Targeted respiratory regulation and precision diaphragm localization improve efficiency and image quality: a comparison between conventional and improved four-dimensional flow cardiac magnetic resonance in hypertrophic obstructive cardiomyopathy patients and healthy volunteers

Introduction

Pulsatile blood flow through the heart and great vessels is multidirectional and multidimensional. The most commonly used tools for assessing cardiovascular blood flow in clinical are Doppler echocardiography (1-3) and two-dimensional (2D) cine phase contrast (PC) cardiac magnetic resonance (CMR) (4-6). However, access to all the directions, regions and phases of such flows has been limited with these two imaging modalities because of their restricted spatial coverage (single-plane/single-slice), inability to quantify three-dimensional (3D) hemodynamic parameters, and operator dependence.

Four-dimensional flow CMR (4D flow CMR) is an advanced imaging technique that provides a comprehensive evaluation of cardiovascular hemodynamics. This capability is essential for evaluating the severity of cardiac conditions and treatment efficacy (7,8). However, the technique can be hindered by prolonged scanning time or less-than-ideal image quality (9,10).

The most common strategy for mitigating respiratory and cardiac motion artifacts in 4D flow CMR involves synchronized electrocardiographic (ECG) gating with the conventional diaphragmatic navigation technique (11). However, the conventional method is susceptible to diaphragmatic drift, which can diminish acquisition efficiency and the effectiveness of motion compensation (12). Consequently, it is essential to improve conventional diaphragmatic navigation to reduce examination time and enhance image quality.

Currently, inefficiency and less-than-ideal image quality of conventional 4D flow CMR are highly correlated with diaphragmatic drift due to irregular breathing patterns (13,14). The implementation of targeted respiratory regulation is anticipated to stabilize the respiratory process, promoting consistent diaphragmatic motion throughout the 4D flow CMR examination. Complementing this method, the balanced steady-state free precession (bSSFP) sequence, known for its superior temporal resolution (15,16), allows for the dynamic monitoring of diaphragmatic fluctuation during respiration. This feature facilitates real-time tracking of the diaphragm and pinpointing its position at the end of exhalation, which is essential for accurate diaphragmatic localization.

We hypothesized that integrating targeted respiratory regulation with accurate diaphragmatic localization, termed improved diaphragmatic navigation, could potentially lead to a reduction in examination time and an enhancement in image quality in 4D flow CMR.

Hypertrophic obstructive cardiomyopathy (HOCM), as a common non-ischemic cardiomyopathy in clinical practice, requires 4D flow CMR for complete hemodynamic profiling due to its complex flow patterns. Therefore, this study aimed to evaluate the potential clinical utility of the improved diaphragmatic navigation method, by comparing the factors related to acquisition time, image quality, and confidence in hemodynamic diagnostic assessments between conventional and improved diaphragmatic navigation in 4D flow CMR. We present this article in accordance with the STROBE reporting checklist (available at https://cdt.amegroups.com/article/view/10.21037/cdt-2025-139/rc).

Methods

Study subjects

Between September 2022 and July 2023, this prospective study initiative sequentially enrolled participants from Guangdong Provincial People’s Hospital who were diagnosed with HOCM and healthy volunteers for 4D flow CMR imaging. Eligibility criteria included the absence of ferromagnetic metallic devices and a resting heart rate of 100 beats per minute or lower. Exclusion criteria were age less than 18 years, or contraindications for undergoing magnetic resonance imaging (MRI) procedures. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Institutional Review Board of Guangdong Provincial People’s Hospital (Guangdong Academy of Medical Sciences) (No. KY2023-883-03), Southern Medical University and informed consent was obtained from all individual participants. Sample size estimation procedure for this study was based on expected differences in actual scan times. Based on formula 1, the possible loss to follow-up rate (expected to be 10%), and to ensure the reliability of the study results, 55 participants (30 is enough) were included in this study.

n = (Za2+Zβ△σ)2[1]

Where the significance level (α) is set at 0.05, and the power (1−β) is 80% (with β=0.20), Z_a/2 is the quantile of the standard normal distribution at α/2. Z_β is the quantile of the standard normal distribution at β. ∆ (100 seconds) is the mean difference in actual scan time between the two methods. σ (160 seconds) is the standard deviation of the actual scan time.

Imaging protocol

To conduct this study, a 3.0-tesla MRI scanner (Ingenia 3.0T, Philips Healthcare, Best, the Netherlands) was used with a 32-channel body phased-array coil and spine coil. This setup was utilized for acquiring 4D flow CMR images, ensuring comprehensive coverage of the heart and major vascular structures. And the navigation signal was captured at the end of the diastolic phase within each cardiac cycle to identify the diaphragmatic dome, utilizing a 6-mm wide acceptance window for navigation. The pencil beam navigator, measuring 100 mm, was aligned above the diaphragmatic dome, ensuring lung-to-liver coverage ratio of 1:1 (17). The imaging protocol parameters for both the conventional and improved methods during 4D flow CMR remained consistent，except the respiratory control (Figure 1).

Figure 1 Overview of conventional and improved diaphragmatic navigation 4D flow CMR imaging protocols. (A) The 4D flow CMR imaging protocol encompasses navigator placement (yellow rectangle) and imaging coverage (white rectangle). (B) Respiratory control protocols for both methods. (C) Positional relationship between the diaphragmatic dome (black-white interface) and the acceptance window (blue double solid lines). In the conventional method, variable degrees of offset exist between the diaphragmatic dome and the acceptance window. In the improved method, the diaphragmatic dome is positioned in the acceptance window with minimal offset. (D) Representative 4D flow CMR images, the upper panel are magnitude images with different degrees of artifacts, and the lower panel is PCA images with similar degrees of visibility. 4D flow CMR, four-dimensional flow cardiac magnetic resonance; bSSFP, balanced steady-state free precession; PCA, phase contrast angiography.

Respiratory control: (I) conventional diaphragmatic navigation: participants were instructed to breathe freely and calmly; (II) improved diaphragmatic navigation: before scanning, participants received targeted respiratory regulation, encompassing: (i) remaining awake and relaxing throughout the process; (ii) keeping the body still and following the breathing rhythm instructions (breathing rhythm was fixed at 20 breaths per minute) on the recording and breathing calmly with small amplitude; and (iii) refraining from coughing. Subsequently, a real-time tracking bSSFP sequence scan (Figure S1) was conducted to determine the diaphragmatic dome’s position at the end of exhalation.

Volunteers underwent 4D flow CMR imaging without gadolinium contrast agent. Patients diagnosed with HOCM underwent 4D flow CMR after late gadolinium enhancement (LGE) scanning. All participants underwent the conventional 4D flow CMR first, followed by the improved 4D flow CMR, to avoid the impact on the results of the improved method caused by the participants’ prior knowledge of the targeted respiratory regulation.

A comprehensive list of parameters for the 4D flow CMR and bSSFP sequence is shown in Table 1.

Data analysis

The datasets were subsequently uploaded to Picture Archiving and Communication Systems (PACS) and analyzed using CVI42 (Circle Cardiovascular Imaging version 5.17, Inc., Calgary, Alberta, Canada). The image analysis was performed independently by three experienced radiologists with more than a decade of experience each, all of whom were blinded to the scanning technique (conventional vs. improved).

Factors related to acquisition time

Navigation offset: navigation offset refers to the perpendicular distance from the diaphragmatic dome apex to the center of the navigation acceptance window (Figure 2A). This metric indicated the accuracy of diaphragmatic localization, with a reduced offset correlating to enhanced accuracy in the localization.

Figure 2 Data quantification and image quality assessment projects and rules. (A) Navigation offset: the perpendicular distance from the diaphragmatic dome, indicated by a white solid line, to the midpoint of the navigation acceptance window, marked by a yellow solid line, is measured within the confines of the blue interval, delineated by a purple solid line. (B) aSNR: on the central cross-section of the 4D flow CMR magnitude image, three ROIs of identical area, depicted in red, are positioned to ascertain the aSNR. Image quality: this encompasses scoring for (C) visibility and (D) artifacts (red triangles mark). Hemodynamics: measurement planes are strategically positioned along the (E) aorta at the (E3) AAo, (E1) Arch, and (E2) DAo. 4D flow CMR, four-dimensional flow cardiac magnetic resonance; AAo, ascending aorta; Arch, aortic arch; aSNR, apparent signal-to-noise ratio; DAo, descending aorta; LPA, left pulmonary artery; MPA, main pulmonary artery; ROI, region of interest; RPA, right pulmonary artery.

Planned scan time: this parameter represented the estimated scan time indicated by the MRI system once the 4D flow CMR protocol was configured. It was determined by the system’s internal calculations.

Actual scan time: this metric reflected the total elapsed time for the 4D flow CMR examination completion, as recorded by an independent timer.

Acquisition efficiency: this was defined as the ratio of the planned scan time to the actual scan time, expressed as a percentage. This measure of efficiency was derived using the formula:

Ea = TpTa×100%[2]

Where E_a is the acquisition efficiency, T_p is the planned scan time, and T_a is the actual scan time.

Image quality

Apparent signal-to-noise ratio: standard SENSE (SENSitivity Encoding) can lead to increased background noise and reduced signal-to-noise ratio (SNR) due to the amplification of noise during the reconstruction process. Consistent with the studies by Fervers et al. (18) and Chen et al. (19), the apparent SNR (aSNR) was used to evaluate image quality variation. For this purpose, three regions of interest (ROIs) of identical dimensions were selected at the central plane of the 4D flow CMR images, specifically: (I) the ascending aorta (AAo), identified at the midpoint between the aortic sinus and the brachiocephalic artery; (II) the aortic arch (Arch), pinpointed at the midpoint between the brachiocephalic artery and the left subclavian artery; and (III) the descending aorta (DAo), located at the midpoint between the aortic isthmus and the diaphragm. The calculation of the aSNR involved dividing the mean signal intensity (µ_tissue) of the tissue within the ROI by the tissue’s standard deviation (σ_tissue) within that ROI, as shown in Figure 2B. The mean aSNR derived from these three distinct regions was considered the representative aSNR for the analysis. The formulas are:

aSNRtissue = μtissueσtissue[3]

aSNR = aSNRAAo+aSNRArch+aSNRDAo3[4]

Where aSNR represents the apparent signal-to-noise ratio, µ represents the signal intensity, and σ represents the standard deviation.

Visibility and artifacts: we implemented a tiered scoring system, ranging from 1 to 4 points. For visibility evaluation, end-diastolic PC angiography (PCA) images of the aorta within the 4D flow CMR scans were acquired with a window width/level of 198/181 (Figure 2C), and for artifacts evaluation, end-diastolic magnitude images were acquired with a window width/level of 1,440/829 (Figure 2D). The detailed scoring criteria is as follows (images were show in Figure S2).

Visibility: 1 point, low signal intensity with poor uniformity; 2 points, relatively higher signal intensity with sub-improved uniformity; 3 points, relatively higher signal intensity with good uniformity; 4 points, high signal intensity with excellent uniformity.

Artifacts: 1 point, severe artifacts with indistinct anatomical structures; 2 points, moderate artifacts with anatomical structures still discernible; 3 points, mild artifacts with better discernment of anatomical structures; 4 points, minimal artifacts with clear and discernible anatomical structures.

Hemodynamic diagnostic confidence

The 4D flow CMR datasets were analyzed using post-processing software CVI42, encompassing the rectification of background phase offsets and velocity aliasing phenomena. For each dataset, ROIs were strategically positioned at distinct aortic segments (Figure 2E) to ascertain the peak systolic velocity (V_peak), maximum pressure gradient (P_max), and volume flow (V). The plane placement of the protocol was delineated as follows: for the AAo, the plane was situated at the division of the primary pulmonary artery (Figure 2, E3); for the Arch, the plane was positioned between the left common carotid and subclavian arteries (Figure 2, E1); and for the DAo, the plane mirrored the level of that for the AAo (Figure 2, E2). Each measurement plane was oriented perpendicularly to the longitudinal axis of the respective aortic segment.

Statistical analysis

The Shapiro-Wilk test was used to determine the normalcy of variable distributions. Normally distributed data were presented as means with standard deviations (means ± SDs) and underwent paired sample t-tests for analysis. Non-normally distributed data were depicted as medians with interquartile ranges [medians (IQRs)] and were compared using the Wilcoxon signed-rank test. For categorical variables, data were represented as frequencies with their respective percentages. The consistency of intra- and inter-observer measurements was evaluated through intraclass correlation coefficients (ICCs) with 95% confidence intervals. Statistical significance was determined at the threshold of two-sided P<0.05 for all conducted tests. The computational analyses were executed using Statistical Product and Service Solutions (SPSS) software (IBM SPSS Statistics for Macintosh, version 26.0), and GraphPad Prism software (version 9.0, San Diego, CA, USA) was used for the graphical representation of the outcomes.

Results

Participant characteristics

This prospective study enrolled 55 participants, comprising 110 4D flow CMR examinations. The cohort included 38 HOCM patients and 17 healthy volunteers. The average age of the participants was 47.91±15.26 years, and the group comprised 23 males and 32 females. A detailed demographic profile of the enrolled participants is presented in Table 2.

Participant flow

Between September 2022 and July 2023, a total of 68 individuals (50 HOCM patients and 18 healthy volunteers) were screened for eligibility. Of these, 13 were excluded: 8 did not meet inclusion criteria (5 with resting heart rate >100 bpm, 3 with ferromagnetic implants), and 5 met exclusion criteria (2 aged <18 years, 3 with MRI contraindications). The remaining 55 participants (38 HOCM patients and 17 healthy volunteers) completed both conventional and improved 4D flow CMR scans, yielding 110 complete datasets for analysis (Figure S3). No dropouts or missing data occurred during the study.

Navigation offset

The mean navigation offset recorded for the conventional method was 14.85±6.97 mm (range, 2–38 mm). In contrast, the mean navigation offset for the improved method was 3.35±2.34 mm (range, 0–10 mm). The reduction in the average navigation offset by 11.51±7.15 mm with the improved compared to the conventional method was statistically significant (P<0.001). These findings are shown in Table 3 and Figure 3A.

Figure 3 Comparative quantitative outcomes of conventional and improved diaphragmatic navigation 4D flow CMR. The panel illustrate the (A) navigation offset, depicts the (B) actual scan time, and represents the (C) acquisition efficiency, with each figure demonstrating statistically significant differences between the conventional and improved methods. In contrast, the panel demonstrates the absence of a significant statistical difference in the (D) aSNR. 4D flow CMR, four-dimensional flow cardiac magnetic resonance; aSNR, apparent signal-to-noise ratio; CONV, conventional; IMP, improved.

Planned scan time

The mean planned scan time for the conventional and improved method were the same, 252.76±51.53 seconds (range, 155–358 seconds).

Actual scan time

The mean actual scan time for the conventional method was 538.89±187.30 seconds (range, 300–1,221 seconds), while that for the improved method was 422.55±88.34 seconds (range, 251–577 seconds). Compared to the conventional method, the improved method reduced the mean actual scan time by 116.35±159.81 seconds, and this difference was statistically significant (P<0.001) (Table 3 and Figure 3B).

Acquisition efficiency

The mean acquisition efficiency of the conventional method was 49.71%±10.72% (range, 18.84–75.00%), while the mean acquisition efficiency of the improved method was 60.15%±5.46% (range, 50.24–74.75%). Compared to the conventional method, the improved method improved the mean acquisition efficiency by 10.44%±9.13% (P<0.001) (Table 3 and Figure 3C).

aSNR

In the aSNR analysis based on ROIs, no significant difference was observed between the conventional and improved methods in all, with respective aSNR values of 10.66±3.60 and 10.44±3.24 (P=0.59) (Table 3 and Figure 3D).

Visibility and artifacts

As shown in Table 3 and Table S1, a visibility score analysis revealed no statistically significant difference between the conventional and improved methods {3 [3–4] vs. 3 [3–4], P=0.15}. Among the participants, 10.91% (6/55) achieved higher scores with the improved method, whereas 3.64% (2/55) had better scores with the conventional method, with most [85.45% (47/55)] exhibiting equivalent scores across both methods.

When evaluating the presence of artifacts, the improved method had the advantage of reducing artifacts, with a median score of 2 (IQR, 2–3) compared to the conventional method’s median score of 2 (IQR, 1–2) (P<0.001). Specifically, 60% (33/55) of the participants had improved scores with the improved method, 5.45% (3/55) with the conventional method, and 34.55% (19/55) showed no difference in scores between the two methods. Figure 4 shows examples of the visibility, artifacts, and post-processing enhancement of the 4D flow CMR images obtained through conventional and improved diaphragmatic navigation.

Figure 4 Comparative analysis of image visibility, artifacts, and post-processing in 4D flow CMR images with conventional and improved diaphragmatic navigation in a 21-year-old female with HOCM. The visual assessment reveals no significant difference in visibility between the conventional method, as shown in (A), and the improved method, as depicted in (E). However, a marked reduction in artifacts is evident in the improved method, illustrated in (F), when juxtaposed with the conventional method’s artifacts, displayed in (B). Furthermore, both navigation techniques exhibit analogous post-processing effects, as observed in the 3D segmentation in (C) and (G), and the streamlined visualization in (D) and (H). 3D, three-dimensional; 4D flow CMR, four-dimensional flow cardiac magnetic resonance; HOCM, hypertrophic obstructive cardiomyopathy.

Hemodynamic diagnostic confidence

Figure 5 and Table 4 show the hemodynamic comparison (V_peak, P_max, V) between the conventional and improved methods for the AAo, Arch and DAo.

Figure 5 Hemodynamic assessments of conventional and improved diaphragmatic navigation 4D flow CMR. This figure presents a comparative analysis of key hemodynamic parameters: (A) V_peak, (B) P_max, and (C) V. No statistically significant differences were observed between the conventional and improved methods across the assessed regions. 4D flow CMR, four-dimensional flow cardiac magnetic resonance; AAo, ascending aorta; Arch, aortic arch; CONV, conventional; DAo, descending aorta; IMP, improved; P_max, maximum pressure gradient; V, volume flow; V_peak, peak systolic velocity.

In the AAo, V_peak values were 152.65±36.98 and 157.40±43.49 cm/s (P=0.29); P_max values were 9.87±4.85 and 10.57±5.95 mmHg (P=0.25); and V values were 4.22±1.01 and 4.18±0.86 L/min (P=0.67).

In the Arch, V_peak values were 107.62±30.71 and 103.48±23.37 cm/s (P=0.19); P_max values were 4.99±2.98 and 4.51±2.01 mmHg (P=0.15); and V values were 3.49±0.85 and 3.50±0.81 L/min (P=0.96).

In the DAo, V_peak values were 107.92±32.37 and 103.64±24.56 cm/s (P=0.06); P_max values were 5.11±3.02 and 4.83±2.46 mmHg (P=0.09); and V values were 2.60±0.65 and 2.57±0.60 L/min (P=0.52).

Consistency analysis

The intra- and inter-observer measurements showed high reliability, with ICCs exceeding 0.8 for all assessments (Table S2). In the context of the conventional diaphragmatic navigation for 4D flow CMR, the intra-observer ICC values ranged from 0.886 to 0.991, while the inter-observer ICC values ranged from 0.882 to 0.994. Similarly, for the improved diaphragmatic navigation method, the intra-observer ICC values ranged from 0.893 to 0.991, with the inter-observer ICC values falling between 0.847 and 0.986.

Discussion

The conventional diaphragmatic navigation for 4D flow CMR imaging is hindered by long scanning times and motion-related artifacts. We demonstrated that the improved diaphragmatic navigation introduced in this study could offer superior performance compared to the conventional method in terms of factors related to acquisition time, image quality, and consistency in hemodynamic diagnostic assessments.

The acquisition efficiency of the improved diaphragmatic navigation in 4D flow CMR introduced in this study surpassed that of the conventional method. The conventional method often achieves acquisition efficiency between 40% and 60%, with an average of 50% (10). This inefficiency is likely due to the free breathing without relatively fixed rhythm and amplitude can cause navigation drift, diminishing acquisition efficiency (12).

To address these challenges, this study introduced two key technical improvements. First, targeted respiratory regulation protocols were implemented, requiring subjects to (I) remain awake and relaxed during pre-scan acclimation to minimize adverse events; (II) maintain body stillness while following breathing rhythm instructions (calm, regular respiration) to standardize diaphragmatic motion and enhance navigator acceptance window alignment; and (III) suppress coughing and stabilize respiratory/cardiac rates for improved scan success. Second, precision diaphragm localization was achieved through a two-step process: real-time tracking of the diaphragmatic dome position at end-expiration using a bSSFP sequence, followed by placement of a pencil-beam navigator with a lung-to-liver coverage ratio of 1:1 at the diaphragm-lung interface to anchor data acquisition triggers.

These measures enhanced the accuracy of diaphragmatic localization and ensured the end-expiration data collection. Because of these improvements, the improved diaphragmatic navigation 4D flow CMR in this study realized an acquisition efficiency ranging from 50.24% to 74.75% (average: 60.15%), which eclipses prior research (10) and offers greater stability, culminating in a reduction of image artifacts.

In our study, artifacts were reduced in images obtained with the improved method, although aortic visibility was comparable to the conventional method. Improved diaphragmatic navigation facilitated the maintenance of a stable respiratory state among participants, enhancing their acclimation to the scanning process and aiding the mitigation of motion artifacts. This aligned with the documented suppressive impact of respiratory navigation techniques on motion artifacts, as reported by Song et al. (20) and Wang et al. (21). Collectively, these observations underscore the positive contribution of improved diaphragmatic navigation to 4D flow CMR image quality enhancement.

Echoing our findings, van Ooij et al. (22) reported similar outcomes when juxtaposing aortic visibility under conventional and refined respiratory navigation gating techniques. Visibility is contingent upon the contrast ratio between the vessel lumen and the surrounding background signal, a factor significantly influenced by flip angle selection (23). The imaging protocols for both conventional and improved diaphragmatic navigation in 4D flow CMR within this study were equivalent, except the respiratory control, ensuring that the flip angle and other imaging parameters remained constant. As a result, no significant difference in visibility was detected between the two methods.

Study limitations

There are several limitations in this study. First, as a single-center study with a small sample size, there is reduced generalizability of the findings. Nonetheless, including both healthy participants and those with HOCM, which is the predominant form of cardiomyopathy, enhanced the representativeness of the study. We intend to further evaluate improved diaphragmatic navigation in 4D flow CMR to encompass a broader spectrum of cardiovascular conditions, thereby expanding the technique’s reliability and reproducibility. Second, the study’s primary objective was to ascertain the practical use of the improved diaphragmatic navigation in 4D flow CMR. While the study did not perform a comparative analysis with alternative respiratory gating methodologies, such as self-gating or respiratory bellows technology (24-33), because these new technologies have not been widely applied to our medical institutions, so diaphragmatic navigation continues to be a prevalent strategy. Therefore, further refinement and enhancement is clinically important.

Conclusions

The improved diaphragmatic navigation in 4D flow CMR, which combines targeted respiratory regulation with accurate diaphragmatic localization, resulted in a reduced examination time, enhanced image quality, and has the potential to improve the efficiency of Guangdong Provincial People’s Hospital in the diagnosis of cardiovascular diseases.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://cdt.amegroups.com/article/view/10.21037/cdt-2025-139/rc

Data Sharing Statement: Available at https://cdt.amegroups.com/article/view/10.21037/cdt-2025-139/dss

Peer Review File: Available at https://cdt.amegroups.com/article/view/10.21037/cdt-2025-139/prf

Funding: This work was supported by Medical Scientific Research Foundation of Guangdong Province of China (grant No. A2024518), the National Natural Science Foundation of China (grant No. 82371903), Guangdong Provincial Science and Technology Planning Project (grant No. 2023B110009), Guangzhou Clinical High-tech, Major, and Distinctive Technology Projects (grant No. 2023P-TS43), and Natural Science Foundation of Guangdong Province (grant No. 2024A1515012087).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://cdt.amegroups.com/article/view/10.21037/cdt-2025-139/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 Institutional Review Board of Guangdong Provincial People’s Hospital (Guangdong Academy of Medical Sciences) (No. KY2023-883-03), Southern Medical University and informed consent was obtained from all individual participants.

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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