Transthoracic Doppler echocardiography of normal tricuspid valve prostheses: comparison between surgical and transcatheter approaches

Introduction

Tricuspid valve (TV) disease, particularly severe tricuspid regurgitation, is being increasingly recognized as a major contributor to morbidity and mortality in patients with heart failure, pulmonary hypertension, or prior left-sided valve surgery (1,2). TV replacement (TVR) remains an indispensable option for patients with these diseases (3). Advances in surgical techniques, including improved prosthetic valve designs and minimally invasive approaches, have enhanced the success rates and long-term prognosis for patients with tricuspid prostheses (4). Surgical TVR with bioprosthetic or mechanical prostheses has historically been the cornerstone of treatment for advanced TV disease, yet carries significant perioperative risks, especially in patients with right ventricular (RV) dysfunction or comorbidities (5-7). Recent advancements in transcatheter TV replacement (TTVR), exemplified by devices such as the Lux-Valve, offer a minimally invasive alternative for high-risk cohorts, yet comparative data on echocardiographic outcomes across prostheses remain sparse (8,9).

The tricuspid annulus’s unique elliptical geometry and dynamic nature pose distinct challenges for prosthetic valve implantation and functional assessment (10). Transthoracic echocardiographic (TTE) parameters after TVR are important for assessing valve function and identifying potential dysfunction. Previous studies have also demonstrated the clinical value of normal tricuspid prostheses with TTE-derived Doppler parameters (11,12). However, there are few studies on the normal reference range of Doppler parameters for surgical bioprosthetic and mechanical valves as compared to those for transcatheter valves. Different valve types produce different echocardiographic Doppler parameters. Clarifying the echocardiographic parameter characteristics of different TV prosthesis types can improve postoperative follow-up accuracy and clinical management effectiveness.

Therefore, this study aimed to systematically analyze the TTE-derived Doppler parameters of surgical bioprosthetic, mechanical, and transcatheter tricuspid prostheses with normal function (Figure 1). The goal was to determine the range and differences in their normal reference values and thus provide a more accurate reference for the management of patients following clinical TVR. We present this article in accordance with the STROBE reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1251/rc).

Figure 1 Comparative analysis of postoperative echocardiographic Doppler parameters among normal tricuspid prostheses, including surgical mechanical valves, surgical bioprosthetic valves, and transcatheter valves. E velocity, early tricuspid diastolic velocity; EOA_TV, effective orifice area of the tricuspid valve; IEOA_TV, indexed effective orifice area of the tricuspid valve; MG_TV, mean gradient of the tricuspid valve; PHT_TV, pressure half-time of the tricuspid valve; TVR, tricuspid valve replacement; VTI_TV, velocity-time integral of the tricuspid valve; VTI ratio, the ratio of VTI_TV to velocity-time integral of the left ventricular outflow tract.

Methods

Patient selection

We searched the picture archiving and communication systems of Union Hospital of Tongji Medical College at Huazhong University of Science and Technology and identified 247 patients aged >18 years who had undergone TVR between January 1, 2012, and October 31, 2024. The inclusion criterion was postoperative echocardiographic assessment following TVR at this center. The majority of patients underwent intraoperative transesophageal echocardiography (TEE) for the evaluation of valve function both before and immediately after the traditional or interventional surgery and were routinely monitored with TTE during follow-up outpatient visits.

Patients with tricuspid prostheses with normal function confirmed by TEE and TTE (the interval between TEE and TTE was no more than 30 days) or without TEE confirmed by more than two TTE follow-ups and without any evidence of functional changes of prostheses were also included in the study.

Of the 247 patients, we excluded 108 who had prosthetic TV dysfunction (including paravalvular regurgitation/transvalvular regurgitation or stenosis; n=42), incomplete echo and clinical data (n=36), heart rate >100 bpm (n=25), more-than-moderate aortic regurgitation (n=4), and left ventricular outflow tract obstruction (n=1). A total of 139 cases were included in this study and were divided into three groups: a surgical bioprosthetic valve group (sB group), a surgical mechanical valve group (sM group), and a transcatheter valve group (T group) (Figure 2). TTE was completed within 30 days of TEE in 112 patients (80.1%) (47 with surgical bioprosthetic valves, 40 with surgical mechanical valves, and 25 with transcatheter valves).

Figure 2 Study flowchart showing the inclusion, exclusion, and grouping of patients. LVOT, left ventricular outflow tract; PACS, picture archiving and communication system; TV, tricuspid valve.

This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments, and was approved by the Ethics Committee of Union Hospital of Tongji Medical College at Huazhong University of Science and Technology (No. 20230086). Informed consent was provided by all individual participants.

Echocardiography

TTE and TEE were both performed with commercial cardiac ultrasound equipment, including the EPIQ 7C, IE33 (Philips, Amsterdam, the Netherlands), and Vivid E9 (GE HealthCare, Chicago, IL, USA) devices. Multiple two-dimensional (2D) planes and acoustic windows, along with color and Doppler assessments, were obtained according to the relevant guidelines (13-15). Three TTE views facilitating the visualization of the TV were acquired from each patient. These included the parasternal long-axis view of the RV inflow, the short-axis view at the level of the aortic valve, the RV-focused apical four-chamber view, and the subcostal view. All TTE views, particularly those from the apex, were adjusted to obtain optimal visualization of the RV and prosthetic TV.

Conventional 2D echocardiographic parameters were measured. The ascending aortic diameter, left atrial end-systolic diameter, interventricular septal thickness, and left ventricular outflow tract diameter (D_LVOT) were measured through the parasternal long axis of the left ventricle during the systolic period. Left ventricular end-diastolic diameter was measured during the diastolic phase. Left ventricular ejection fraction was measured with the conventional biplane Simpson method from apical two- and four-chamber views with manual endocardial border tracing.

The pulmonary artery (PA) diameter was measured during the systolic phase on the short-axis view. The right atrial end-systolic diameter and RV end-diastolic diameter were measured on the apical four-chamber view. The RV fractional area change was calculated with the following formula: RV fractional area change = (RV end-diastolic area − RV end-systolic area)/RV end-diastolic area × 100%.

Continuous-wave Doppler imaging was employed to capture the flow and regurgitant jet signals in the apical four-chamber view and RV inflow views (Figure 3). All acquired images were digitally archived for subsequent offline analysis via TomTec imaging software (TomTec Imaging Systems, Unterschleissheim, Germany). The peak velocity of the left ventricular outflow tract (V_LVOT) was measured via spectral Doppler images of the apical five-chamber view, while the velocity-time integral (VTI) of LVOT (VTI_LVOT), and the peak velocity of the pulmonary valve (V_PA) were measured via spectral Doppler ultrasound in the long axial section of the PA.

Figure 3 TTE two-dimensional, color Doppler, and continuous Doppler images of three groups of normal tricuspid prostheses (A-C: sB group; D-F: sM group; G-I: T group). sB group, surgical bioprosthetic valve group; sM group, surgical mechanical valve group; T, transcatheter valve group. TTE, transthoracic echocardiographic; VTI, velocity-time integral.

The mean gradient of the TV (MG_TV), velocity-time integral of the TV (VTI_TV), E velocity of the TV, and pressure half-time of the TV (PHT_TV) were calculated across three consecutive cardiac cycles and averaged. The ratio of VTI_TV to the VTI of the left ventricular outflow tract (VTI ratio) was calculated as follows: VTI ratio = VTI_TV/VTI_LVOT (11). Stroke volume (SV) was calculated as follows: SV = VTI_LVOT × LVOT area. The effective orifice area of TV (EOA_TV) was obtained through the continuity equation as follows: EOA_TV = SV/VTI_TV. The indexed effective orifice area of the TV (IEOA_TV) was calculated as follows: IEOA_TV = EOA_TV/body surface area. For patients with atrial fibrillation, measurements were averaged over five cardiac cycles.

Statistical analysis

The normality of data distribution was evaluated through the use of graphical methods and the Shapiro-Wilk test. Continuous variables are presented as the mean ± standard deviation (SD) or as the median and interquartile range, depending on their distribution. For continuous variables, the independent samples t-test or Mann-Whitney test was used to compare two independent groups where applicable. For three independent groups, a one-way analysis of variance was used for normally distributed data, while the Kruskal-Wallis test was applied for data that did not follow a normal distribution. The χ² test was used to compare categorical variables, which are expressed as numbers and percentages, across different groups. The normal reference ranges for Doppler parameters in this study were established with the central 95% interval of measurements in accordance with standard statistical methods for biological parameter estimation. Eighteen participants were randomly selected to evaluate the level of agreement for both intra- and interobserver variability. This assessment was conducted with Bland–Altman analysis to quantify the limits of agreement. The second observer was kept blind to the first observer’s measurements to avoid bias in the assessment. Furthermore, the initial observer conducted the analysis again after 1 month for the assessment of intraobserver consistency and to reduce possible recall bias. All statistical analyses were conducted with R version 4.3.1 (The R Foundation for Statistical Computing). A two-sided P value <0.05 was considered statistically significant.

Results

Patient characteristics

This study included 62 cases of surgical bioprosthetic valves, 52 cases of surgical mechanical valves, and 25 cases of transcatheter valves. In the sB valve group, there were 21 (33.9%) males, aged 45.1±14.3 years, with a mean body surface area (BSA) of 1.63±0.16 kg/m². In the sM group, there were 24 (46.2%) males, aged 48.3±11.1 years, with a BSA of 1.68±0.16 kg/m². In the T group, there were 4 (16.0%) males, aged 62.2±6.8 years, with a BSA of 1.59±0.19 kg/m², and 19 cases had accompanying atrial fibrillation (Table 1). Patients in the T group were significantly older than those in the sM group and sB (P<0.001). The 4 (16.0%) male patients in the T group represented a significant difference from the other two groups (4 in the T group, 21 in the sM group, and 24 in the sB group; P<0.001). The incidence of atrial fibrillation in the sM group was significantly higher than that in the sB group (65.38% vs. 41.94%; P<0.05). The incidence of atrial fibrillation was highest in the T group (76.00%), followed by the sB group (41.94%) and sM group (65.38%) (P<0.05). Other clinical indicators did not differ significantly between the groups (P>0.05).

The etiology of TVR is summarized in Table S1. The primary etiology included Ebstein malformation, TV prolapse, TV repair, and prosthetic TV dysfunction. The secondary etiology included rheumatic heart disease, infective endocarditis, left heart valve replacement, atrial septal defect, ventricular septal defect, pacemaker installation, atrial fibrillation, and postoperative congenital heart disease; a few patients with TVR had an unclear etiology. Among the patients, 49 (11 with surgical bioprosthetic valves, 18 with surgical mechanical valves, and 20 with transcatheter valves, accounting for 35.3%) had accompanying TV regurgitation after left heart valve replacement, which was the most common cause of TVR, followed by Ebstein malformation in 18 cases (11 with surgical bioprosthetic valves and 7 with surgical mechanical valves, accounting for 12.9%) and rheumatic heart disease in 15 cases (8 with surgical bioprosthetic valves, 6 with surgical mechanical valves, and 1 with a transcatheter valve, accounting for 10.8%).

According to the statistical summary of TVR combined with other valve operations, simple TVR was the most common procedure, occurring in 60 patients (36 with surgical bioprosthetic valves, 19 with surgical mechanical valves, and with 5 transcatheter valves, accounting for 43.2%), followed by TVR combined with mitral valve replacement and TVR combined with aortic valve replacement. Combined valve procedures may not be performed simultaneously with TVR. Table S2 summarizes the final status of the concomitant valve procedures for all patients. All bioprosthetic valves used in our hospital were from Medtronic (Galway, Ireland), mechanical valves were from Abbott Laboratories (Chicago, IL, USA), and all transcatheter valves were Lux-Valves from Jenscare Scientific Co (Ningbo, China).

Comparison of the 2D parameters of TTE

The 2D parameters of each group were analyzed and compared (Table 1). The ascending aortic diameter of the T group (3.40±0.42 cm) was significantly different from that of the sB group (3.03±0.58 cm) and the SM group (3.11±0.50 cm) (P<0.05). The left atrial end-systolic diameter of the T group (5.45±1.07 cm) and sM group (4.75±1.18 cm) was significantly different from that of the sB group (4.32±2.05 cm) (P<0.001). The interventricular septal thickness of the T group was significantly greater than that the sB group (P<0.05). The PA of the sB group was significantly different from that of the T group and the sM group (P<0.05). The other 2D parameters, including left ventricular end-diastolic diameter, D_LVOT, left ventricular ejection fraction, right atrial end-systolic diameter, RV end-diastolic diameter, and RV fractional area change, were not significantly different between the three groups (P>0.05).

Comparison of TTE Doppler parameters between the three groups

The Doppler parameters of each group were analyzed and compared (Table 1), with the results being visualized in a box plot (Figure 4). Compared with the sB group, the sM group and T group exhibited significantly lower VTI_TV, VTI ratio, and PHT_TV, but a significantly higher EOA_TV (P<0.05). The MG_TV of the sM group was statistically lower than that of the sB group (P<0.05). Compared with that in sB group, the IEOA_TV in the T group was significantly higher (P<0.05). However, V_LVOT, V_PA, SV, VTI_LVOT, and E velocity did not differ significantly between the groups (P>0.05).

Figure 4 Box plot for the distribution of Doppler parameters of the tricuspid valve in three groups. *, P<0.05. EOA_TV, effective orifice area of the tricuspid valve; IEOA_TV, indexed effective orifice area of the tricuspid valve; MG_TV, mean gradient of the tricuspid valve; PHT_TV, pressure half-time of the tricuspid valve; VTI_TV, velocity-time integral of the tricuspid valve; VTI_LVOT, velocity-time integral of the left ventricular outflow tract.

Comparative analysis of valve sizes

To address the potential influence of prosthesis size, a further analysis was performed within each valve type group despite an unbalanced sample size. The results indicated a decrease in MG_TV and an increase in EOA_TV with greater size. However, there was no statistically significant difference between the groups in this regard (P>0.05). In the T group and the sM group, no significant differences between sizes were observed for any of the parameters (P>0.05). A notable exception was found in the sB group, in which valves with a 27-mm diameter demonstrated a significantly higher VTI_TV compared to those with a 31-mm diameter (P<0.05). This hemodynamic finding was consistent with the baseline anatomy of the patients, as recipients of 27-mm diameter bioprosthetic valves also had a significantly smaller ascending aortic diameter (P<0.05). No other parameters differed significantly across sizes in the sB group (P>0.05).

Normal range and dysfunction threshold of Doppler parameters

According to the 95% confidence interval, the normal range of prosthetic TV Doppler parameters was obtained (Table 2). We further calculated the mean + 2SD or mean − 2SD for each Doppler parameter as the cutoff value for probable TV prosthesis dysfunction (Table 2). For the tricuspid surgical bioprosthetic valve, the normal ranges for each Doppler parameter were as follows: E velocity, 1.40–1.59 m/s; MG_TV, 3.90–4.93 mmHg; VTI_TV, 41.8–47.2 cm; PHT_TV, 135.8–157.8 ms; VTI ratio, 2.03–2.31; EOA_TV, 1.44–1.69 cm²; and IEOA_TV, 0.92–1.09 cm²/m². Meanwhile, the cutoff values of probable surgical tricuspid bioprosthetic valve dysfunction were as follows: E velocity, ≥2.22 m/s; MG_TV, ≥8.30 mmHg; VTI_TV, ≥66.7 cm; PHT_TV, ≥235.2 ms; VTI ratio, ≥3.44; EOA_TV ≤0.54 cm²; and IEOA_TV ≤0.36 cm²/m².

For the tricuspid surgical mechanical valve, the normal ranges for each Doppler parameter were as follows: E velocity, 1.40–1.58 m/s; MG_TV, 3.08–3.93 mmHg; VTI_TV, 34.6–39.9 cm; PHT_TV, 106.7–122.8 ms; VTI ratio, 1.70–2.04; EOA_TV, 1.73–2.10 cm²; and IEOA_TV, 1.08–1.31 cm²/m². Moreover, the cutoff values suggesting possible tricuspid surgical mechanical prosthetic valve dysfunction were as follows: E velocity, ≥2.17 m/s; MG_TV, ≥6.65 mmHg; VTI_TV, ≥57.3 cm; PHT_TV, ≥172.7 ms; VTI ratio, ≥3.13; EOA_TV, ≤0.54 cm²; and IEOA_TV, ≤0.29 cm²/m².

The established normal reference ranges (95% confidence interval) for transcatheter tricuspid prostheses were as follows: E velocity, 1.21–1.51 m/s; MG_TV, 2.58–4.83 mmHg; VTI_TV, 32.7–40.4 cm; PHT_TV, 107.5–132.2 ms; VTI ratio, 1.60–1.99; EOA_TV, 1.80–2.44 cm²; and IEOA_TV, 1.15–1.54 cm²/m². The thresholds indicative of possible transcatheter TV dysfunction were as follows: E velocity, ≥2.10 m/s; MG_TV, ≥9.16 mmHg; VTI_TV, ≥55.3 cm; PHT_TV, ≥179.6 ms; VTI ratio, ≥2.73; EOA_TV ≤0.58 cm²; and IEOA_TV, ≤0.40 cm²/m².

Repeatability test

Doppler parameters (VTI_TV and PHT_TV) from 18 patients were analyzed to validate the reproducibility of parametric measurements. The consistency between and within observers was visualized in Bland-Altman plots (Figure 5). There was good agreement within and between groups.

Figure 5 Bland-Altman analysis chart of intra-observer and inter-observer consistency. PHT_TV, pressure half-time of the tricuspid valve; SD, standard deviation; VTI_TV, velocity-time integral of the tricuspid valve.

Discussion

To the best of our knowledge, this study is the first to conduct a systematic comparative analysis of early postoperative echocardiographic Doppler parameters among surgical mechanical valves, surgical bioprosthetic valves, and transcatheter valves. Our findings revealed differences in hemodynamic performance and established reference ranges for Doppler hemodynamic parameters for these three valve types, providing crucial insights for individualized valve selection and postoperative evaluation.

Accurate assessment of tricuspid prostheses remains a critical yet underexplored area in cardiovascular imaging, especially for transcatheter tricuspid prostheses. In recent years, with the continuous development of TTVR technology, a growing number of patients have benefited from this minimally invasive treatment method (16-18). The monitoring of tricuspid prostheses and the reference value of postoperative echocardiography are particularly important for the continuous improvement of postoperative effects. However, previous studies have predominantly focused on surgical TV, with virtually no data on transcatheter TV evaluation being available (19,20). The related research, including the seminal work by Connolly et al., has primarily analyzed isolated parameters such as MG and PHT, neglecting integrative metrics such as VTI ratio (19). Subsequently, Blauwet et al. reported postoperative hemodynamic profiles using multidimensional dynamic Doppler parameters, including the PHT_TV, MG_TV, VTI_TV, VTI ratio, EOA_TV, and IEOA_TV, for both surgical mechanical TV and surgical bioprosthetic TV (21,22). However, there are few studies on the characteristics of Doppler echocardiographic parameters associated with TTVR due to it being a relatively novel technique. This underscores the need for comprehensive hemodynamic evaluation frameworks, which our study addresses through multidimensional analysis of three distinct tricuspid prosthesis types.

Building on this methodological foundation, our comparative analysis revealed significant demographic and pathophysiological distinctions between the different valve groups. Our initial comparative analysis was systematically conducted across three valve groups, with both baseline clinical characteristics and conventional 2D echocardiographic parameters being examined. The age of patients in the T group was significantly higher than that in the other two groups, and the proportion of males was lower. This may be related to the current focus of TTVR indications on high-risk, older patients who cannot tolerate open heart surgery (23,24). Additionally, the incidence of atrial fibrillation in the T group was significantly higher, which is consistent with previous research (25,26). This phenomenon may be attributable to the predominant application of TTVR in older adult, high-risk surgical candidates, a population demonstrating significantly worsened heart conditions as compared to conventional surgical candidates. Furthermore, this pathophysiological correlation may also explain the observed echocardiographic profile in the T cohort, which demonstrated significantly elevated measurements of ascending aortic diameter, left atrial end-systolic diameter, interventricular septal thickness, and PA when compared to surgical valve recipients. These baseline differences highlight the importance of context-specific parameter interpretation.

To establish clinically actionable thresholds, we delineated normal Doppler parameter ranges through rigorous statistical analysis. For the surgical bioprosthetic TV, the cutoff values of probable surgical tricuspid bioprosthetic valve dysfunction were similar to those reported previously (21,22). For the surgical mechanical TV, our cutoff values were higher in comparison with those in previous work (22), including for E velocity (2.17 vs. 1.9 m/s), MG_TV (6.65 vs. 6 mmHg), VTI_TV (57.3 vs. 43 cm), PHT_TV (172.7 vs. 122 ms), and VTI ratio (3.13 vs. 2.0). This discrepancy may be due to differences in the size of the tricuspid prosthetic mechanical valves in the study population. The sizes of tricuspid prosthetic mechanical valves in this study included only diameters of 27, 29, and 31 but not 33 mm. Additionally, Blauwet et al. (21,22) excluded patients with prosthesis-patient mismatch from the process of establishing the cutoff value, which is a potential reason why our results may be different. Importantly, for transcatheter tricuspid prostheses, our study is the first to establish the normal ranges of echocardiographic Doppler parameters, as well as the cutoff values for valve dysfunction. These data provide an important reference for clinical tricuspid prosthetic valve evaluation, especially for transcatheter TVs, for which clinical studies are scarce.

Regarding interprosthesis variations, our data revealed hemodynamic patterns that align with known engineering characteristics. The differences in echocardiographic Doppler parameters between the three types of tricuspid prostheses in this study were similar to those of previous studies (21,22). Our results indicated that the MG_TV in the sM group was lower than that in the sB group and the T group, demonstrating its low-resistance blood flow characteristics, which are closely related to the rigid leaflet design and a larger EOA (21,22). Moreover, the sB group showed higher values on VTI_TV, VTI ratio, and PHT_TV, suggesting greater transvalvular flow velocity and energy loss, possibly due to the inherent flexibility of biological valves (21,22). Meanwhile, the T group had a higher IEOA_TV than did the other two groups, reflecting the advantage of the sutureless ring design of the Lux-Valve in improving the EOA (27). Although the T group exhibited a lower MG compared with the sB group (3.70±2.73 vs. 4.40±1.95 mmHg), the difference was not statistically significant. This may reflect the generally low MG across the TV, as the larger EOA of the transcatheter valve group did not translate into a significant change in transvalvular pressure gradient. These findings collectively demonstrate the complex interplay between prosthesis design and hemodynamic performance, providing evidence for supporting personalized valve selection.

Study limitations

The limitations of this study include the single-center, retrospective design and the relatively small sample size, especially for the patients with the transcatheter tricuspid prosthesis. Additionally, gender was imbalanced in T group and may influence the results of this study. Future investigations could focus on whether there are differences between gender and valve parameters. Finally, the data in this study were mainly derived from three specific types of valves, including the transcatheter TV, which was exclusively the Lux-Valve. This may affect the generalization of the study results to other types of valves. In the future, multicenter prospective studies, incorporating more valve types, can be conducted to verify the stability of the threshold.

Conclusions

This study established a Doppler echocardiographic reference framework for assessing normal tricuspid prostheses, including surgical bioprosthetic, mechanical, and transcatheter valves. The 95% reference intervals and dysfunction thresholds generated in this study provide critical benchmarks for postoperative surveillance. These findings underscore the necessity of applying valve-type-specific evaluation criteria in clinical practice.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1251/rc

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1251/dss

Funding: This work was supported by the National Natural Science Foundation of China (Nos. 82371990, 82001852, 82202194) and the Natural Science Foundation of Hubei Province (No. 2023AFB772).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-1251/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 Union Hospital of Tongji Medical College at Huazhong University of Science and Technology (No. 20230086), and informed consent was taken 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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