which outlines ethical principles for medical research involving human participants. All participants were informed of the procedures and provided written informed consent.

## Funding

This study was funded by a public grant managed by the French National Research Agency, under the 3rd PIA, and integrated into the France 2030 plan, with the following reference: ANR-21-RHUS-0011.

## Data availability

The data that support the findings of this study are available from the corresponding author (SA), upon reasonable request.

## Appendix

A sensitivity analysis was performed to assess the influence of the prescribed breathing boundary conditions on the simulated hemodynamics. Specifically, the magnitude of the imposed displacement was varied by ±20% with respect to the reference configuration at expiration (Table 4).

<table><caption>**Table 4:** Sensitivity analysis for different breathing deformations (±20%) showing renal mean flow rate $\bar{Q}$ and peak flow rate $Q_{max}$ (in brackets) for Patient 1 pre-fEVAR.</caption><thead><tr><th>Patient</th><th>Artery</th><th>Condition</th><th>Q&#773; (Q<sub>max</sub>) [ml/s]</th><th>% Variation in Q&#773;</th><th>% Variation in Q<sub>max</sub></th></tr></thead><tbody><tr><td rowspan="3">Pat. 1</td><td rowspan="3">RRA</td><td>pre-EVAR (BC expiration)</td><td>7.44 (35.10)</td><td>-</td><td>-</td></tr><tr><td>pre-EVAR (BC exp. -20%)</td><td>7.44 (35.10)</td><td>0%</td><td>0%</td></tr><tr><td>pre-EVAR (BC exp. +20%)</td><td>7.36 (34.87)</td><td>-1.0%</td><td>-0.6%</td></tr><tr><td rowspan="3">Pat. 1</td><td rowspan="3">LRA</td><td>pre-EVAR (BC expiration)</td><td>7.18 (25.56)</td><td>-</td><td>-</td></tr><tr><td>pre-EVAR (BC exp. -20%)</td><td>7.42 (26.37)</td><td>+3.3%</td><td>+3.1%</td></tr><tr><td>pre-EVAR (BC exp. +20%)</td><td>6.94 (24.44)</td><td>-3.3%</td><td>-4.4%</td></tr></tbody></table>

These variations in the imposed displacements lead to minimal changes in the main hemodynamics trends, namely on the mean and peak flow rate though the RA with respect to our baseline. Increasing the Breathing Boundary Conditions by 20% (more intense/forced expiration) leads to only a slight reduction in both mean and peak flow rates in the RRA and LRA.
Conversely, decreasing the Breathing Boundary Conditions by 20% (less intense expiration) leads to a marginal increase in mean and peak flow rates in the renal arteries compared to the reference.

A sensitivity analysis by varying the inlet inflow by ±10% was performed, while we assumed no significant changes downstream, at the renal outlets. The sensitivity analysis showed an increase in renal flow rate of approximately 14% for both the renal arteries when the inflow was increased, and a decrease of about 6% when the inflow was reduced (Table 5). As expected, the solution is sensitive to the imposed boundary conditions.

<table><caption>**Table 5:** Sensitivity analysis for inlet velocity waveform (±10%) showing renal mean flow rate $\bar{Q}$ and peak flow rate $Q_{max}$ (in brackets) for Patient 1 pre-fEVAR.</caption><thead><tr><th>Patient</th><th>Artery</th><th>Condition</th><th>Q&#773; (Q<sub>max</sub>) [ml/s]</th><th>% Variation in Q&#773;</th><th>% Variation in Q<sub>max</sub></th></tr></thead><tbody><tr><td rowspan="3">Pat. 1</td><td rowspan="3">RRA</td><td>pre-EVAR (BC inlet)</td><td>7.5 (35.56)</td><td>-</td><td>-</td></tr><tr><td>pre-EVAR (BC inlet +10%)</td><td>8.8 (40.3)</td><td>+17.3%</td><td>+13.3%</td></tr><tr><td>pre-EVAR (BC inlet -10%)</td><td>7.0 (33.6)</td><td>-6.7%</td><td>-5.5%</td></tr><tr><td rowspan="3">Pat. 1</td><td rowspan="3">LRA</td><td>pre-EVAR (BC inlet)</td><td>7.3 (25.96)</td><td>-</td><td>-</td></tr><tr><td>pre-EVAR (BC inlet +10%)</td><td>8.1 (29.2)</td><td>+10.8%</td><td>+12.5%</td></tr><tr><td>pre-EVAR (BC inlet -10%)</td><td>6.9 (24.6)</td><td>-5.6%</td><td>-5.2%</td></tr></tbody></table>

The details of TAWSS maps generation for each artery are shown in Figure 9. As specified in the Materials and Methods section, the artery is unrolled and cut, starting from a reference point P0 located at the cranial proximal artery. From this point, following the direction of the centerline, the TAWSS map is obtained by completely unrolling the vessel, with the $\theta$ angle reported in the plots varying from $-\pi$ to $+\pi$.
<figure><img src="image_10.png" /><figcaption>**Fig. 9:** Details for the generation of the TAWSS maps, showing the reference point $P_0$, the angle theta, the radius $r$, and the centerline. These elements define the local cylindrical coordinate system (r, theta, s) used for mapping, where r is the local radius of the vessel, and s is the position along the centerline.</figcaption></figure>
References

[1] Dansey, K.D., Varkevisser, R.R.B., Swerdlow, N.J., Li, C., Guerre, L.E.V.M., Liang, P., Marcaccio, C., O'Donnell, T.F.X., Carroll, B.J., Schermerhorn, M.L.: Epidemiology of endovascular and open repair for abdominal aortic aneurysms in the united states from 2004 to 2015 and implications for screening. Journal of Vascular Surgery **74**(2), 414-424 (2021) https://doi.org/10.1016/j.jvs.2021.01.044

[2] Biancari, F., Catania, A., D'Andrea, V.: Elective endovascular vs. open repair for abdominal aortic aneurysm in patients aged 80 years and older: systematic review and meta-analysis. European Journal of Vascular and Endovascular Surgery **42**(5), 571-576 (2011) https://doi.org/10.1016/j.ejvs.2011.07.011

[3] Scurr, J.R., McWilliams, R.G.: Fenestrated aortic stent grafts. Seminars in Interventional Radiology **24**(2), 211-220 (2007). https://pmc.ncbi.nlm.nih.gov/articles/PMC3036411

[4] Varkevisser, R.R.B., O'Donnell, T.F.X., Swerdlow, N.J., Liang, P., Li, C., Ultee, K.H.J., Pothof, A.B., De Guerre, L.E.V.M., Verhagen, H.J.M., Schermerhorn, M.L.: Fenestrated endovascular aneurysm repair is associated with lower perioperative morbidity and mortality compared with open repair for complex abdominal aortic aneurysms. Journal of Vascular Surgery **69**(6), 1670-1678 (2019) https://doi.org/10.1016/j.jvs.2018.08.192

[5] Cox, K., Yip, H.C.A., Geragotellis, A., et al.: Endovascular solutions for abdominal aortic aneurysms: Fenestrated, branched and custom-made devices. Vascular and Endovascular Surgery **59**(1), 64-75 (2023) https://doi.org/10.1177/15385744231185606

[6] Nejim, B., Arhuidese, I., Rizwan, M., Khalil, L., Locham, S., Zarkowsky, D., Goodney, P., Malas, M.B.: Concurrent renal artery stent during endovascular infrarenal aortic aneurysm repair confers higher risk for 30-day acute renal failure. Journal of Vascular Surgery **65**(4), 973-981 (2017) https://doi.org/10.1016/j.jvs.2016.10.112

[7] Deslarzes-Dubuis, C., Tran, K., Colvard, B.D., Lee, J.T.: Renal stent complications and impact on renal function after standard fenestrated endovascular aneurysm repair. Annals of Vascular Surgery **72**, 106-113 (2021) https://doi.org/10.1016/j.avsg.2020.10.020. Epub 2020 Nov 27

[8] Silva, J., Tonheiro, J., Rodrigues, F.: The “silent enemy” called renal artery stenosis: A mini-review. Journal of Vascular Diseases **4**(1), 10 (2025) https://doi.org/10.3390/jvd4010010

[9] Zhang, Z.: Renal Artery Stenosis and Occlusion. https://www.msdmanuals.com/professional/genitourinary-disorders/renovascular-disorders/renal-artery-stenosis-and-occlusion (2025)

[10] Vagaonescu, T.D., Dangas, G.: How to diagnose, how to treat: renal artery stenosis-diagnosis and management. Journal of Clinical Hypertension (Greenwich) **4**(5), 363-370 (2002) https://doi.org/10.1111/j.1524-6175.2002.01455.x
[11] Eagleton, M.J., Follansbee, M., Wolski, K., Mastracci, T., Kuramochi, Y.: Fenestrated and branched endovascular aneurysm repair outcomes for type ii and iii thoracoabdominal aortic aneurysms. Journal of Vascular Surgery **63**(4), 930–942 (2016) https://doi.org/10.1016/j.jvs.2015.10.095. Epub 2016 Jan 11

[12] Daye, D., Walker, T.G.: Complications of endovascular aneurysm repair of the thoracic and abdominal aorta: evaluation and management. Cardiovascular Diagnosis and Therapy **8**(Suppl 1) (2017). https://cdt.amegroups.org/article/view/16911

[13] Ashorobi, D., Ameer, M., Fernandez, R.: Thrombosis. In: StatPearls. StatPearls Publishing, Treasure Island (FL) (2024). https://pubmed.ncbi.nlm.nih.gov/30860701/

[14] Modi, K., Soos, M.P., Mahajan, K.: Stent thrombosis. In: StatPearls. StatPearls Publishing, Treasure Island (FL) (2023). https://www.ncbi.nlm.nih.gov/books/NBK441908/

[15] Mayo, R.P., Yaakobovich, H., Finkelstein, A., Shadden, S.C., Marom, G.: Numerical models for assessing the risk of leaflet thrombosis post-transcatheter aortic valve-invalve implantation: Risk of leaflet thrombosis post viv tavi. R Soc Open Sci **7**(12) (2020) https://doi.org/10.1098/rsos.201838

[16] Manning, K.B., Nicoud, F., Shea, S.M.: Mathematical and computational modeling of device-induced thrombosis. Current Opinion in Biomedical Engineering **20** (2021) https://doi.org/10.1016/j.cobme.2021.100349

[17] Kim, S.H., Litt, H.I.: Surveillance imaging following endovascular aneurysm repair: State of the art. Seminars in Interventional Radiology **37**(4), 356–364 (2020) https://doi.org/10.1055/s-0040-1715882

[18] Smith, T., Quencer, K.: Best practice guidelines: Imaging surveillance after endovascular aneurysm repair. AJR American Journal of Roentgenology **214**(5), 1165–1174 (2020) https://doi.org/10.2214/AJR.19.22197

[19] Chaikof, E.L., Dalman, R.L., Eskandari, M.K., Patel, M.S., Schermerhorn, M.L., Starnes, B.W., *et al.*: The society for vascular surgery practice guidelines on the care of patients with an abdominal aortic aneurysm. Journal of Vascular Surgery (2018) https://doi.org/10.1016/j.jvs.2017.10.044

[20] Morell-Hofert, D., Gruber, L., Gruber, H., Glodny, B., Gruber, I., Loizides, A.: Contrast-enhanced ultrasound after endovascular aortic repair: Supplement and potential substitute for ct in early- and long-term follow-up. Annals of Vascular Surgery (2024) https://doi.org/10.1016/j.avsg.2023.11.040

[21] AbuRahma, A.F., Srivastava, M., Mousa, A.Y., Dearing, D.D., Hass, S.M., Campbell, J.R., Dean, L.S., Stone, P.A., Keiffer, T.: Critical analysis of renal duplex ultrasound parameters in detecting significant renal artery stenosis. Journal of Vascular Surgery **56**(4), 1052–105910601 (2012) https://doi.org/10.1016/j.jvs.2012.03.036
[22] Desberg, A.L., Paushter, D.M., Lammert, G.K., Hale, J.C., Troy, R.B., Novick, A.C., Nally, J.V.J., Weltevreden, A.M.: Renal artery stenosis: Evaluation with color doppler flow imaging. *Radiology* **177**(3), 749–753 (1990) https://doi.org/10.1148/radiology.177.3.2243982

[23] Kohler, T., Zierler, R., Martin, R., Nicholls, S., Bergelin, R., Kazmers, A., Beach, K., Strandness, D.J.: Noninvasive diagnosis of renal artery stenosis by ultrasonic duplex scanning. *Journal of Vascular Surgery* **4**(5), 450–456 (1986) https://doi.org/10.1067/mva.1986.av50040450. https://pubmed.ncbi.nlm.nih.gov/3534324/

[24] Zierler, R.E., Bergelin, R.O., Davidson, R.C., Cantwell-Gab, K., Polissar, N.L., Strandness, D.E.: A prospective study of disease progression in patients with atherosclerotic renal artery stenosis. *American Journal of Hypertension* **9**(11), 1055–1061 (1996) https://doi.org/10.1016/0895-7061(96)00196-3

[25] Harvin, H.J., Verma, N., Nikolaidis, P., Hanley, M., Dogra, V.S., Goldfarb, S., Gore, J.L., Savage, S.J., Steigner, M.L., Strax, R., Taffel, M.T., Wong-You-Cheong, J.J., Yoo, D.C., Remer, E.M., Dill, K.E., Lockhart, M.E., Urologic Imaging, E.P., Imaging, V.: Acr appropriateness criteria® renovascular hypertension. *Journal of the American College of Radiology* **14**(11S), 540–549 (2017) https://doi.org/10.1016/j.jacr.2017.08.040

[26] Fernandez, L.J.: Renal ultrasound in arterial systemic hypertension. *Journal of Radiological Science* **49**(1), 26–32 (2024) https://doi.org/10.4103/jradiolsci.JRADIOLSCI-D-23-00036

[27] Chi, Y.-W., White, C.J., Thornton, S., Milani, R.V.: Ultrasound velocity criteria for renal in-stent restenosis. *Journal of Vascular Surgery* (2009) https://doi.org/10.1016/j.jvs.2008.12.066

[28] Bakker, J., Beutler, J.J., Elgersma, O.E.H., Lange, E.E., Kort, G.A.P., Beek, F.J.: Duplex ultrasonography in assessing restenosis of renal artery stenosis. *Cardiovascular and Interventional Radiology* **22**, 475–480 (1999) https://doi.org/10.1007/s002709900435

[29] Wen, J., Liu, X., Lei, J., Wang, J., Chen, X., Zheng, T., Yuan, D.: Hemodynamics in renal arteries with partial coverage after endovascular aneurysm repair affected by renal orientations. *Medical Nonlinear Dynamics*, 100224 (2023) https://doi.org/10.1016/j.medntd.2023.100224

[30] Kandail, H., Hamady, M., Xu, X.Y.: Comparison of blood flow in branched and fenestrated stent-grafts for endovascular repair of abdominal aortic aneurysms. *Journal of Endovascular Therapy* **22**(4), 578–590 (2015) https://doi.org/10.1177/1526602815587261

[31] Kandail, H., Hamady, M., Xu, X.Y.: Effect of a flared renal stent on the performance of fenestrated stent-grafts at rest and exercise conditions. *Journal of Endovascular Therapy* **23**(5), 809–820 (2016) https://doi.org/10.1177/1526602816651425
[32] Tran, K., Yang, W., Marsden, A., Lee, J.T.: Patient-specific computational flow modelling for assessing hemodynamic changes following fenestrated endovascular aneurysm repair. JVS-Vascular Science **2**, 53–69 (2021) https://doi.org/10.1016/j.jvssci.2020.11.032

[33] Tran, K., Deslarzes-Dubuis, C., DeGlise, S., Kaladji, A., Yang, W., Marsden, A.L., Lee, J.T.: Patient-specific computational flow simulation reveals significant differences in paravisceral aortic hemodynamics between fenestrated and branched endovascular aneurysm repair. JVS-Vascular Science **5**, 100183 (2024) https://doi.org/10.1016/j.jvssci.2023.100183

[34] Ben-Ahmed, S., Bakel, T.M.J., Rosset, E., Fassot, G., Albertini, J.-N., Avril, S., Figueroa, C.A.: Patient-specific analysis of renal artery hemodynamics after evar with fenestrated or branched versus parallel stent-graft techniques for renal vascularization (2022). Available at SSRN: https://ssrn.com/abstract=4010580 or http://dx.doi.org/10.2139/ssrn.4010580

[35] Lin, W.-C.P., Doyle, M.G., Amon, C.H., Forbes, T.L.: Patient-specific computational fluid dynamics simulations before and after fenestrated endovascular aneurysm repair. Journal of Vascular Surgery (2020) https://doi.org/10.1016/j.jvs.2020.04.437

[36] Velde, L., Donselaar, E.J., Groot Jebbink, E., Boersen, J.T., Lajoinie, G.P.R., Vries, J.-P.P.M., Zeebregts, C.J., Versluis, M., Reijnen, M.M.P.J.: Partial renal coverage in endovascular aneurysm repair causes unfavorable renal flow patterns in an infrarenal aneurysm model. Journal of Vascular Surgery **66**(5), 1507–1516 (2017) https://doi.org/10.1016/j.jvs.2017.05.092. Copyright © 2017 by the Society for Vascular Surgery

[37] Suh, G.Y., Choi, G., Herfkens, R.J., Dalman, R.L., Cheng, C.P.: Respiration-induced deformations of the superior mesenteric and renal arteries in patients with abdominal aortic aneurysms. Journal of Vascular and Interventional Radiology **24**(7), 1035–1042 (2013) https://doi.org/10.1016/j.jvir.2013.04.006

[38] Corvo, A., Avril, S., Aliseda, A., Haulon, S., Chassagne, F.: Computational simulation of respiration-induced deformation of renal arteries after evar. Annals of Biomedical Engineering (2025) https://doi.org/10.1007/s10439-025-03806-y

[39] Yuan, G., Drost, N.A., McIvor, R.A.: Respiratory rate and breathing pattern. McMaster Univ. Med. J **10**(1), 23–25 (2013). https://www.mangalam.nl/wp-content/uploads/2018/12/Breathing-Pattern.pdf

[40] Grünwald, A., Korte, J., Wilmanns, N., al.: Intraventricular flow simulations in singular right ventricles reveal deteriorated washout and low vortex formation. Cardiovascular Engineering and Technology **13**, 495–503 (2022) https://doi.org/10.1007/s13239-021-00598-9

[41] Les, A.S., Yeung, J.J., Schultz, G.M., Herfkens, R.J., Dalman, R.L., Taylor, C.A.: Supraceliac and infrarenal aortic flow in patients with abdominal aortic aneurysms:
Mean flows, waveforms, and allometric scaling relationships. Cardiovascular Engineering and Technology **1**(1), 10–10071323901000048 (2010) https://doi.org/10.1007/s13239-010-0004-8

[42] Moore, J.E.J., Ku, D.N.: Pulsatile velocity measurements in a model of the human abdominal aorta under resting conditions. Journal of Biomechanical Engineering **116**(3), 337–346 (1994) https://doi.org/10.1115/1.2895740

[43] Pellerito, J.S., Revzin, M.V.: Ultrasound assessment of native renal vessels. In: Radiology Key. https://radiologykey.com/ultrasound-assessment-of-native-renal-vessels

[44] House, M.K., Dowling, R.J., King, P., Gibson, R.N.: Using doppler sonography to reveal renal artery stenosis: an evaluation of optimal imaging parameters **173**(3), 761–765 https://doi.org/10.2214/ajr.173.3.10470919

[45] Mortazavinia, Z., Arabi, S., Mehdizadeh, A.R.: Numerical investigation of angulation effects in stenosed renal arteries. Journal of Biomedical Physics & Engineering **4**(1), 1–8 (2014). https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4258856/

[46] Chiu, J.-J., Chien, S.: Effects of disturbed flow on vascular endothelium: pathophysiological basis and clinical perspectives. Physiological Reviews **91**(1), 327–387 (2011) https://doi.org/10.1152/physrev.00047.2009

[47] Cheng, C.P., Suh, G.Y., Kim, J.J., Holden, A.: Cardiac pulsatility– and respiratory-induced deformations of the renal arteries and snorkel stents after snorkel endovascular aneurysm sealing. Journal of Endovascular Therapy **26**(4), 556–564 (2019) https://doi.org/10.1177/1526602819856363