The role of fast approximate estimation displacement forces in prediction of stent-graft-related endoleaks after endovascular abdominal aortic aneurysm repair

Introduction

Endovascular aneurysm repair (EVAR) has become the mainstream option for infrarenal abdominal aortic aneurysms (AAAs) in patients with suitable anatomy and a reasonable life expectancy (1,2). However, EVAR is still limited because of the specific complications and high rate of reintervention (3). Therefore, an understanding of the mechanisms of EVAR failure and delicate preoperative planning of EVAR are essential to improve prognosis.

Adequate and durable sealing is vital to sustain EVAR success, which, from a mechanical perspective, is a combined result of the stent graft (SG) fixation force and displacement force (DF). Blood flow through the SG exerts a force on the entire wall of the SG called DF, which was associated with migration of SGs and stent-graft-related endoleaks (SGELs) (type I and type III) (4). Both migration and SGELs are associated with sealing failure and late aneurysm rupture (5,6). While the fixation force, mainly consists of radial force of self-expanding SG, prevents the migration of SG (4). Therefore, the evaluation of DF and fixation force is helpful for better assessment of risk of complications after EVAR.

Current preoperative planning of EVAR relies predominantly on preoperative imaging protocols (1,2,7), with computed tomography angiography (CTA) being the standard in most cases, which ignores the effects of local hemodynamic environment. The limitations of image-based geometric protocols have motivated the development of mechanical approaches for more accurate prediction of EVAR complications (8,9). SG oversizing ratio (OSR) is the most commonly used parameter in clinical practice for SG radial force evaluation and SG size selection based on preoperative diameter measurement for landing zones. Computational fluid dynamics (CFDs) simulations have been validated as a reliable approach for accurately assessing the post-EVAR hemodynamic environment and predicting the risk of SGEL (10,11). As for DF, the patient-specific DF was calculated through the CFD approach by integrating the SG surface pressure and wall shear stress (WSS) (12-14). While the CFD approach yields a relatively accurate DF, this procedure is complicated, time-consuming, and challenging to incorporate into clinical practice due to its reliance on three-dimensional (3D) models of post-deployment SG for analysis.

Notably, a previous study suggested that DF is largely driven by pressure direction changes at the SG ends, which are determined by patient-specific morphology (15). Based on the finding, a method for estimating DF using patient-specific aorto-iliac morphological parameters was introduced in this study. This approach eliminates the necessity for complex CFD simulations of complete 3D post-deployment SG models, making preoperative estimation of patient-specific DF feasible.

In this study, a simplified formula proposed by the previously work was applied to calculate the patient-specific DF (15). The aim was to investigate and validate the effect of the simplified momentum quantitative DF on risk of SGEL after EVAR. Furthermore, we sought to develop a risk prediction model based on DF and OSR parameters to predict risk of SGEL and guide SG selection. The hypothesis was that the DF might be associated with risk of SGEL after EVAR and could serve as a useful tool to improve clinical decision-making in preoperative EVAR planning. We present this article in accordance with the STROBE reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1349/rc).

Methods

Study design

This case-control study was conducted based on a retrospective cohort database of patients with infrarenal AAA at West China Hospital from July 2011 to May 2020. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the institutional review board of West China Hospital (No. 1705, 2023) and individual consent for this retrospective analysis was waived.

Study population

Patients who had undergone EVAR with bifurcated main body and iliac limb SGs deploying in common iliac arteries or external iliac arteries were included. The exclusion criteria were as follows: (I) inflammatory aneurysms, pseudoaneurysms or dissecting aneurysms; (II) aneurysms repaired by cuff SGs; (III) reintervention for previous repair; and (IV) absence of preoperative CTA.

Case patients were identified as those who had SGEL (type I and type III) after EVAR. The SGEL was diagnosed by color duplex ultrasound and further confirmed by CTA. Control patients were matched to the case group by age and sex using Rstudio (R version 4.1.3, package Matchlt 4.5.3). From the matched cohort, the most appropriate patients were selected for inclusion in the control group at a case-to-control ratio of 1:2. In total, 148 patients were included as the control group. The patient selection process is illustrated in Figure S1.

Anatomical parameters and stent oversizing

The 3D vascular models and the central lumen lines were reconstructed using commercial software (MIMICS v21.0, Materialise Inc., Belgium). The distal edge of SG (zero reference point of distal landing zones) was identified retrospectively on the pre-operative CTA 3D reconstruction models using digital subtraction angiography (DSA) as a reference, and the reference plane of the proximal landing zone was identified through a similar approach. Figure S2 and Appendix 1 have shown the specific methods of reconstruction (validated internally, see Figure S3 and Appendix 1). Morphological data were collected for all patients, including neck diameter, percentage of severe neck angulation (SNA) (16), AAA diameter (maximum diameter of aneurysm sac), maximum diameter of iliac arteries, and pelvic artery index (PAI) of tortuosity (16,17). According to Oliveira et al., SNA was defined as meeting any of the following criteria: (I) neck length >15 mm with β >75°; (II) α >60°; or (III) neck length >10 mm with β >60° or α >45° (16). PAI was defined as the length of the pelvic artery, measured along the vessel centerline from the aortic bifurcation to the origin of the common femoral artery, divided by the straight-line distance between these two landmarks (18). All diameters were measured in slices perpendicular to the center line as described in a previous study (16). OSR was computed as the ratio of the diameter difference between SG and the landing artery (infrarenal aorta and bilateral iliac arteries). Two experienced vascular surgeons measured the parameters using an established protocol on the preoperative CTA. All diameters were measured from the outer wall to outer wall perpendicular to the path of the aorta or iliac arteries (17,19).

Simplified momentum quantitative DF

Previous study examined how changes in momentum and pressure drop contribute to the DF, and found that changes in momentum and pressure between the outlet and inlet were almost negligible (15). Thus, the formula can be simplified as:

DF→=p(A1n1→+A2n2→+A3n3→)[1]

where DF→ represents the DF vector, p is the systolic blood pressure, A_i is the cross-section area, and ni→ is the cross-section unit normal vector with positive value inward the SG, as shown in Figure 1. Therefore, by combining the patient-specific blood pressure and the cross-sectional area of the inlet and outlets, we were able to obtain the DF efficiently.

Figure 1 Schematic diagram of different components of the displacement forces. DF, displacement force.

The estimated DF was presented in two formats, a Cartesian coordinate view with components DF_x, DF_y, and DF_z, and an orthogonal view with components that are orthogonal to the inlet and outlets (proximal DF_orthogonal for proximal neck and right DF_orthogonal, left DF_orthogonal for bilateral iliac limb), as shown in Figure 1. Thus, the magnitude and direction of the DF can be presented as a real number, where positive values indicated DF inward the SG, and negative values indicate the opposite direction.

Statistical analysis

Continuous data were presented as means ± standard deviation (SD) or as median [interquartile range (IQR)]. Categorical data were presented as frequency (%). All variables were compared between groups using Student’s t-tests or Mann-Whitney U test for continuous data, and chi square test or Fisher’s exact test for categorical data. Multiple imputation was adopted to handle missing data for covariables.

Receiver operating characteristic (ROC) curve analysis was used to assess the discrimination ability of different geometric and mechanical parameters on SGEL. The confidence interval (CI) of area under the curve (AUC) was estimated using Bootstrap resampling (replicate times =500). Highest Youden index was used to identify the appropriate cut-off value of the ROC curve. Calibration analysis was performed using the calibration curve and Hosmer-Lemeshow test.

Multivariate logistic regression analysis was performed to calculate the odds ratio (OR) and related 95% CI for SGEL by exposure to DF parameters and morphology parameters. Clinically relevant factors, including DF parameters (DF_magnitude, proximal DF_orthogonal, left DF_orthogonal, and right DF_orthogonal) and OSR parameters (proximal neck OSR, right limb OSR, and left limb OSR) were included, and factors with a P value less than 0.1 in the univariate analysis were incorporated in the variable selection using LASSO regression, and then further simplified by stepwise Akaike information criterion (AIC) algorithm. Finally, the correlation between variables and the issue of multicollinearity were considered. The multivariable models were constructed as follows: model 1 included the OSR parameters of proximal and bilateral distal landing zones; model 2 consisted of the OSR parameters and the anatomical parameters of landing zones, which represented the most commonly used preoperative planning parameters in clinical practice; model 3 combined model 1 and DF magnitude that were significantly associated with risk of SGEL; model 4 combined model 1 and DF with three components that are orthogonal to the inlet and outlets, with consideration of DF acting on each cross section. Additionally, net reclassification improvement (NRI) and integrated discrimination improvement (IDI) statistics were adopted to compare the performance of all predictive models. Sensitivity analysis was performed in the subgroup analysis involving patients with SNA or ectatic distal landing zone (defined as maximal diameter >17 mm). R Version 4.1.3 (http://www.R-project.org) was utilized for statistical analysis.

Results

Baseline characteristics

A total of 964 patients were reviewed according to the inclusion and exclusion criteria, and 217 patients were finally enrolled in the study (Figure S1). Of the 217 patients, 69 were diagnosed with SGEL, comprising 26 (37.7%) T1AEL, 48 (69.6%) T1BEL and 7 (10.1%) T3EL. The control group consisted of 148 patients who exhibited no evidence of SGEL within 12 months after EVAR.

Baseline characteristics of the case-control cohort are summarized in Table 1. The mean age of the SGEL and non-SGEL groups was 70.0±8.3 and 70.4±7.8 years, respectively. There were no significant differences in demographic features or comorbidity profiles between the SGEL and non-SGEL groups. The median ultrasound or CTA follow-up after EVAR was 39 (IQR, 23–65) months for the SGEL group and 38 (IQR, 19–58) months for the control group (P=0.545). Other details are shown in Table 1.

Landing zone parameters

A comparison of aneurysm and landing zone anatomical measurements was performed between the SGEL and non-SGEL cohorts, as outlined in Table 1. Notably, neck diameter (22.2±3.0 vs. 20.8±2.4 mm, P<0.001) and right distal landing zone diameter (14.6±3.6 vs. 13.5±3.2 mm, P=0.015) were significantly larger in the SGEL group. A higher degree of tortuosity was observed in the left iliac arteries of patients with SGEL (1.29±0.23 vs. 1.23±0.16, P=0.042), although no significant differences were noted in the right iliac arteries. Additionally, a trend towards increased prevalence of severely angulated necks was observed in the SGEL cohort, though statistical significance was not reached (42.0% vs. 30.2%, P=0.100).

OSR parameters and risk of SGEL

OSR parameters were evaluated to assess their association with SGEL following EVAR. In patients with SGEL, the median OSR of the proximal landing zone, the right distal landing zone, and the left distal landing zone was significantly smaller than that in the non-SGEL group, as shown in Table 1. The optimal thresholds for OSR were determined to be 20% for the proximal landing zone, 8% for the right distal landing zone, and 14% for the left distal landing zone. Lower OSR values were associated with an increased risk of SGEL following EVAR, as outlined in Table 2 and Table S1.

DF parameters

DF parameters revealed significant disparities between the SGEL and non-SGEL groups, as presented in Table 1. Patients with SGEL exhibited a substantially larger resultant DF magnitude compared to those without SGEL [5.73 (4.17, 7.65) vs. 4.77 (3.57, 6.00) N, P=0.003]. In the Cartesian coordinate view, DF in anterior (y-component) direction formed the major component in the overall cohort. Notably, DF in the anterior direction (y-component) was elevated in the SGEL cohort [−3.89 (−5.74, −2.50) vs. −2.84 (−4.26, −2.02) N, P=0.007], while the mean z-component of DF demonstrated an elevated caudal orientation in the non-SGEL group compared with the SGEL group [−1.83 (−3.42, −0.36) vs. −0.38 (−1.99, 0.72) N, P<0.001].

DF acting orthogonal to the SG inlet (normal to the neck cross section, directed inward toward the SG with positive values) and outlets (normal to the bilateral iliac cross sections, directed inward toward the SG with positive values) was also calculated. DFs orthogonal to the right and left outlets were significantly higher in the SGEL group, measuring 2.87 (0.83, 4.85) and 2.29 (0.67, 5.06) (both P<0.001). However, DF orthogonal to the proximal inlet was slightly higher in the non-SGEL group [2.87 (1.49, 4.71) vs. 3.62 (2.09, 4.76) N, P=0.061]. After adjustment for SNA, maximal aneurysm diameter, diameters of landing zones, and PAI, patients with higher magnitudes of DF directed inward toward the SG inlet exhibited a reduced risk of SGEL following EVAR (OR =0.758; 95% CI: 0.60–0.95; P=0.017), while patients with a higher inward-directed distal DF towards the SG showed an increased risk of SGEL after EVAR (right: OR =1.219, 95% CI: 1.019–1.458, P=0.030; left: OR =1.223, 95% CI: 1.035–1.444, P=0.018). Other details are shown in Table 2.

Comparison of predictive models with and without DF parameters

Comparative analysis of predictive models with and without DF parameters revealed superior performance for the model incorporating DF parameters. Notably, the AUC was higher for the DF-inclusive model, suggesting enhanced discriminatory capability in identifying patients at risk for SGEL following EVAR. The AUC improved significantly from 0.78 to 0.86 with the inclusion of DF parameters in the model. Additionally, the model incorporating DF parameters demonstrated improvements with NRI increasing by 0.61 (95% CI: 0.34–0.89; P<0.001) and IDI by 0.12 (95% CI: 0.06–0.17; P<0.001), as shown in Table 3 and Figure 2A.

Figure 2 Comparison of the discriminant ability to predict SGEL of different models combining DF parameters with classic OSR models. (A) Overall population. (B) Subgroup of patients with severe aneurysmal neck angulation. (C) Subgroup of patients with ectatic distal landing zone. (D) Nomogram comprising DF and OSR parameters. AUC, area under the curve; CI, confidence interval; DF, displacement force; LZ, landing zone; OSR, oversizing ratio; SGEL, stent-graft-related endoleak; SNA, severe neck angulation.

Similarly, subgroup analysis in patients with SNA demonstrated improvements in discriminant abilities (AUC =0.893; 95% CI: 0.81–0.98), with NRI and IDI improvements of 0.595 (P=0.011) and 0.155 (P=0.001). In patients with an ectatic distal landing zone, discriminant ability also improved (AUC =0.841; 95% CI: 0.75–0.94), with NRI and IDI improvements of 0.637 (P=0.006) and 0.109 (P=0.014), respectively, as shown in Table 3, Figure 2B,2C. Table S2 provides more detailed information on discrimination analysis for different prediction models. A nomogram comprising DF and OSR was constructed to facilitate the estimation SGEL risk (Figure 2D). The calibration curves demonstrated good agreement between the predicted probability and the actual occurrence rate of SGEL in both the overall population and subgroups (Figure S4).

Discussion

The hemodynamic environment results from the combined geometric characteristics of patient-specific aorto-iliac morphology, and effective preoperative planning for EVAR should consider both geometric and mechanical parameters. This study validates a clinician-friendly method for approximating flow-induced DF, which can be integrated into preoperative planning.

The direction of DF is not always aligned with blood flow. A retrograde DF at the distal end (in the cranial direction or inward toward the stent) was found to increase the risk of SGEL. Interestingly, retrograde DF in the distal landing zone was observed in most cases in this study, challenging preconceived notions. Consistent with our findings, flow-induced forces in SGs were measured under pulsatile conditions in experimental studies, and the authors found that the distal end of the SG might be subject to a retrograde DF measuring 1.6–6.9 N (20,21). Similarly, DF in the cranial direction was also found in mathematical and mechanical analyses (22). Proximal migration was also observed in a clinical study, which occurred in 75.0% (54/72) migrated stent limbs (23). All the evidence above points to the fact, that the distal end of SG might be subjected to a DF opposite to blood flow.

Various SG designs, including “hook” structures, have been developed to mitigate migration in the proximal landing zone. The force necessary to cause migration of the proximal portion of the graft was significantly larger in those with proximal fixation hooks (about 6–10 N), and the device was easier to be dragged to proximal than distal (24). This could explain why large caudal DF did not increase the risk of SGEL while the cranial DF did. However, the distal end of most commercial SGs lacks such preventive features, rendering retrograde DFs particularly detrimental by increasing the likelihood of complications.

A larger OSR may assist in addressing poor anatomical morphology and hemodynamic conditions. However, clinical practices exhibit substantial variability, with conflicting evidence regarding the optimal OSR to avert complications such as late type I endoleak, landing zone dilatation, and limb occlusion. Therefore, it is essential to carefully consider the patient-specific degree of SG oversizing to reduce the risk of SGEL (19), particularly with consideration of local hemodynamic conditions in preoperative EVAR planning. However, incorporating DF evaluation into EVAR planning continues to be limited by the time-consuming CFD analyses in most previous studies, and it remains challenging to apply in clinical practice due to its reliance on 3D models of post-deployment SG for analysis. Thus, a morphology-based mechanical parameter might be more favorable and practical.

Previous studies have reported that the simplified momentum quantitative DF consistently reflected the DF pattern calculated by CFD (15,25). Based on the simplified formula, it could be seen that the direction of DF was determined by section area and normal vectors of the proximal neck and distal landing zone, providing a method for estimating DF based on patient-specific anatomical parameters of the landing zones. Meanwhile, this could also explain why geometric factors like wide aneurysm neck, ectatic iliac artery, SNA, and aorto-iliac angulation are associated with increased risk of endoleak in many studies (26-29).

To build the prediction model for SGEL, the fixation force was also considered. In this study, the fixation force mainly consisted of the stent radial force, which was associated with the stent oversizing. A multivariate prediction model was developed using DF orthogonal to the inlet and outlets’ sections and OSR of each landing zone. The model performed well in predicting SGEL, and all parameters can be easily measured during routine preoperative assessment of landing zone diameters on 3D-reconstructed CTA images. The model proposed in this study provides recommendations for selecting SG OSR based on biomechanical parameters. This approach reduces reliance on indiscriminate oversizing standards and facilitates the formulation of more tailored stent selection strategies for individual patients.

Currently, the assessment of DF following EVAR primarily relies on postoperative CTA images, which makes it challenging to evaluate patient-specific DFs preoperatively and incorporate them into surgical planning. A previous study has demonstrated that the simplified DF is highly consistent with the DF calculated using CFD (13), while this study further reveals that the DFs estimated from preoperative CTA images can effectively predict the risk of SGEL in patients after EVAR. Based on preoperative imaging, postoperative DF can be rapidly estimated by combining systolic blood pressure with morphological measurements. This simple and efficient approach enables clinicians to assess DF and design a surgical plan that minimizes the risk of SGEL.

The current study is subject to several limitations. Firstly, its retrospective design as a case-control study introduces the potential for selection bias, despite efforts to match by age and gender and exclude patients with short-term follow-up. Thus, the results should be confirmed by further prospective cohort studies. Secondly, the manual process involved in measurement procedures may not be efficient enough. However, this method can be easily integrated into various automated measurement processes, improving convenience and accuracy. Thirdly, this study did not account for deformation effects induced by stent deployment. Although the methods provided offer an estimation of the DF pattern, which was also used in another study (25), this simplification overlooks the influence of the specific spatial configuration of the stent on internal flow dynamics. Additionally, the effects of pressure drop between the proximal and distal ends were not taken into account during the calculations, which may have affected the results. These aspects will be addressed in future research using four-dimensional (4D) flow magnetic resonance imaging technology to measure real-time flow patterns in patients received EVAR.

Conclusions

This study highlights the important role of DF parameters in predicting SGEL and validates their efficacy in clinical cohorts. The introduction of a clinician-friendly method for estimating DF, as demonstrated in this study, offers a valuable tool for predicting SGEL occurrence, aligning well with the practical preoperative clinical decision-making in EVAR planning. Despite the valuable insights, several limitations exist. Future research could address these limitations by employing larger sample sizes and longer follow-up periods to further validate findings.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1349/rc

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1349/dss

Funding: This work was supported by the National Natural Science Foundation of China (grant No. 82300542) and Postdoctor Fund of West China Hospital, Sichuan University (grant No. 2023HXBH108).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1349/coif). C.W. reports that this study was funded by the National Natural Science Foundation of China (grant No. 82300542). T.W. reports that this study was supported by the Postdoctor Fund of West China Hospital, Sichuan University (grant No. 2023HXBH108). The other authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by institutional review board of West China Hospital (No. 1705, 2023) and individual consent for this retrospective analysis was waived.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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