Using finite element analysis to obtain the pressure gradient between the left renal vein and the inferior vena cava: a new method for the diagnosis and follow-up of patients with nutcracker syndrome

Introduction

Nutcracker syndrome (NCS), also known as left renal vein (LRV) entrapment syndrome, is caused by the compression of the LRV between the abdominal aorta (AA) and the superior mesenteric artery (SMA), or by mechanical compression of the LRV between the AA and the spine. It presents with hematuria, orthostatic proteinuria, left flank or abdominal pain, and left-sided varicocele (1).

Due to the lack of a unified diagnostic standard and the nonspecific nature of its symptoms, diagnosing NCS is challenging. Common diagnostic methods include Doppler ultrasound (DUS), computed tomography angiography (CTA), and renal venography. However, DUS results can be influenced by operator judgment, and the ultrasound probe may inadvertently compress the LRV, affecting the accuracy of diameter and flow velocity measurements (2,3). Meanwhile, although CTA can clearly visualize the anatomical relationships among the LRV, AA, SMA, and branching vessels, demonstrate the compression site in the LRV, reveal downstream LRV dilation, and exclude other causes of NCS, it does not provide information on LRV pressure gradients (4-6).

Currently, the “gold standard” for diagnosing NCS is measuring the pressure gradient between the LRV and the inferior vena cava (IVC), with a gradient greater than 3 mmHg considered diagnostic (3,7). Although renal venography yields more accurate diagnostic information, it is an invasive procedure. Non-invasive approaches based on CTA-derived 3D reconstruction and computational fluid dynamics have recently been explored as potential tools to assess NCS hemodynamics (8). However, it remains unclear whether finite element analysis (FEA) can reliably predict the LRV-IVC pressure gradient, has sufficient diagnostic accuracy, or can be applied for longitudinal follow-up. Larger studies are needed to address these questions.

Therefore, we retrospectively enrolled 46 patients who underwent both abdominal CTA and LRV pressure measurement. From their CTA data, we reconstructed patient-specific 3D models of the AA, SMA, and LRV, then used ANSYS software (Ansys, Canonsburg, PA, USA) to perform hemodynamic simulations of the LRV and calculate the simulated pressure gradient (SPG) between the LRV and the IVC. We compared these SPG values to the true pressure gradient (TPG) between the LRV and the IVC obtained via direct LRV pressure measurement to assess their clinical value. Our aim was to introduce a novel, reliable, non-invasive diagnostic and follow-up tool for NCS, potentially reducing the need for invasive examinations. We present this article in accordance with the STARD reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-aw-2141/rc).

Methods

Study population

This study was approved by The Third Affiliated Hospital of Sun Yat-sen University Ethics Review Committee (No. II2025-044) and conducted in accordance with the Declaration of Helsinki and its subsequent amendments. Informed consent was provided by all the participants included in the study.

From January 2022 to January 2025, a total of 47 patients underwent renal venography for assessment of the LRV pressure gradient, of whom 46 also underwent abdominal CTA. After excluding one patient who did not undergo CTA, 46 patients who received both abdominal CTA and renal venography were included in the final analysis. Among these, 35 patients were classified into the NCS group based on the following diagnostic criteria: (I) macroscopic or microscopic hematuria with left-sided abdominal pain; (II) mostly isomorphic red blood cells on phase-contrast microscopy; (III) demonstration of the nutcracker phenomenon on contrast-enhanced computed tomography (CT) of both kidneys (described in the report); and (IV) most importantly, LRV venography showing an LRV-IVC pressure gradient >3 mmHg (3,9,10). The exclusion criteria were as follows: (I) prior or current compression or displacement of major abdominal vessels by abdominal masses or spinal deformities; (II) other causes of hematuria, proteinuria, flank pain, scrotal pain, oligospermia, or varicocele; and (III) other diseases affecting LRV hemodynamics, such as congenital vascular anomalies (11).

Data acquisition and analysis

Imaging data acquisition

Enhanced CT scans were performed using 128-slice or 256-slice CT scanners (Siemens Healthcare, Erlangen, Germany) or a 128-slice IQon Spectral CT scanner (Philips, Amsterdam, the Netherlands). Patients were positioned supine, with the scanning range from the diaphragm to the pubic symphysis. Scanning parameters included 80–120 kVp, 150–300 mAs, 0.6–1.25 mm pitch, 512×512 matrix, and 1–3 mm slice thickness. Iodinated contrast (Ioversol, Guerbet, Villepinte, France; 350 mg/mL) was administered at 4 mL/s via the median cubital vein using a high-pressure injector at a dose of 1.2 mL/kg. All images were saved in Digital Imaging and Communication in Medicine (DICOM) format for analysis.

All patients underwent renal venography to determine the TPG. Patients remained supine throughout the procedure, with the pressure sensor leveled at the right atrium and measurements recorded in mmHg. A right jugular vein approach was used for catheter insertion: after placing a 4-F sheath over a guidewire, a single-curved catheter was advanced to the LRV. Pressure measurements were then obtained from both the stenotic site of the LRV and the IVC.

Imaging analysis

Imaging data were analyzed using VolumeShop software (Huibaitu Technology, Nanjing, China) by 2 experienced urologists, blinded to clinical data and diagnoses. In case of disagreement, a senior physician was consulted. The analysis included: (I) the LRV diameter ratio (the hilum segment to the aortomesenteric segment); (II) presence of the “beak sign” and measurement of the beak angle; and (III) aortomesenteric angle on the sagittal plane. The LRV diameter ratio was the ratio of the diameter of the LRV at the renal hilum to that of the aortomesenteric portion on the axial plane, used to assess LRV dilation (12); the beak angle was defined as the angle formed by the anterior and posterior walls of the LRV at the narrowed segment between the AA and the SMA (Figure 1) (12); and the aortomesenteric angle was measured between the proximal SMA and the AA at the LRV level (12).

Figure 1 Measurement diagram of beak angle (12). (I) A line is drawn between the center of the AA and the SMA and the intersecting points of this line with the anterior wall (point A) and the posterior wall (point B) of the LRV are marked. (II) The point along the aorta where the posterior wall of the LRV first becomes tangential (point D) is marked and a line is drawn connecting this point to point B. (III) The point on the anterior wall of the LRV where the narrowing first occurs (point C) is marked and a line is then drawn connecting point A and point D. (IV) The angle at the intersection of the 2 lines BC and AD is measured. AA, abdominal aorta; LRV, left renal vein; SMA, superior mesenteric artery.

Construction of the LRV model and FEA

3D reconstruction of the LRV

CT data were imported into MIMICS 21.0 (Materialise, Leuven, Belgium) for 3D model generation from 2D tomographic images, enabling clear visualization of the lesion site. Preprocessing—such as threshold segmentation and dynamic region growing—was performed on the imported CT images to isolate the LRV, SMA, and AA, followed by mask creation and 3D model generation (8). The resulting model was then imported into 3-matic 13.0 (Materialise) for mesh optimization, including smoothing, denoising, subdividing, and repairing the mesh, to facilitate subsequent FEA (13). The model generation workflow and the final model are shown in Figure 2.

Figure 2 Reconstruction and smoothing of 3D models. (A-C) The 3D reconstruction process of the vascular model. (D) The vascular model smoothed using 3-matic software.

FEA

In NCS patients, the compression and deformation of the LRV require a denser mesh in high-curvature regions to improve FEA accuracy, as mesh density directly affects the error margin in calculations, enabling more precise analysis of key deformation areas.

After meshing, the model was imported into the FLUENT module of ANSYS 17.2 software, where the blood-flow inlet, outlet, and computational domain were defined. Blood was assumed to be a Newtonian, incompressible fluid, and the vessel was considered impermeable. Flow was assumed to be laminar and steady, with the vascular wall treated as smooth, non-slip, and rigid (8). The blood density was set to 1,060 kg/m³, and the viscosity was set to 0.02943 Pa·s (8). The velocity at the inlet boundary was defined as 0.3 m/s (14), and the outlet boundary was assigned a pressure of 1,492 Pa (15,16). The default unit for the MESH file was millimeters, and the residual was set to 10⁻⁴. The computation automatically ceased once the residual reached this threshold. The corresponding model assumptions and boundary conditions are listed in Table 1.

Statistical analysis

Continuous variables are presented as mean ± standard deviation (SD) or interquartile range (IQR), whereas categorical variables are expressed as frequencies (percentages). Chi-squared tests were conducted to compare categorical data between groups. The Shapiro-Wilk test was used to assess the normality of continuous variables. Independent-samples t-tests compared demographic data, imaging parameters, and TPG between groups. For 8 patients who underwent surgery, paired t-tests evaluated changes in SPG and TPG before and after the procedure. Receiver operating characteristic (ROC) curve analyses were conducted to determine the diagnostic performance of imaging parameters and the SPG for NCS. Optimal cutoff values were identified to maximize sensitivity and specificity, and the area under the ROC curve (AUC) along with its 95% confidence interval (CI) were calculated. All statistical analyses were performed using SPSS 22.0 (IBM Corp., Armonk, NY, USA), with a P value <0.05 considered statistically significant.

Results

Demographic characteristics

Table 2 presents the demographic characteristics of the enrolled patients. After excluding one patient who did not undergo CTA, a total of 46 patients who received renal venography were included in the final analysis. Of these, 35 were diagnosed with NCS, with the remaining 11 serving as controls. No significant differences were observed between the two groups in mean age (P=0.20) or sex distribution (P=0.59). In the NCS group, the most common chief complaint was gonadal varices (45.71%). In contrast, 6 (54.54%) control patients had LRV compression detected during routine physical exams, and only 1 (9.09%) presented with hematuria. In addition, the body mass index (BMI) in the NCS group was significantly lower than that in the control group (18.2±1.9 vs. 20.3±2.4 kg/m², P<0.05).

Imaging findings

Table 3 presents the imaging findings of the enrolled patients. Compared with controls (44.0±19.8°), patients with NCS had a significantly smaller aortomesenteric angle (21.2±11.4°, P=0.01), but a significantly higher LRV diameter ratio (6.4±2.5 vs. 3.8±3.1, P=0.02) and beak angle (38.7±14.9° vs. 25.2±12.4°, P=0.02). In addition, the beak sign was present in 29 NCS patients, whereas only 2 controls exhibited this sign (P<0.01). The TPG was also significantly higher in the NCS group than in the control group (5.5±1.9 vs. 2.4±0.4 mmHg, P<0.01).

3D LRV modeling and FEA results

3D model of the LRV

Figure 3 presents 3D reconstructions of the LRV generated with MIMICS and 3-matic. Compared with the control group, patients with NCS exhibited marked compression of the aortomesenteric segment, resulting in a significantly narrowed lumen and pronounced dilation of the distal LRV.

Figure 3 Reconstruction models for normal patients and NCS patients. (A,C) The reconstruction models of normal patients (33 years old, BMI =17.9 kg/m², α=69.9°). The ratios of LRV diameters are 1.1. (B,D) The models of NCS reconstruction (45 years old, BMI =23.1 kg/m², α=15.8°). The ratios of LRV diameters are 9.6. (C,D) The LRV. BMI, body mass index; LRV, left renal vein; NCS, nutcracker syndrome.

FEA of LRV model

Meshing

In FEA, the accuracy of calculations depends on the mesh elements, where cells represent spatial discretization and nodes are crucial for evaluating physical quantities. The mesh data for the LRV models in both groups are presented in Table 4 and Figure 4. No significant difference was observed between the two groups in terms of model meshing (P>0.05).

Figure 4 Grid division of 3D left renal vein models. (A,C) The left renal vein of normal patient models. The mesh nodes and cells of the model are 67,030 and 21,248. (B,D) The left renal vein of nutcracker syndrome patients. The mesh nodes and cells of the model are 106,797 and 31,556.

FEA results of the LRV

Figures 5,6 and Table 5 present the pressure, velocity, and wall shear contours derived from FEA. NCS patients exhibited lower pressure at the stenosis site compared to controls, with higher blood flow velocity and wall shear contours. The pressure, velocity, and wall shear contours in NCS demonstrated a more pronounced gradient, with the lowest pressure at the stenosis site and the highest velocity and wall shear contours, extending from the stenosis center toward both ends of the LRV. In contrast, no significant gradient was observed in the pressure distribution or velocity in the control group.

Figure 5 Hemodynamic results of control group. (A,E) The pressure distribution vectors in the LRV. (B,F) The streamlines of the blood flow in the LRV. (C,G) The blood flow in the LRV. (D,H) The wall shear contours distribution in the LRV. LRV, left renal vein.

Figure 6 Hemodynamic results of nutcracker syndrome group. (A,E) The pressure distribution in the LRV. (B,F) The streamlines of the blood flow in the LRV. (C,G) The blood flow in the renal vein vectors. (D,H) The wall shear contours distribution in the LRV. LRV, left renal vein.

Consistency between TPG and SPG

Among 35 NCS patients, TPG was 5.5±1.9 mmHg and SPG was 5.6±3.9 mmHg, showing no significant difference (P>0.05). In our center, 8 NCS patients who underwent LRV transposition were followed up 3 months post-surgery, at which time their TPG was remeasured. These 8 patients were part of our own clinical cohort and were not related to the 8 patients reported by Tang et al. (8). All 8 patients reported significant improvement in hematuria, proteinuria, and flank pain, with reduced TPG (5.37±1.8 vs. 2.1±0.8 mmHg, P<0.01) and SPG (6.78±6.4 vs. 1.5±0.9 mmHg, P<0.05) (Figure 7A). Importantly, no significant difference was found between TPG and SPG before or after surgery (Figure 7B).

Figure 7 Consistency of TPG and SPG. (A) The changes in preoperative and postoperative TPG and SPG in 8 NCS patients. (B) The consistency of preoperative and postoperative TPG and SPG. *, P<0.05; ***, P<0.001. NCS, nutcracker syndrome; Post, postoperative; Pre, preoperative; SPG, simulated pressure gradient; TPG, true pressure gradient.

Diagnostic value of various indicators

Table 6 presents the optimal cutoff values from ROC analysis, including sensitivities and specificities. The beak sign showed 74.32% sensitivity and 90.91% specificity, whereas the beak angle at 32.7° had 81.82% sensitivity and 74.29% specificity. The aortomesenteric angle at 26.7° had 80.00% sensitivity and 72.73% specificity. The LRV diameter ratio at 5.0 had the lowest sensitivity (71.43%) but the highest specificity (81.82%). Notably, SPG at 3.3 mmHg had high sensitivity (81.82%) and specificity (80.00%), with AUCs of 0.803 for the LRV diameter ratio and 0.808 for SPG (Figure 8).

Figure 8 ROC curves for diagnostic parameters of nutcracker syndrome. AUC, area under the curve; CI, confidence interval; LRV, left renal vein; ROC, receiver operating characteristic; SMA, superior mesenteric artery.

Discussion

Owing to the lack of a unified standard, the exact prevalence of NCS remains controversial (17). Studies suggest that NCS exhibits a bimodal incidence pattern, peaking at 10–14 years and again at 30–40 years (18,19). In this study, the mean BMI of NCS patients (18.2±1.9 kg/m²) was significantly lower than that of the control group (20.3±2.4 kg/m²), which aligns with previous findings (20). Here, the mean age of NCS patients was 18.0±7.0 years, and 45.71% sought treatment for gonadal varices, followed by flank pain (25.71%). Although commonly reported to peak at 10–14 years, the slightly higher age of onset observed in this study could be attributed to the lower BMI in these patients, which reduces retroperitoneal fat and exacerbates vascular compression. Significant reductions in BMI often occur in late adolescence, and some children may not seek medical attention until symptoms are pronounced, delaying diagnosis until age 18. The pathogenesis of NCS is thought to be multifactorial. A key predisposing factor is the rapid increase in height and vertebral growth during puberty, which narrows the aortomesenteric angle and compresses the LRV (3). Low BMI and loss of retroperitoneal fat further reduce the cushion around the LRV, aggravating venous compression; in some patients, symptoms may improve with weight gain (7,17,19). Elevated LRV pressure can also lead to the development of collateral pathways via the gonadal and lumbar veins, contributing to gonadal varices and pelvic congestion, and may cause hematuria, flank pain, and orthostatic proteinuria through venous rupture, renal hemodynamic changes, and visceral pain mechanisms (3). Future large-scale, multicenter prospective studies—encompassing broader age ranges and incorporating BMI, anatomical variations, and other relevant factors—are warranted to clarify the age-specific incidence and contributing factors of NCS.

The aortomesenteric angle in NCS is often less than 40°, and an angle below 35° confirms the diagnosis. In addition, the LRV diameter ratio is usually >4.9 in NCS, which was also observed in our cohort (7,21,22). Kim et al. first described the “beak sign” and beak angle, reporting the beak sign in 91.7% of NCS patients (12). Similarly, 82.86% of patients in our NCS group showed a beak sign, compared with only 2 patients in the non-NCS group, and the mean beak angle was 38.7±14.9°, closely matching Kim et al.’s data. Together, these findings support the diagnostic utility of the aortomesenteric angle, LRV diameter ratio, and beak-related features in NCS.

FEA provides comprehensive, non-invasive hemodynamic insights into NCS, guiding clinical diagnosis and treatment. Tang et al. first applied CTA-based 3D reconstruction combined with FEA in a small cohort of 8 NCS patients to estimate blood flow characteristics and the LRV-IVC pressure gradient, suggesting that computational fluid dynamics may serve as a non-invasive tool for hemodynamic assessment in NCS. However, that study was limited by the small sample size and the lack of systematic comparison with invasively measured trans-pressure gradients, which precluded a robust evaluation of its diagnostic performance. The hemodynamic characteristics of the LRV in this study align with those reported by Tang et al. (8). Moreover, previous studies have shown that in NCS, blood flow velocity at the LRV stenosis ranges from 0.68 to 1.42 m/s, whereas velocity at the proximal LRV measures 0.12 to 0.28 m/s, yielding a ratio greater than 4.1 as a diagnostic criterion for NCS, which aligns with our results simulated by FEA (Table 5) (2,3,12,23). Since the gonadal vein was not included in the blood flow simulation, the SPG may be slightly elevated relative to the TPG due to the influence of gonadal venous outflow.

FEA revealed no significant difference between the SPG and the TPG. In practice, the evaluation of treatment outcomes for NCS often focuses on symptomatic improvement, auxiliary examination results, and changes in the TPG (24). Conservative management is typically recommended initially for NCS patients, whereas surgical intervention is reserved for those with severe symptoms (3). Common surgical approaches include LRV transposition, intravascular stent placement, and extravascular stent placement (25-29). Nevertheless, symptom resolution can be subjective, with the most objective indicator of therapeutic efficacy being the postoperative TPG, which is invasive and unsuitable for frequent follow-up. This study employed FEA to monitor 8 patients following LRV transposition. Notably, the SPG remained consistent with the TPG both before and after surgery (Figure 7B), suggesting that FEA provides a viable noninvasive and objective tool for assessing postoperative outcomes in NCS while reducing the financial burden on patients.

SPG obtained via FEA demonstrated superior diagnostic value compared with the beak angle and the LRV diameter ratio, and its performance was comparable to that of the beak sign. The cut-off values for the LRV diameter ratio (5.0) and beak angle (32.7°) in this study were similar to those reported by Kim et al., and both demonstrated high diagnostic value (11,12,22). However, compared with traditional measures, FEA is more objective and less susceptible to the operator bias often encountered with ultrasound and CTA.

To date, TPG is widely regarded as the gold-standard diagnostic criterion for NCS (4,7,30). However, TPG measurement is invasive, impractical for routine clinical use, and typically reserved for severe cases. In this study, patient-specific LRV models were reconstructed from CTA data, and FEA was employed to determine the SPG. At a cutoff value of 3.3 mmHg, the SPG demonstrated an AUC of 0.808, along with relatively high sensitivity (81.82%) and specificity (80.00%). These findings suggest that FEA may facilitate earlier identification of NCS, enabling prompt intervention in severe cases.

This study has several limitations. First, FEA relies on high-quality CTA datasets with adequate resolution. In our investigation, 2 patient datasets were excluded due to poor image quality, resulting in inaccurate 3D models. This requirement for advanced imaging may limit the broader applicability of our method, particularly in centers with limited imaging resources, and thus represents an important practical limitation of this technique. Second, our simulations assumed a rigid vascular wall and did not account for respiratory motion or vessel compliance, potentially impacting SPG accuracy. Future studies should include vascular elasticity, respiratory motion, and pulsatile flow to improve simulation realism. Moreover, due to the indications for LRV pressure measurement surgery, control group patients typically undergo pressure measurement after symptoms or CTA indicated LRV compression (as healthy patients typically do not undergo LRV venography), which may result in the inclusion of mild NCS that could have gone unrecognized in the control group and only 11 controls were recruited. In fact, the TPG in the control group in this study was 2.4±0.4 mmHg, slightly higher than the normal range reported in the literature (0–1 mmHg) (3), which could impact the accuracy of the cutoff values for each diagnostic indicator and for SPG. The small sample size may have broadened the normal TPG range.

Despite some limitations, this single-center study includes one of the largest NCS cohorts with confirmed TPG measurements. It offers a first-time comparison of SPG and TPG before and after LRV transposition surgery. The SPG, with an AUC of 0.808, demonstrates high diagnostic performance. SPG, derived through FEA, provides a non-invasive, reliable method for diagnosing NCS and monitoring post-treatment outcomes. A standardized workflow reduces operator bias, and with further advancements, SPG may become a key tool in NCS diagnosis and management.

Conclusions

This study demonstrates that the SPG calculated through FEA can serve as a non-invasive diagnostic metric for NCS, offering high diagnostic accuracy. As an objective hemodynamic parameter, SPG minimizes the potential subjectivity associated with imaging measurements and presents a promising tool for early screening, treatment decisions, and follow-up in NCS.

Acknowledgments

We thank The Third Affiliated Hospital of Sun Yat-sen University for providing the research data and all the staff and participants.

Footnote

Reporting Checklist: The authors have completed the STARD reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-aw-2141/rc

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-aw-2141/dss

Funding: This article was supported by the National Natural Science Foundation of China (No. 81772752) and Guangdong Natural Science Foundation (No. 2023A1515012925).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-aw-2141/coif). J.D. reports payments were made to him from National Natural Science Foundation of China and Guangdong Natural Science Foundation. 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. This study was approved by The Third Affiliated Hospital of Sun Yat-sen University Ethics Review Committee (No. II2025-044) and conducted in accordance with the Declaration of Helsinki and its subsequent amendments. Informed consent was obtained from all the participants included in the study.

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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