Skip to main content
Scientific Reports logoLink to Scientific Reports
. 2025 Dec 9;16:2332. doi: 10.1038/s41598-025-32033-7

Hamstring strength and hip mobility associated with pain and disability in lumbar instability

Tomasz Kuligowski 1, Agnieszka Dębiec-Bąk 1, Błażej Cieślik 2,
PMCID: PMC12816697  PMID: 41366102

Abstract

Chronic low back pain (LBP) has been hypothesized to involve lumbar instability, yet the roles of hamstring strength and hip mobility remain underexplored. While earlier studies focused on hamstring tightness, this study examined how these factors are strongly associated with pain and disability in young adults with lumbar instability. A case-control study was conducted on 129 participants (67 symptomatic, 62 asymptomatic) aged 18–35 years. Hamstring strength was assessed using the NordBord dynamometer, while hip mobility was measured using a goniometer. Pain intensity and disability were evaluated using the Numeric Pain Rating Scale and Oswestry Disability Index. Hamstring strength showed a strong negative correlation with pain (r = -0.71, p < 0.001) and disability (r = -0.72, p < 0.001). Regression analysis confirmed hamstring strength and hip mobility as key correlates of LBP severity. Cutoff values were determined for hamstring strength (Female: 178.0 N; Male: 197.5 N), hip internal rotation (Female: 23°; Male: 18°), and hip extension (Female: 21°; Male: 19°). Hamstring strength and hip mobility are key correlates of pain and disability in young adults with clinically defined lumbar instability. Candidate thresholds showed apparent in-sample discrimination and should be interpreted as hypothesis-generating rather than diagnostic.

Keywords: Lumbar instability, Low back pain, Hamstring strength, Hip mobility, Physiotherapy

Subject terms: Rehabilitation, Quality of life

Introduction

Recent research increasingly examines the relationship between low back pain (LBP) and lumbar spine instability13. Lumbar instability is commonly described as the spine’s inability to maintain controlled displacement under physiological loads, which may contribute to pain and disability4,5. Building on this framework, growing attention has turned to peripheral factors such as hamstring strength and hip mobility, which may influence symptoms and functional outcomes in young adults with LBP. A growing body of evidence highlights the burden of chronic LBP, with lifetime prevalence estimates as high as 57.8%6. Among the many contributing factors, altered muscle strength, flexibility, and overall physical function have received increasing attention710. In particular, impairments in hamstring performance and hip mobility are thought to play an important role in functional limitations and disability, making them relevant clinical targets for investigation1113. LBP has multifactorial underpinnings, with disc-degenerative changes and altered trunk-hip muscle performance frequently reported in association with symptoms14,15. In addition, previous studies have noted links with degenerative changes, muscle morphology, and specific clinical tests2,16. Together, this literature highlights the importance of considering both structural and functional aspects, while drawing attention to measurable factors such as hamstring strength and hip mobility that may be clinically relevant in young adults with LBP.

Research indicates that lumbar instability can manifest across diverse populations, with risk factors such as age, sex, and specific physical conditions playing a role17. Targeted exercise programs, particularly core stability and corrective strengthening routines, have been associated with modest but clinically meaningful reductions in excessive lumbar lordosis, although effect sizes remain heterogeneous across trials18,19. Observational and interventional studies also suggest that individuals with chronic LBP often exhibit reduced hip range of motion (ROM) and that programs emphasizing core stability and hip strength can improve functional abilities compared with controls2022. These findings support the clinical relevance of hip mobility and related muscular performance in the context of lumbar stability.

The role of hamstring function in lumbopelvic mechanics has also been discussed. Tight hamstrings may influence pelvic tilt and lumbar posture23,24, although it remains unclear whether these changes are causal or compensatory. Beyond flexibility, broader hamstring performance, including strength, has been linked to functional outcomes. For example, targeted hamstring exercises have been associated with improvements in balance and stability in individuals with LBP25. These observations support examining hamstring strength as a clinically relevant factor in relation to pain and disability.

Despite growing interest in the relationship between muscle properties and LBP, significant gaps remain. While some studies have examined the effects of hamstring tightness on lumbar mechanics, the role of hamstring strength in relation to pain and disability is less clear. For instance, hypotheses that hamstring shortness could weaken the gluteus maximus and influence lumbopelvic function have not been substantiated with direct empirical data26. Other studies have described compensatory mechanisms of hamstring tightness in relation to lumbar motion, though clear relationships remain uncertain27,28. In addition, cut-off values for hamstring strength and hip mobility measures have not been established. These gaps highlight the need for further investigation into how hamstring strength and hip ROM relate to pain and disability in young adults. Therefore, the primary aim was to compare hamstring strength and hip range of motion between young adults with non-specific LBP and age-matched asymptomatic controls. The secondary aim was to examine associations of hamstring strength and hip range of motion with pain intensity and disability. The exploratory aim was to derive candidate cut-off values for hamstring strength and hip range of motion that may differentiate symptomatic from asymptomatic individuals, treated as hypothesis generating and not as evidence of diagnostic validity.

Methods

Study design

This case–control study was conducted between July and December 2024 in accordance with the Declaration of Helsinki and was approved by the Institutional Review Board of the Wroclaw University of Health and Sport Sciences, Poland (No. 19/2024). Written informed consent was obtained from all participants. Before enrolment, participants were informed about the study procedures and their right to decline or withdraw at any time. Reporting followed the STROBE checklist29.

Participants

Participants were assigned to either the symptomatic group (SYM), comprising patients with low back pain and clinical signs of lumbar instability, or to the control group (CON), consisting of age-matched healthy individuals recruited from the university population. The SYM group included patients attending a private physiotherapy clinic who exhibited positive results on both the Passive Lumbar Extension (PLE) test and the Painful Catch sign30,31. Lumbar instability was operationally defined as a positive outcome on both tests, and only individuals meeting this criterion were classified as symptomatic. In contrast, the CON group consisted of asymptomatic individuals without a history of low back pain, matched by age.

To be eligible, participants had to be between 18 and 35 years old and report non-specific low back pain that had persisted—or recurred without a pain-free interval—for at least six consecutive weeks. They were required to have experienced an average pain intensity of 3 or higher (on a 0–10 Numeric Pain Rating Scale) during the week prior to screening, and to score at least 12% on the Oswestry Disability Index (ODI), indicating minimal disability across daily living domains such as lifting, sitting, standing, and personal care. Exclusion criteria encompassed, degenerative disc disease symptoms, radiculopathy or radicular pain, severe spinal issues (e.g., metastatic disease, fractures), significant spinal deformities, previous surgeries in the spinal, hip, or knee regions, lower limb muscle conditions (e.g., trauma), tumors, or any other disorders that could affect the results. Additionally, individuals involved in professional sports or currently undergoing treatment were excluded.

Outcome measures and procedures

A licensed physiotherapist with over 12 years of experience in manual therapy, adhering to the International Federation of Orthopaedic Manipulative Physical Therapists (IFOMPT) standards, conducted all assessments throughout the study.

Hamstring strength

All participants underwent hamstring strength evaluation, using the noninvasive NordBord device (VALD Performance, Australia). The NordBord is a validated tool for measuring eccentric knee flexor strength, with studies reporting high reliability (coefficients of variation: 5.8%–8.5%, intraclass correlation: 0.83–0.90)3234. It has been validated against traditional isokinetic dynamometers, offering a reliable and accessible option for assessing hamstring function35,36.

The Nordic hamstring exercise (NHE) was used for assessment, with participants kneeling on a padded board and their ankles secured above the lateral malleolus37,38. This setup immobilizes the lower limbs, ensuring accurate force measurement. Participants leaned forward in a controlled descent, engaging their hamstring muscles to resist the motion39,40. The NordBord recorded eccentric force output, enabling precise strength analysis.

For data collection, participants completed a warm-up set, followed by three consecutive maximal bilateral NHE repetitions. They maintained a neutral trunk and hip position, with hands crossed over the chest. Peak force values from each repetition were averaged for statistical comparisons. To minimize bias, no verbal encouragement was provided, and pain levels were assessed using a visual analog scale (VAS), with no reported discomfort.

Test–retest reliability for the NordBord has been reported with intraclass correlation coefficient (ICC) values between 0.83 and 0.9041. The standard error of measurement is approximately 20 Newtons, and the minimal detectable change at the 95% confidence level is estimated at around 60 Newtons. Currently, no minimal clinically important difference (MCID) has been established for hamstring strength in this population.

Oswestry disability index questionnaire (ODI)

The Polish version of the ODI was used to assess disability42. The ODI has ten sections scored 0 to 5. The summed raw score 0 to 50 is converted to a 0 to 100% score by multiplying by two, so 1 raw point equals 2% points. We report ODI on the 0 to 100 scale. In the Polish validation, test–retest reliability was excellent, with ICC of 0.97, standard error of measurement approximately 3.5% points, and minimal detectable change at the 95% level (MDC95) of about 10% points43. For chronic low back pain, we use an absolute MCID of 10% points on the 0 to 100 scale, equivalent to 5 raw points44, acknowledging method-dependent variability45.

Pain intensity measurement

The Numeric Pain Rating Scale (NPRS Pain) is an 11-point scale used to measure pain intensity in participants from the SYM group during ADLs on the same day as other procedures. The NPRS scale was applied according to the procedure46,47. The NPRS has excellent reliability, with ICC values reported around 0.96. The standard error of measurement is approximately 0.7 points, and the minimal detectable change at the 95% confidence level is about 2 points48. The accepted MCID for chronic low back pain is also 2 points.

Hip range of motion

Each patient’s hip range of motion (internal rotation, external rotation, and extension) was assessed with a goniometer. Hip flexion was not measured since no pathology is typically observed in young individuals. After the examiner demonstrated the movement, each participant performed two un-recorded practice repetitions through their full comfortable range; hip IR, ER and EXT were then measured three times with a handheld goniometer. The mean of the three values was used for analysis. The goniometer’s reliability for measuring hip range of motion is deemed very high, with Cronbach α values reaching a minimum of 0.9049. Reported test–retest reliability for goniometric hip range-of-motion measurements ranges from 0.80 to 0.91. The standard error of measurement is typically 2 to 4 degrees, with a minimal detectable change of 6 to 11 degrees depending on the specific motion assessed. No minimal clinically important difference has been established for hip range of motion.

Power analysis

To evaluate the statistical robustness of the primary group comparisons, a post hoc power analysis was conducted using G*Power 3.1 software. The analysis focused on the between-group difference in hamstring strength, which represented the primary outcome of interest. Based on the observed means (SYM: 158.84 ± 38.55 N; CON: 245.23 ± 27.21 N), the calculated standardized effect size (Cohen’s d) was 2.58, indicating a very large effect. Given the sample sizes of 67 (SYM) and 62 (CON) participants, and assuming a two-tailed α level of 0.05, the achieved power (1 – β) exceeded 0.99. This result confirms that the study was highly powered to detect the observed group difference in hamstring strength. Similarly, post hoc analyses of the correlation (r = − 0.72) between hamstring strength and disability and the multiple regression model of pain intensity (R² = 0.64) also demonstrated power levels exceeding 0.99.

Data analysis

Data were analyzed using JASP version 0.19.3 (University of Amsterdam, The Netherlands), and R (R version 4.4.2, The R Foundation for Statistical Computing Platform). Continuous variables were reported as mean and standard deviation (SD). The Shapiro-Wilk test was used to assess the distribution of quantitative data. Independent samples t-tests were applied for normally distributed variables, while non-normally distributed variables were analyzed using Mann-Whitney U tests. Correlation analysis was conducted using Pearson’s correlation for normally distributed variables and Spearman’s rank correlation for non-normally distributed variables.

A multiple linear regression analysis was performed to estimate cross-sectional associations of hamstring strength (and asymmetry) with pain (NPRS) and disability (ODI). These models estimate associations and do not imply prediction or causality. Pairwise correlation tests were used to evaluate the assumption of a linear relationship between the independent and outcome variables. Receiver operating characteristic (ROC) analyses were conducted to derive in-sample candidate thresholds for hamstring strength, hip internal rotation, and hip extension that separated symptomatic from asymptomatic participants. The area under the ROC curve (AUC) quantified discrimination within this dataset, and Youden’s J was used to identify candidate cutoff values. These analyses are hypothesis-generating, no external reference standard was used, and the thresholds are not clinically validated. Accordingly, ROC analyses are presented as apparent in-sample discrimination only.

Structural equation modeling (SEM) was used to estimate contemporaneous associations among clinically measured variables and outcomes in lumbar instability. The model included bilateral hamstring strength (Newtons), hip mobility (internal rotation, external rotation, extension; degrees), pain intensity (Numerical Pain Rating Scale, 0–10), and functional disability (Oswestry Disability Index). We specified paths (associations) from hamstring strength and hip mobility to pain and disability, and from pain to disability. Standardized coefficients (β) were interpreted as cross-sectional associations; where relevant, we report model-implied indirect associations via pain intensity (i.e., products of standardized paths). No causal or mediated-effect inferences were drawn.

Correlation, regression, and ROC analyses were conducted in the full sample (n = 129; symptomatic and asymptomatic) to examine continuous relationships between physical measures (hamstring strength, hip mobility) and patient-reported outcomes (pain, disability). SEM was performed in the symptomatic subgroup (n = 67) to enhance model stability and clinical relevance. Statistical significance was set at α < 0.05.

Results

Participants characteristics

The study comprised 129 participants, including 65 females (50.4%) and 64 males (49.6%). The symptomatic group consisted of 67 individuals, while the control 62. The descriptive statistics of the study participants are summarized in Table 1. The mean age of participants was 27.57 ± 4.64 years (range: 18–35 years), with a mean height of 173.02 ± 9.34 cm and weight of 73.21 ± 12.70 kg. The mean BMI was 24.41 ± 3.44 kg/m², indicating that the majority of participants were within the normal to overweight range. Regarding physical measures, the mean hamstring strength was 200.36 ± 54.74 N, with values ranging from 95.5 N to 321.5 N. Hip mobility measurements showed mean internal rotation of 23.08 ± 9.76 degrees and mean hip extension of 20.00 ± 5.37 degrees. Clinical outcomes revealed a mean pain intensity (NPRS) of 3.57 ± 2.97 points on a 0–10 scale, while the mean disability score (ODI) was 33.13 ± 26.63, indicating mild to moderate functional limitations in the study population.

Table 1.

Participants characteristics.

Variable Total (n = 129) SYM (n = 67) CON (n = 62) p value
Age 27.57 ± 4.64 27.30 ± 4.67 27.87 ± 4.63 0.48
Height [cm] 173.02 ± 9.35 170.18 ± 8.09 176.08 ± 9.70 < 0.001
Body mass [kg] 73.21 ± 12.70 66.72 ± 9.06 80.23 ± 12.38 < 0.001
BMI 24.41 ± 3.44 23.07 ± 2.92 25.85 ± 3.39 < 0.001
Hamstrings L [N] 203.64 ± 56.02 161.66 ± 38.09 249.02 ± 31.41 < 0.001
Hamstrings R [N] 197.08 ± 56.02 156.03 ± 44.03 241.44 ± 25.23 < 0.001
Hamstrings asymmetry 2.59 ± 13.18 2.61 ± 17.15 2.56 ± 6.80 0.21
Hamstrings mean [N] 200.36 ± 54.74 158.84 ± 38.55 245.23 ± 27.21 < 0.001
Hamstrings [N/kg] 2.75 ± 0.68 2.40 ± 0.53 3.13 ± 0.61 < 0.001
Hip IR [°] 23.08 ± 9.76 16.43 ± 6.58 30.26 ± 7.23 < 0.001
Hip ER [°] 36.20 ± 8.74 37.33 ± 7.98 34.98 ± 9.41 0.12
Hip EXT [°] 20.00 ± 5.37 15.81 ± 3.00 24.53 ± 3.25 < 0.001
NPRS [0–10] 3.57 ± 2.97 6.02 ± 1.95 0.92 ± 0.86 < 0.001
ODI 33.13 ± 26.63 55.25 ± 17.61 9.22 ± 5.85 < 0.001

As shown in Table 1, between-group comparisons (SYM vs. CON) revealed significant differences in hamstring strength and hip mobility, with lower values observed in the symptomatic group. These comparisons provide the basis for subsequent within-group analyses in the SYM cohort.

BMI: Body Mass Index; L: left; R: Right; IR: Internal Rotation; ER: External Rotation; EXT: extension; NPRS: Numeric Pain Rating Scale; ODI: Oswestry Disability Index; Values presented as mean ± Standard Deviation; p value as a result of U Mann-Whitney test.

Correlation analysis

Correlation analysis (Fig. 1) revealed strong associations between strength parameters and clinical outcomes in individuals with low back pain. Hamstring strength demonstrated the strongest negative correlations with both pain intensity (r = −0.71, p < 0.001) and disability (r = −0.72, p < 0.001), indicating that lower hamstring strength was associated with higher levels of pain and disability. Similarly, hip extension mobility showed strong negative correlations with both pain intensity (r = −0.71, p < 0.001) and disability (r = −0.69, p < 0.001), while hip internal rotation also demonstrated substantial negative correlations with pain intensity (r = −0.59, p < 0.001) and disability (r = −0.64, p < 0.001). The analysis also revealed significant intercorrelations among physical parameters, with moderate positive correlations between hamstring strength and both hip internal rotation (r = 0.53, p < 0.001) and hip extension (r = 0.61, p < 0.001), suggesting a potential interaction between muscle strength and joint mobility. Additionally, a strong positive correlation was observed between pain intensity and disability (r = 0.82, p < 0.001), supporting the close relationship between these clinical outcomes. These findings collectively suggest that impairments in hamstring strength and hip mobility are strongly associated with both pain and functional limitations in individuals with low back pain, highlighting the potential importance of these parameters in clinical assessment and treatment planning.

Fig. 1.

Fig. 1

This heatmap visualization represents the strength and direction of relationships between variables, with darker blue colors indicating stronger negative correlations and darker red colors indicating stronger positive correlations. Note: Analyses shown were conducted on the full sample (n = 129).

Physical measures across pain categories

The distribution of physical measures across different pain severity categories revealed distinct patterns, as illustrated in Fig. 2. Participants were stratified into three pain categories based on their NPRS scores: mild (0–3), moderate (4–6), and severe (7–10). Analysis showed that individuals with severe pain had significantly lower hamstring strength (mean difference: 84.72 N, p < 0.001) compared to those with mild pain. Similarly, hip mobility measures demonstrated a gradient across pain categories, with the severe pain group showing reduced hip internal rotation (mean difference: 14.02 degrees, p < 0.001) and hip extension (mean difference: 8.25 degrees, p < 0.001) compared to the mild pain group. These findings strongly support the hypothesis that physical impairments are more pronounced in individuals experiencing greater pain intensity.

Fig. 2.

Fig. 2

Distribution of physical measures across pain intensity (NPRS) and disability (ODI) categories. Note: Analyses shown were conducted on the full sample (n = 129).

The boxplots in Fig. 2 illustrate the relationships between physical parameters and clinical outcomes, specifically pain intensity and disability categories. The left column of the figure shows the relationships with pain intensity categories (Mild: NPRS ≤ 3, Moderate: NPRS 4–7, Severe: NPRS > 7), while the right column depicts the relationships with disability categories (Minimal: ODI ≤ 20%, Moderate: ODI 21–40%, Severe: ODI > 40%). Statistical analysis revealed significant differences across both pain and disability categories for all physical measures. For hamstring strength, significant differences were observed across pain categories (F = 64.58, p < 0.001), with mean values decreasing from mild (236.39 N) to moderate (162.12 N) and severe (150.85 N) pain. A similar pattern was found across disability categories (F = 133.35, p < 0.001), with means declining from minimal (246.35 N) to moderate (157.87 N) and severe (156.05 N) disability. Hip internal rotation also showed significant differences across pain categories (F = 36.62, p < 0.001), with means decreasing from mild (28.49°) to moderate (17.79°) and severe (14.47°) pain, and across disability categories (F = 59.66, p < 0.001), with means declining from minimal (29.95°) to moderate (18.93°) and severe (15.80°) disability. Similarly, hip extension exhibited strong differences across pain categories (F = 107.32, p < 0.001), with means decreasing from mild (23.96°) to moderate (15.35°) and severe (15.71°) pain, and across disability categories (F = 110.79, p < 0.001), with reductions from minimal (24.37°) to moderate (15.33°) and severe (15.98°) disability. These findings demonstrate that participants with higher pain intensity and greater disability consistently exhibited lower hamstring strength and reduced hip mobility. The relationships were statistically significant for all physical parameters, with particularly strong effects observed for hamstring strength and hip extension. The parallel patterns observed across both pain and disability categories suggest that physical impairments are strongly associated with both symptoms and functional limitations.

β: unstandardized regression coefficient; SE: standard error; CI: confidence interval; NPRS: Numerical Pain Rating Scale; ODI: Oswestry Disability Index. Analyses were cross-sectional (n = 129). Coefficients reflect in-sample associations and do not imply prediction or causality.

Table 2 presents the results of multiple regression analyses examining associations of physical measures with pain intensity (NPRS) and disability (ODI). For pain intensity, the model explained 64.4% of the variance (R² = 0.64, p < 0.001), with significant negative explanatory variables including hamstring strength (β = −0.02, p < 0.001), hip internal rotation (β = −0.06, p = 0.008), and hip extension (β = −0.208, p < 0.001). Similarly, for disability, the model accounted for 66.2% of the variance (R² = 0.66, p < 0.001), with hamstring strength (β = −0.002, p < 0.001), hip internal rotation (β = −0.01, p < 0.001), and hip extension (β = −0.02, p < 0.001) showing significant inverse associations. These findings highlight strong cross-sectional associations of reduced hamstring strength and hip mobility with both pain and disability, with hip extension showing the largest effect sizes in both models.

Table 2.

Multiple linear regression: variables associated with pain intensity and disability.

Independent variables β SE t p 95% CI R² F
NPRS 0.64 75.5
Hamstring strength (N) −0.02 0.004 −5.408 < 0.001 [−0.028, −0.013]
Hip internal rotation (°) −0.06 0.02 −2.692 0.008 [−0.095, −0.014]
Hip extension (°) −0.21 0.04 −5.27 < 0.001 [−0.287, −0.130]
ODI 0.66 81.65
Hamstring strength (N) −0.002 0.01 −5.481 < 0.001 [−0.003, −0.001]
Hip internal rotation (°) −0.01 0.002 −4.135 < 0.001 [−0.011, −0.004]
Hip extension (°) −0.02 0.003 −4.536 < 0.001 [−0.022, −0.009]

Relationship between physical measures and pain

Further analysis of the relationship between physical measures and pain intensity revealed clear trends, as shown in Fig. 3. The scatterplot demonstrates a significant inverse relationship between hamstring strength and pain intensity, with a correlation coefficient of r = −0.38 (p < 0.001). Similarly, hip extension showed a strong negative correlation with pain (r = −0.38, p < 0.001). The relationship remained significant even after adjusting for potential confounders such as age and BMI (adjusted R² = 0.34, p < 0.001).

Fig. 3.

Fig. 3

Relationship between hamstring strength, hip extension, and pain intensity. This scatterplot illustrates the complex interplay between physical measures and pain. The color gradient represents pain intensity levels, with darker colors indicating higher pain scores. The surface plot visualizes the combined association of hamstring strength and hip extension with pain intensity, highlighting the importance of both factors in pain presentation. Note: Analyses shown were conducted on the full sample (n = 129).

SEM results

To better understand the direct and indirect relationships between physical factors and clinical outcomes, a comprehensive SEM analysis was conducted. The results, visualized in Fig. 4, revealed significant associations from physical measures to both pain and disability. In the cross-sectional regression model, hamstring strength showed the largest magnitude independent association with pain intensity (β = −0.38, p < 0.001), with a comparable association for hip extension (β = −0.38, p < 0.001) and hip internal rotation (β = −0.18, p = 0.008). The model also demonstrated significant direct effects on disability, with pain intensity showing the strongest relationship (β = 0.47, p < 0.001). The total effects on disability, which include both direct and indirect associations, were substantial for all physical measures: hamstring strength (−0.38), hip internal rotation (−0.27), and hip extension (−0.32). The model’s fit indices indicated good overall fit (CFI = 0.97, RMSEA = 0.06), supporting the validity of the proposed relationships.

Fig. 4.

Fig. 4

SEM analysis model with standardized coefficients. This comprehensive diagram illustrates the complex network of relationships between physical factors, pain intensity, and disability. Arrows represent directional relationships, with standardized path coefficients indicating the strength and direction of each relationship. Solid lines represent statistically significant paths (p < 0.05), while the thickness of the lines corresponds to the magnitude of the relationship. Note: Analyses shown were conducted on the SYM group only sample (n = 67).

AUC: Area Under Curve; IR: Internal Rotation; EXT: Extension. Note: Analyses shown were conducted on the full sample (n = 129). Apparent performance, no external validation; thresholds are candidate values only.

Table 3 presents apparent in-sample discrimination for symptom status using three physical measures, stratified by sex, with candidate threshold values. For hamstrings strength, the general cutoff was established at 197.5 N (sensitivity = 0.91, specificity = 0.97, AUC = 0.96), with females showing a lower optimal threshold at 178.0 N and males matching the general cutoff at 197.5 N. Hip internal rotation demonstrated varying thresholds, with a general cutoff of 23.0° matching the female-specific value, while males showed a lower threshold at 18.0°. Hip extension revealed a general cutoff of 19.0° (matching the male-specific value), while females demonstrated better discrimination at 21.0°.

Table 3.

In-sample discrimination (ROC) for symptom status.

Measure Cutoff Sensitivity Specificity AUC Youden’s J p
Total
Hamstrings Strength 197.5 N 0.91 0.97 0.96 0.88 < 0.001
Hip IR 23.0° 0.87 0.77 0.91 0.64 0.30
Hip Extension 19.0° 0.82 1.00 0.98 0.82 0.11
Female
Hamstrings strength 178.0 0.95 1.00 0.99 0.95
Hip IR [°] 23.0 0.86 0.87 0.95 0.73
Hip EXT [°] 21.0 0.98 0.87 0.98 0.85
Male
Hamstrings strength 197.5 0.84 1.00 0.91 0.84
Hip IR [°] 18.0 0.68 1.00 0.91 0.68
Hip EXT [°] 19.0 0.88 1.00 0.98 0.88

Figure 5 presents the ROC curves stratified by sex for each physical parameter. The curves indicate apparent in-sample discrimination (AUCs > 0.90) across measures. Hamstrings strength showed the highest discriminative ability in females (AUC = 0.99) with a nearly perfect ROC curve shape, while maintaining excellent accuracy in males (AUC = 0.91). Hip extension demonstrated apparent in-sample discrimination in both sexes (AUC = 0.98 for females, AUC = 0.98 for males), with curves showing steep initial slopes indicating optimal sensitivity-specificity trade-offs. Hip internal rotation, while still showing excellent discrimination (AUC = 0.95 for females, AUC = 0.91 for males), demonstrated slightly lower but clinically meaningful diagnostic accuracy. Notable sex-specific patterns emerged: males consistently showed perfect specificity (1.00) across measures, while females demonstrated more balanced sensitivity-specificity trade-offs. These patterns suggest that sex-specific candidate cutoffs may provide more precise reference points for future hypothesis-generating work.

Fig. 5.

Fig. 5

ROC curves for hamstring strength and hip range of motion. Note: Analyses shown were conducted on the full sample (n = 129). Apparent in-sample performance; no external validation.

Discussion

This study compared hamstring strength and hip ROM in young adults with and without LBP. Individuals with LBP exhibited lower hamstring strength and reduced hip mobility, and these measures were significantly associated with higher pain and disability. These are cross-sectional, in-sample findings and do not establish diagnostic validity or causality. Together, the results support hamstring strength and hip mobility as clinically relevant correlates of pain and disability. Hamstring strength showed a strong inverse association with both outcomes, and hip extension and internal rotation discriminated LBP status in ROC analyses. These observations align with prior work implicating muscle performance and hip biomechanics in LBP50.

The relationship between hamstring function and lumbopelvic mechanics is well established, though most prior studies have focused on flexibility rather than strength. The present findings extend this evidence by showing that reduced hamstring strength is significantly associated with higher pain and disability, providing complementary insight beyond flexibility measures. Prior studies on hamstring flexibility and lumbopelvic posture report mixed associations with alignment and motion, while links to pain are inconsistent; our results complement this literature by focusing on hamstring strength and hip ROM and their associations with pain and disability5153.

Hamstring activity and length have been linked to changes in pelvic orientation and lumbar posture. For example, Park and Jung (2021) reported that individuals with shortened hamstrings showed greater anterior pelvic tilt and altered spinal curvatures54, while Han et al. (2016) found associations between limited hamstring length and increased posterior pelvic tilt, affecting sagittal alignment55,56. Such findings highlight the influence of hamstring properties on lumbopelvic posture, although their direct relationship to pain outcomes remains debated. In this context, our results add to the literature by focusing on hamstring strength as a factor associated with pain and disability, complementing previous flexibility-focused research. Collectively, flexibility studies suggest links between hamstring properties and lumbopelvic posture, although direct relationships with pain remain debated. Our findings complement this literature by showing that hamstring strength – alongside hip ROM – was associated with pain and disability in young adults.

The concept of hip–spine syndrome highlights the close interaction between hip and lumbar function. Limitations in hip motion have been associated with compensatory movement patterns in the lumbar spine, which may influence symptoms of LBP. Redmond et al., in a systematic review, reported frequent alterations in hip ROM among patients with LBP and noted that treatments addressing hip pathology were often accompanied by improvements in back pain57. Similarly, Kim et al. found that hip mobilization exercises reduced symptoms in individuals with chronic non-specific LBP, underscoring the potential clinical relevance of hip impairments58. Supporting evidence also shows that patients with LBP commonly demonstrate reduced hip internal rotation and hip abductor weakness59. Nishimura and Miyachi observed that increased lumbar mobility in the presence of hip restriction was associated with pain sensitivity60, and Khoury et al. described abnormal hip conditions as leading to compensatory pelvic and lumbar adaptations61. Taken together, these studies reinforce the importance of considering hip mobility when evaluating LBP. In line with this evidence, the present results showed that reduced hip extension and internal rotation were associated with pain and disability in young adults.

Clinical implications

This study provides valuable insights for clinicians, highlighting the importance of assessing and addressing hamstring strength and hip mobility in individuals with LBP. Given the observed associations between these physical measures and clinical outcomes, rehabilitation protocols may benefit from emphasizing strength and mobility-based exercises rather than relying on passive stretching alone. By incorporating targeted strength training and hip mobilization strategies, clinicians can develop more comprehensive treatment plans tailored to young adults with LBP.

Limitations and future research

While this study provides valuable insights, several limitations should be acknowledged. The cross-sectional design precludes causal inferences, and the sample characteristics may limit generalizability. Hamstring weakness and limited hip mobility may either contribute to, or arise as consequences of, pain and disability in individuals with lumbar instability; in this study, lumbar instability was operationally defined using clinical screening tests (PLE/painful catch), and no imaging or other gold-standard reference was used. The sample consisted of volunteers from a physiotherapy clinic, which may not represent the general population. Identifying reliable strength and ROM threshold values would require larger and more diverse cohorts, and ROC-derived cut-offs should be regarded as exploratory rather than validated diagnostic criteria. Minimal clinically important differences (MCIDs) for hamstring strength (NordBord) and goniometric hip ROM have not been established; therefore, we emphasize reliability indices (SEM/MDC) and interpret thresholds as exploratory. Future research should use longitudinal designs to clarify causal relationships, evaluate the effectiveness of interventions targeting hamstring strength and hip mobility, and consider additional variables (e.g., core strength, flexibility). The ODI score may also be analyzed in more detail when stratified into specific sections. Reported links between hamstrings and lordosis largely stem from correlational studies or multifaceted interventions; future work should incorporate more specific assessments, including imaging, to clarify these relationships.

Conclusion

In summary, this study suggests that hamstring strength and hip mobility have a strong association with pain and disability in young adults with lumbar instability, where hamstring strength, hip mobility, and lumbar instability were operationally defined using clinical screening tests. These findings suggest the potential value of incorporating these measures into clinical assessment and rehabilitation planning, while acknowledging that causal inferences cannot be drawn from this cross-sectional design. Future studies should aim to confirm clinically relevant cut-off values for hamstring strength and hip mobility in larger and more diverse populations, with particular attention to external validation and the exploratory nature of thresholds.

Author contributions

Conceptualization: T.K., Methodology: T.K. and B.C., Validation: A.D-B., Formal analysis: T.K. and A.D-B., Writing - Original Draft: T.K. and B.C., Writing - Review & Editing: A.D-B., Supervision: B.C., Project administration: T.K. All authors reviewed the manuscript.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

  • 1.Demoulin, C., Distrée, V., Tomasella, M., Crielaard, J. M. & Vanderthommen, M. Lumbar functional instability: a critical appraisal of the literature. Ann. Readaptation Med. Phys. Rev. Sci. Soc. Francaise Reeducation Fonct Readaptation Med. Phys.50, 677–684 (2007). [DOI] [PubMed] [Google Scholar]
  • 2.Seyedhoseinpoor, T. Importance of lumbar instability in the study of associations between muscle Morphology, pain, and disability in chronic low back pain. Am. J. Phys. Med. Rehabil. 104, 31–37 (2024). [DOI] [PubMed] [Google Scholar]
  • 3.Seyedhoseinpoor, T., Sanjari, M. A., Taghipour, M., Dadgoo, M. & Mousavi, S. J. Spinopelvic malalignment correlates to lumbar instability and lumbar musculature in chronic low back pain-an exploratory study. Sci. Rep.14, 31974 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 4.Panjabi, M. M. The stabilizing system of the spine. Part II. Neutral zone and instability hypothesis. J. Spinal Disord. 5, 390–396; discussion 397 (1992). [DOI] [PubMed]
  • 5.Panjabi, M. M. Clinical spinal instability and low back pain. J. Electromyogr. Kinesiol.13, 371–379 (2003). [DOI] [PubMed] [Google Scholar]
  • 6.Perveen, A. Hamstring tightness among individuals with neck and low back pain: A Cross-Sectional study in a public sector Institute of Karachi. J. Pak Med. Assoc.73, 1598–1602 (2023). [DOI] [PubMed] [Google Scholar]
  • 7.Chatprem, T., Puntumetakul, R., Kanpittaya, J., Selfe, J. & Yeowell, G. A diagnostic tool for people with lumbar instability: a criterion-related validity study. BMC Musculoskelet. Disord. 22, 976 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 8.Iguchi, T. et al. Age distribution of three radiologic factors for lumbar instability: probable aging process of the instability with disc degeneration. Spine28, 2628–2633 (2003). [DOI] [PubMed] [Google Scholar]
  • 9.Kanemura, A. et al. The influence of sagittal instability factors on clinical lumbar spinal symptoms. J. Spinal Disord Tech.22, 479–485 (2009). [DOI] [PubMed] [Google Scholar]
  • 10.Leone, A., Guglielmi, G., Cassar-Pullicino, V. N. & Bonomo, L. Lumbar intervertebral instability: a review. Radiology245, 62–77 (2007). [DOI] [PubMed] [Google Scholar]
  • 11.Golbakhsh, M., Hamidi, M. A. & Hassanmirzaei, B. Pelvic incidence and lumbar spine instability correlations in patients with chronic low back pain. Asian J. Sports Med.3, 291–296 (2012). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 12.Puntumetakul, R. et al. The effects of core stabilization exercise with the abdominal Drawing-in maneuver technique versus general strengthening exercise on lumbar segmental motion in patients with clinical lumbar instability: A randomized controlled trial with 12-Month Follow-Up. Int. J. Environ. Res. Public. Health. 18, 7811 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 13.Rathod, A., Garg, B. K. & Sahetia, V. M. Lumbar rocking test: A new clinical test for predicting lumbar instability. J. Craniovertebral Junction Spine. 10, 33–38 (2019). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 14.Seo, H. R. & Kim, S. W. The effects of gyrotonic expansion system exercise and trunk stability exercise on muscle activity and lumbar stability for the subjects with chronic low back pain. J. Exerc. Rehabil. 15, 129–133 (2019). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 15.Wang, Z. Mechanical factors regulate annulus fibrosus (AF) injury repair and remodeling: A review. Acs Biomater. Sci. Eng.10, 219–233 (2023). [DOI] [PubMed] [Google Scholar]
  • 16.Ferrari, S., Manni, T., Bonetti, F., Villafañe, J. H. & Vanti, C. A literature review of clinical tests for lumbar instability in low back pain: validity and applicability in clinical practice. Chiropr. Man. Ther.23, 14 (2015). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 17.Farrokhi, M. R., Yadollahikhales, G. & Gholami, M. Treatment of 44 cases with lumbar spine stenosis and degenerative instability: outcomes of surgical intervention. Iran. J. Neurosurg.3, 79–88 (2017). [Google Scholar]
  • 18.González-Gálvez, N., Gea-García, G. M. & Marcos-Pardo, P. J. Effects of exercise programs on kyphosis and lordosis angle: A systematic review and meta-analysis. PloS One. 14, e0216180 (2019). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 19.Shalamzari, M. H., Henteh, M. A., Shamsoddini, A. & Ghanjal, A. Comparison of the effects of core stability and whole-body electromyostimulation exercises on lumbar lordosis angle and dynamic balance of sedentary people with hyperlordosis: a randomized controlled trial. BMC Sports Sci. Med. Rehabil. 16, 91 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 20.Kim, B. & Yim, J. C. Stability and hip exercises improve physical function and activity in patients with Non-Specific low back pain: A randomized controlled trial. Tohoku J. Exp. Med.251, 193–206 (2020). [DOI] [PubMed] [Google Scholar]
  • 21.Yasunaga, Y. et al. Biofeedback physical therapy with the hybrid assistive limb (HAL) lumbar type for chronic low back pain: A pilot study. Cureus14, e23475 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 22.Lee, S. & Kim, S. Y. Comparison of chronic Low-Back pain patients hip range of motion with lumbar instability. J. Phys. Ther. Sci.10.1589/jpts.27.349 (2015). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 23.Cejudo, A., Centenera-Centenera, J. M. & Santonja-Medina, F. The potential role of hamstring extensibility on sagittal pelvic Tilt, sagittal spinal curves and recurrent low back pain in team sports players: A gender perspective analysis. Int. J. Environ. Res. Public. Health. 18, 8654 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 24.Jandre Reis, F. J. & Macedo, A. R. Influence of hamstring tightness in Pelvic, lumbar and trunk range of motion in low back pain and asymptomatic volunteers during forward bending. Asian Spine J.9, 535–540 (2015). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 25.Shamsi, M., Mirzaei, M., Shahsavari, S., Safari, A. & Saeb, M. Modeling the effect of static stretching and strengthening exercise in lengthened position on balance in low back pain subject with shortened hamstring: a randomized controlled clinical trial. BMC Musculoskelet. Disord. 21, 809 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 26.Rabiei, P., Namin, B. G., Nasermelli, M. H., Marjomaki, O. & Mazloum, V. The effects of functional training on pain, Function, and performance in Taekwondo players with mechanical low back pain. Health9, 1176–1189 (2017). [Google Scholar]
  • 27.Arab, A. M. & Nourbakhsh, M. R. Hamstring muscle length and lumbar lordosis in subjects with different lifestyle and work setting: comparison between individuals with and without chronic low back pain. J. Back Musculoskelet. Rehabil. 27, 63–70 (2014). [DOI] [PubMed] [Google Scholar]
  • 28.Kanishka, G. K. et al. Influence of hamstring tightness on the functions of lumbar and pelvic regions among sewing machine operators in a garment factory of Colombo district. J. Coll. Community Physicians Sri Lanka. 7, 315–321 (2021). [Google Scholar]
  • 29.Cuschieri, S. The STROBE guidelines. Saudi J. Anaesth.13, S31 (2019). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 30.Kasai, Y., Morishita, K., Kawakita, E., Kondo, T. & Uchida, A. A new evaluation method for lumbar spinal instability: passive lumbar extension test. Phys. Ther.86, 1661–1667 (2006). [DOI] [PubMed] [Google Scholar]
  • 31.Ombregt, L. A System of Orthopaedic Medicine: Third Edition (Elsevier, 2013).
  • 32.Jones, S. J. M. et al. Strength development and Non-contact lower limb injury in academy footballers across age groups. Scand. J. Med. Sci. Sports. 31, 679–690 (2020). [DOI] [PubMed] [Google Scholar]
  • 33.Wezenbeek, E. et al. Impact of (Long) COVID on athletes’ performance: A prospective study in elite football players. Ann. Med.55, 2198776 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 34.Wille, C. M. et al. Preseason eccentric strength is not associated with hamstring strain injury: A prospective study in collegiate athletes. Med. Sci. Sports Exerc.54, 1271–1277 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 35.Koukouras, D. The Nordbord usefulness in football: A systematic review of the pros and cons. Hum. Mov.25, 64–85 (2024). [Google Scholar]
  • 36.Ribeiro-Alvares, J. B., Santos Oliveira, G., de Lima-E-Silva, F. X. & Baroni, B. M. Eccentric knee flexor strength of professional football players with and without hamstring injury in the prior season. Eur. J. Sport Sci.21, 131–139 (2020). [DOI] [PubMed] [Google Scholar]
  • 37.Behan, F. P., Opar, D. A., Vermeulen, R., Timmins, R. G. & Whiteley, R. The Dose–response of pain throughout a nordic hamstring exercise intervention. Scand. J. Med. Sci. Sports. 33, 542–546 (2023). [DOI] [PubMed] [Google Scholar]
  • 38.Bishop, C., Manuel, J., Drury, B., Beato, M. & Turner, A. N. Assessing eccentric hamstring strength using the nordbord: Between-Session reliability and interlimb asymmetries in professional soccer players. J. Strength. Cond Res.36, 2552–2557 (2022). [DOI] [PubMed] [Google Scholar]
  • 39.Fernandes, J., Morán, J., Clarke, H. & Drury, B. The influence of maturation on the reliability of the nordic hamstring exercise in male youth footballers. Transl Sports Med.3, 148–153 (2019). [Google Scholar]
  • 40.Jones, M. J. et al. Low load with BFR vs. High load without BFR eccentric hamstring training have similar outcomes on muscle adaptation. J. Strength. Cond Res.37, 55–61 (2022). [DOI] [PubMed] [Google Scholar]
  • 41.Opar, D. A., Piatkowski, T., Williams, M. D. & Shield, A. J. A novel device using the nordic hamstring exercise to assess eccentric knee flexor strength: A reliability and retrospective injury study. J. Orthop. Sports Phys. Ther.43, 636–640 (2013). [DOI] [PubMed] [Google Scholar]
  • 42.Fairbank, J. C. & Pynsent, P. B. Oswestry Disabil. Index. Spine25, 2940–2952 (2000). [DOI] [PubMed] [Google Scholar]
  • 43.Miekisiak, G. et al. Validation and cross-cultural adaptation of the Polish version of the Oswestry disability index. Spine38, E237–243 (2013). [DOI] [PubMed] [Google Scholar]
  • 44.Ostelo, R. W. J. G. et al. Interpreting change scores for pain and functional status in low back pain: towards international consensus regarding minimal important change. Spine33, 90–94 (2008). [DOI] [PubMed] [Google Scholar]
  • 45.Solomito, M. J., Kia, C. & Makanji, H. The minimal clinically important difference for the Oswestry disability index substantially varies based on calculation method: implications to Value-Based care. Spine50, 707 (2025). [DOI] [PubMed] [Google Scholar]
  • 46.Chiarotto, A. et al. Core outcome measurement instruments for clinical trials in nonspecific low back pain. Pain159, 481–495 (2018). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 47.Chiarotto, A. et al. Measurement properties of visual analogue Scale, numeric rating Scale, and pain severity subscale of the brief pain inventory in patients with low back pain: A systematic review. J. Pain. 20, 245–263 (2019). [DOI] [PubMed] [Google Scholar]
  • 48.Farrar, J. T., Young, J. P., LaMoreaux, L., Werth, J. L. & Poole, M. R. Clinical importance of changes in chronic pain intensity measured on an 11-point numerical pain rating scale. Pain94, 149–158 (2001). [DOI] [PubMed] [Google Scholar]
  • 49.Nussbaumer, S. et al. Validity and Test-Retest reliability of manual goniometers for measuring passive hip range of motion in femoroacetabular impingement patients. BMC Musculoskelet. Disord. 11, 194 (2010). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 50.Pizol, G. Z., Miyamoto, G. C. & Cabral, C. M. N. Hip biomechanics in patients with low back pain, what do we know? A systematic review. BMC Musculoskelet. Disord. 25, 415 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 51.Saranraj, P., Durai, S., Susmitha, P., Balasuburamaniam, A. & Sujitha, G. The effectiveness of comprehensive corrective exercise program along with Janda’s approach and Lacrosse ball massage technique in the improvement of posture in subjects with lower crossed syndrome. Indian Journal of Natural Science.15, 78683–78687 (2024).
  • 52.Król, A., Polak, M., Szczygieł, E., Wójcik, P. & Gleb, K. Relationship between mechanical factors and pelvic Tilt in adults with and without low back pain. J. Back Musculoskelet. Rehabil. 30, 699–705 (2017). [DOI] [PubMed] [Google Scholar]
  • 53.Allam, N. M. et al. The association of hamstring tightness with lumbar lordosis and trunk flexibility in healthy individuals: gender analysis. Front. Bioeng. Biotechnol.11, 1225973 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 54.Park, D. & Jung, S. Effects of hamstring self-stretches on pelvic mobility in persons with low back pain. Phys. Ther. Rehabil Sci.9, 140–148 (2020). [Google Scholar]
  • 55.Han, H. I., Choi, H. S. & Shin, W. S. Effects of hamstring stretch with pelvic control on pain and work ability in standing workers. J. Back Musculoskelet. Rehabil. 29, 865–871 (2016). [DOI] [PubMed] [Google Scholar]
  • 56.Cejudo, A. Lower-Limb range of motion predicts sagittal spinal misalignments in children: A Case-Control study. Int. J. Environ. Res. Public. Health. 19, 5193 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 57.Redmond, J. M., Gupta, A., Hammarstedt, J. E., Stake, C. E. & Domb, B. G. The hip-spine syndrome: how does back pain impact the indications and outcomes of hip arthroscopy? Arthrosc. J. Arthrosc. Relat. Surg. Off Publ Arthrosc. Assoc. N Am. Int. Arthrosc. Assoc.30, 872–881 (2014). [DOI] [PubMed] [Google Scholar]
  • 58.Kim, B. R., Kang, T. W. & Kim, D. H. Effect of proprioceptive neuromuscular facilitation stretching on pain, hip joint range of Motion, and functional disability in patients with chronic low back pain. Phys. Ther. Rehabil Sci.10, 225–234 (2021). [Google Scholar]
  • 59.San-Emeterio-Iglesias, R., De-la-Cruz-Torres, B., Romero-Morales, C. & Minaya-Muñoz, F. Effect of Ultrasound-Guided percutaneous neuromodulation of sciatic nerve on hip muscle strength in chronic low back pain sufferers: A pilot study. J. Clin. Med.11, 6672 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 60.Nishimura, T. & Miyachi, R. Relationship between low back pain and lumbar and hip joint movement in desk workers. J. Phys. Ther. Sci.32, 680–685 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 61.Khoury, A., Hatem, M., Bowler, J. & Martin, H. D. Hip–spine syndrome: rationale for ischiofemoral impingement, femoroacetabular impingement and abnormal femoral torsion leading to low back pain. J. Hip Preserv Surg.7, 390–400 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.


Articles from Scientific Reports are provided here courtesy of Nature Publishing Group

RESOURCES