A study on predicting additional axillary lymph node positivity in breast cancer patients with positive sentinel lymph node to avoid axillary lymph node dissection
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Key findings
• This study developed a prediction model based on clinical and pathological features (age, number of positive sentinel lymph nodes, vascular tumor thrombus, preoperative axillary lymph node diameter) to assess axillary lymph node metastasis risk in breast cancer patients with positive sentinel lymph nodes. The model demonstrated good predictive efficacy [area under the curve (AUC) = 0.760] and fit.
What is known and what is new?
• Previous research has highlighted the importance of sentinel lymph node biopsy in minimizing axillary lymph node dissection (ALND) complications. However, the decision to exempt ALND in patients with positive sentinel lymph nodes remains controversial.
• This study introduces a novel prediction model integrating multiple clinical-pathological factors, offering a more individualized approach to ALND exemption.
What is the implication, and what should change now?
• The model provides clinicians with a practical tool to identify low-risk patients for ALND exemption, potentially reducing surgery-related complications and improving quality of life. Implementation of this model into clinical practice could guide more personalized treatment strategies, emphasizing the need for preoperative risk assessment and multidisciplinary collaboration in breast cancer management.
Introduction
Breast cancer has become one of the most common malignant tumors among women worldwide (1,2). Its incidence rate has remained consistently high. Breast cancer has several malignant clinical features such as strong invasiveness and metastasis, high recurrence rate, and short survival period, etc. (3). However, with the advancement of medical technology and the diversification and precision of treatment strategies, the mortality rate of breast cancer patients has been significantly improved. Currently, breast cancer is gradually transforming from a fatal disease to a chronic condition that can be controlled through long-term management.
During the treatment of breast cancer, the management of axillary lymph nodes is particularly crucial. The status of axillary lymph node metastasis is an important factor in assessing tumor stage, formulating treatment plans, and predicting disease prognosis (4). It has a profound impact on the postoperative health condition and quality of life of the patients (5). Traditionally, standard axillary lymph node dissection (ALND) has been the primary method for assessing the status of axillary lymph nodes. However, this surgery can lead to a series of serious complications, such as limited range of motion in the affected upper limb, lymphedema, and neuralgia (6). These complications significantly reduce the long-term quality of life of patients. Therefore, how to reduce unnecessary ALND surgeries, lower postoperative complications, and improve the quality of life of patients has become an important research direction in the current field of breast cancer treatment.
In recent years, with a deeper understanding of the biological behavior of breast cancer, scholars have begun to consider downgrading the management of axillary lymph nodes, that is, based on the specific conditions of patients, exempting or reducing the use of ALND. Especially with the wide application of sentinel lymph node biopsy (SLNB), minimally invasive assessment of axillary lymph nodes has become possible, and the risk of complications is significantly lower than that of ALND (7). SLNB detects the status of sentinel lymph nodes to predict the metastasis of axillary lymph nodes, thereby guiding subsequent treatment decisions. In the selection of surgical methods for most breast cancer patients with negative axillary lymph nodes, ALND has been replaced by SLNB surgery (8). Currently, in clinical practice, the presence or absence of positive sentinel lymph nodes is often used as a criterion to determine whether ALND (axial lymph node dissection) is necessary (9,10). This strategy has to some extent reduced the usage rate of ALND. However, in actual clinical practice, doctors have observed that some patients have positive sentinel lymph nodes, but after undergoing ALND, they found that the axillary lymph nodes were not positive. Therefore, in recent years, some scholars have begun to question whether patients with positive sentinel lymph nodes on the same side still need to undergo routine ALND (11). The research by SENOMAC provides evidence to support the exemption of ALND for patients with low tumor burden in sentinel lymph nodes (12). Some studies have explored the possibility of further exempting SLNB by using imaging techniques such as ultrasound (13). Therefore, relying solely on the positive status of the sentinel lymph nodes to assess whether ALND should be performed may have limitations and cannot accurately predict the risk of axillary lymph node metastasis.
There is still controversy regarding the treatment plan for axillary lymph nodes in breast cancer patients. The research on how to predict more accurately, precisely, and conveniently whether patients with positive sentinel lymph nodes during breast cancer surgery can be exempted from ALND still has limitations. Constructing a prediction model based on clinical and pathological features to explore the feasibility of exempting ALND for patients with positive sentinel lymph nodes during breast cancer surgery is of great significance. In the lymph node dissection part of breast cancer surgery, the surgeon will first perform a SLNB, and then decide whether to perform ALND based on the results of the SLNB. Our research focuses on how surgeons should proceed with the surgery based on the results of SLNB during the operation. Therefore, our study utilizes preoperative and intraoperative variables to apply to intraoperative decisions. In view of this, this study aims to construct a prediction model based on clinical and pathological features to deeply explore the feasibility of exempting ALND for patients with positive sentinel lymph nodes during breast cancer surgery. This study hopes to provide a more individualized prediction tool for clinicians to guide the management of axillary lymph nodes in breast cancer patients, so as to ensure the treatment effect while minimizing surgical complications and improving the quality of life of patients, with the aim of providing a theoretical basis for further revealing the feasibility of exempting ipsilateral ALND for breast cancer patients with positive sentinel lymph nodes. We present this article in accordance with the TRIPOD reporting checklist (available at https://gs.amegroups.com/article/view/10.21037/gs-2026-1-0115/rc).
Methods
Case collection
The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of Liuzhou People’s Hospital Affiliated to Guangxi Medical University (the approval ethics ID: KY 2025-242-01). All patients provided written informed consent. Retrospectively, 133 breast cancer patients diagnosed by histopathology in the Breast and Thyroid Surgery Department of Liuzhou People’s Hospital from January 2023 to August 2025 were collected. All patients were pathologically diagnosed with breast cancer, had no neoadjuvant therapy before surgery, had positive SLNB during the operation, underwent ALND, and had complete clinical data such as preoperative blood biochemical tests. At the same time, this study excluded cases with axillary-related diseases or surgical history, those with a history of breast cancer radiotherapy, those allergic to methylene blue or mitoxantrone hydrochloride, those who received neoadjuvant therapy before surgery, and those whose SLNB failed to detect the sentinel lymph nodes.
During the surgical procedures of all the patients involved in this study, the method of local injection of tracer was used to precisely trace the sentinel lymph nodes. The specific operation is as follows: in the tissue of the outer upper quadrant of the breast, multiple appropriate sites were selected, and methylene blue and mitoxantrone hydrochloride were prepared as tracer solutions. The solutions were injected locally into the skin using an injection needle. After the injection, wait for 20 minutes to allow the tracer to fully diffuse in the lymphatic system, so that the target lymphatic vessels and sentinel lymph nodes can be fully stained blue. During the surgery, based on the blue-stained lymphatic vessels and sentinel lymph nodes, 3 to 7 sentinel lymph nodes were excised for biopsy.
Data collection
Extract the following patient information from the electronic medical records: (I) basic patient data (gender, age, etc.); (II) preoperative breast color Doppler ultrasound (location of the tumor, maximum diameter, number, maximum diameter and number of axillary lymph nodes, etc.); (III) pathological data [human epidermal growth factor receptor 2 (HER-2), estrogen receptor (ER), progesterone receptor (PR), Ki-67, vascular tumor thrombus]; vascular tumor thrombus refers to the embolus formed after cancer cells invade blood vessels or lymphatic vessels, which is a high risk factor for tumor metastasis, suggesting that cancer may have the ability to metastasize to distant sites; (IV) surgical details (number of sentinel lymph nodes positive during the operation, positive rate of axillary lymph nodes during the operation); (V) preoperative blood tests within one week before the operation; (VI) in this study, the proportion of missing data was relatively low, so the missing data were simply deleted.
Statistical analysis
For count data, they are expressed as [number (%)]. The differences between groups are analyzed using the Chi-squared test or Fisher’s exact test. For measurement data that follow a normal distribution and have homogeneity of variance, they are represented as (mean ± standard deviation), and the comparison between the two groups is conducted using the independent sample t-test. For measurement data that do not follow a normal distribution or have heterogeneity of variance, they are expressed as [median (lower quartile, upper quartile)], and the comparison between the two groups is performed using non-parametric tests. The factors with statistical significance in the univariate Logistic regression analysis are included in the multivariate Logistic regression analysis, and the collinear factors are excluded to establish the multivariate Logistic regression model. Statistical analysis was performed by SPSS 25.0 software. A P<0.05 is considered statistically significant.
Results
Baseline characteristics
This study initially screened 671 breast cancer patients, and finally included 133 patients. Among them, 83 were included in the ALND (−) group and 50 in the ALND (+) group (Figure 1). This study explored the differences in clinical and pathological characteristics between the ALND (−) and ALND (+) groups (Table 1). A total of 133 SLN-positive patients who underwent breast cancer surgery and met the eligibility criteria for ALND were included in this study. Among them, 76% (n=83) had negative axillary lymph nodes after ALND, while 24% (n=50) underwent ALND and had positive axillary lymph nodes.
Table 1
| Characteristics | ALND (−) (n=83) | ALND (+) (n=50) | P value |
|---|---|---|---|
| Sex | 0.38 | ||
| Male | 83 (62.4) | 49 (36.8) | |
| Female | 0 (0.0) | 1 (0.8) | |
| Age (years) | 53.398±12.652 | 59.4±12.58 | 0.009 |
| Number of positive sentinel lymph nodes | 1 (1.0, 2.0) | 2 (1.0, 4.0) | <0.001 |
| Number of sentinel lymph nodes | 6 (4.0, 8.0) | 5 (4.00, 7.75) | 0.15 |
| Combined with carcinoma in situ | 0.10 | ||
| No | 19 (14.3) | 18 (13.5) | |
| Yes | 64 (48.1) | 32 (24.1) | |
| Vascular tumor thrombus | 0.004 | ||
| No | 53 (39.8) | 19 (14.3) | |
| Yes | 30 (22.6) | 31 (23.3) | |
| HER2 | 0.09 | ||
| IHC (non-staining) | 12 (9.0) | 12 (9.0) | |
| IHC (1+) | 28 (21.1) | 12 (9.0) | |
| IHC (2+) | 33 (24.8) | 14 (10.5) | |
| IHC (3+) | 10 (7.5) | 12 (9.0) | |
| ER (%) | 90 (80.0, 95.0) | 75 (0, 90.0) | 0.004 |
| PR (%) | 70 (25.0, 90.0) | 5 (0, 75.0) | <0.001 |
| Ki-67 (%) | 30 (20.0, 40.0) | 30 (22.5, 50.0) | 0.10 |
| Side of the disease | 0.20 | ||
| Left | 37 (27.8) | 28 (21.1) | |
| Right | 46 (34.6) | 22 (16.5) | |
| Preoperative axillary lymph node diameter (mm) | 0 (0.0, 12.0) | 11 (0.0, 18.0) | 0.005 |
| Preoperative tumor diameter (mm) | 18 (14.45, 29) | 20 (12.25, 28) | 0.79 |
| Testosterone (nmol/L) | 0.812 (0.5575, 1.115) | 0.648 (0.318, 1.065) | 0.03 |
| Serum prolactin determination (mIU/L) | 493 (306.1, 774.5) | 445.45 (311.2, 783.62) | 0.93 |
| Determination of serum follicle-stimulating hormone (IU/L) | 20.16 (5.405, 58.07) | 46.355 (28.825, 65.53) | 0.04 |
| Serum luteinizing hormone determination (IU/L) | 16.83 (5.22, 31.665) | 28.635 (17.018, 38.645) | 0.02 |
| Estradiol (pmol/L) | 79.97 (18.35, 273.3) | 60.065 (27.525, 132.5) | 0.44 |
| Progesterone (nmol/L) | 0.922 (0.3205, 1.71) | 0.632 (0.3435, 1.865) | 0.97 |
Data are presented as n (%), median (IQR), or mean ± SD. ALND, axillary lymph node dissection; cALND, complete ALND; ER, estrogen receptor; HER2, human epidermal growth factor receptor 2; IHC, immunohistochemistry; IQR, interquartile range; PR, progesterone receptor; SD, standard deviation.
In the comparison of the two groups of clinical pathological parameters, the patients in the ALND (+) group were statistically older, with an average age of 59.4 years (Table 1). In the comparison of lymph nodes, the ALND (+) group had more positive sentinel lymph nodes and larger preoperative axillary lymph node diameters than the ALND (−) group (Table 1). Moreover, the number of vascular tumor thrombi, serum follicle-stimulating hormone measurement levels, and serum luteinizing hormone measurement levels in the ALND (+) group were also significantly higher (Table 1). Additionally, there were also significant differences in ER, PR, and testosterone measurement levels between the two groups (Table 1).
Logistic regression analysis
Firstly, through single-factor analysis in this study, it was found that the ALND (−) and ALND (+) groups had significant differences in Age, Number of positive sentinel lymph nodes, vascular tumor thrombus, ER, PR, preoperative axillary lymph node diameter, and serum luteinizing hormone determination (Table 2). Further, in the multivariate analysis, it was shown that there were significant correlations in age, number of positive sentinel lymph nodes, vascular tumor thrombus, and preoperative axillary lymph node diameter between the two groups (Table 2).
Table 2
| Characteristics | Total (N) | Univariate analysis | Multivariate analysis | |||
|---|---|---|---|---|---|---|
| OR (95% CI) | P value | OR (95% CI) | P value | |||
| Age | 133 | 1.038 (1.009–1.068) | 0.01* | 1.052 (1.013–1.092) | 0.008** | |
| Number of positive sentinel lymph nodes | 133 | 1.824 (1.332–2.500) | <0.001*** | 1.734 (1.086–2.770) | 0.02* | |
| Number of sentinel lymph nodes | 133 | 0.916 (0.810–1.037) | 0.17 | |||
| Combined with carcinoma in situ | 133 | |||||
| No | 37 | Reference | ||||
| Yes | 96 | 0.528 (0.244–1.142) | 0.11 | |||
| Vascular tumor thrombus | 133 | |||||
| No | 72 | Reference | Reference | |||
| Yes | 61 | 2.882 (1.395–5.956) | 0.004** | 2.798 (1.035–7.567) | 0.04* | |
| HER2 | 133 | |||||
| IHC (non-staining) | 24 | Reference | Reference | |||
| IHC (2+) | 47 | 0.424 (0.154–1.171) | 0.10 | 0.569 (0.142–2.277) | 0.43 | |
| IHC (1+) | 40 | 0.429 (0.150–1.222) | 0.11 | 0.642 (0.152–2.704) | 0.55 | |
| IHC (3+) | 22 | 1.200 (0.376–3.826) | 0.76 | 0.406 (0.066–2.495) | 0.33 | |
| ER | 133 | 0.979 (0.968–0.989) | <0.001*** | 0.992 (0.975–1.009) | 0.35 | |
| PR | 133 | 0.981 (0.971–0.991) | <0.001*** | 0.991 (0.975–1.008) | 0.29 | |
| Ki-67 | 133 | 1.016 (0.997–1.035) | 0.10 | |||
| Side of the disease | 133 | |||||
| Left breast | 65 | Reference | ||||
| Right breast | 68 | 0.632 (0.312–1.281) | 0.20 | |||
| Preoperative axillary lymph node diameter (mm) | 133 | 1.049 (1.010–1.090) | 0.01* | 1.059 (1.005–1.115) | 0.03* | |
| Preoperative tumor diameter (mm) | 133 | 0.999 (0.972–1.027) | 0.96 | |||
| BMI | 132 | 1.016 (0.947–1.090) | 0.66 | |||
| Serum prolactin determination | 115 | 1.000 (0.999–1.001) | 0.86 | |||
| Determination of serum follicle-stimulating hormone | 115 | 1.013 (1.000–1.026) | 0.05 | 0.995 (0.967–1.025) | 0.76 | |
| Serum luteinizing hormone determination | 115 | 1.030 (1.005–1.055) | 0.02* | 1.025 (0.969–1.084) | 0.38 | |
| Estradiol | 115 | 0.999 (0.997–1.001) | 0.26 | |||
| Progesterone | 115 | 0.999 (0.965–1.034) | 0.96 | |||
*, P<0.05; **, P<0.01; ***, P<0.001. BMI, body mass index; cALND, complete axillary lymph node dissection; CI, confidence interval; ER, estrogen receptor; HER2, human epidermal growth factor receptor 2; IHC, immunohistochemistry; OR, odds ratio; PR, progesterone receptor.
Build a predictive model
In this study, four clinical pathological parameters that were correlated between the ALND (−) and ALND (+) groups in the multivariate analysis were selected: age, number of positive sentinel lymph nodes, vascular tumor thrombus, and preoperative axillary lymph node diameter. Based on these four clinical case pathological parameters, a prediction model was constructed (Figure 2). The receiver operating characteristic (ROC) curve of this prediction model showed an area under the curve (AUC) of 0.760 [95% confidence interval (CI): 0.677–0.843] (Figure 3). Furthermore, this study further evaluated the model through the diagnostic calibration curve, and the results showed that the C-index was 0.760 and the model fit was good as analyzed by the Hosmer-Lemeshow Goodness of Fit test (Figure 4).
Discussion
Breast cancer treatment has entered a comprehensive and precise diagnosis and treatment era. However, ALND, as a key surgical procedure in breast cancer diagnosis and treatment, may cause serious complications such as lymphedema after breast cancer surgery, thereby negatively affecting the quality of life of patients (14-16). Clinical studies have confirmed that it is possible to preserve the axilla in some patients with low-load axillary positive lymph nodes. Moreover, the “de-escalation” approach of exempting ALND without increasing radiotherapy is also being explored. This study, with breast cancer patients who did not undergo preoperative neoadjuvant chemotherapy as the research subjects, aims to explore and evaluate the possible factors for exempting ALND for ipsilateral sentinel positive lymph nodes.
Among the clinical and pathological features available before the operation, our research results showed that the patients in the ALND (+) group had older age, larger preoperative axillary lymph node diameters, higher levels of serum follicle-stimulating hormone, and higher levels of serum luteinizing hormone than those in the ALND (−) group. Among the clinical and pathological features available before the operation, our research results showed that the patients in the ALND (+) group had older age, larger preoperative axillary lymph node diameters, higher levels of serum follicle-stimulating hormone, and higher levels of serum luteinizing hormone than those in the ALND (−) group. At the same time, the levels of ER, PR, and testosterone in the ALND (+) group were significantly lower. At the same time, the levels of ER, PR, and testosterone in the ALND (+) group were significantly lower. In recent years, many studies have shown that in the research on axillary lymph nodes of breast cancer, the size of the lymph nodes can be used to predict axillary lymph node metastasis (17). Especially the short-axis diameter of the axillary lymph nodes (18). This study also found that the diameter of axillary lymph nodes before surgery can be used to predict axillary lymph node metastasis. This might be because when lymph node metastasis occurs, the lymph nodes tend to enlarge. Though axillary ultrasound has a sensitivity and specificity of 75.7% and 92.9%, respectively, it has its limitations in certain subtypes such as the invasive lobular cancers (19,20). It is worth noting that in this study, patients with low expression of ER and PR were more likely to be exempt from ALND. In previous studies, the correlation between ER, PR and axillary lymph node metastasis remains controversial. Some scholars believe that low expression of ER and PR can indicate a higher risk of axillary lymph node metastasis (21,22). Some scholars also believe that high expression of ER and PR may indicate a higher risk of axillary lymph node metastasis (23,24). As mentioned in many studies, the HER2-enriched subtype and the triple-negative subtype are more aggressive and have a higher rate of metastasis (22,25). Currently, the regulatory mechanisms of ER and PR expression levels and axillary lymph node metastasis are not clear and still need further exploration. Combining these research findings with our results indicate that clinicians can assess the possibility of ALND based on preoperative indicators, thereby enabling more adequate preoperative preparations and clinical interventions.
In 2025, the American Society of Clinical Oncology (ASCO) once again proposed recommendations for the management of axillary surgery in breast cancer: for early-stage breast cancer patients without lymph node metastasis or with only 1–2 sentinel lymph node metastases and who undergo breast-conserving surgery and whole breast radiotherapy, ALND is not recommended (26). At the same time, studies such as IBCSG23-01, Z0011 and AMAROS have provided evidence to support the exemption of ALND for patients with SLN micrometastasis and 1–2 macroscopic metastases in the axilla with low tumor burden (27-29). The results of this study also show that the number of positive sentinel lymph nodes, as a preoperative predictive indicator that can be obtained during the operation, indicate that when there are 0–1 positive sentinel lymph nodes, the patient can be exempted from ALND. However, when the patient has 2 or more positive sentinel lymph nodes, the patient still needs to undergo ALND. The number of positive sentinel lymph nodes is a crucial indicator for breast cancer surgery. In clinical practice, surgeons must consider the significant evaluation value of this indicator for ALND, as well as the strategies for physical examination of axillary lymph nodes, imaging abnormalities, and radiotherapy after exemption from ALND.
In previous studies, vascular tumor thrombus has been regarded as an important factor influencing lymph node metastasis (30,31). In the research conducted by Fu et al., it was found that vascular tumor thrombus is an independent risk factor and predictor for axillary lymph node metastasis in breast cancer patients (32). Vascular tumor thrombi are often included as part of the routine postoperative pathological results. In this study, it was found that they were more likely to occur in the ALND (+) group. We speculate that after the formation of vascular tumor thrombi, the permeability of the vessel wall was changed, providing adhesion sites for tumor cells, thereby obtaining the pathways and conditions for lymph node metastasis, and ultimately increasing the possibility of lymph node metastasis.
Based on the results of single-factor and multi-factor analyses, in this study, four factors including age, the number of positive sentinel lymph nodes, vascular tumor thrombus, and preoperative axillary lymph node diameter were integrated to construct a prediction model for axillary lymph node metastasis in breast cancer patients with positive sentinel lymph nodes during surgery. The AUC value of this prediction model was 0.760, indicating that these indicators can effectively distinguish whether patients need to undergo ALND and also suggesting the possibility of this research’s prediction model as an auxiliary tool for clinicians to predict axillary lymph node metastasis in patients with positive sentinel lymph nodes during surgery. Additionally, we used the diagnostic calibration curve to evaluate this prediction model. The results showed that this model was meaningful and accurate. Therefore, this risk prediction model can identify potential high-risk patients with axillary lymph node metastasis through common clinical pathological indicators at an early stage. This prediction model can provide a simple and rapid diagnostic auxiliary tool for clinicians, thereby providing guidance for the selection of surgical methods for patients, which is crucial for the management of axillary lymph nodes in patients with positive sentinel lymph nodes and breast cancer.
Although this study has made certain progress in exploring the feasibility of exempting ALND for patients with positive sentinel lymph nodes during breast cancer surgery, it still has limitations such as a limited sample size and a single source which may affect the generalizability of the results, sample selection bias due to missing information during data collection, the predictive model being based on retrospective data and lacking prospective validation, failure to deeply analyze the interaction between multiple factors, and inability to assess long-term prognosis due to lack of long-term follow-up. Future research needs to improve in these aspects.
Conclusions
In conclusion, age, the number of positive sentinel lymph nodes, vascular tumor thrombus, and preoperative axillary lymph node diameter all play significant roles in assessing the occurrence of axillary lymph node metastasis in breast cancer patients with positive sentinel lymph nodes during surgery. The prediction model established by these indicators in this study can preliminarily predict the risk of axillary lymph node metastasis in breast cancer patients with positive sentinel lymph nodes during surgery. It can provide a practical and effective prediction tool for clinicians to screen and identify patients with axillary lymph node metastasis from breast cancer with positive sentinel lymph nodes during surgery and formulate more individualized treatment plans.
Acknowledgments
None.
Footnote
Reporting Checklist: The authors have completed the TRIPOD reporting checklist. Available at https://gs.amegroups.com/article/view/10.21037/gs-2026-1-0115/rc
Data Sharing Statement: Available at https://gs.amegroups.com/article/view/10.21037/gs-2026-1-0115/dss
Peer Review File: Available at https://gs.amegroups.com/article/view/10.21037/gs-2026-1-0115/prf
Funding: This work was supported by
Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://gs.amegroups.com/article/view/10.21037/gs-2026-1-0115/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. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of Liuzhou People’s Hospital Affiliated to Guangxi Medical University (approval ethics ID: KY 2025-242-01). All patients provided written 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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