Analysing The Cross-Section of The Abdominal Aortic Aneurysm Neck and Its Effects on Stent Deployment

Stent graft devices for the treatment of abdominal aortic aneurysms (AAAs) are being increasingly used worldwide. Yet, during modelling and optimization of these devices, as well as in clinical practice, vascular sections are idealized, possibly compromising the effectiveness of the intervention. In this study, we challenge the commonly used approximation of the circular cross-section of the aorta and identify the implications of this approximation to the mechanical assessment of stent grafts. Using computed tomography angiography (CTA) data from 258 AAA patients, the lumen of the aneurysmal neck was analysed. The cross-section of the aortic neck was found to be an independent variable, uncorrelated to other geometrical aspects of the region, and its shape was non-circular reaching elliptical ratios as low as 0.77. These results were used to design a finite element analysis (FEA) study for the assessment of a ring stent bundle deployed under a variety of aortic cross-sections. Results showed that the most common clinical approximations of the vascular cross-section can be a source of significant error when calculating the maximum stent strains (underestimated by up to 69%) and radial forces (overestimated by up to 13%). Nevertheless, a less frequently used average approximation was shown to yield satisfactory results (5% and 2% of divergence respectively).

for endoleak type I. For that, finite element analysis (FEA) models have been extensively used in the literature, thoroughly examining and optimizing mechanical aspects of medical significance.
In most of these studies, vessels are treated as idealized tubes with a circular cross-section, yet the assumption of circularity is challenged when examining CTA scans of the aorta [13][14][15] . It is indeed true that in clinical practice, medical doctors consider the aortic cross section to be circular and its radius is usually approximated either with the minimum radius 16 or the maximum radius 17,18 appearing on the medical imaging data. Yet the consequences of this practice have not been evaluated in the EVAR context.
Almost every investigation of the mechanical response of stent deployment is carried out assuming circular boundary geometries (for some recent examples refer to [19][20][21][22]. Even where analysis of plaque is attempted [23][24][25] or patient specificness in taken into account 26 , the assumption of a circular luminal cross-section is usually maintained. Recognising the need to move away from such idealizations, some researchers 27 have proposed the development of tools that can take into account all geometrical irregularities of vessels, while others have developed such algorithms 28 when reconstructing the aortic geometry from 2D data. However, to the authors' knowledge, no thorough investigation has ever been conducted to quantify either the cross-sectional shape variations of the human abdominal aorta or its effects on stent graft deployment.
Herein, the circularity assumption is challenged by investigating the cross-section of the neck of the AAA. The significance of this region to the EVAR is critical since it directly affects the proximal end of the stent graft, which is primarily responsible for preventing endoleaks and migration. The effects of the vascular cross-section on the exerted forces and strains of the stent are also examined via FEA, because of their importance to sealing and fatigue life.

Results
ctA Study. We examined pre-op computed tomography angiography (CTA) scans from 258 AAA patients that subsequently underwent EVAR. For each patient, a proximal and a distal image of the proximal AAA neck was acquired and the luminal shape was extracted (Fig. 1). In each cross-section, the circularity factor (CF) and elliptical ratio (ER) were used as metrics of shape. The results are summarised in Table 1. Furthermore, using 5 points of interest per case (Fig. 2), an additional four variables related to the aneurysmal neck, were examined. Table 2 reports the median and range of them, while histograms of all examined variables are provided as Supplementary Information.
Average CF and average ER were compared to each other. The metrics had a Pearson's correlation value of 0.684, suggesting that the shape factors are producing similar values to each other, hence no significantly rough boundaries were present in the intima. More interestingly, neither of the two metrics strongly correlated to any of the additional variables of the aneurysmal neck and only CF presented a very weak correlation of 0.161 with angle α.
When comparing the values of the metrics on the two planes of the cross-section of the aortic neck (i.e. the relation between the proximal and the distal cross-section), only a weak correlation appears (ρ = 0.237 for CF and ρ = 0.206 for ER), suggesting that, if possible, the study of two cross-sections in the aortic neck's region should be pursued.
Neither ER nor CF was found to follow a normal distribution, an expected result since both metrics have an upper limit of 1. Furthermore, no shape metric had a statistically significant difference between the genders, despite differences in the neck length, which was statistically significantly bigger in males (23.0 mm vs 16.0 mm for females), as well as the average neck diameter (23.5 mm vs 21.25 mm).
In general, CF was high, suggesting the smoothness of the intima. And while the median average ER was also high (closely resembling a circle), in instances, ER got as low as 0.77 (Fig. 3). This highlights the need for special patient specific attention when designing and modelling stent grafts, since the AAA neck is the most proximal region of endograft contact and is primarily responsible for adequate EVAR anchoring and sealing. The effect of such a cross-section on the deployment of an endograft was subsequently examined. feA deployment study. A FEA model was used to explore the effects non-circular cross-sections have on deployed stents (Fig. 4). A model of a ring stent bundle, found in devices like the Anaconda TM (Terumo Aortic, Glasgow, UK), was deployed in a number of elliptical vessels, as well as complementary circular ones. All cross-sectional configurations are reported in Table 3: every ellipsis was associated with a minor, a major and an average circle, each of which corresponds to a different clinical approximation of the lumen (Fig. 4b). Note that the values of Table 3 correspond to the original build of the vessels, hence refer to the unpressurized state. Note also that the most extreme of these cases was designed so that when pressurized, the most severe ER of the CTA study would be approximated.
In all models examined, the maximum strain of the ring stent bundle increased while the elliptical ratio decreased (Fig. 5 top). The worst case ellipse ( = . ER 0 75) had a maximum strain of 0.0415 and if the major axis approximation was followed, the strain would be underestimated by 69%. At the average elliptical ratio (ER 0 94 = . ), this value dropped to 40%, still yielding a significant error. In contrast, the minor axis approximation would result in a 62% overestimation at ER = 0.89 (elliptical ratio that results in 33% oversize) and 21% at ER 0 94 = . . Regarding the average circle, an underestimation was also observed but it was significantly smaller: 5% at ER 0 75 = . and 3.5% at ER 0 94 = . . A smaller variation was observed for the chronic outward force (COF) (Fig. 5 bottom). The major axis approximation overestimated COF by 13.1% at the worst case ellipse and by 1.8% at the average ellipse. In contrast, the minor circle underestimated COF by 7.3% at the 0.89 ratio and by 2.5% at the 0.94 ratio. The average circle laid 0.8% above the extreme elliptical value and 2.2% above the average one.
www.nature.com/scientificreports www.nature.com/scientificreports/ When examining the differences that arise once the deployment angle of the endograft changes (angle of rotation about luminal axis), results are less sensitive. COF does not change more than 1% at any configuration ( Fig. 6 bottom) while maximum strain stays below a 4% variation (Fig. 6 top) for most of the configurations.
Finally, it is interesting to note that similar to the effect the vessel has on the stent, the stent affects the cross section of the vessel as well. In all simulations, the post-deployment shape of the lumen was significantly altered by the bundle ring, hence conforming into a circular shape (Fig. 7). The most extreme cross section constructed had an ER = 0.65 when unpressurized: upon pressurization this ratio increased to 0.75 and after the ring deployment it was further raised to 0.966.

Discussion
The cross-section of the AAA neck was extensively examined through the study of 258 AAA patients, challenging the assumption of circularity. Results showed that the median average ER did not lie far from the circle, yet aneurysmal necks with very elliptical cross-sections were identified as well. Furthermore, the lack of correlation between the shape metrics used and other geometrical variables of the AAA neck, indicate that special attention needs to be taken for the aortic neck's luminal shape in a patient by patient manner.
The scans used for vascular measurements should ideally be perpendicular to the centreline of the vessel. Nevertheless, axial scans are sometimes used in clinical practice 29 . In such cases, the smallest measurement of the luminal diameter is considered an appropriate approximation of the true diameter 30 , yet the errors introduced with this approximation are not minimal. It has been shown that the use of axial scans leads to statistically significant overestimations of the aneurysmal size when compared to scans transverse to the vessel 31 . Even if the scan orientation is perpendicular to the lumen though, when non-circular target vessels are identified, specialists make use of approximate diameters to plan the EVAR and decide upon the most suitable endograft. Nevertheless, as already mentioned, it is not rare that stents fail to anchor or seal appropriately, incidents that might be aided by non-circular aortic cross-sections. Utilizing the CTA study, a thorough examination was conducted exploring the effects the cross-sectional shape of the vessel has on a stent model and both the COF and (especially) the strains were found to be significantly affected.  www.nature.com/scientificreports www.nature.com/scientificreports/ The major axis approximation was found to underestimate the maximum strain by 69% at the most extreme ER and the total radial force overestimated by 13%. In contrast, the minor axis approximation overestimated the maximum strain by up to 62% and underestimated the total radial force by up to 7%. These two approaches represent the most common approximation of the vascular cross-section and if followed, can be the source of significant errors during EVAR planning. On the other hand, the average circle produced a much better estimation of the maximum strain and overestimated the COF by a maximum of 2.2% when compared to the respective elliptical shapes. This is important, since the underestimation of strains can cause unexpected fatigue fractures and result in the loss of structural integrity of the device while the overestimation of radial forces may lead to unforeseen loss of stent/vessel sealing. As a result, the average circle can be safely used to calculate these variables, when a CT perpendicular to the aortic centreline is considered.  www.nature.com/scientificreports www.nature.com/scientificreports/ When examining the axial deployment angle of the endograft, it was demonstrated that the COF and maximum strains were practically unaffected by it. Furthermore, it was calculated that the post-deployment shape of the lumen, being strongly affected by the bundle ring, significantly increased its ER, diverging only by 3.4% from a circle even in the most extreme elliptical case.
The CT scans obtained for this study reflect a specific group of AAA patients, i.e. those who are suitable for EVAR. Nevertheless, given that the results of this analysis are relevant to EVAR interventions only, the nonrepresentation of the AAA population suitable for open repair is not considered a limitation. In the future, pre-and post-EVAR data should ideally be analysed in parallel, to examine if vascular non-circularity can be a predictor of endoleaks or migration. Despite this omission though, it is believed that the variables examined herein already improve our current understanding of the geometry of the aortic anatomy and bring new insight  Table 3. Cross-section specifications of the FEA vessel. Values are reported in mm at 0 mmHg (unpressurized state). The major circle has a constant radius of 9.98 mm.  www.nature.com/scientificreports www.nature.com/scientificreports/ to the topic. It is recommended that future stent graft analyses take into account variations in the target vessel geometry, since the use of non-idealized cross-sections can have a measurable effect on the functional performance of these devices. It is also recommended that medical practitioners use average aortic diameters during EVAR planning. The accurate sizing of the endografts will result in optimized device functionality and reduced EVAR complications.  www.nature.com/scientificreports www.nature.com/scientificreports/ Methods ctA study. The data used herein, were collected by the core laboratory M2S, Inc. West Lebanon, NH, USA in the period May 2009 to July 2011 as part of the non-randomized Anaconda stent graft investigational device exemption (IDE) pivotal study, approved by the U.S. Food and Drug Administration (registration number: NCT00612924 in the U.S. National Library of Medicine 32 ) in accordance with relevant guidelines and regulations. All patients provided their informed consent. For the purposes of the current study, preoperative (baseline) imaging data from 258 patients (222 (86%) men, 34 (13%) women and 2 (1%) unspecified) aged between 51 and 88 years were used. Data were supplied to us anonymised, with age and gender being the only descriptors of the patients. The inclusion criteria of the original study were: • Infrarenal AAA ≥ 4.0 cm in diameter, or AAA growth ≥1.0 cm/year • Iliac artery distal fixation sites ≥20 mm in length • Ability to preserve at least one internal iliac artery • Femoral/Iliac artery's size and morphology should be compatible with the appropriate delivery system (6 mm, 6.67 mm or 7.67 mm in diameter) Patients with thrombus, calcification and/or plaque ≥2 mm in thickness and/or 50% continuous coverage of the vessel's circumference in the intended fixation site were excluded. Pre-op data were supplied to us anonymised, with age and gender being the only descriptors of the patient and m2s Preview v4.0.1 software was used to assess them.
For our study, 2 CTA images were considered per patient, one at the proximal end of the AAA's neck (immediately below the lower renal) and one at its distal end, right before the aneurysm (Fig. 1). All images were acquired at a plane perpendicular to the aortic centreline. This is important, since the original (axial) scans are not, in general, transverse to the axis of the vessel and can make cross-sections appear non-circular or asymmetric even if they are not, especially if significant tortuosity is present.
Inside most AAAs, there is usually intraluminal thrombus (ILT) and regions of calcification. The irregularity of ILT and calcification is vast and random, yet it is reasonable to assume that deployed stents crush ILT and part of the calcified layer, especially when ballooning is employed for this reason exactly. As a result, thrombus and calcification were not included in the current analysis.
For each CTA image, a cross-section boundary that included the lumen, the calcified and the thrombotic region was manually drawn. This allowed the definition of the intima wall's inner border. The images of these borders alone were then manipulated with a Matlab script (version R2015b, MathWorks), turned into binary format and filled to create a 1-colour 2D surface. In each final surface two metrics were applied to quantify their divergence from circularity.
The first metric used was the circularity factor, defined as: (1) 2 where A = area and P = perimeter of the examined surface. This metric is affected by ovality as well as irregular (i.e. jagged or rough) edges and for a circle gets a maximum value of 1. The second metric was the elliptical ratio and for the calculation of it, as a first step, the evaluation of an equivalent ellipse (same second moment of area as the original surface) was necessary. Given the ellipse, elliptical ratio is defined as: 1 2 R where R1 semi minor axis of the ellipse and 2 = − = semi-major axis of the ellipse (Fig. 1d2). By averaging the values of each metric for the proximal and the distal cross-section, average CF and average ER could be acquired to represent each AAA neck.
An additional 4 variables were considered in the region of the AAA's neck, in order to reveal any possible correlations between the shape of the neck and its luminal outline. The Average Neck Diameter, calculated as the average value of two neck diameters, one at the distal renal artery (P3) and one right before the proximal end of the AAA (P4), the Neck Length, defined as the centreline distance between points P3 and P4 and the angles a and b, calculated from the points (P1, P2, P4) and (P2, P4, P5) respectively, were examined (Fig. 2). Note that the measurements of the Average Neck Diameter and Neck Length were conducted by trained technicians of M2S, as part of the initial clinical investigation.
Finally, the shape metric data, along with the neck-related variables, were statistically analysed using SPSS, version 25. Normality was tested according to the Shapiro-Wilk test. Correlation between the examined variables was investigated with a 2-tailed Pearson correlation test at the 0.01 significance level. Lastly, the difference of medians between the genders was examined with the non-parametric median test for 2 independent medians at the 0.05 significance level. feA deployment study. Utilizing the results of the CTA study, a numerical analysis of the non-circularity of the aorta was conducted. More specifically, a series of 19 elliptical and "equivalent-circle" vascular sections in the range of ER values identified previously was considered as target vessels of EVAR. A FEA stent model was assembled, compacted and deployed in each vascular section, and mechanical assessment followed. The FEA stent model used had been previously developed and validated 33 ; it is a ring stent bundle model, typical of the Scientific RepoRtS | (2020) 10:4673 | https://doi.org/10.1038/s41598-020-61578-y www.nature.com/scientificreports www.nature.com/scientificreports/ structural units found in the Anaconda TM endograft. In brief, it consists of a series of straight overlapping Nitinol wires that curve into a ring shape, to take into account the strains induced by the manufacturing process. The material parameters of Nitinol and the ring specifications used herein are summarized in Tables 4 and 5 respectively.
The neck of the aneurysm was represented by a straight tube with length twice the ring diameter and original thickness of 1.9 mm. By altering the semi-minor axis, R 1 , of the cross-section, the elliptical ratio was adjusted according to Eq. (2) (Fig. 4).
Starting from the value of 1, representing a circle, 6 more equidistant ratios were examined down to the value of 0.65, which when pressurized increased to 0.75, i.e. close to ER = 0.77, the most extreme ratio identified in the patient dataset (Table 3). Taking into account the geometrical shape of the ring, for each ellipse, 3 cases were studied, each one considering a different deployment position (Fig. 4b): (i) with the peaks and valleys of the ring being aligned with the axes of the cross-section, (ii) with the ring peaks at 22.5° angle and (iii) with the ring peaks at 45°. For symmetry reasons, the 0° and 45° are the extreme cases of rotation about the axial direction of the vessel. Additionally, two more cases were examined for each ratio different to 1: a circular cross-section with radius equal to R 1 , called minor circle, and a circular cross-section with radius + R R 2 1 2 , called average circle. The reason for examining the circular cases was to compare the ellipses with the results that would occur if common circular approximations were followed. The original circle represents the case of approximating the ellipse with its major axis, the minor circle corresponds to the minor axis approximation and the average circle lies in between.
In each vascular section, the ring model was deployed assuming a friction coefficient µ = 0.3. The vessel was pressurised between diastole (P d = 80 mmHg) and systole (P s = 160 mmHg) for 5 cycles that allowed the system to settle. The maximum mean strain developed on the ring between systole and diastole was exported along with the COF (calculated by summing the radial component of all forces produced by the ring on the vascular surface) at the end of the systolic phase. The boundary conditions applied to the ring are summarized below (refer to Fig. 4a, for point definitions).
During compaction: x = Displacement 0 for points B, D y Displacement 0 for point E (11) z = A 10% oversize (percentage by which a stent is larger than the target vessel) at the time-weighted arterial blood pressure P m = 106.7 mmHg, defined as: was initially assumed. This oversize relates only to the initial circular vessel (major circle). Since the same ring was used for all vessel models, greater oversize ratios were acquired for all cases but the first. For the smallest average circle, oversize was 33% while for the smallest minor circle 69%. Nevertheless, because it is highly unlikely that a surgeon would plan an EVAR at 69% oversize, a maximum of 33% oversize was assumed for the minor circle as well. Hence, results above this region were not taken into account in post-processing and were only illustrated with dotted lines in the figures created. It should also be noted that when altering the radius of the vessel, the thickness of the vessel was altered too, so that each aortic section exhibited the same stiffness. The material model of the vessel used was linear elastic and homogeneous. The material parameters are reported in Table 6 and were adjusted to produce a 4.2% radial strain on the vessel when stented, representing an extreme pulsatility scenario. As already mentioned, no thrombus or calcification were taken into account because of their versatile manifestation, the avoidance of such regions during EVAR planning, the fact that for the most part they get crushed during EVAR deployment, and the surprising range of stiffness values found in the literature (the elastic modulus for calcification ranges from 40 MPa 34 up to 22.7 GPa 35 ) making their accurate modelling questionable.
Finally, all simulations were run on Abaqus (version 6.13-2, Dassault Systemes Simulia Corp., RI, USA), on 12 Xeon © CPUs of a desktop computer (3.40 GHz, 64 GB) and the analysis time was between 83 to 290 minutes, depending on the vessel size.

Data availability
All datasets associated with this manuscript are available in FIGSHARE (https://doi.org/10.6084/ m9.figshare.11742792) and from the corresponding author upon reasonable request.