Correlation between contrast-enhanced T2 fluid-attenuated inversion recovery enhancement and dynamic contrast-enhanced magnetic resonance imaging permeability in brain metastases

Introduction

The number, location, and size of brain metastases play critical roles in determining therapeutic strategies for the patient (1,2). Changes in the number of brain metastases directly influence radiotherapy planning, including treatment field size, radiation dose, and choice of treatment modality (3,4). Therefore, accurate identification of the number and spatial distribution of metastatic lesions on imaging plays a critical role in guiding personalized treatment planning.

However, different imaging sequences exhibit varying levels of sensitivity in detecting brain metastases. The T2 fluid-attenuated inversion recovery (FLAIR) sequence possesses a certain T1-weighted effect, allowing lesions to exhibit contrast enhancement on T2 FLAIR images following gadolinium administration (5). Previous studies have compared the detection rates of brain tumor lesions between contrast-enhanced T2 FLAIR (CE-T2 FLAIR) and contrast-enhanced T1-weighted imaging (CE-T1WI), and found that the degree of enhancement of the same lesion differed between CE-T2 FLAIR and CE-T1WI images (6,7), thereby resulting in different detection rates. In vitro experiments (8) have shown that CE-T2 FLAIR is highly sensitive to low concentrations of gadolinium contrast agent; that is, when the gadolinium concentration is low, the CE-T2 FLAIR signal is higher than that of CE-T1WI, whereas when the concentration is high, the CE-T2 FLAIR signal is lower than that of CE-T1WI. However, few studies have quantitatively reported the relationship between the intralesional gadolinium concentration and the signal intensity (SI) as well as the degree of enhancement on CE-T2 FLAIR in vivo.

The concentration of contrast agent within a lesion is primarily related to tumor vascular permeability (9): the higher the vascular permeability, the higher the intralesional contrast agent concentration, and vice versa. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can quantitatively analyze lesion vascular permeability (10). The parameters volume transfer constant (K^trans) and reverse volume transfer constant (K_ep) are the optimal indicators for reflecting vascular permeability of lesions (11), and can indirectly reflect the deposition of contrast agent within the lesion.

Therefore, this study applied DCE-MRI sequences to qualitatively and quantitatively analyze the relationship between intralesional gadolinium concentration and the degree of enhancement on CE-T2 FLAIR in brain metastases, aiming to explore the diagnostic value of CE-T2 FLAIR in brain metastases. We present this article in accordance with the STROBE reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1998/rc).

Methods

Patients

The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of The First Affiliated Hospital of Kunming Medical University (approval No. [2023] Lunshen L No. 206), and the requirement for individual consent for this retrospective analysis was waived. Cranial MRI images from January 2018 to July 2024 of patients with a history of extracranial primary malignant tumors and confirmed brain metastases that had been performed at our hospital were retrospectively collected. The inclusion criteria were as follows: (I) lesions located in the brain parenchyma, with MRI examinations including T1WI, T2-weighted imaging (T2WI), T2 FLAIR, DCE-MRI, CE-T1WI, and CE-T2 FLAIR sequences; (II) presence of an extracranial primary malignant tumor confirmed by pathology through surgery or biopsy; (III) diagnosis of intracranial metastatic lesions confirmed by surgical pathology or a 2-month follow-up, with follow-up confirmation criteria defined as (12): changes in the size of existing lesions on follow-up MRI, enlargement or reduction of lesions after radiotherapy and/or chemotherapy, or occurrence of new enhancing lesions; (IV) patients who had not received radiotherapy, chemotherapy, or cranial surgery before the initial MRI examination; and (V) absence of other primary intracranial tumors. The exclusion criterion was poor quality of cranial MRI images.

A total of 43 patients with 80 brain metastases were finally included. The primary malignant tumors were lung cancer (n=33), breast cancer (n=2), rectal cancer (n=2), esophageal cancer (n=1), other gastrointestinal cancer (n=2), endometrial carcinoma (n=1), alveolar soft part sarcoma (n=1), and malignant lymphoma (n=1) (Table 1).

Imaging techniques

All examinations were performed using GE Discovery MR 750 3.0 T superconducting MR scanner (GE Healthcare, Chicago, IL, USA) with a 32-channel head coil. Patients were placed in the supine position with head-first scanning mode. Conventional T1WI, T2WI, and T2 FLAIR sequences were acquired first. DCE-MRI was then initiated immediately after contrast administration (acquisition time, 5 min 58 s), followed by contrast-enhanced brain volume imaging (CE-BRAVO; 4 min 37 s) or three-plane CE-T1WI (axial, coronal, and sagittal; 1 min 30 s, 1 min 20 s, and 1 min 20 s, respectively), and finally CE-T2 FLAIR (2 min 33 s). Contrast-enhanced scans were performed with gadopentetate dimeglumine (Gd-DTPA) at a dose of 0.2 mL/kg.

The MRI acquisition protocols and parameters were standardized as follows: T2WI: repetition time (TR) =4,869 ms, echo time (TE) =116 ms, number of excitations (NEX) =1.5, field of view (FOV) =240×240 mm², slice thickness =5.0 mm, interslice gap =1.0 mm. T1WI: TR =2,500 ms, TE =24 ms, NEX =1.5, FOV =240×240 mm², slice thickness =5.0 mm, interslice gap =1.0 mm. T2 FLAIR: TR =9,000 ms, TE =95 ms, NEX =1.0, FOV =240×240 mm², slice thickness =4.0 mm, interslice gap =0.0 mm. Three-dimensional (3D) BRAVO: TR =8.5 ms, TE =3.2 ms, NEX =1.0, slice thickness =1.0 mm, FOV =256×256 mm², matrix =256×256. The acquisition parameters for CE-T1WI and CE-T2 FLAIR were identical to those of their corresponding unenhanced sequences.

DCE-MRI was performed using a fast spoiled gradient recalled echo (FSPGR) sequence with the following parameters: TR =5.3 ms, TE =1.0 ms, FOV =260×174.2 mm², matrix =256×192, slice thickness =5.0 mm, interslice gap =0.0 mm. Before dynamic scanning, three pre-enhancement flip angle (FA) scans (4°, 8°, and 15°) were performed, each consisting of 10 phases with a temporal resolution of 2 s and a total scan time of 20 s per FA. Dynamic scanning was then conducted with a FA of 15°, acquiring 180 continuous phases with a temporal resolution of 2 s and a total scan time of 5 min 58 s.

Image assessment

After scanning, all image data were transferred to the Picture Archiving and Communication System (PACS) and analyzed and measured by two radiologists. For contrast ratio (CR) and percentage increase (PI), three circular regions of interest (ROIs; 30–50 voxels) were drawn within the enhancing solid tumor component on the slice with the largest solid area, and their mean was used for analysis. For DCE-MRI, three hotspot ROIs (30–50 voxels) were placed within the enhancing solid tumor parenchyma, and their average was taken as the representative K^trans and K_ep for each lesion. All ROIs avoided necrosis, hemorrhage, cystic/necrotic components, and large vessels.

Measurement of tumor size

The maximum tumor diameter (TD_max) of all metastases was measured in combination with CE-T2 FLAIR and CE-T1WI.

Assessment of the degree of enhancement of metastatic tumors on CE-T2 FLAIR

The SI CR and the PI in SI of the metastatic tumors on CE-T2 FLAIR were calculated. Calculation formula: (I) CR: CR = (SI_lesion − SI_NWM)/SI_NWM × 100%, wherein SI_lesion represents the SI of the enhanced lesion parenchyma, and SI_NWM represents the SI of the normal white matter adjacent to the tumor after enhancement; and (II) PI: PI = (SI_{CE-T2 FLAIR} − SI_{native T2 FLAIR})/SI_{native T2 FLAIR} × 100%, wherein SI_{CE-T2 FLAIR} represents the SI after enhancement, and SI_{native T2 FLAIR} represents the SI before enhancement. PI was used to assess the true increase in enhancement between pre- and post-contrast images, minimizing the influence of the intrinsically high SI present on native T2 FLAIR (8,13).

Quantitative parameters measurement in DCE-MRI

Quantitative analysis and pharmacokinetic modeling of the DCE-MRI data were performed using the GenIQ perfusion analysis software on the GE Advantage Workstation (AW) version 4.6 platform (GE Healthcare). Motion correction was performed automatically by the software on the raw DCE-MRI images. Individual arterial input functions (AIFs) were automatically or semi-automatically identified by the post-processing software for each patient, typically in the basilar artery or middle cerebral artery. DCE-MRI parameters (K^trans and K_ep) were generated based on the extended Tofts pharmacokinetic model (14-16).

Visual assessment and subsequent lesion grouping

In vitro experiments have shown that the tissue SI corresponding to the same gadolinium concentration differs between CE-T2 FLAIR and CE-T1WI images (8): when the gadolinium concentration is relatively low, the tissue SI on CE-T2 FLAIR is higher than that on CE-T1WI; when the gadolinium concentration increases to a certain level, the tissue SIs on the two sequences become similar; with a further increase in gadolinium concentration, the tissue SI on CE-T2 FLAIR decreases and becomes lower than that on CE-T1WI.

Since visual assessment is simple and straightforward, in this study, lesions were classified into three different contrast concentration groups based on the visual assessment of the difference in enhancement between CE-T1WI and CE-T2 FLAIR: Group A (Figure 1, A1-D1): lesions with markedly higher enhancement on CE-T2 FLAIR than on CE-T1WI, representing the low-concentration group; Group B (Figure 1, A2-D2): lesions with little difference in enhancement between CE-T2 FLAIR and CE-T1WI, representing the medium-concentration group; Group C (Figure 1, A3-D3): lesions with markedly higher enhancement on CE-T1WI than on CE-T2 FLAIR, representing the high-concentration group.

Figure 1 T1WI, T2 FLAIR, CE-T1WI, CE-T2 FLAIR, K_ep, and K^trans images. (A1-F1) A 23-year-old female with brain metastasis from gastrointestinal neuroendocrine carcinoma. The lesion shows no enhancement on CE-T1WI but significant enhancement on CE-T2 FLAIR. Quantitative analysis reveals K^trans=0.073 min⁻¹ and K_ep=0.114 min⁻¹, indicating low tumor vascular permeability. (A2-F2) A 67-year-old male with brain metastasis from right lung adenocarcinoma. The lesion exhibits significant enhancement on CE-T1WI and moderate enhancement on CE-T2 FLAIR. Quantitative analysis shows K^trans=0.520 min⁻¹ and K_ep=0.640 min⁻¹, suggesting moderate tumor vascular permeability. (A3-F3) A 22-year-old male with brain metastasis from soft tissue alveolar sarcoma. The lesion demonstrates significant enhancement on CE-T1WI but no appreciable post-contrast signal elevation on CE-T2 FLAIR. Quantitative analysis reveals K^trans=0.768 min⁻¹ and K_ep=1.451 min⁻¹, reflecting high tumor vascular permeability. CE-T1WI, contrast-enhanced T1-weighted imaging; CE-T2 FLAIR, contrast-enhanced T2 fluid-attenuated inversion recovery; K_ep, reverse volume transfer constant; K^trans, volume transfer constant; T1WI, T1-weighted imaging; T2 FLAIR, T2 fluid-attenuated inversion recovery.

Statistical analysis

Statistical analysis was performed using the software SPSS 26.0 (IBM Corp., Armonk, NY, USA). Normally distributed data were expressed as mean ± standard deviation (SD), whereas non-normally distributed data were expressed as median [interquartile range (IQR)]. Measurement reproducibility was assessed using the intraclass correlation coefficient (ICC): it was considered “poor” if ICC was less than 0.40, “moderate” when ICC was ≥0.40 but <0.75, and “good” with ICC >0.75. The CR, PI, TD_max, and DCE-MRI parameters (K^trans and K_ep) measured by the two radiologists in this study showed good consistency (ICC range, 0.826–0.998; all P<0.001).

First, differences in K^trans, K_ep, CR, PI, and TD_max among different contrast concentration groups were compared to determine statistical significance. The Kruskal-Wallis test was used for comparisons among the three groups, and the Mann-Whitney U test was used for subsequent pairwise comparisons, with Bonferroni correction applied. A P value <0.05 was considered statistically significant. Second, a quantitative analysis was performed to evaluate the relationship between intralesional contrast agent concentration and CE-T2 FLAIR lesion SI as well as post-contrast enhancement degree: the correlations of K^trans and K_ep values with CR and PI values for all lesions were analyzed using Spearman’s test. A P value <0.05 was considered statistically significant. The correlation coefficient was defined as follows: r≥0.70, high correlation; 0.40<r<0.70, moderate correlation; r≤0.40, low correlation.

Results

Intergroup comparisons

The number of lesions in each group was as follows: Group A (low-contrast concentration group), 17 lesions; Group B (moderate-contrast concentration group), 45 lesions; and Group C (high-contrast concentration group), 18 lesions. Significant differences were observed among the three groups in K^trans, K_ep, CR, PI, and the TD_max (P<0.05) (Table 2).

Pairwise comparisons (Figure 2) revealed the following: Group A had significantly higher CR and PI values than Group B (Z=3.403, P<0.01; Z=3.642, P<0.01) and Group C (Z=6.029, P<0.01; Z=6.357, P<0.01), but lower K^trans and K_ep values than Group B (Z=3.075, P<0.01; Z=3.166, P<0.01) and Group C (Z=5.920, P<0.01; Z=5.747, P<0.01). Group B had higher CR and PI values than Group C (Z=3.837, P<0.01; Z=3.991, P<0.01), but lower K^trans and K_ep values than Group C (Z=4.039, P<0.01; Z=3.738, P<0.01). The TD_max in Groups A and B were significantly smaller than they were in Group C (Z=3.325, P<0.01; Z=2.789, P<0.01), whereas no significant difference in lesion size was observed between Groups A and B (P>0.05).

Figure 2 Pairwise comparisons of (A) K_ep, (B) K^trans, (C) CR, (D) PI, and (E) TD_max among Groups A, B, and C. Group A: low-contrast concentration group; Group B: moderate-contrast concentration group; Group C: high-contrast concentration group. Statistical significance is indicated as follows: *, P≤0.05; **, P≤0.01; ***, P≤0.001; ns, no significant difference (P>0.05). CR, contrast ratio; K_ep, reverse volume transfer constant; K^trans, volume transfer constant; PI, percentage increase; TD_max, maximum tumor diameter.

Correlation analysis

The CR value was moderately negatively correlated with K^trans and K_ep values (r=−0.467, P<0.001; r=−0.526, P<0.001). Similarly, the PI value was moderately negatively correlated with K^trans value (r=−0.658, P<0.001) and highly negatively correlated with K_ep value (r=−0.716, P<0.001) (Figure 3).

Figure 3 In Spearman correlation analysis, CR showed a moderate negative correlation with K^trans (r=−0.467, P<0.001) and K_ep (r=−0.526, P<0.001), whereas PI showed a moderate negative correlation with K^trans (r=−0.658, P<0.001) and a strong negative correlation with K_ep (r=−0.716, P<0.001). CR, contrast ratio; K_ep, reverse volume transfer constant; K^trans, volume transfer constant; PI, percentage increase.

Discussion

Since the DCE-MRI parameters K_ep and K^trans can quantify vascular permeability and indirectly reflect lesion contrast agent concentration (11,17), this study qualitatively and quantitatively analyzed the relationship between intralesional gadolinium concentration and the degree of enhancement on CE-T2 FLAIR based on DCE-MRI. It addressed the question raised in previous human studies regarding why the detection rates of brain tumors differ between CE-T2 FLAIR and CE-T1WI (6,7), and explored the diagnostic value of CE-T2 FLAIR in intracranial metastases.

The qualitative results of this study showed that when intralesional K^trans and K_ep values were relatively low, the CR and PI values of the lesions on CE-T2 FLAIR were higher, and CE-T2 FLAIR demonstrated the lesions better than CE-T1WI (Figure 1, A1-F1); when intralesional K^trans and K_ep values were relatively moderate, the CR and PI values of the lesions on CE-T2 FLAIR were moderate, and both CE-T2 FLAIR and CE-T1WI could clearly demonstrate the lesions (Figure 1, A2-F2); when intralesional K^trans and K_ep values were relatively high, the CR and PI values of the lesions on CE-T2 FLAIR were significantly reduced, and CE-T1WI demonstrated the lesions better than CE-T2 FLAIR (Figure 1, A3-F3). These findings suggest that, when tumor vascular permeability is low, CE-T2 FLAIR demonstrates the lesions better than CE-T1WI, and CE-T1WI may miss lesions; when tumor vascular permeability is very high, CE-T1WI demonstrates the lesions better than CE-T2 FLAIR, and CE-T2 FLAIR may miss lesions. Previous human studies have reported inconsistent conclusions regarding the detection rates of brain tumors between CE-T2 FLAIR and CE-T1WI (18-20), which may be attributed to differences in tumor composition across studies. Tumors with higher aggressiveness and faster growth have higher microvascular density and higher vascular permeability (21). Since most metastases have high vascular permeability, CE-T1WI can detect the majority of lesions in routine diagnostic practice; however, it may miss a small number of lesions with low vascular permeability. Moreover, relevant studies have indicated that CE-T2 FLAIR is more effective than CE-T1WI in differentiating small subcortical metastases from enhancing vessels, providing an advantage in the evaluation of cortical surface lesions (22,23). Therefore, when performing MRI examinations in patients with brain metastases, CE-T2 FLAIR scanning should be conducted following routine CE-T1WI, in order to minimize the risk of missing lesions with low vascular permeability and cortical surface lesions.

In addition, the results of this study suggest that in routine practice, a simple and feasible visual assessment can be used to roughly evaluate intralesional vascular permeability based on the difference in enhancement between CE-T1WI and CE-T2 FLAIR. Under normal conditions, the blood-brain barrier (BBB) maintains the stability of the brain microenvironment and thus protects brain tissue, but under pathological conditions, it hinders the application of certain drugs (24). A CE-T1WI-dominant enhancement pattern may correspond to lesions with higher vascular permeability, thereby facilitating drug entry into the tumor and potentially improving treatment efficacy, whereas a CE-T2 FLAIR-dominant enhancement pattern may reflect relatively lower permeability and more limited drug penetration, potentially resulting in poorer therapeutic response—a hypothesis that requires further validation in future studies. However, enhancement on both CE-T1WI and CE-T2 FLAIR is also affected by the post-contrast delay (25). Yuh et al. reported that a 10-min delay after contrast injection improved the detection of brain metastases smaller than 10 mm (26). In our study, CE-T1WI/CE-BRAVO was acquired at approximately 6 min and CE-T2 FLAIR at around 10 min after injection, which may have partly contributed to better lesion detection on CE-T2 FLAIR. This difference in acquisition timing should be considered when interpreting our results and represents a methodological limitation of the study.

The quantitative results of this study showed that the CR values of lesions on CE-T2 FLAIR were moderately negatively correlated with K^trans and K_ep values; PI values were moderately negatively correlated with K^trans values and highly negatively correlated with K_ep values. These findings are broadly consistent with those reported by Jin et al. (16). Accordingly, we more modestly frame our study as a confirmatory/validation extension of the prior conclusions. Notably, DCE pharmacokinetic parameters in our study were derived using the e-Tofts model. Compared with the standard Tofts model, the e-Tofts model incorporates the plasma volume fraction (V_p) and decomposes tissue contrast-agent concentration into intravascular and extravascular extracellular space (EES) components (14). Prior work suggests that the e-Tofts model may be more appropriate for permeability quantification in lesions with high perfusion and/or high blood volume (27). The observation of the same correlation pattern under this alternative modeling assumption provides more robust support for the phenomenon and may improve its to clinical image interpretation. In addition, DCE parameters were extracted using a multi-slice hotspot ROI approach on parametric maps, with values averaged across ROIs, which is more likely to capture characteristic tumor permeability features while partially accounting for intratumoral heterogeneity (28). A previous study has also compared hotspot vs. large-tumor ROIs for correlating DCE metrics with histopathology and found stronger associations with microvascular indices for some parameters when derived from hotspot ROIs, suggesting that hotspot-based measurements may better reflect the vascular characteristics of key pathological regions (29).

Despite quantitatively explaining the relationship between vascular permeability of brain metastases and the degree of lesion enhancement on CE-T2 FLAIR, this result was only partially consistent with the gadolinium concentration-SI curve of CE-T2 FLAIR in vitro (8,22). In the in vitro curve of gadolinium concentration vs. tissue SI on CE-T2 FLAIR, when the contrast concentration is low, the tissue SI on CE-T2 FLAIR increases with increasing contrast concentration; when the contrast concentration rises to a certain level, the tissue SI on CE-T2 FLAIR decreases with further increases in contrast concentration. In the pharmacokinetic study of gadolinium contrast agent in humans by Spinazzi et al. (30), volunteers were administered gadolinium contrast agent intravenously at a dose of 0.2 mmol/kg, and plasma samples were collected at scheduled intervals to measure gadolinium concentration. The results showed that within 30 min, the plasma concentration of the gadolinium contrast agent remained no lower than 0.5 mmol/L. Therefore, in this study, for metastases with a greater degree of BBB disruption, the amount of contrast agent passing through was larger and contrast agent continuously accumulated in the lesions, resulting in higher intralesional contrast concentration; whereas for metastases with less severe BBB disruption, the amount of contrast agent passing through was smaller, resulting in lower intralesional contrast concentration. For extremely low concentrations of contrast agent, the ability of CE-T2 FLAIR to detect changes in tissue SI is limited. In addition, only a small number of such cases were included in this study (n=17), and thus, the relationship between tissue SI on CE-T2 FLAIR and contrast concentration at lower levels could not be accurately demonstrated.

The results of this study also showed that there was no statistically significant difference in the TD_max of lesions between Groups A and B, but the TD_max of lesions in Groups A and B were significantly smaller than those in Group C. Among them, Group A lesions had the smallest TD_max with relatively low vascular permeability, whereas Group C lesions had the largest TD_max with relatively high vascular permeability. This result suggests that when brain metastases are relatively small, their vascular permeability is lower and the intralesional contrast concentration is lower; whereas when brain metastases become significantly larger, their vascular permeability markedly increases and the intralesional contrast concentration markedly increases. Therefore, CE-T2 FLAIR has a particular advantage in detecting small metastases, whereas for large metastases it is inferior to CE-T1WI.

This study has several limitations. First, analyses were performed at the lesion level without patient-level adjustment or mixed-effects modeling, so within-patient correlation and confounding cannot be fully excluded. Second, although the acquisition order was standardized, post-contrast delay may still have influenced enhancement characteristics. Third, only patients with complete MRI sequences were included, which may have introduced selection bias and could limit generalizability. Fourth, although primary lung cancer accounted for about two-thirds of the cohort and no significant association was found between primary site (lung vs. non-lung) and CE-T2 FLAIR enhancement group (χ²=1.26, P=0.53), this population heterogeneity may still affect external validity. Finally, most brain metastases were confirmed by imaging follow-up rather than surgery or histopathology.

Conclusions

This study revealed that the vascular permeability of brain metastases in vivo is an important factor influencing the difference in enhancement between CE-T2 FLAIR and CE-T1WI, and that CE-T2 FLAIR has greater advantages than CE-T1WI in demonstrating metastases with low vascular permeability. Therefore, for patients suspected of having brain metastases, CE-T2 FLAIR scanning can serve as an important supplement to CE-T1WI.

Acknowledgments

The authors would like to express their sincere gratitude to their mentors and colleagues for their invaluable guidance and unwavering support throughout the research process and manuscript preparation.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1998/rc

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1998/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-2025-1998/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 The First Affiliated Hospital of Kunming Medical University (approval No. [2023] Lunshen L No. 206), and the requirement for 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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