2.1 Participants

A total of 572 typically developing children aged 6–15 years were recruited from neighboring primary and secondary schools. “Typical development” was defined as the absence of diagnosed neurological and musculoskeletal diseases and disorders. Participants with a history of trauma or injuries affecting passive ROMs were excluded from the data analysis, as determined through interviews with the participants and their parents.

All participants and their legal guardians provided written informed consent before participating in the study. The study adhered to the principles outlined in the Declaration of Helsinki and received approval from the ethics committee of the authors’ affiliated institutions.

2.2 Measurement procedures

All measurements were conducted in the exercise therapy room of the authors' affiliated institutions. The participants’ height, weight, body mass index (BMI), lower limb length, and passive ROMs were assessed. Passive ROMs were assessed by four physiotherapists with over 5 years of experience in the pediatric field. Assistants aided with the measurements when necessary. A 30 cm stainless steel 180° goniometer (Yasuda Ltd., Tokyo, Japan) was used for the measurements, which included hip flexion, hip extension (Thomas test), knee flexion, knee extension, popliteal angle, ankle dorsiflexion in knee flexion, ankle dorsiflexion in knee extension, and ankle plantar flexion. In the Thomas test, one hip was flexed in the supine position until the anterior superior iliac spine aligned just above the posterior superior iliac spine. Subsequently, the angle between the long axis of the thigh of the other lower limb and the perpendicular line connecting the anterior and posterior superior iliac spines was measured (Fig. 1).¹⁶ For the popliteal angle measurement, the angle between the extended line of the long axis of the thigh and the long axis of the lower leg was measured during the passive extension of the knee joint, with the hip joint maintained at a 90° flexion position (Fig. 1).¹³ The other joints were measured following the guidelines outlined in the “Joint Range of Motion Indication and Measurement Methods” by the Japanese Orthopaedic Association Corporation and the Japanese Association of Rehabilitation Medicine (Table 1).¹⁷

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Fig. 1 Methods of measuring the Thomas test (a) and popliteal angle (b).

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2.3 Data analysis

To examine developmental changes in lower limb ROMs among school-age children, participants were categorized into four age groups: 6–7 years (189 participants), 8–9 years (147 participants), 10–11 years (124 participants), and 12–15 years (112 participants). Since the difference between ROM measurements in the left and right lower limbs of all participants was less than 5°, mean ROM values for both limbs were used for analysis.

The mean and median ROM values for each group were calculated. The normality of the data distribution was assessed using the Shapiro–Wilk's test. All measurements for lower limb ROMs did not show a normal distribution. Consequently, the Kruskal–Wallis test was used to analyze differences in ROMs between the age groups. Additionally, the Mann–Whitney U test was conducted to evaluate sex-related differences in each ROM, and the significance level was set at 5 %. For the popliteal angle, two standard deviations (SD) were calculated along with the mean and median values for each group. Based on previous studies, hamstring tightness was determined when the popliteal angle exceeded 2 SDs from the mean.¹⁰ All statistical analyses were conducted using EZR Ver. 1.37 (Saitama Medical Center, Jichi Medical University, Saitama, Japan),¹⁸ a graphical user interface for R (The R Foundation for Statistical Computing, Vienna, Austria).

3.1 Age-related differences in ROMs

Table 2 presents the participants’ characteristics. Table 3 and Fig. 2 display the results of the test examining the differences between the various age groups. In hip flexion, the values for the 12–15 year group were significantly lower than those for the other three groups (12–15 vs. 6–7 years: p < 0.001; 12–15 vs. 8–9 years: p < 0.001; 12–15 vs. 10–11 years: p = 0.031). No significant group differences were found in the hip extension (Thomas test) values (p = 0.243). For knee flexion (10–11 vs. 6–7 years: p = 0.024; 12–15 vs. 6–7 years: p = 0.025) and knee extension (10–11 vs. 6–7 years: p = 0.002; 12–15 vs. 6–7 years: p = 0.014), the values in the 10–11 and 12–15 year groups were significantly lower than those in the 6–7 year group. The popliteal angle exhibited significantly higher values in the 12–15 year group than in the other three groups (12–15 vs. 6–7 years: p < 0.001; 12–15 vs. 8–9 years: p = 0.020; 12–15 vs. 10–11 years: p = 0.020). Regarding ankle dorsiflexion in knee flexion (8–9 vs. 6–7 years: p = 0.005; 10–11 vs. 6–7 years: p = 0.002; 12–15 vs. 6–7 years: p < 0.001) and ankle dorsiflexion in knee extension (8–9 vs. 6–7 years: p = 0.007; 10–11 vs. 6–7 years: p < 0.001; 12–15 vs. 6–7 years: p < 0.001), the other groups exhibited significantly lower values compared to the 6–7 year group. Moreover, the values for ankle plantar flexion in the 10–11 year group were significantly lower than those in the 6–7 and 8–9 year groups (10–11 vs. 6–7 years: p = 0.001; 10–11 vs. 8–9 years: p = 0.023).

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Fig. 2 Box-and-whisker plot showing the medians and interquartile ranges of ROMs in each age group. ∗p < 0.05.

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3.2 Sex differences in ROMs

Table 4 shows the results of the tests examining sex differences in each passive ROMs. Significant sex differences for passive ROMs were observed for hip flexion (p < 0.001) and the popliteal angle in the 6–7 year group (p = 0. 001), popliteal angle in the 8–9 year group (p = 0.003), and knee flexion in the 10–11 year group (p = 0.050).

3.3 Popliteal angle details

Among the items in which sex differences in passive ROMs were observed, the differences were less than 5°, except for the popliteal angle. Conversely, only the popliteal angle showed a value of 12.5°, which is considered a clinically significant difference. Therefore, we conducted an additional validation focusing on the popliteal angle The mean, 2 SD, median, minimum, and maximum values of the popliteal angle for each age group based on sex were presented in Table 5.

4.1 Passive lower limb ROM in school-age children

BMIs in each group were align with the statistics reported for BMI values of school-age children in Japan.¹⁹ With the exception of hip extension and ankle dorsiflexion in knee extension, the obtained ROM values were aligned with previous studies.

Compared to the mean value of 12.5° reported by Mudge et al. for children aged 4–16,¹³ the mean ROM for hip extension was 0.2° for our study participants. Mudge et al. used a modified version of the Thomas test, in which participants were placed at one end of an examination table to allow measurement of hip extension angles beyond a neutral position.¹³ However, the Thomas test used to measure hip extension ROM in our study had an upper limit of 0° of detectable hip extension angle, as it was performed in the supine position on a flat floor. Although the Thomas test is effective for assessing the degree of hip flexion contracture, assessing ROM above 0° hip extension is challenging. Notably, 95 % of our study participants recorded a 0° hip extension, suggesting that the ceiling effect of the Thomas test resulted in a lower value than the participants’ original hip extension ROM. Therefore, evaluating hip extension ROM using a modified version of the Thomas test may be preferable.

For ankle dorsiflexion ROM in the knee extension, Mudge et al. reported a mean value of 21.3° for children aged 4–16 years.¹³ In this study, the mean value for the 6–7 year group, which showed the widest ROM, was 16.6°, a difference of less than 5° from that reported in a previous study. Conversely, the other age groups showed a difference of more than 5°, with values of 13.9° for the 8–9 year group, 13.0° for the 10–11 year group, and 10.8° for the 12–15 year group. A large variation in ankle dorsiflexion ROM in knee extension has been observed among previous studies,^20,21 and this variation has been attributed to differences in measurement methods.¹³ To measure ankle dorsiflexion in knee extension in this study, the ankle joint was dorsiflexed to its maximum extent, with the knee joint held in extension in the supine position. Conversely, in Mudge et al., the initial measurement position was the prone position, with the knee joint flexed at 90° and maximally extended, while the ankle joint was held in maximum dorsiflexion in this position.¹³ The forces applied to the ankle joint may vary between measurements conducted in supine and prone positions. Additionally, if the knee joint flexed at 90° is used as the starting limb position for measurement, the ankle dorsiflexion angle may be measured when the knee joint is not maximally extended due to the influence of the gastrocnemius muscle, a biarticular muscle spanning the knee and ankle joints. These could account for the differences observed in ankle dorsiflexion ROM in knee extension between the present study and previous studies. Considering that ROM values differ based on the measurement method, employing the values obtained using the same measurement method for the reference values for ROMs is recommended.

4.2 Age-related differences in passive lower limb ROMs in school-age children

The findings of this study revealed a tendency for ROMs to decrease with age across all measurement items, excluding hip extension. Previous studies have reported that lower limb ROMs in children decrease with age,^7,8 aligning with our study results. The absence of this trend in hip extension ROM could be due to the ceiling effect of the Thomas test, as mentioned above. Mudge et al. found significantly lower values for hip extension ROM in typically developing children aged 12–16 years compared to participants aged 4–7 years,¹³ indicating that hip extension ROM tends to reduce during school age. This finding suggests that lower limb ROMs in typically developing children tend to decrease during school age. However, the only differences between the age groups in this study that were greater than 5° were observed in the popliteal angle and ankle dorsiflexion in knee extension. Consequently, the degree of age-related changes in passive ROMs may vary between joints.

4.3 Sex differences in passive lower limb ROM in school-age children

In this study, significant sex differences in passive ROMs were observed in hip flexion and the popliteal angle in the 6–7 year group, the popliteal angle in the 8–9 year group, and knee flexion in the 10–11 year group. Notably, the only sex difference exceeding 5° was found in the popliteal angle of the 8–9 year group, with girls demonstrating greater flexibility than boys. A previous study reported a 5°–10° sex difference in popliteal angle, with girls showing greater flexibility than boys.¹⁰ Conversely, some reports found no sex differences in hip and ankle ROMs,¹⁵ suggesting that the effect of sex differences on lower limb ROMs may vary across joints. Considering the findings of previous studies with our study results, it can be inferred that for lower limb ROMs, the effect of sex on the popliteal angle is significant. Consequently, using a sex-matched reference value for the popliteal angle is recommended.

4.4 Popliteal angle as a reference value for hamstring tightness in school-age children

Kuo et al. examined changes in the popliteal angle among typically developing children aged 0–16.¹⁰ They reported that the popliteal angle plateaued at 6 years and remained at an average of 35° after that. Subsequently, they showed that a popliteal angle of 55° or more, which is more than 2 SDs from the mean, serves as the reference value for hamstring tightness requiring treatment. In this study, the mean + 2 SD values of the popliteal angle for boys were 55.6° in the 6–7 year group, 64.8° in the 8–9 year group, 63.3° in the 10–11 year group, and 66.6° in the 12–15 year group. The corresponding values for girls were 54.8° for the 6–7 year group, 52.4° for the 8–9 year group, 52.4° for the 10–11 year group, and 69.4° for the 12–15 year group. Based on Kuo et al.’s criteria for hamstring tightness,¹⁰ the thresholds for boys in Japan should be 55° or more for ages 6–7, 65° or more for ages 8–11, and 70° or more for ages 12–15. Similarly, for girls, the hamstring tightness thresholds should be 55° or more for ages 6–11 and 70° or more for ages 12–15.

4.5 Study limitations

One limitation of this study is its cross-sectional nature, which hindered the establishment of a causal relationship between ROMs and aging. Additionally, the specific tissues involved in ROM changes are unclear, as we did not investigate the organic changes occurring in these tissues. Therefore, longitudinal studies exploring changes in ROMs over time and basic studies investigating the organic changes in joint components are required to clarify age-related changes in ROMs.