Multimodal quantitative ultrasound assessment of perioperative neck muscle alterations in patients with cervical spondylosis

Introduction

Cervical spondylosis (CS), also referred to as cervical spine degenerative disease, arises from degenerative changes of the cervical spine. It can result in severe manifestations that impair an individual’s work ability and quality of life, and has thus emerged as a global health concern (1). Anterior cervical spine surgery is a well-established surgical approach for treating CS, offering advantages such as minimal surgical trauma, reliable efficacy, and effective restoration of the cervical physiological lordosis (2). For perioperative assessment of neck function, the Japanese Orthopedic Association (JOA) score and the Neck Disability Index (NDI) are commonly used for functional evaluation, whereas the Visual Analogue Scale (VAS) is the most frequently employed method for assessing patient-reported discomfort (3). However, these assessment tools lack objective quantitative data and are characterized by low sensitivity and poor reproducibility.

Previous studies on CS have predominantly focused on intervertebral discs, nerve roots, and the spinal cord, often overlooking the role of cervical muscles in the onset and progression of the condition (4). Compared with healthy individuals, patients with CS are more prone to muscle fatigue and stiffness of the muscles surrounding the cervical spine. Postoperatively, patients are required to wear cervical collars to maintain spinal stability (5); however, prolonged cervical collar use may be associated with neck muscle stiffness, which may lead to neck pain and restricted cervical mobility. Elucidating the changes in neck muscles during the perioperative period in patients with CS may provide valuable insights for preoperative assessment, postoperative follow-up, treatment response evaluation, and determination of optimal cervical collar wearing duration.

Multimodal ultrasound has been used to study various neuromuscular diseases. Conventional ultrasound enables measurement of muscle echo intensity, muscle thickness, muscle penetration angle, and muscle cross-sectional area (6), whereas shear wave elastography (SWE) allows for the real-time quantification of muscle stiffness (7). Several previous studies have used SWE to quantitatively measure shear wave velocity (SWV) in cervical paraspinal muscles in healthy individuals and have confirmed the reproducibility of such measurements (8-10). Nevertheless, there remains a paucity of research on the use of multimodal ultrasound for the quantitative assessment of neck muscles in patients with CS.

This study aimed to apply multimodal ultrasound to investigate differences in neck muscle thickness and stiffness between patients with CS and healthy controls (HC), and to examine changes in neck muscle stiffness associated with varying durations of cervical collar wear, thereby providing clinical guidance for determining the optimal duration of postoperative cervical collar use. We present this article in accordance with the STROBE reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2026-1-0212/rc).

Methods

This study was approved by the Ethics Committee of West China Hospital of Sichuan University (approval No. 2022[394]), and was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. Informed consent was provided by all participants for the publication of this study and accompanying images.

Study participants

A total of 40 patients with CS who underwent anterior cervical spine surgery at the Department of Orthopedics, West China Hospital of Sichuan University, between September 2021 and December 2022 were included in the case group. The inclusion criteria were as follows: a diagnosis of CS evaluated by an orthopedic surgeon as meeting the surgical criteria; age older than 18 years; and satisfactory compliance with the examination. Concurrently, 40 healthy volunteers were recruited as the HC group, according to the following inclusion criteria: absence of neck pain or discomfort in the preceding 6 months; age older than 18 years; and satisfactory compliance with the examination. The exclusion criteria applied to both groups were as follows: pregnancy; history of neck trauma or surgery; use of medications that may affect muscle structure and function (such as glucocorticoids and muscle relaxants); diseases that affect upright posture (such as scoliosis and ankylosing spondylitis); systemic diseases that may affect muscles (such as rheumatic diseases and autoimmune disorders, and metabolic diseases); skin scarring at the ultrasound examination site; and unsatisfactory compliance with the examination. All participants were right-handed.

Of the enrolled patients, 18 who completed postoperative ultrasound follow-up were randomly allocated into two groups: Group A, in which patients wore a cervical collar for 1 month, and Group B, in which patients wore one for 3 months. The cervical collar was worn in strict accordance with the treating physician’s instructions. No additional physical therapy was administered. Allocation was carried out using a random number table; after randomly selecting a starting number, patients assigned odd numbers were allocated to Group A and those assigned even numbers were allocated to Group B (Figure 1). The follow-up assessors were blinded to group allocation and, during each examination, were unaware of the patient’s assigned group.

Figure 1 Flowchart of participant enrollment and allocation.

Ultrasound procedure

An experienced sonographer performed ultrasound of the neck muscles of all participants, acquired the images, and conducted the measurements. A previous study from our group demonstrated good intra- and inter-rater reliability, with intraclass correlation coefficients (ICCs) exceeding 0.75 for ultrasound measurements of neck muscle thickness and SWV (11). In the current study, postoperative ultrasound assessment was repeated at 3 and 6 months in patients who underwent surgery for CS.

Ultrasound examination

The ultrasound equipment used was the Aixplorer system (SuperSonic Imagine, Aix-en-Provence, France) with the SuperLinear SL10-2 transducer. The superficial musculoskeletal preset was selected. The depth was fixed at 3–4 cm, and the focus zone was adjusted to the target muscle layer. When the SWE color map was stable, a region of interest (ROI) was defined using a Q-box (diameter, 1–3 mm, trapezius and longus capitis, 1 mm; splenius capitis, semispinalis capitis, semispinalis cervicis, multifidus and longus colli, 2 mm; sternocleidomastoid, 3 mm) and placed within a region of uniform elasticity signal. The elasticity scale was adjusted to 0–180 kPa to obtain standardized images.

Based on the studies of Xie et al. (8), Ghamkhar et al. (12) and a preliminary study from our group (11), eight muscles of the right posterior and anterior cervical regions were selected for measurement (Figures 2-5). For the posterior cervical muscle group, participants were seated facing away from the examiner, with the neck fully exposed, looking straight ahead, and the neck and shoulders maintained in a neutral position (0° on a goniometer), breathing calmly. Preliminary palpation was performed to locate the C7 spinous process. The probe was placed transversely to identify the level of the spinous process, then moved 2 cm lateral to the spinous process and cranially to the C4 level. In the transverse plane, the cross-sections of the trapezius, splenius capitis, semispinalis capitis, semispinalis cervicis, and multifidus were identified at this level, and the thickness of each muscle (cm) was measured. The probe was then orientated along the long axis of the muscle to measure the mean SWV (m/s). All measurements were performed in triplicate, and the mean value was recorded. Measurements were also obtained in the forward flexion position (+40° on the goniometer) and cervical extension position (−10° on the goniometer) using the same protocol. For the anterior cervical muscle group, participants were positioned supine without a pillow, breathing calmly. The ultrasound probe was placed at 2 cm below the superior aspect of the thyroid cartilage, laterally displaced 2 cm to the level of C5–C6, to visualize the sternocleidomastoid, longus capitis, and longus colli, and their thicknesses were measured. The probe was then orientated along the long axis of each muscle to measure the SWV. Measurements were also obtained in the lateral flexion position (±30° on the goniometer) using the same protocol.

Figure 2 Probe positions and corresponding thickness measurements of the posterior cervical muscles in different positions. (A-C) The neutral position, forward flexion position, and extension position, respectively. (D-F) The ultrasound measurements of posterior cervical muscle thickness in the corresponding positions (from superficial to deep: trapezius, splenius capitis, semispinalis capitis, semispinalis cervicis, and multifidus). These images are published with the patient’s consent.

Figure 3 Probe positions and corresponding thickness measurements of the anterior cervical muscles in different positions. (A,B) The neutral position and deflection position, respectively. (C,D) The ultrasound measurements of anterior cervical muscle thickness in the corresponding positions (sternocleidomastoid, longus capitis, and longus colli). These images are published with the patient’s consent.

Figure 4 Probe positions and corresponding SWV measurements of the posterior cervical muscles in different positions. (A-C) The neutral position, forward flexion position, and extension position, respectively. (D-I) SWV measurements of the trapezius and splenius capitis in the corresponding positions, respectively. These images are published with the patient’s consent. SD, standard deviation; SWV, shear wave velocity.

Figure 5 Probe positions and corresponding SWV measurements of the anterior cervical muscles in different positions. (A,B) The neutral position and the deflection position, respectively. (C-F) The SWV measurements of sternocleidomastoid and longus capitis in the corresponding positions, respectively. These images are published with the patient’s consent. SD, standard deviation; SWV, shear wave velocity.

Statistical analysis

Statistical analyses were performed using the software SPSS 26.0 (IBM Corp., Armonk, NY, USA). Continuous data were expressed as mean ± standard deviation (SD) for normally distributed variables and as median (interquartile range) for non-normally distributed variables. Between-group differences in continuous variables were assessed using the independent samples t-test or t’-test for normally distributed data, and the Wilcoxon rank-sum test or Mann-Whitney U test for non-normally distributed data. Categorical data were expressed as frequency n (%), and between-group differences were assessed using the chi-squared (χ²) test. A generalized estimating equation (GEE) model was used to evaluate the effect of cervical collar wearing duration on neck muscle thickness and SWV. Statistical significance was set at P<0.05; all tests were two-tailed.

Results

Basic clinical characteristics of the case and control groups

In this study, 40 patients with CS were included in the case group and 40 healthy volunteers in the HC group. No statistically significant differences were observed between the two groups in terms of sex ratio, age, or body mass index (BMI). The mean age was 46.00±8.66 years in the case group and 46.08±11.00 years in the HC group (P=0.973). The male-to-female ratio was 21:19 in the case group and 23:17 in the control group (P=0.658). The mean BMI was 23.45±3.05 kg/m² in the case group and 23.81±2.67 kg/m² in the HC group (P=0.569) (Table 1).

Comparison of ultrasound parameters between the case and control groups

Muscle thickness

For the posterior cervical muscles, in the neutral position, the case group showed significantly greater trapezius thickness (0.18 vs. 0.15 cm, P=0.008), whereas significantly reduced thickness was observed in the splenius capitis (0.44 vs. 0.54 cm, P<0.001), semispinalis capitis (0.35 vs. 0.59 cm, P<0.001), semispinalis cervicis (0.59 vs. 0.72 cm, P<0.001), and multifidus (0.81 vs. 0.91 cm, P<0.001). In the forward flexion position, the case group continued to exhibit significantly reduced thickness in the semispinalis capitis (0.32 vs. 0.50 cm, P<0.001), semispinalis cervicis (0.54 vs. 0.59 cm, P=0.012), and multifidus (0.73 vs. 0.81 cm, P=0.010), but greater trapezius thickness (0.17 vs. 0.15 cm, P=0.025). In the extension position, similar trends were observed for the trapezius (0.20 vs. 0.16 cm, P=0.001), semispinalis capitis (0.38 vs. 0.55 cm, P<0.001), semispinalis cervicis (0.59 vs. 0.64 cm, P=0.013), and multifidus (0.80 vs. 0.87 cm, P=0.004) (Table 2).

For the anterior cervical muscles, in neutral position, the case group showed significantly reduced thickness in the longus capitis (0.21 vs. 0.30 cm, P<0.001) and longus colli (0.66 vs. 0.75 cm, P<0.001), but no significant difference in the sternocleidomastoid (P=0.485). In the deflection position, similar reductions persisted for longus capitis (0.23 vs. 0.30 cm, P=0.006) and longus colli (0.59 vs. 0.65 cm, P=0.002), whereas sternocleidomastoid thickness remained comparable between groups (P=0.267) (Table 3).

Muscle stiffness

For the posterior cervical muscles, in the neutral position, no significant differences in SWV were found for any of the posterior muscles (all P>0.05). In the forward flexion position, the case group demonstrated significantly lower SWV in the trapezius (3.33 vs. 3.69 m/s, P=0.015), splenius capitis (3.30 vs. 3.63 m/s, P=0.008), semispinalis capitis (3.50 vs. 4.75 m/s, P<0.001), semispinalis cervicis (4.75 vs. 5.53 m/s, P<0.001), and multifidus (4.79 vs. 5.57 m/s, P<0.001). In the extension position, the case group had significantly higher SWV in the splenius capitis (2.26 vs. 1.92 m/s, P=0.008), whereas no significant differences were observed for the remaining posterior muscles (all P>0.05) (Table 2).

No significant differences in SWV were found in the neutral position for any anterior cervical muscle (all P>0.05). By contrast, in the deflection position, the case group exhibited significantly lower SWV in the sternocleidomastoid (2.74 vs. 3.47 m/s, P=0.001), longus capitis (3.13 vs. 4.05 m/s, P<0.001), and longus colli (3.63 vs. 4.52 m/s, P<0.001) (Table 3).

Baseline clinical characteristics of the 1- and 3-month cervical collar group

A total of 18 patients with CS completed postoperative ultrasound follow-up, with nine patients in Group A (1-month cervical collar wear) and nine in Group B (3-month cervical collar wear). No significant differences were observed between the two groups at baseline. The mean age was 46.78±9.80 years in Group A and 47.61±8.07 years in Group B (P=0.782). The male-to-female ratio was 2:7 in Group A and 3:6 in Group B (P=0.738). The mean BMI was 24.05±3.00 kg/m² in Group A and 24.25±3.46 kg/m² in Group B (P=0.853). Preoperative VAS scores were 3.61±1.20 and 3.11±1.53, respectively (P=0.282). Preoperative JOA scores were 13.22±0.88 and 13.33±0.91, respectively (P=0.711). Preoperative NDI scores were 21.06±3.89 and 21.17±3.11, respectively (P=0.925). The preoperative Cobb angle was 4.65°±8.46° in Group A and 10.88°±10.96° in Group B, with a difference that approached but did not reach statistical significance (Table 4).

Comparison of ultrasound parameters between 1- and 3-month cervical collar groups

Of the 18 patients who completed follow-up, nine were allocated to Group A (n=9) and nine to Group B (n=9). The mean values of anterior and posterior cervical muscle thickness and stiffness measured preoperatively in each group were used as baseline references. The ratios of

changes in muscle thickness and stiffness at 3 and 6 months of follow-up were calculated to reflect longitudinal trends.

A GEE model was used to evaluate the effects of group, muscle type, cervical position, time, and their interactions on cervical muscle thickness and stiffness. For muscle thickness, no significant main effects or interaction effects were observed: group effect (Wald χ²=2.396; P=0.122), muscle type effect (Wald χ²=3.607; P=0.058), position effect (Wald χ²=1.097; P=0.778), time effect (Wald χ²=3.178; P=0.075), and group × time interaction (Wald χ²=3.503; P=0.061). For stiffness, a significant group effect was found (Wald χ²=13.306; P<0.001), indicating that cervical collar wearing duration significantly influenced stiffness. No other significant effects were observed for stiffness: muscle type effect (Wald χ²=0.020; P=0.888), position effect (Wald χ²=0.239; P=0.971), time effect (Wald χ²=0.000; P=0.995), and group × time interaction (Wald χ²=1.483; P=0.223) (Table 5).

To further identify factors independently associated with cervical muscle stiffness, a GEE model was fitted. Compared with Group A (reference), Group B showed significantly higher stiffness [β=0.122; 95% confidence interval (CI): 0.049 to 0.196; Wald χ²=10.77; P=0.001]. Muscle type (anterior vs. posterior cervical muscles, reference: posterior) was not significantly associated with stiffness (β=0.016; 95% CI: −0.104 to 0.135; Wald χ²=0.065; P=0.799). For cervical position, no significant differences were observed relative to the respective neutral position references. For the posterior cervical muscles, the forward flexion position (β=−0.008; 95% CI: −0.091 to 0.074; Wald χ²=0.037; P=0.848) and cervical extension position (β=0.006; 95% CI: −0.090 to 0.103; Wald χ²=0.017; P=0.896) were not significant. For the anterior cervical muscles, the deflection position (β=−0.023; 95% CI: −0.124 to 0.078; Wald χ²=0.205; P=0.651) was also not significant. Time (6 vs. 3 months, reference: 3 months) did not demonstrate a significant effect (β=−0.019; 95% CI: −0.058 to 0.020; Wald χ²=0.901; P=0.343) (Table 6).

Changes in cervical muscle thickness and stiffness over time

Figure 6 shows the changes in cervical muscle thickness at 3 and 6 months postoperatively. In Group A, thickness remained stable from 3 to 6 months (mean difference =0.001; 95% CI: −0.052 to 0.054; adjusted P>0.99). In Group B, thickness decreased slightly, but not significantly (mean difference =−0.055; 95% CI: −1.131 to 0.004; adjusted P=0.081). No significant between-group differences were observed, with the exception of the comparison between Group B at 6 months and Group A at 3 months (mean difference =−0.060; 95% CI: −1.203 to 0.000; adjusted P=0.049), indicating a marginal between-group difference at this specific time point. Overall, no consistent or clinically meaningful changes in muscle thickness were observed over time or between groups.

Figure 6 Longitudinal changes in cervical muscle thickness at 3 and 6 months postoperatively in patients who wore a cervical collar for 1 month (Group A) and 3 months (Group B).

Regarding cervical muscle stiffness, within-group changes over time were not significant in either group: Group A (mean difference =−0.119; 95% CI: −0.071 to 0.034; adjusted P>0.99) or Group B (mean difference =0.019; 95% CI: −0.044 to 0.081; adjusted P>0.99). By contrast, at 3 months postoperatively, the SWV ratio of Group A was significantly lower than that of Group B (mean difference =−0.122; 95% CI: −0.221 to −0.024; adjusted P=0.006); at 6 months postoperatively, the SWV ratio of Group A remained significantly lower than that of Group B (mean difference =−0.160; 95% CI: −0.280 to −0.040; adjusted P=0.003) (Figure 7). These findings suggest that a longer duration of postoperative cervical collar wear, compared with 1 month, may be associated with increased cervical muscle stiffness, an effect that appeared to persist for several months after collar removal.

Figure 7 Longitudinal changes in cervical muscle SWV at 3 and 6 months postoperatively in patients who wore a cervical collar for 1 month (Group A) and 3 months (Group B). SWV, shear wave velocity.

Discussion

The cervical spine is a complex structure, and neck muscles play a critical role in maintaining cervical stability and facilitating movement (13,14). The annual incidence of CS has been increasing. This study used multimodal ultrasound to quantitatively evaluate cervical muscle thickness and stiffness, with the aim of deepening the understanding of neck muscle changes in CS and providing potential support for early diagnosis, follow-up, and treatment response evaluation in this population.

Muscle thickness

The present study found that most neck muscles (except the sternocleidomastoid and splenius capitis in the flexion and extension positions) differed in thickness between the groups. Patients with CS exhibited significantly reduced deep cervical muscle thickness compared with HC. Specifically, semispinalis capitis thickness was 41% lower (0.35 vs. 0.59 cm), longus colli 12% lower (0.66 vs. 0.75 cm), and multifidus 11% lower (0.81 vs. 0.91 cm). By contrast, the superficial trapezius was paradoxically thicker in the case group (0.18 vs. 0.15 cm, +20%). This pattern of deep muscle atrophy with relative superficial preservation or hypertrophy suggests a compensatory mechanism. Previous studies have shown that superficial neck muscle size does not differ between patients with chronic neck pain and healthy individuals in a relaxed state; however, differences emerge under loading conditions (11). This may reflect atrophy and insufficient activation of the deep neck extensors under load, leading to compensatory overactivity of the superficial extensors. Rezasoltani et al. (15) reported reduced semipinalis capitis thickness in patients with chronic neck pain, consistent with the present findings. Hodges et al. (16) observed that following nerve root injury, the corresponding multifidus undergoes atrophy, and a similar mechanism may operate in the cervical spine. The deep neck extensors are innervated by spinal nerves, and spinal cord compression (reduced anteroposterior diameter) can result in denervation atrophy. Deep neck flexors are important for maintaining cervical lordosis and segmental stability; therefore, changes in their thickness may affect spinal structure and posture. Ghamkhar et al. (12) and Javanshir et al. (17) also found that the longus colli was thinner in patients with chronic neck pain, further supporting the presence of structural changes in deep cervical muscles. These differences in muscle thickness—particularly the pattern of deep muscle atrophy with superficial hypertrophy—suggest a functional imbalance that may compromise segmental stability and has implications for rehabilitation planning. Furthermore, ultrasound measurement of muscle thickness may provide valuable information to guide clinical treatment and rehabilitation assessment.

Muscle stiffness

In the neutral position, no significant stiffness differences were observed between the groups. However, under postural loading (forward flexion and deflection), patients consistently showed lower stiffness than HC, with differences ranging from 14% to 26% depending on the muscle and cervical posture. For example, in the forward flexion position, semispinalis capitis stiffness was 26% lower in the case group (3.50 vs. 4.75 m/s), and longus colli stiffness in the deflection position was 20% lower (3.63 vs. 4.52 m/s). Muscle stiffness varied with posture, consistent with previous reports (18,19). Chan et al. (20) also noted postural differences in multifidus stiffness in patients with chronic low back pain. The finding that cervical paraspinal muscles demonstrate lower stiffness in patients with CS is consistent with the observation of Li et al. (21), who reported reduced rectus abdominis stiffness in patients with chronic non-specific lower back pain, suggesting that prolonged chronic pain may be associated with reduced core muscle mechanical properties and stability. By contrast, Taş et al. (22) found no difference in splenius capitis stiffness between groups, possibly owing to differences in participant positioning (prone in their study vs. seated with cervical extension in the present study). These findings indicate that stiffness assessment under postural loading conditions may be more diagnostically informative than assessment in the neutral position, and that rehabilitation strategies may benefit from focusing on restoring the ability to generate appropriate muscle tension during movement, rather than on resting muscle properties alone.

Postoperative cervical collar duration

Traditionally, 3 months of cervical immobilization has been recommended to allow for bony fusion; however, accumulating evidence suggests that prolonged cervical collar use does not correlate with fusion rates and may reduce the quality of life and result in neck muscle atrophy (23-25). Nevertheless, the optimal collar wearing duration remains controversial. The present study demonstrated that cervical muscle thickness did not change significantly from 3 to 6 months in either group, and between-group differences did not reach statistical significance. The absence of a significant thickness change suggests that within a 3-month observation window, cervical collar use does not produce measurable muscle atrophy as detected by ultrasound thickness measurement. Alternatively, the small sample size may have had insufficient statistical power to detect small to moderate effects. By contrast, patients who wore a cervical collar for 3 months (Group B) showed significantly higher stiffness at both 3 and 6 months postoperatively than those who wore one for 1 month (Group A). These results are consistent with findings reported in the literature (23-25). Following confirmation of bony stability, prolonged cervical collar use should therefore be minimized. However, these findings are based on a small sample size and should be interpreted as preliminary. Adequately powered, large-scale randomized trials are warranted.

Limitations

This study has several limitations. First, the sample size of patients who completed follow-up was relatively small, attributable to the long follow-up period and the impact of the coronavirus disease 2019 (COVID-19) pandemic. Second, all participants were right-handed, and findings may not be generalizable to left-handed individuals. Third, the follow-up duration was relatively short, and longer-term longitudinal observations, along with complementary imaging modalities such as magnetic resonance imaging (MRI), are required to further validate the findings.

Conclusions

This study demonstrated distinct differences in cervical muscle thickness and stiffness in patients with CS, which may have implications for perioperative assessment. Patients who wore a cervical collar for 3 months showed higher muscle stiffness than those who wore one for 1 month, suggesting that prolonged postoperative cervical collar use may be associated with increased muscle tension; however, owing to the small sample size (n=18), these findings are preliminary and should be interpreted with caution. Prolonged cervical collar use should be minimized when clinically feasible, and adequately powered, large-scale randomized trials are warranted.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2026-1-0212/rc

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2026-1-0212/dss

Funding: This study was supported by the National Key R&D Program of China (No. 2023YFC2410802), the National Natural Science Foundations of China (No. 82572249), and the Sichuan Science and Technology Program (No. 2025YFHZ0232).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2026-1-0212/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. This study was approved by the Ethics Committee of West China Hospital of Sichuan University (approval No. 2022[394]), and was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. Informed consent was obtained from all participants for the publication of this study and accompanying images.

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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