Combining 3D iterative image reconstruction and deep learning to improve image quality of knee joint MRI fast sequences: a focus on meniscal injury evaluation
Introduction
The knee joint is an important weight bearing joint in the human body. With factors such as aging, obesity, trauma, and the diversification of social activities, knee joint diseases such as osteoarthritis (1,2), meniscal injuries (3), and ligament injuries (4,5) caused by acute and chronic injuries have become significant challenges in the medical field. These diseases restrict patients’ functional abilities and mobility, reducing their quality of life (6,7). Currently, over 100 million people worldwide have knee joint diseases, and this number is expected to increase further, posing a serious threat to human health. Therefore, the rapid and accurate diagnosis of knee joint lesions is of great significance for targeted clinical treatment.
Magnetic resonance imaging (MRI) has the advantages of multi parameter, multi directional, non-invasive imaging, good tissue contrast, and high spatial resolution, making it the preferred examination method for evaluating injuries to structures such as the knee meniscus, ligaments, and cartilage. Studies have shown that MRI has a sensitivity and specificity of over 90% in diagnosing meniscal tears, anterior cruciate ligament (ACL) and posterior cruciate ligament (PCL) injuries, with an accuracy rate of 92% for meniscal injuries and 89% for ligament injuries. In the field of non-invasive examination of knee joint lesions, this method can be called the “gold standard” and has important clinical value (8,9). Currently, the commonly used sequences for knee joint examinations include proton density-weighted imaging (PDWI), T1-weighted imaging (T1WI), and T2-weighted imaging (T2WI) based on fast spin echo (FSE) (10,11), among which PDWI and T1WI sequences have the greatest diagnostic value for knee joint diseases such as knee arthritis, ligament injuries, and meniscal lesions. Studies have shown that T1WI has irreplaceable advantages in observing low signal bone damage, bone marrow lesions, osteoarthritis, and bone tumor screening (12-15). Schafer et al. comprehensively demonstrated that the PDWI sequence exhibits a sensitivity and specificity of approximately 90% and 98%, respectively, in diagnosing meniscal tears. Its diagnostic performance closely aligns with arthroscopic findings and is superior to that of other imaging sequences (16). Therefore, T1WI and PDWI sequences have become the best observation sequences for diseases such as meniscal injuries, tears, and bone marrow edema except for arthroscopic examinations. However, the acquisition time for scanning these sequences on a 1.5 T magnetic resonance (MR) scanner is about 7–9 minutes, which not only reduces the efficiency of the equipment, but also may cause some patients to have reduced cooperation due to maintaining a fixed position for a long time, affecting image quality and diagnostic accuracy. Therefore, improving scanning efficiency to address both workflow constraints and patient comfort concerns is of paramount importance for clinical knee MRI.
At present, several MRI accelerated acquisition technologies are in clinical use. Among these, parallel imaging (PI) techniques, such as GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA), are widely adopted to reduce scan time by undersampling k-space data. Although compressed sensing (CS) represents another acceleration paradigm that employs pseudo-random undersampling and nonlinear reconstruction, this study utilized acceleration solely based on PI. A primary challenge with PI-accelerated acquisitions is the potential for reduced image quality, including decreased signal-to-noise ratio (SNR) and increased artifacts. To address this, advanced image reconstruction techniques are essential. Various three-dimensional (3D) iterative image reconstruction technologies have been developed such as non-local means, singular value decomposition, sparse representation, machine learning-based technologies, and combinations of these technologies (17-20). These methods can significantly shorten the examination time without compromising image quality. However, few studies have applied such advanced reconstruction techniques to knee joint MRI, and those that have not received sufficient attention. Therefore, this study investigated a hybrid reconstruction approach implemented using a specific commercial software (iQMR™, Medic Vision Imaging Solutions Ltd., Tirat Carmel, Israel). This approach processes PI-accelerated data through a model-based iterative reconstruction algorithm that incorporates a compressed sensing and total variation (CS-TV) minimization constraint to suppress artifacts and enforce data consistency. Subsequently, the output is fed into a deep learning (DL) module for perceptual image enhancement, establishing a machine learning-assisted 3D iterative image enhancement system. It uses nonlinear, volumetric image reconstruction algorithms, and through artificial intelligence (AI) assistance, leverages statistical prior knowledge of MRI data to restore the details and quality of images obtained from accelerated acquisition (21). This can significantly shorten the scanning time while significantly improving the SNR and image quality of fast sequences. We present this article in accordance with the STROBE reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1845/rc).
Methods
The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by Institutional Ethics Committee of Chongqing Emergency Medical Center (No. 2025-70, issued 23 Apr 2025) and the requirement for individual consent for this analysis was waived due to the retrospective nature.
Participants
This retrospective study was approved by the Ethics Committee of our hospital (2025 Ethics Approval No. 70, issued 23 Apr 2025). As this was a retrospective study, informed consent was not required.
Patients with knee pain who were admitted to the Central Hospital Affiliated to Chongqing University from June 2023 to June 2024 were retrospectively included. The inclusion criteria were as follows: (I) aged ≥18 years; (II) patients clinically suspected of having knee joint diseases; (III) patients without contraindications to MR examination; and (IV) patients who could fully cooperate with the examination. The exclusion criteria were as follows: (I) patients with general contraindications to MRI examination; (II) patients with severe motion artifacts or metal artifacts that could not meet the diagnostic requirements; and (III) patients with severe claustrophobia.
MR image acquisition
All cases underwent MRI using a 1.5 T magnetic resonance scanner (uMR560, Shanghai United Imaging Healthcare Co., Ltd., Shanghai, China) with a 12-channel dedicated knee receiving coil (Shanghai United Imaging Healthcare Co., Ltd.). First, conventional T1WI and PDWI sequences were acquired with the following parameters: (I) T1WI [repetition time (TR): 782 ms; echo time (TE): 11.52 ms; voxel size: 0.73×0.51×4 mm3; bandwidth: 190 kHz/pixel; echo train length (ETL): 2; number of excitations (NEX): 1; acceleration factor: 0]; (II) PDWI (TR: 4,488 ms; TE: 21.88 ms; voxel size: 0.70×0.56×4 mm3; bandwidth: 200 kHz/pixel; ETL: 16; NEX: 1; acceleration factor: 0). For the fast sequences, the acceleration factors of T1WI and PDWI were increased to 3 and 2, respectively, with other parameters remaining unchanged. In this study, both the T1WI and PDWI sequences were acquired using two-dimensional (2D) acquisition. For acceleration, these sequences employed techniques based on PI. Specifically, the PI technique used was GRAPPA, which is k-space-based and represents a novel partially parallel acquisition (PPA) method that accelerates image acquisition using a radiofrequency (RF) coil array for spatial encoding (22). Furthermore, the sampling schemes were designed based on the GRAPPA framework. In this approach, the center point of the acquired k-space data was fully sampled, whereas the periphery of the k-space data employed equally spaced random sampling.
Image reconstruction
“The ‘Fast’ group images were generated by applying the standard GRAPPA reconstruction directly to the accelerated k-space data. The ‘After Processing’ group images were generated by feeding the same accelerated k-space data into the iQMR™ software for the hybrid reconstruction process described below. All accelerated sequence images in this study were reconstructed offline using the iQMR™ DL reconstruction software (version 1.2). This software implements an integrated hybrid reconstruction pipeline, with the specific workflow detailed below.
First, parallel imaging-based initial reconstruction (utilizing an autocalibrating GRAPPA algorithm) is performed on the raw accelerated k-space data to rapidly generate an initial image and estimate coil sensitivity profiles. Subsequently, model-based iterative reconstruction is executed by solving an optimization problem that includes a data fidelity term and a total variation regularization term. This enforces strict physical consistency between the reconstructed image and the original undersampled data, thereby effectively suppressing aliasing artifacts and noise. Finally, the output from the iterative reconstruction is fed into a dedicated deep convolutional neural network (CNN) for perceptual quality enhancement. The core architecture of this network draws inspiration from the residual learning blocks within the generator of the Super-Resolution Generative Adversarial Network (SRGAN) proposed by Ledig et al. (23). However, its training objective is specifically tailored for this application, employing a hybrid loss function that combines pixel-level fidelity with high-level feature similarity (24). This design aims to significantly improve the visual sharpness, tissue contrast, and textural realism of the image, rather than merely increasing resolution.
Qualitative image analysis
Two radiologists with 10 years of experience in reading MRI images of the osteoarticular system independently performed qualitative analysis on the IMPAX Client workstation (Version: 6.5.3.3009 2015, AGFA HealthCare, Mortsel, Belgium). The radiologists were blinded to clinical information and sequence types. The overall quality of conventional sequences, original images of fast sequences, and reconstructed images of fast sequences was evaluated, with each category assessed using a 5-point Likert scale. The weighted Kappa test was used to calculate the inter rater agreement.
Quantitative image analysis
SNR and CNR of tissues around the knee joint in conventional sequences, original images of fast sequences, and reconstructed images of fast sequences were calculated and analyzed. On the sagittal T1WI and PDWI of the knee joint, elliptical regions of interest (ROIs) with areas of approximately 0.5, 0.5, 0.1, 0.1, 0.1, and 0.1 cm2 were placed in the medial femoral condyle, medial head of the gastrocnemius muscle, infrapatellar fat pad, suprapatellar bursa effusion, patellar cartilage, and posterior cruciate ligament, respectively, to measure the corresponding signal intensity (SI) values. Each site was measured continuously three times to obtain the average SI value of the ROI. Then, the standard deviation (SD) of background noise outside the knee joint was measured using an ROI of the same size, and the SNR of each tissue was calculated respectively. Meanwhile, the CNR for T1WI and PDWI was calculated as (SI of suprapatellar bursa effusion SI of patellar cartilage)/SD at the patellar cartilage level. Intraclass correlation coefficient (ICC) analysis was used to calculate the inter rater agreement. It should be noted that for images reconstructed using DL, their noise distribution no longer conforms to simple Rayleigh or Gaussian models. Consequently, the SNR and CNR values calculated based on the standard deviation of background regions in this study should primarily be interpreted as relative indicators reflecting the overall signal-to-noise performance and contrast/texture characteristics of the images, intended for inter-sequence comparison rather than as absolute measures of physical SNR and CNR.
Stoller classification assessment
Two radiologists, who were blinded to clinical data, respectively observed the conventional sequences, original images of fast sequences, and reconstructed images of fast sequences to determine the corresponding scores. The weighted Kappa test was used to calculate the inter rater agreement. The flow chart of our study is shown in Figure 1.
Statistical analysis
Statistical analysis was performed using R4.0 software (R Foundation for Statistical Computing, Vienna, Austria). The Shapiro-Wilk test was used to evaluate the normal distribution of quantitative values. If the data conformed to a normal distribution, they were expressed as mean ± SD, and the independent samples t-test was used; if they did not conform to a normal distribution, they were expressed as median [interquartile range (IQR)], and the independent samples Wilcoxon rank-sum test was used. For consistency testing, the ICC and Kappa test were used to assess the consistency between the two radiologists. A value <0.2 indicates poor consistency; a value between 0.2 and 0.4 indicates fair consistency; a value between 0.4 and 0.6 indicates moderate consistency; a value between 0.6 and 0.8 indicates substantial consistency; and a value between 0.8 and 1.0 indicates almost perfect consistency.
Results
A total of 116 patients were included in this study, with 53 males (45.7%) and 63 females (54.3%), aged 21–80 years (53.7±16.9 years). Each patient underwent three imaging series for both T1WI and PDWI: (I) conventional fully-sampled sequences; (II) accelerated sequences reconstructed with standard GRAPPA (labeled ‘Fast’); and (III) accelerated sequences processed with the iQMR™ software using the same undersampled data as group 2 (labeled ‘After Processing’). Each patient had 3 sets of data. The acquisition time of conventional T1WI and PDWI sequences was 92 seconds and 158 seconds, respectively, whereas that of fast T1WI and PDWI sequences was 31 seconds and 53 seconds, respectively, which were shortened by 66.304% and 66.455%, respectively. The achieved reduction in scan time approximately corresponds to the applied acceleration factors (R=3 for T1WI and R=2 for PDWI), considering the overhead for auto-calibration signals.
Comparison of qualitative image evaluation
Statistical results showed that after post-processing of the fast sequence images, the SNR was significantly improved (P<0.05), which was comparable to that of the conventional sequence images. After the fast sequences were processed by iterative reconstruction and DL, the image quality received significantly higher scores from both reviewers compared with conventional images, and the proportion of high quality images (scored 4–5) was better (P<0.05). The internal reliability between the two reviewers was substantial, with Kappa values ranging from 0.767 to 0.914 (Figure 2). In the evaluation of meniscus Stoller classification, the internal reliability between the two reviewers was also substantial, with Kappa values ranging from 0.767 to 0.914 (Figure 3).
Comparison of quantitative image evaluation
Statistical results showed that after post processing of the fast sequence images, the SNR was significantly improved (P<0.05), which was comparable to that of the conventional sequence images. The ICC analysis results ranged from 0.709 to 0.926 (Figure 4 and Table 1). There was no statistically significant difference in CNR among the three groups of images in both T1WI and PDWI sequences (P>0.05) (Figure 5 and Table 1).
Table 1
| Category | Series | Conventional | Fast | After processing |
|---|---|---|---|---|
| Medial condyle of the femur | T1WSNR | 117.8 (100.6, 133.8) | 94.5 (78.9, 109.0) | 117.2 (102.5, 137.5) |
| PDWSNR | 82.9 (71.6, 98.0) | 64.9 (57.3, 78.2) | 86.0 (72.8, 98.5) | |
| Medial head of the gastrocnemius | T1WSNR | 55.1 (48.3, 65.2) | 42.9 (34.8, 53.8) | 55.9 (47.3, 65.5) |
| PDWSNR | 180.5 (159.9, 201.1) | 162.8 (142.6, 178.8) | 188.8 (163.0, 208.0) | |
| Infrapatellar fat pad | T1WSNR | 203.7 (179.9, 233.1) | 182.7 (156.2, 209.4) | 212.6 (183.8, 243.3) |
| PDWSNR | 154.8 (131.7, 176.5) | 136.0 (112.7, 158.5) | 156.7 (135.6, 186.6) | |
| Suprapatellar bursa effusion | T1WSNR | 73.3 (61.4, 94.8) | 63.4 (52.4, 79.3) | 74.4 (61.2, 97.5) |
| PDWSNR | 344.8 (309.6, 406.0) | 308.3 (264.4, 379.3) | 363.8 (308.5, 427.5) | |
| Patellar cartilage | T1WSNR | 84.2 (71.0, 97.8) | 70.3 (57.7, 84.2) | 84.9 (70.9, 103.2) |
| PDWSNR | 227.2 (193.4, 266.7) | 196.5 (173.3, 228.2) | 239.7 (206.0, 281.9) | |
| Posterior Cruciate Ligament | T1WSNR | 55.3 (45.8, 63.8) | 48.8 (38.8, 55.3) | 54.8 (44.0, 69.6) |
| PDWSNR | 113.3 (93.4, 136.6) | 95.9 (79.0, 123.3) | 128.3 (98.3, 149.4) | |
| Suprapatellar bursa effusion-patellar cartilage | T1WCNR | −7.1 (−23.6, 11.0) | −5.1 (−18.5, 12.1) | −4.6 (−24.6, 18.3) |
| PDWCNR | 118.7 (58.0, 182.4) | 107.5 (46.1, 183.4) | 111.1 (50.5, 191.3) |
Data are presented as median (interquartile range). The SNR and CNR of the medial femoral condyle, medial head of gastrocnemius, infrapatellar fat pad, suprapatellar bursa effusion, patellar cartilage, and posterior cruciate ligament relative to surrounding tissues were analyzed using the independent samples Wilcoxon rank-sum test. CNR, contrast-to-noise ratio; PDWI, proton density-weighted imaging sequence; SNR, signal-to-noise ratio; T1WI, T1-weighted imaging sequence.
Discussion
The primary challenge in accelerating knee MRI lies in maintaining diagnostic image quality—particularly for fine structures like the menisci—while substantially reducing scan time. Although PI, exemplified by GRAPPA, provides a fundamental acceleration mechanism, images reconstructed with PI alone are often prone to residual noise and aliasing artifacts, which can degrade diagnostic confidence. This study employed a hybrid reconstruction pipeline integrating PI acceleration with a model-based iterative reconstruction (IIR) and a subsequent DL enhancement module. The observed restoration of image quality, achieving parity with conventional sequences in semi-quantitative meniscal grading, can be attributed to the complementary roles of this integrated approach. The model-based IIR component, utilizing total variation regularization, enforces strict consistency between the reconstructed image and the originally acquired undersampled k-space data. This process effectively suppresses incoherent aliasing artifacts and noise amplification inherent to PI, providing a physically grounded foundation for the reconstruction. Subsequently, the dedicated DL module, trained with objectives that combine pixel-level fidelity and perceptual similarity (24), acts on this initial estimate. It is specifically designed to recover fine textural details and enhance edge sharpness—features critical for the clear delineation of internal meniscal architecture and tear morphology—that may be attenuated or lost in the linear PI reconstruction or during the regularization step of IIR. This synergistic framework, where IIR ensures data fidelity and DL recovers high-frequency details, aligns with emerging methodological paradigms that combine physical models with data-driven priors for optimized inverse problem solving (25). Our quantitative findings are consistent with this mechanistic interpretation. The significant improvement in SNR for the accelerated post-processed images, reaching levels comparable to those of conventional sequences, results from the combined effect of noise suppression through IIR regularization and intelligent signal recovery via the DL network’s learned priors. Furthermore, the maintained CNR across all three groups suggests that the hybrid pipeline preserves the relative signal differences between tissues (e.g., fluid and cartilage), which is crucial for diagnostic contrast. This balance between SNR recovery and CNR preservation under acceleration is corroborated for the knee by recent work demonstrating the clinical non-inferiority of DL-reconstructed accelerated protocols (26). The high inter-reader agreement (Kappa values 0.767–0.914) in Stoller grading between conventional and accelerated post-processed images directly supports the clinical utility of this approach for meniscal assessment, achieving a ~66% reduction in scan time without compromising grading consistency.
In this study, the acquired fast sequence images were sent to the server, where 3D iterative technology combined with DL was used for denoising, image sharpening, enhancement processing, as well as for the suppression of noise and the recovery of underlying tissue signal. Through continuous iteration, the optimal accelerated post processing group images were generated, significantly improving image quality. In clinical practice, good image quality and clear display of internal structures of lesions are crucial for evaluating knee joint lesions. The post-processed images of fast sequences performed excellently in terms of overall image quality, significance of knee joint lesions, and display of internal structures of lesions. The results of this study showed that in T1WI and PDWI sequences, the post-processed fast sequence images received significantly higher scores from both reviewers, especially in the proportion of high quality images with scores of 4–5. Meanwhile, the Kappa test results for the meniscus Stoller scores between the conventional group and the accelerated post-processing group ranged from 0.767 to 0.914, indicating a high degree of consistency. This suggests that under the premise of greatly shortening the examination time, the fast sequence ensures image quality through 3D iteration and DL, improves work efficiency, and achieves the ability of the conventional group to evaluate knee joint lesions. Aggarwal et al. showed that the combination of iterative reconstruction optimization and DL for MRI undersampled reconstruction can achieve an acceleration effect of about 5–10 times (27). Liu et al. proposed a general framework combining iterative reconstruction and DL, which unfolds iterative optimization steps (such as conjugate gradient method) into neural network layers to ensure data consistency and improve reconstruction quality (28). Therefore, the combination of IIR and DL breaks through traditional limitations, and can achieve image quality comparable to that obtained by conventional sequences under the 1.5T magnetic field intensity, realizing a balance between “speed and quality”.
This study found that the SNR of both T1-weighted and PD-weighted images in the fast sequences demonstrated a significant improvement after post-processing and were comparable to those of the conventional sequences. This indicates that IIR restores images from undersampled k space data through iterative optimization and enforces data consistency, ensuring that the reconstructed k space is consistent with the original sampling points in each iteration to avoid over smoothing or distortion. Furthermore, the dedicated DL module, trained in a supervised manner, enables its convolutional layers to capture multi-scale features, repairing the subtle structures of cartilage edges or ligaments that may be lost in traditional IIR. Meanwhile, they learn noise distribution from a large amount of training data to distinguish real signals from noise, thereby improving SNR. Finally, through physics-guided DL and accelerated iterative convergence, the data consistency layer of IIR is embedded into the neural network, ensuring that the reconstruction results conform to physical laws while retaining details. Therefore, the combination of IIR and DL, through the collaborative optimization of physical constraints and data driven approaches, achieves SNR comparable to that of conventional sequences in knee joint T1WI and PDWI imaging (29). This technology not only shortens the scanning time but also provides a new tool for the accurate diagnosis of early cartilage injuries and ligament lesions. By virtue of the collaborative optimization between physical models and DL, this technology breaks through the “SNR-time-resolution” triangular limitation of traditional accelerated imaging, and shows significant advantages especially in the visualization of fine structures such as menisci and ligaments. In this study, there was no statistically significant difference in CNR among the conventional sequences, fast sequences, and post-processed fast sequences (P>0.05), suggesting that this technology can effectively maintain good CNR while shortening the scanning time. The possible reasons are as follows: the accelerated group effectively retains key signal information while shortening the scanning time through reasonable acceleration factors and k space sampling strategies; meanwhile, iterative reconstruction can suppress high frequency noise introduced by undersampling, maintaining CNR close to that of conventional sequences. On the basis of the accelerated group, the accelerated post-processing group, through data-driven learning, specifically repairs the noise and artifacts in the accelerated images and retains tissue contrast; at the same time, some algorithms combine iterative optimization with DL to ensure that the reconstruction results not only conform to k space data consistency but also retain anatomical details, thus effectively maintaining image CNR. Feng et al. studied the impact of different acceleration factors (2–8 times) on cardiac cine MRI, proposed the optimal acceleration strategy in dynamic scenarios, and showed that under 4-fold acceleration, CNR had no significant difference from that of conventional sequences (30). Foti et al. evaluated indicators such as CNR and diagnostic confidence of DL reconstruction in knee joint MRI, showing that it is equivalent to conventional sequences and can effectively suppress motion artifacts and high frequency noise (31).
Although this study demonstrates promising results for meniscal injury evaluation, several considerations limit the immediate generalization of the conclusions. First, the diagnostic task was confined to meniscal Stoller grading—a well-established and frequently used metric. The performance of this accelerated and processed protocol for diagnosing other clinically crucial knee pathologies, such as ACL or PCL tears, collateral ligament injuries, or subtle cartilage defects, remains unverified. These structures differ in contrast, morphology, and pathological presentation. Although the improved SNR and maintained CNR are beneficial, dedicated studies evaluating diagnostic accuracy (e.g., sensitivity, specificity) for these specific entities are necessary before broader clinical adoption. The choice to focus initially on the meniscus was based on its high clinical prevalence and the availability of a robust semi-quantitative grading system (Stoller) for validation.
Second, the evaluation was limited to T1WI and PDWI sequences, without encompassing a full spectrum of MRI sequences. Third, only images from a 1.5 T MRI system were included, leaving the applicability to other field strengths (e.g., 3.0 T) unexplored. Finally, the sample size was relatively small, and no longitudinal follow-up was performed to assess clinical outcomes. In future studies, more samples and sequences will be included for dynamic follow up, and devices with different field strengths will be used under accelerated conditions. Through algorithm optimization and parameter adjustment, the clinical value of this technology will be further verified.
Conclusions
In summary, the accelerated technology based on 3D iterative image reconstruction supplemented by DL can significantly improve the image quality of knee joint MRI fast sequences, shorten the examination time, enhance work efficiency, reduce operating costs, and optimize examination resources, which is worthy of clinical promotion and application.
Acknowledgments
None.
Footnote
Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1845/rc
Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1845/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-2025-1845/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 Institutional Ethics Committee of Chongqing Emergency Medical Center (No. 2025-70, issued 23 Apr 2025) and individual consent for this analysis was waived due to the retrospective nature.
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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