Non-invasive risk stratification of immunoglobulin A nephropathy and crescent formation using contrast-enhanced ultrasound combined with serological markers

Introduction

Immunoglobulin A nephropathy (IgAN) is the most prevalent primary glomerulonephritis globally and a leading cause of end-stage renal disease (1,2). Its clinical manifestations are highly heterogeneous, ranging from isolated hematuria with preserved renal function to progressive proteinuria, renal insufficiency, and even end-stage renal disease. This heterogeneity highlights the importance of early identification of pathological activity and disease severity (3).

Among the pathological features of IgAN, crescent formation has special clinical significance. Crescents reflect active glomerular injury and are usually associated with a more aggressive disease course, higher inflammatory burden, and poorer renal prognosis. Therefore, the ability to identify patients at increased risk of crescent formation is crucial for risk stratification, treatment selection, and follow-up intensity.

Although renal biopsy remains the diagnostic gold standard, its invasiveness and sampling variability restrict repeated use in routine practice. Non-invasive tools for identifying patients with a high probability of IgAN and for stratifying crescent risk may therefore support earlier risk assessment and clinical decision-making.

Contrast-enhanced ultrasound (CEUS) provides real-time quantitative assessment of renal microcirculation without ionizing radiation or nephrotoxic contrast agents (4,5). Compared with traditional gray-scale ultrasound, CEUS can provide dynamic functional information about renal perfusion. Parameters derived from time-intensity curves (TICs), such as peak enhancement (PE), wash-in rate (WiR), and wash-in perfusion index (WiP), have shown correlations with histopathological severity (6-10). Integrating these with serological markers like estimated glomerular filtration rate (eGFR) and urine albumin-to-creatinine ratio (UACR) could enhance diagnostic and prognostic accuracy.

In this study, we aimed to (I) examine the associations between CEUS parameters, serological biomarkers, and Oxford MEST-C (mesangial hypercellularity, endocapillary hypercellularity, segmental sclerosis, tubular atrophy/interstitial fibrosis, crescent formation) scores, with a focus on crescents; (II) develop predictive models for IgAN diagnosis and crescent formation; and (III) determine whether combining CEUS with clinical biomarkers improves diagnostic performance compared with clinical-only or CEUS-only models. We present this article in accordance with the TRIPOD reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2026-1-0025/rc).

Methods

Patient selection and ethics approval

This retrospective study included patients who visited the Department of Nephrology, Huashan Hospital, Fudan University, for persistent proteinuria, hematuria, or unexplained renal impairment between February 28, 2023, and May 9, 2024, and who were considered by clinicians to have clear indications for renal biopsy.

Inclusion criteria were as follows: (I) age ≥18 years; (II) chronic kidney disease (CKD) diagnosed according to Kidney Disease: Improving Global Outcomes (KDIGO) guidelines, defined as evidence of kidney injury (including proteinuria, hematuria, or imaging abnormalities) and/or eGFR <60 mL/min/1.73 m² lasting ≥3 months; (III) CKD stage 1–5 with a biopsy-confirmed pathological diagnosis; and (IV) CEUS examination completed within 7 days before renal biopsy, with stable clinical status and no acute change in renal function during the examination period.

Exclusion criteria were as follows: (I) acute kidney injury at enrollment; (II) marked fluctuation in renal function within 1 month before examination (eGFR change >30%); (III) an interval of more than 7 days between CEUS examination and renal biopsy; and (IV) poor CEUS image quality that precluded quantitative analysis.

A total of 184 eligible patients were included. The sample size was based on the number of eligible patients available during the study period. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. This retrospective study was approved by the Ethics Committee of Huashan Hospital, Fudan University (Approval No. KY2024-730), and all patients provided informed consent. Among the 184 patients who completed renal biopsy, 94 were diagnosed with IgAN and 90 were diagnosed with non-IgAN kidney diseases.

Among the 94 patients with IgAN, crescent status was defined according to the Oxford classification C score. Patients with C1 or C2 lesions were assigned to the crescent subgroup, whereas patients with C0 lesions were assigned to the non-crescent subgroup. Each subgroup included 47 patients.

Clinical and laboratory data collection

Demographic information (age and gender) and laboratory values, including eGFR calculated using the CKD-EPI equation, serum creatinine, urea, albumin, and UACR, were recorded within 7 days before biopsy.

Contrast-enhanced ultrasound examination

Examinations were performed using a Siemens ACUSON Sequoia (Siemens Healthineers) color Doppler ultrasound system with a 1–6 MHz convex array probe for CEUS at low mechanical index. After conventional B-mode imaging, 1.0 mL of SonoVue (Bracco, Milan, Italy) was injected intravenously via the antecubital vein, followed by a 5 mL normal saline flush. Valid 90-second CEUS videos were recorded and saved in Digital Imaging and Communications in Medicine (DICOM) format.

CEUS videos in DICOM format were analyzed using VueBox 7.0 software with cortex-to-medulla normalization. CEUS analysis was performed independently without knowledge of pathological results. The regions of interest (ROI) consisted of one elliptical area (approximately 4 mm × 3 mm) in the renal cortex and one in the renal medulla, placed in the mid renal cortex (red) and mid renal medulla (blue) closest to the probe, respectively (Figure 1A). The software generated TICs (Figure 1B), which reflected dynamic changes in renal cortical and medullary microcirculatory perfusion. ROI placement was performed by an experienced radiologist and reviewed by a second investigator.

Figure 1 CEUS ROI sampling, cortex-to-medulla normalization, and TIC parameter extraction. (A) ROI sampling in the renal cortex and medulla and cortex-to-medulla normalization. (B) TIC-based extraction of quantitative CEUS parameters, including PE, RT, WiR, and WiP. CEUS, contrast-enhanced ultrasound; FT, fall time; mTT, mean transit time; PE, peak enhancement; ROI, region of interest; RT, rise time; TIC, time-intensity curve; TTP, time to peak; WiAUC, wash-in area under the curve; WiP, wash-in perfusion index; WiR, wash-in rate; WoAUC, wash-out area under the curve; WoR, wash-out rate.

CEUS TIC analysis generated a series of renal perfusion parameters, including rise time (RT), time to peak (TTP), fall time (FT), mean transit time (mTT), PE, wash-in area under the curve (WiAUC), wash-out AUC (WoAUC), WiR, WiP, wash-out rate (WoR), and wash-in and wash-out AUC (WiWoAUC). The definitions of the key parameters are shown in Figure 1B: PE was defined as the maximum peak intensity above baseline (dB), RT as the time required for the signal to increase from 10% to 100% of PE(s), FT as the time required for the signal to decrease from PE to baseline(s), TTP as the time from contrast agent arrival to PE(s), WiR as the slope of the ascending segment (dB/s), WiP as PE/RT (dB/s), and WoR as the slope of the descending segment (dB/s). mTT, WiAUC, WoAUC, and WiWoAUC were also recorded. Only curves with a goodness of fit ≥85% were included.

The cortex-to-medulla ratio was used as a normalization index to quantify renal microcirculation. This approach was adopted for two reasons. First, CEUS parameters are affected by technical factors, including contrast-agent dose, injection speed, machine gain, imaging depth, and probe angle, as well as individual factors such as blood pressure, cardiac function, cardiac output, and respiratory motion. Second, renal blood flow is distributed unevenly, with the cortex receiving approximately 90% of renal blood flow and the medulla approximately 10%. Decreased cortical microcirculation is an early and important feature of CKD, whereas medullary perfusion impairment tends to occur later and may be less pronounced. Cortex-to-medulla normalization may therefore reduce technical and physiological variability and improve data stability and comparability. Each subject was measured twice using the same method, and the average value was used for statistical analysis.

Renal biopsy and histopathological evaluation

All patients underwent ultrasound-guided percutaneous renal biopsy under local anesthesia, and renal tissue samples were obtained using a 16 G biopsy needle. The samples were fixed in 10% neutral buffered formalin, embedded in paraffin, and examined by light microscopy and immunofluorescence. Pathological assessment was performed by experienced pathologists who were blinded to CEUS findings. All patients with IgAN were newly diagnosed, untreated cases without recurrence.

The diagnosis of IgAN was based on renal biopsy findings, characterized by predominant IgA deposition in the glomerular mesangium on immunofluorescence together with compatible light microscopic findings. According to renal biopsy pathology, CKD patients were divided into the IgAN group and the non-IgAN group. Pathological lesions in IgAN were evaluated using the Oxford MEST-C scoring system, including mesangial hypercellularity (M), endocapillary hypercellularity (E), segmental sclerosis (S), tubular atrophy/interstitial fibrosis (T), and crescent formation (C).

According to the MEST-C scoring system in the Oxford classification, crescents in IgAN patients were graded: C0: no crescents; C1: crescents involving <25% of glomeruli; C2: crescents involving ≥25% of glomeruli. In this study, C1 + C2 grades were defined as the crescent formation group (1,2).

Statistical analysis

SPSS 25.0 (IBM, USA) and R 4.1.0 (R Foundation, Vienna) were used for statistical analysis. All statistical tests were two-tailed, and P<0.05 was considered statistically significant. Normality was assessed using the Shapiro-Wilk test. Normally distributed continuous variables were expressed as mean ± standard deviation and compared using independent-samples t-tests. Non-normally distributed variables were expressed as median (interquartile range) and compared using the Mann-Whitney U test. Categorical variables were expressed as n (%) and compared using the Chi-squared test or Fisher’s exact test, as appropriate. Spearman correlation analysis was used to evaluate associations with MEST-C scores.

Univariate logistic regression was used to screen potential predictors. Variables with P<0.05 in univariate analysis were entered into multivariable logistic regression. Before multivariable analysis, multicollinearity was assessed using the variance inflation factor (VIF), with VIF <5 indicating no significant multicollinearity. Final predictors were retained according to their multivariable associations with each endpoint, which explains why different CEUS parameters entered different models. Independent predictors of IgAN diagnosis and crescent formation were identified, and odds ratios (ORs) with 95% confidence intervals (CIs) were calculated. Diagnostic models were constructed based on multivariable logistic regression results and visualized as nomograms.

Model performance was evaluated using receiver operating characteristic (ROC) curves, and AUCs, 95% CIs, sensitivity, and specificity were calculated. Positive predictive value (PPV) and negative predictive value (NPV) were derived from sensitivity, specificity, and the observed prevalence of each endpoint in the study cohort. Calibration curves were generated to evaluate agreement between predicted and observed probabilities. Decision curve analysis (DCA) was used to assess clinical net benefit. Optimal cut-off values were determined using the Youden index. DeLong tests were used for pairwise comparisons between ROC curves. Bootstrap resampling was used for internal validation.

Results

Baseline characteristics and CEUS metrics

Among the 184 patients, 94 were diagnosed with IgAN. Compared with non-IgAN patients, IgAN patients were significantly younger (40.3±12.8 vs. 49.4±15.1 years; P<0.001) and had lower eGFR (78.0±33.4 vs. 90.3±47.5 mL/min/1.73 m²; P=0.045), lower UACR, and higher albumin levels (P=0.021; Table 1). Among non-IgAN cases, membranous nephropathy (15.2%), lupus nephritis (7.1%), focal segmental glomerulosclerosis (6.0%), Henoch-Schonlein purpura nephritis (3.8%), diabetic nephropathy (3.3%), and other pathological types (13.6%) were confirmed. Crescent formation varied across diagnoses, with the highest prevalence in Henoch-Schonlein purpura nephritis (71.4%) and lupus nephritis (23.1%). No crescents were observed in membranous nephropathy, focal segmental glomerulosclerosis, or diabetic nephropathy (Table 2). CEUS showed that PE, WiR, and WiP were significantly lower in the IgAN group (all P<0.05; Table 3). The inclusion of several non-IgAN pathological entities allowed further evaluation of the crescent prediction model in the entire cohort.

Correlation analysis

Spearman correlation analysis demonstrated partial significant associations between Oxford classification scores [mesangial hypercellularity (M), endocapillary hypercellularity (E), segmental sclerosis (S), tubular atrophy/interstitial fibrosis (T), and crescent formation (C)] and both serological markers (eGFR and serum creatinine) and CEUS parameters (PE, WiR, and WiP) (P<0.05), indicating that CEUS metrics reflect histopathological severity (Table 4).

Construction of IgAN diagnosis model and nomogram

The diagnostic model for IgAN identified age, eGFR, UACR, and WiR as independent predictors (P<0.05; Table 5). A corresponding nomogram was developed based on these variables to estimate the probability of IgAN (Figure 2A). The model showed moderate discrimination, with an AUC of 0.78 (95% CI: 0.72–0.85; Figure 2B). Calibration and decision curve analyses showed acceptable agreement between predicted and observed probabilities and suggested potential clinical utility (Figure 2C,2D).

Figure 2 Nomogram and validation for IgAN diagnosis. (A) Nomogram for IgAN diagnosis based on age, eGFR, UACR, and WiR. (B) ROC curve for IgAN diagnosis (AUC 0.78, 95% CI: 0.72–0.85). (C) DCA demonstrating the net clinical benefit for IgAN diagnosis. (D) Calibration plot assessing the agreement between predicted and actual probability for IgAN diagnosis. AUC, area under the curve; CI, confidence interval; DCA, decision curve analysis; eGFR, estimated glomerular filtration rate; IgAN, immunoglobulin A nephropathy; ROC, receiver operating characteristic; UACR, urine albumin-to-creatinine ratio; WiR, wash-in rate.

The combined model achieved an AUC of 0.78 (95% CI: 0.72–0.85), which was higher than that of the clinical model (AUC 0.64, 95% CI: 0.55–0.72) and the CEUS-only model (AUC 0.63, 95% CI: 0.55–0.71).

Pairwise comparisons using DeLong tests are shown in Table S1. The combined model was significantly superior to both the clinical model and the CEUS-only model, whereas no significant difference was observed between the clinical model and the CEUS-only model. These findings suggest that CEUS alone should not replace conventional clinical variables, but that it may provide incremental information when combined with clinical variables.

Construction of crescent formation diagnosis model and nomogram in IgAN, and subgroup analysis by renal function

For crescent formation prediction in IgAN, age and WiP were identified as independent predictors (P<0.05; Figure 3A). A nomogram was constructed to assess the risk of crescent formation in patients with IgAN. ROC analysis yielded an AUC of 0.74 (95% CI: 0.64–0.85; Figure 3B; Table 6), indicating moderate discrimination. Calibration and decision curve analyses showed acceptable agreement between predicted and observed probabilities and suggested potential clinical utility (Figure 3C,3D).

Figure 3 Nomogram and validation for crescent formation risk. (A) Nomogram for crescent formation risk based on age and WiP. (B) ROC curve for crescent formation prediction (AUC 0.74, 95% CI: 0.64–0.85). (C) DCA demonstrating the net clinical benefit for crescent formation prediction. (D) Calibration plot assessing the agreement between predicted and actual probability for crescent formation prediction. AUC, area under the curve; CI, confidence interval; DCA, decision curve analysis; ROC, receiver operating characteristic; WiP, wash-in perfusion index.

The AUC of the combined model was 0.74 (95% CI: 0.64–0.85), while the AUC of the clinical model was 0.64 (95% CI: 0.52–0.75) and that of the CEUS-only model was 0.62 (95% CI: 0.51–0.74). The CEUS-only model showed relatively higher sensitivity, while the clinical model had higher specificity. The combined model provided a more balanced performance profile, indicating that these two types of variables provide complementary information.

According to Table S1, the combined model was significantly superior to both the clinical model and the CEUS-only model. No significant difference was observed between the clinical model and the CEUS-only model, suggesting that the added value of CEUS lies mainly in its combination with clinical markers rather than in its independent use.

Subgroup analysis showed that nomogram performance was higher in patients with preserved renal function (eGFR ≥60 mL/min/1.73 m²) and lower in patients with advanced CKD. This pattern may be explained by diffuse and homogeneous microvascular impairment in advanced CKD, which reduces perfusion heterogeneity detectable by CEUS.

Construction of crescent formation diagnosis model and nomogram in the entire cohort

For crescent formation prediction in the entire cohort, age and RT were identified as independent predictors (P<0.05; Table 7; Figure 4A). A nomogram was constructed to assess the risk of crescent formation across the entire cohort. ROC analysis yielded an AUC of 0.72 (95% CI: 0.64–0.81; Figure 4B). Calibration and decision curve analyses further confirmed good agreement between predicted and observed probabilities and supported the clinical utility of the model (Figure 4C,4D).

Figure 4 Nomogram and validation for crescent formation in the entire cohort. (A) Nomogram for crescent formation based on clinical and CEUS-derived parameters. (B) ROC curve for crescent formation prediction (AUC 0.72, 95% CI: 0.64–0.81). (C) DCA demonstrating the net clinical benefit for crescent formation prediction. (D) Calibration plot assessing the agreement between predicted and actual probability for crescent formation prediction. AUC, area under the curve; CEUS, contrast-enhanced ultrasound; CI, confidence interval; DCA, decision curve analysis; ROC, receiver operating characteristic; RT, rise time.

The AUC of the combined model was 0.72 (95% CI: 0.64–0.81), which was higher than that of the clinical model (0.64, 95% CI: 0.55–0.73) and the CEUS-only model (0.60, 95% CI: 0.51–0.69). Compared with the IgAN subgroup, the overall discrimination of the entire cohort was slightly lower. This reduction in performance is likely attributable to the heterogeneous pathophysiological mechanisms underlying crescent formation across different renal diseases. Nevertheless, the combined model remained the best-performing method.

DeLong tests showed that the combined model was significantly superior to the CEUS-only model and also outperformed the clinical model, with statistical significance or marginal significance depending on the comparison (Table S1). These results suggest that CEUS may add information when crescent formation is evaluated across a broader disease spectrum, although the magnitude of improvement remained moderate.

Comparison of model performance at each endpoint

Table 8 compares the diagnostic performance of the clinical, CEUS-only, and combined models across all three endpoints, including AUC, sensitivity, specificity, PPV, and NPV. Overall, the combined model consistently achieved the highest AUC than the clinical-only and CEUS-only models, supporting the incremental value of the integrated modeling strategy. ROC curves for the three models at each endpoint are displayed in Figure 5A-5C, with curves labeled as Combined, Clinical, and CEUS models. The renal-function subgroup results are summarized in Table 9, and the corresponding ROC curves are shown in Figure 6.

Figure 5 ROC curves comparing clinical, CEUS, and combined models across different endpoints. (A) IgAN diagnosis. (B) Crescent formation in IgAN. (C) Crescent formation in the entire cohort. CEUS, contrast-enhanced ultrasound; CI, confidence interval; IgAN, immunoglobulin A nephropathy; ROC, receiver operating characteristic.

Figure 6 ROC curves stratified by renal function. eGFR, estimated glomerular filtration rate; ROC, receiver operating characteristic.

The corresponding pairwise statistical comparisons are summarized in Table S1. In summary, these analyses support the conclusion that CEUS provides additional information beyond conventional clinical variables at multiple clinically relevant endpoints, but the moderate AUC values indicate that the models should be considered supportive rather than definitive diagnostic tools.

Discussion

The main finding of this study is that CEUS may add diagnostic information when integrated with conventional clinical variables. Quantitative CEUS parameters (PE, WiR, and WiP) were associated with Oxford MEST-C scores, suggesting that CEUS can capture microvascular perfusion changes related to IgAN, particularly in fibrotic (T) and crescentic (C) lesions (6,7,11). By integrating these parameters with serological markers, we developed nomograms for IgAN diagnosis (AUC 0.78) and crescent prediction (AUC 0.74). These AUC values indicate moderate discrimination rather than high diagnostic accuracy, and the models should therefore be interpreted as exploratory supportive tools. Differences in the selected predictors across models may reflect endpoint-specific pathophysiological mechanisms and were determined by multivariable regression. The pre-test probability of IgAN in this cohort was relatively high (51.1%), exceeding that reported in many Western populations. This difference may reflect regional epidemiology and biopsy indications, and it may limit the generalizability of the proposed nomogram in populations with a lower prevalence of IgAN. Future multicenter studies should include more diverse populations for external validation. Reduced WiP in crescentic cases may reflect capillary disruption and consequent ischemia, which can contribute to progressive fibrosis. The normalized CEUS metrics used in this study may reduce inter-individual variability and strengthen links with histopathology compared with non-normalized measurements (4,5,11). Previous studies have also developed radiomic or clinical nomograms for predicting crescent formation in IgAN (12,13). Similarly, a CEUS-based nomogram has been reported for evaluating glomerulosclerosis in transplanted kidneys, supporting the feasibility of integrating quantitative CEUS metrics for non-invasive renal pathological assessment (14).

Another important consideration is the heterogeneity of the non-IgAN control group. Crescent formation across different renal diseases may arise through different pathological mechanisms, and renal perfusion patterns may also vary by disease type. This heterogeneity makes biological interpretation more complex and may partly explain why the crescent model performed slightly less well in the entire cohort than in the IgAN subgroup. Nevertheless, the combined model remained the best-performing strategy, suggesting that CEUS may have broader exploratory utility beyond a single pathological subtype, although disease-specific models may provide higher discrimination.

From a clinical perspective, the proposed nomograms may be useful in selected settings, but several practical constraints should be considered. The models are not intended to replace renal biopsy, which remains the diagnostic gold standard. Instead, they may assist pre-biopsy risk stratification and patient selection. Compared with radiomics, magnetic resonance imaging (MRI)-based approaches, and established clinical prediction models, CEUS has the advantages of real-time microvascular assessment and avoidance of nephrotoxic contrast agents. However, it also requires specific equipment, trained operators, standardized acquisition, and post-processing expertise. Cost, availability, and operator dependence may limit routine implementation, particularly outside centers with CEUS experience. For IgAN diagnosis, the model may help identify CKD patients with suspected glomerular disease who have a higher probability of biopsy-confirmed IgAN. For crescent prediction, the models may help identify patients at increased risk of active pathological injury. CEUS may also have potential value for longitudinal assessment or relapse monitoring in selected patients, although biopsy remains indispensable when diagnostic confirmation is required.

The subgroup analysis by renal function provided clinically relevant information. Better performance in patients with preserved renal function suggests that CEUS may be particularly useful in earlier disease stages, when microvascular changes remain heterogeneous enough to distinguish pathological states. In advanced CKD, diffuse and overlapping perfusion impairment may reduce the specificity of CEUS-derived parameters. This pattern supports the potential role of CEUS as an auxiliary tool in earlier rather than later CKD stages. However, blood pressure, disease duration, and other factors affecting renal microcirculation may still have influenced CEUS parameters and should be considered in future prospective studies.

This study has several strengths, including a diverse CKD cohort, standardized CEUS quantification, and internal validation. Several limitations should also be acknowledged. First, this was a retrospective single-center study, which may introduce selection bias and limit generalizability because patient selection and biopsy indications may differ between hospitals. Second, the sample size was relatively small for prediction-model development, especially for crescent and renal-function subgroup analyses. Third, no external validation was performed, and the nomograms require independent confirmation in larger multicenter cohorts. Fourth, formal interobserver or intraobserver reproducibility analysis for ROI placement and CEUS parameter extraction was not performed, although ROI placement was reviewed by a second investigator. Fifth, missing data were handled using complete-case analysis, which may introduce bias if missingness was not random. Sixth, because of the cross-sectional design, the prognostic value of CEUS for long-term renal outcomes could not be evaluated. Future prospective studies should include external validation, reproducibility assessment, detailed calibration statistics, optimism-corrected performance estimates, and prespecified clinical threshold analyses.

Conclusions

CEUS provides microvascular perfusion information that may complement conventional clinical biomarkers. In this exploratory single-center study, models combining CEUS and clinical variables showed better performance than clinical-only and CEUS-only models for diagnosing IgAN and predicting crescent formation, although discrimination was moderate. These findings suggest that CEUS may serve as a promising supportive tool for pre-biopsy risk stratification and crescent formation prediction in CKD, but external validation is required before routine clinical use.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the TRIPOD reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2026-1-0025/rc

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2026-1-0025/dss

Funding: None.

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2026-1-0025/coif). The 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 conducted in accordance with the Declaration of Helsinki and its subsequent amendments. This study was approved by the Ethics Committee of Huashan Hospital, Fudan University (Approval No. KY2024-730), and all patients provided informed consent.

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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