Validity and reliability of inertial measurement units for measuring gait kinematics in older adults across varying fall risk levels and walking speeds

Abstract

Background

This study aimed to determine whether the validity and reliability of inertial measurement units (IMUs) in measuring lower extremity joint kinematics differed among different walking velocities and varying fall risk older adults.

Methods

Forty-five older adults were categorized into low and high fall risk. Lower extremity joint angles during walking were simultaneously measured using inertial measurement units (IMUs) and an optical motion capture (OMC) system across slow, preferred, and fast walking speeds. The Coefficient of Multiple Correlation (CMC) was employed to assess waveform consistency, while systematic error (SE) was calculated to quantify deviations. For discrete kinematic parameters, Pearson’s correlation coefficient (r), intra-class correlation coefficients (ICCs), and root mean square error (RMSE) were computed. A two-way analysis of variance utilizing statistical parametric mapping methods was conducted to compare differences in lower extremity joint angles across fall risk categories and varying walking speeds.

Results

For lower extremity joint waveforms, IMUs demonstrated very good to excellent validity (low fall risk: CMC = 0.872–0.957, SE = 4.8°-9.6°; high fall risk: CMC = 0.894–0.974,SE = 4.5°-6.9°) and reliability (within-raters: low fall risk: CMC = 0.924–0.982, SE = 3.9°–6.5°; high fall risk: CMC = 0.914–0.974, SE = 1.0°–2.5°; between-raters: low fall risk: CMC = 0.953–0.981, SE = 2.2°–5.9°; high fall risk: CMC = 0.903–0.985, SE = 1.7°–2.2°) for joint kinematics in the sagittal plane across various walking velocities in both low and high fall risk individuals. For discrete parameters, r values of peak joint angles and ROM measured by IMUs and OMC system were generally higher in the sagittal plane compared to the frontal and transverse planes. ICC values between within-raters and between-raters comparisons ranged from moderate to excellent, with RMSE values between 2.1°- 8.4° for both within-rater and between-rater comparisons in the sagittal plane. There are significant differences in the joint angles of lower limbs between different fall risk groups and different walking speeds in specific gait cycle intervals.

Conclusion

IMUs are valid and reliable for measuring joint kinematics both low- and high-fall risk older adults across different walking speeds. However, caution is warranted when interpreting data from the frontal and transverse planes. Additionally, high fall risk individuals had smaller joint angles, while faster walking speeds increased joint angles during specific gait cycles.

Introduction

Falls pose a significant health risk to older adults, may leading to both fatal and non-fatal injuries, pain, fractures, functional impairments, and psychological distress [1]. According to the report of World Health Organization (WHO) (2022) [2], 30% of community-dwelling adults aged 60 and above experience falls, with the rate rising to 40-50% for those over 80. Preventing falls requires a comprehensive assessment of individual, environmental, behavioral, and socio-economic factors [2]. In clinical practice, fall risk is commonly assessed using standardized tools, including self-reported fall history, performance-based tests such as the Timed Up and Go (TUG) test, fall risk questionnaires such as the Morse Fall Scale [3] and gait analysis.

Gait, which involves the coordination of sensory, neural, and motor systems, is quantified through gait parameters and the measurement of an individual’s walking patterns, serves as a key biomechanical factor in assessing the risk of falls. Gait analysis methods typically include observation, scale-based assessments, and instrumented-based measurement [4,5,6]. While the first two methods are commonly used in clinical settings due to their ease of implementation, their reliability and validity are limited by assessor and subject variability. In contrast, instrumented methods that provide precise measurements of movement trajectories overcome these limitations [7], though they are often restricted by high costs and limited portability. This has led to a growing interest in wearable technologies, which combine precision and portability, as promising alternatives for assessing gait and postural control in older adults.

Inertial Measurement Units (IMUs), composed of accelerometers, gyroscopes, and magnetometers, have gained attention for their ability to capture and analyze gait data efficiently. Due to their small size, light weight, and affordability, IMUs offered a promising alternative to traditional gold-standard tools for gait monitoring and fall risk assessment in older adults. Studies have shown that IMUs offer good to excellent validity and reliability in measuring gait spatiotemporal parameters in older populations [8,9,10,11,12,13]. However, their ability to accurately measure three-dimensional kinematics across the full gait cycle, previous research had mixed results. A considerable number of studies [14,15,16] only recommend the use of IMUs in the sagittal plane for kinematic measurement of lower extremity joints, and hold a negative attitude towards the use of frontal and transverse planes. However, some studies [17, 18] have used more advanced algorithms to reduce static calibration errors and cumulative integral errors to infer more accurate IMUs orientation and position, making IMUs a satisfactory measurement tool.

Additionally, previous studies exploring the reliability and validity of IMUs as a measure of lower limb walking kinematics did not conduct subgroup analyses of fall risk or walking speed, which may limit recommendations for more detailed application of IMUs. Older adults with varying fall risk levels often exhibit distinct walking patterns, such as shorter stride lengths, longer stance times, smaller lower extremity joint ranges of motion, and greater gait variability [19,20,21,22]. These differences may affect gait stability and coordination, influencing the kinematics of lower extremity joints during walking. Therefore, it is crucial to examine the reliability and validity of IMUs in measuring the lower extremity joint angles of individuals with different fall risk levels. Additionally, walking speed plays a significant role in gait kinematics. Slower or faster walking speeds often result in substantial changes in joint angles, stride length, and gait cycle duration. Slower speeds are associated with smaller stride lengths and greater gait instability, while faster speeds bring higher joint loading and dynamic balance challenges [23, 24]. These gait characteristics are closely linked to fall risk [3, 25], particularly in older adults, where the effects may be more pronounced.

Therefore, the aim of this study is to determine whether the validity and reliability of inertial measurement units (IMUs) in measuring lower extremity joint kinematics differed across different walking velocities during varying fall risk older adults. Initially, the study assessed the concurrent validity and reliability of IMUs for lower extremity kinematics across different fall risk levels and walking speeds. Subsequently, for results which achieve good to excellent reliability and validity, differences of lower extremity kinematics between different fall risk groups and walking speeds were explored.

Unlike previous studies that primarily examined the validity and reliability of IMUs in a general older adult population, this study uniquely investigated how IMUs performance varied across different fall risk levels and walking speeds. Most existing research didn’t conduct subgroup analyses based on fall risk levels or walking speeds, which may limit the applicability of their findings in clinical practice. By addressing this gap, our study provides a more detailed evaluation of IMUs in gait assessment, offering insights that can improve fall risk stratification and personalized interventions for older adults. The hypotheses of this study are: (1) the reliability and validity of IMUs in measuring lower extremity joint angles in older adults may differ across varying fall risk levels and walking speeds; (2) lower extremity joint angles in older adults vary in specific gait cycle intervals across different fall risk levels and walking speeds.

Methods

Participants

The sample size for the Pearson correlation analysis was calculated using G*Power software, assuming a medium effect size of 0.4, a significance level of 0.05, and a desired power of 0.80. Based on these parameters, a minimum sample size of 44 participants was recommended.

The study recruited 45 older adults (aged 65 years and above), who met the inclusion criteria of (1) right-leg dominant (2), independent walking ability. Participants were excluded if they had (1) neurological disorders (e.g., Parkinson’s disease, stroke) (2), significant cardiovascular or musculoskeletal conditions that impaired mobility (e.g., severe osteoarthritis, recent lower limb fractures or surgeries within the past six months),(3) individuals reporting severe pain or asymmetrical left-right claudication that visibly affected their gait. Ethical approval was granted by the Ethics Committee of Shanghai University of Sport (Approval No. 102772023RT132), and informed consent was obtained from all participants. It is confirmed that this study adhered to the guidelines set forth in the Declaration of Helsinki for experiments involving human participants.

Fall risk stratification

According to the adapted STEADI algorithm [26], participants were initially screened through three key questions: (1) Do you feel unstable while standing or walking? (2) Are you worried about falling? (3) Have you fallen in the past year? Following this, participants underwent the Timed Up and Go (TUG) test, with observations made on their gait and balance.

If a participant answers “no” to all three questions and scores less than 12 s on the TUG test, without any observed issues with gait or balance, they are classified as “Low Fall Risk.” Conversely, if a participant answers “yes” to any of the three questions, and/or scores 12 s more on the TUG test, or/and exhibits any problems with gait or balance, they are categorized as “High Fall Risk.”

Equipment and procedure

All participants wore standardized shoes (FEIYUE, model DF/1-334, China) in their preferred size. They were instructed to walk along a 10-meter straight pathway at three distinct velocities: self-selected comfortable velocity, slow velocity (80% ± 10% of the comfortable velocity), and fast velocity (as quickly as possible). For each velocity condition, participants were required to complete at least 10 valid steps. To prevent fatigue, a 2-minute rest period was provided between trials at different velocities.

The Inertial Measurement Units (IMUs) used in this study were part of the STT system from the Basque Country, Spain. This advanced system consists of seven IMUs, each equipped with a triaxial accelerometer (range ± 16 g), gyroscope (range ± 1200°/s), and magnetometer (range ± 1.3 Gs). The IMUs measured kinematic data at a sampling frequency of 100 Hz. According to the manufacturer’s guidelines, the IMUs were strategically placed as follows: one on the sacrum along the midline of the back at approximately the S1 level, and bilaterally on the anterior mid-thigh, anterior upper shank, and dorsum of the foot (Fig. 1). Prior to data collection, participants were instructed to stand still with their feet parallel, toes pointing straight forward, and the distance between the feet equal to the width of their shoulders. Participants maintained an upright, motionless stance during this period to complete proper sensor calibration.

Fig. 1

Inertial Measurement Units and Marker Placement. (A) Participant wearing inertial measurement units and markers. (B) Front view of the 3D model showing IMU fixed positions (orange circles) and reflective marker positions. (C) Back view of the 3D model showing IMU fixed positions (orange circles) and reflective marker positions

According to Plug-in Gait Reference Guide, a total of 44 retroreflective markers were placed bilaterally on the anatomical marker sites of head, trunk, pelvis, and both lower limbs of the participants (Fig. 1). Before the formal gait tests, a static calibration trial in a neutral upright position was recorded. The optical motion capture (OMC) system consisted of an eight-camera high-velocity motion capture system (Qualisys Track Manager, Qualisys, Gothenburg, Sweden) with a sampling frequency of 100 Hz.

For the validity assessment, each participant made a single visit to the laboratory. Reflective markers and inertial measurement units (IMUs) were affixed to designated anatomical sites on the participants’ bodies. Subsequently, participants executed walking trials at three distinct velocities, ensuring that a minimum of 10 valid steps were captured for each velocity condition.

To assess reliability, participants visited the laboratory on two separate occasions, spaced one week apart. On the first visit, Rater A affixed all IMUs, instructed the participants to complete the walking tests, and subsequently removed the IMUs. Approximately 30 min later, Rater B reattached the IMUs, and the participants repeated the walking tests. During the second visit, one week later, Rater A again affixed the IMUs and instructed the participants to repeat the walking tests.

Data analysis

The gait cycle was time-normalized to 100 discrete points, with the cycle defined as beginning at the initial ground contact of one foot and ending at the subsequent contact of the same foot. For each participant, all outcome measures were calculated as the ensemble mean of 10 consecutive gait cycles.

Ground reaction force (GRF) was not used to identify gait cycle events due to equipment limitations and cost considerations. Instead, gait events were determined using a marker-based kinematic method within the optical motion capture (OMC) system. This method has been widely applied in gait analysis and aligns with previous studies that have proposed kinematic algorithms for gait event detection [27, 28]. Marker-based trajectory data for the hip, knee, and ankle joints were processed using Visual3D software (C-Motion Inc.). The events of right foot contact (RON) and right foot off (ROFF) were determined by analyzing the vertical velocity of the right heel marker relative to the posterior superior iliac spine marker. RON was defined as the moment the vertical velocity of the right heel transitioned from negative to positive, marking initial ground contact. ROFF was defined as the transition from positive to negative velocity, indicating the moment the right foot left the ground. These transitions were identified by calculating the first difference of the vertical velocity signal and detecting sign changes. IMUs kinematic data were processed using the iSen software (2023 version, Spain), which automatically computed joint angles based on embedded algorithms. Data synchronization between the IMUs and the optical motion capture system was achieved through an external synchronization module that ensured simultaneous data collection at a sampling rate of 100 Hz [15]. To correct systematic discrepancies of joint angle waveforms between systems, an offset correction was applied by computing the mean difference in joint angles over the entire gait cycle and subtracting this offset from the IMU-derived signals [17, 29].

Key discrete parameters were also extracted for analysis, including foot strike angles, maximum angles, minimum angles, and range of motion (ROM) for the hip, knee, and ankle joints across the stance phase, swing phase, and entire gait cycle.

Statistical analysis

Statistical analyses were conducted using MATLAB (Version 2021a; MathWorks Inc., Natick, MA, USA). Demographics data was presented as mean ± standard deviation (SD), Shapiro-Wilk test was used to assess normality distribution of data.

For waveforms consistency, the Coefficient of Multiple Correlation (CMC) was used to assess the similarity in waveform patterns [17, 29, 30]. CMC values quantified the similarity of waveform patterns, interpreted as weak (< 0.65), moderate (0.65–0.75), good (0.75–0.85), very good (0.85–0.95), and excellent (≥ 0.95) [17]. CMC was calculated both before and after offset correction during validity analysis. Systematic Error (SE) was computed to represent the average deviation between the waveforms, offering insight into the systematic differences between time-series joint angles. To assess the statistical significance of differences in joint angle waveforms before and after offset correction, we employed Statistical Parametric Mapping (SPM) analysis using SPM1D in MATLAB.

For discrete parameters, such as peak joint angles and range of motion, Pearson’s correlation coefficient (r) was used to assess the trend consistency between IMUs-based and OMC-based measurements, as it quantifies the strength of the linear relationship between the two systems. Additionally, intraclass correlation coefficients (ICC) were computed to evaluate the absolute agreement between the two systems. Correlations were categorized as 0 ~ 0.19 very weak; 0.2 ~ 0.39 weak; 0.4 ~ 0.59 moderate; 0.6 ~ 0.79 strong; 0.8 ~ 1.0 very strong, and RMSE quantified the average magnitude of errors. Reliability analyses focused on both between-raters (raterA1 versus rater B1) and within-raters (raterA1 versus rater A2) consistency. Intra-class correlation coefficients (ICCs) with 95% confidence intervals (95% CI) were calculated using a two-way random single-measure model. ICCs were classified as poor (0–0.49), moderate (0.50–0.749), good (0.75–0.899), and excellent (≥ 0.90). In addition, root mean square errors (RMSE) were also computed to quantify the difference in discrete parameters during both validity and reliability analysis.

In addition, lower extremity joint angle waveforms which performed good in both validity and reliability analysis, were compared across fall risk (low fall risk vs. high fall risk) and walking speeds (normal vs. fast vs. slow) with a continuous 2-way analysis of variance through statistical parametric mapping (SPM). The significant level was set at p-value < 0.05.

Results

Demographics

As shown in Table 1, a total of 45 older adults were recruited. Among them, 22 individuals were categorized as “Low Fall Risk”, 23 individuals were categorized as “High Fall Risk”. As shown in Table 1, the TUGT durations (p = 0.005, 95%CI: -5.225, -1.036) and number of fall(s) history (p = 0.005, 95%CI: -2.208, -1.925) of high fall risk older adults were larger significantly than low fall risk. In other demographic indicators, there was no significant difference between the two groups.

Table 1 Participants’ characteristics

The walking speeds measured under different conditions are summarized in Table 1. For normal walking velocity, the low fall risk group averaged 1.20 ± 0.16 m/s, compared to 1.17 ± 0.20 m/s for the high fall risk group (p = 0.044, 95%CI: 0.392, 28.903). During fast walking, the respective speeds were 1.46 ± 0.13 m/s and 1.35 ± 0.22 m/s (p = 0.003, 95%CI: 7.934, 36.233). In slow walking conditions, the speeds were 0.99 ± 0.14 m/s and 0.94 ± 0.16 m/s (p = 0.047, 95%CI: 0.169, 24.270) for the low and high fall risk groups, respectively. These findings indicate that the high fall risk group exhibited significantly slower walking speeds across all tested conditions.

Validity analysis

Joint angle waveforms

As shown in Figs. 2, 3 and 4, the CMC values of the joint angle waveform of the two measurement systems showed similar trends under different walking speeds. Before offset correction, very good validities were shown for the hip joint across all speeds in sagittal plane (low fall risk: CMC = 0.925–0.946, high fall risk: CMC = 0.933-0950) and knee joint waveform (low fall risk: CMC = 0.915–0.949, high fall risk: CMC = 0.957–0.966), while good validity for the ankle joint waveform (low fall risk: CMC = 0.829–0.846, high fall risk: CMC = 0.843–0.847). After offset correction, very good to excellent CMC for all joints across all speeds in the sagittal plane (low fall risk: CMC = 0.872–0.957, high fall risk: CMC = 0.894–0.974) (Figs. 5, 6 and 7).

Fig. 2

Joint angle waveforms during gait cycle measured by the inertial measurement units before offset correction and optical reference system at normal walk speed for both low and fall risk older adults

Fig. 3

Joint angle waveforms during gait cycle measured by the inertial measurement units before offset correction and optical reference system at fast walk speed for both low and fall risk older adults

Fig. 4

Joint angle waveforms during gait cycle measured by the inertial measurement units before offset correction and optical reference system at slow walk speed for both low and fall risk older adults

Fig. 5

Joint angle waveforms during gait cycle measured by the inertial measurement units after offset correction and optical reference system at normal walk speed for both low and fall risk older adults

Fig. 6

Joint angle waveforms during gait cycle measured by the inertial measurement units after offset correction and optical reference system at fast walk speed for both low and fall risk older adults

Fig. 7

Joint angle waveforms during gait cycle measured by the inertial measurement units after offset correction and optical reference system at slow walk speed for both low and fall risk older adults

The hip joint angle waveforms in the frontal plane showed weak to moderate correlations between the two systems across different speeds (before offset correction: low fall risk: CMC:0.589–0.705, high fall risk: CMC = 0.567–0.589; after offset correction: low fall risk: CMC:0.684–0.767, high fall risk: CMC = 0.611–0.633). In both frontal and transverse planes, the CMC values of other joint angle waveforms between the two systems were weak, which indicates that there was obvious variability between the two systems both before and after offset correction.

The SE values of all joint angle waveforms in the sagittal plane across different walking speeds were slightly reduced (Figs. 2, 3, 4, 5, 6 and 7) (before offset correction: low fall risk: 5.6°-10.3°, high fall risk: 5.4°-7.6°; after offset correction: low fall risk: 4.8°-9.6°, high fall risk: 4.5°-6.9°). The SE values of all joint angle waveforms in the frontal plane before the offset correction were in the ranges of 4.4°-6.8° and 4.301°-7.7° in low and high fall risk individuals, after offset correction, they were in the ranges of 4.1°-6.1° and 4.5°-6.8°, respectively.

The results of the SPM analysis revealed that joint angle waveforms before and after offset correction exhibited significant differences in specific phases of the gait cycle (p < 0.05). Additional File 1 presents the SPM statistical maps, with significant regions (p < 0.05) highlighted by shaded regions.

Discrete parameters

After offset correction, the correlation coefficients (r values) and ICCs of discrete parameters between the IMUs and OMC systems improved slightly across all joints and planes, with the sagittal plane consistently demonstrating the highest agreement (Additional file 2–3). For the hip joint, correlations ranged from moderate to strong in the sagittal plane (0.469–0.877), while lower agreement was observed in the frontal (0.316 to 0.704) and transverse planes (0.346–0.835). Slow walking velocities produced the highest correlations for the hip joint, particularly in the sagittal plane, where r values reached up to 0.877. Similarly, for the knee joint, moderate correlations were observed in the sagittal plane (0.363–0.924), with the frontal and transverse planes showing slightly lower but comparable ranges (0.329–0.781 and 0.379–0.838, respectively). The ankle joint followed a similar pattern, with the sagittal plane displaying the strongest correlations (0.420–0.831) and the frontal and transverse planes exhibiting more variability. Notably, slow velocities resulted in stronger agreement across most conditions, with the frontal plane for the ankle joint achieving correlations as high as 0.817 under this condition. Notably, ROM parameters showed the highest correlation in the sagittal plane for hip joint (r = 0.749–0.763), whereas for the ankle joint, ROM in the sagittal plane reached r = 0.702–0.752, indicating strong agreement even across varying walking velocities.

The Root Mean Square Error (RMSE) analysis also demonstrated slight improvements after offset correction (Additional File 1). For the hip joint, RMSE values decreased from ranges of 3.3°–9° (sagittal), 2.9°–6.3° (frontal), and 3.2°–11.7° (transverse) before correction to 3.2°–8.4° (sagittal), 3°–6.1° (frontal), and 3.9°–9.4° (transverse) after correction. For the knee joint, RMSE values decreased from 5.2°–10.5° (sagittal), 4.5°–7.6° (frontal), and 5.6°–9.8° (transverse) before correction to 4.5°–9.6° (sagittal), 3.7°–6.4° (frontal), and 4.5°–8.6° (transverse) after correction. For the ankle joint, RMSE values decreased from 3.8°–7.6° (sagittal), 5.3°–8.8° (frontal), and 3.9°–8.7° (transverse) before correction to 3.4°–5.9° (sagittal), 4.8°–8.2° (frontal), and 3.2°–6.9° (transverse) after correction.

Reliability analysis

Joint angle waveforms

As shown in Figs. 8, 9 and 10, the CMC values of joint angle waveforms across different walking speeds in the sagittal plane showed vary good to excellent reliability (within-raters: low fall risk: CMC = 0.924–0.982, high fall risk: CMC = 0.914–0.974; raterA1-rater B1: low fall risk: CMC = 0.953–0.981, high fall risk: CMC = 0.903–0.985). In the frontal and transverse plane, the reliabilities of joint angle waveforms were generally moderate to good (within-raters: low fall risk: CMC = 0.599–0.802, high fall risk: CMC = 0.616-857;between-raters: low fall risk: CMC = 0.608–0.936, high fall risk: CMC = 0.601–0.908), except for the knee joint in the frontal plane (within-raters: low fall risk: CMC = 0.393–0.564, high fall risk: CMC = 0.318–0.468;between-raters: low fall risk: CMC = 0.652–0.708, high fall risk: CMC = 0.604–0.684).

Fig. 8

Joint angle waveforms during gait cycle measured by the inertial measurement units in both within-raters and between-raters comparisons at normal walk speed for both low and fall risk older adults

Fig. 9

Joint angle waveforms during gait cycle measured by the inertial measurement units in both within-raters and between-raters comparisons at fast walk speed for both low and fall risk older adults

Fig. 10

Joint angle waveforms during gait cycle measured by the inertial measurement units in both within-raters and between-raters comparisons at slow walk speed for both low and fall risk older adults

The SE values of joint angle waveforms in the sagittal plane across different speeds were in the ranges of 2.2°–6.5° (within-raters: 3.9°–6.5°; between-raters:2.2°–5.9°) and 1.0°–2.5° (between-rater: RMSE = 1.0°–2.5°; between day: RMSE = 1.7°–2.2°) for all joints in low fall risk and high fall risk individuals, respectively.

Discrete parameters

Additional File 4 presents results from the ICCs of discrete parameters for the between-raters and within-raters reliability. For discrete parameters, the within-raters reliability across different walking velocities was moderate to excellent (Hip: ICC = 0.741–0.927; knee: ICC = 0.719–0.919; ankle: ICC = 0.669–0.889) in the sagittal plane, poor to good (Hip: ICC = 0.165–0.827; knee: ICC = 0.061–0.606; ankle: ICC=-0.055-0.812) in the frontal plane and poor to good (Hip: ICC = 0.455–0.834; knee: ICC = 0.562–0.807; ankle: ICC = 0.571–0.843) in the transverse plane. Additionally, the between raters reliability across different walking velocities was poor to excellent (Hip: ICC = 0.416–0.942; knee: ICC = 0.548–0.925; ankle: ICC = 0.482–0.936) in the sagittal plane, moderate to excellent (Hip: ICC = 0.668–0.947; knee: ICC = 0.562–0.807; ankle: ICC = 0.863–0.943) in the frontal plane and poor to excellent (Hip: ICC = 0.54–0.949; knee: ICC = 0.367–0.922; ankle: ICC = 0.483–0.952) in the transverse plane.

Additional File 5 presents results from the RMSE of discrete parameters for the between-raters and within-raters reliability. For the hip joint, RMSE values were in the ranges of 4.0°–7.2° (sagittal), 3.0°–6.2° (frontal), and 3.5°–7.2° (transverse) for within-raters comparisons; 2.1°–8.4° (sagittal), 1.7°–3.9° (frontal), and 2.3°–6.8° (transverse) for between-raters comparisons. For the knee joint, RMSE values were in the ranges of 3.8°–7.5° (sagittal), 2.8°–8.8° (frontal), and 4.6°–6.3° (transverse) for within-raters comparisons; 3.3°–8.0° (sagittal), 2.5°–5.8° (frontal), and 2.8°–7.4° (transverse) for between-raters comparisons. For the ankle joint, RMSE values were in the ranges of 2.6°–5.8° (sagittal), 3.2°–8.6° (frontal), and 4.8°–6.9° (transverse) for within-raters comparisons; 2.2°–5.7° (sagittal), 2.4°–4.7° (frontal), and 2.9°–7.2° (transverse) for between-raters comparisons.

Comparisons among fall risk and walking speeds

Since IMUs has been confirmed in the above results to have good reliability and validity performance on the sagittal plane in measuring the lower limb joint angle at different speed in the two groups of people, we only analyzed the main effect and interaction of sagittal speed * fall risk. As shown in Fig. 11 (A), SPM analysis results showed that fall risk had a significant main effect on hip/knee/ankle joints (F values for hip/knee/ankle joints = 7.190/8.183/8.371, all p values < 0.05), post-analysis showed that compared with the low fall risk group, the elderly in the high fall risk group had a smaller hip flexion/extension angle in the gait cycle of 3.9–27.2%, 55.5–64.7%, respectively, a smaller knee flexion angle in the gait cycle of 11.2–33.0%, and 89.1–91.5%, a smaller ankle plantarflexion angle in the gait cycle of 64.5 to 78.7%. As shown in Fig. 11 (B), walking speed also had significant main effects on hip, knee and ankle joints (F values for hip/knee/ankle joints = 5.017/5.581/5.686, all p values < 0.05). Post-analysis showed that compared with slow walking, fast walking had greater hip extension angle at the gait cycle of 38.1-67.7%, greater knee flexion angle at the gait cycle of 0-32.4%, greater ankle dorsiflexion angle at the gait cycle of 0–45.0%, 88.6-99.0%, and greater ankle plantar flexion angle at the gait cycle of 54.4-64.7%. In addition, compared with slow walking, normal walking had greater ankle dorsiflexion/plantar flexion angles in the gait cycle of 0-37.2% and 92.2–99.0%, respectively. Compared with normal speed walking, fast walking had a greater angle of ankle dorsiflexion at 11.5–13.0%. At each joint angle, no significant fall risk * speed interaction was found. (F values for hip/knee/ankle joints = 5.017/5.581/5.686, all p values > 0.05).

Fig. 11

(A) Joint angle waveforms comparisons between low and high fall risk individuals (mean [SD]). (B) Joint angle waveforms comparisons among normal, fast and slow walk speeds (mean [SD]). The gray shadows represent significant differences in joint angle waveforms among different walking speeds/fall risks groups

Discussion

This study demonstrated that IMUs provide accurate and reliable measurements in the sagittal plane for lower extremity joint kinematics during walking, with strong waveform consistency and low systematic errors. However, IMUs exhibited limitations in the frontal and transverse planes, showing weaker correlations and higher errors for both joint waveforms and discrete parameters, particularly during swing phase. In addition, compared with low fall risk individuals, high fall risk elderly exhibited smaller joint angles in sagittal plane during specific gait cycles. Compared with slow walking speed, fast walking speed exhibited lager joint angles in sagittal plane. These findings suggest that IMUs are well-suited for clinical applications where sagittal plane kinematics are of primary interest, such as assessing gait patterns and monitoring rehabilitation progress, but caution is advised when interpreting data from the frontal and transverse planes.

Validity

This study provides a novel contribution by validating IMUs system for gait kinematics assessment against an OMC system across different walking speeds and fall risk levels. Unlike previous validation studies that primarily focus on young or healthy adults, our findings highlight the accuracy of IMUs in populations with varying fall risks, thereby providing a more targeted evaluation of the IMUs system’s applicability in fall risk assessment.

In terms of waveform consistency reflected by the CMC values, not surprisingly, the sagittal plane demonstrated strong agreement for the hip, knee, and ankle joints, both before and after offset correction in both groups. In both frontal and transverse planes, the CMC values of lower joint angle waveforms between the two systems in both groups were weak, which indicates that there was obvious variability between the two systems both before and after offset correction. In line with previous studies [14, 16, 17], the present findings confirmed again that IMUs provide reliable measurements in the sagittal plane. This is likely due to the larger range of motion and the stable movement patterns observed in this plane during walking, where forward-backward accelerations and angular velocities predominate. IMUs, being particularly sensitive to these signals, capture and process sagittal movements with higher fidelity. Conversely, the frontal and transverse planes involve smaller and more complex joint movements, which are more prone to soft tissue artifacts, sensor misalignment, and external interferences, leading to lower CMC values. Although algorithmic optimization has improved accuracy in these planes to some extent [31], challenges remain in capturing the subtle and rapid transitions that characterize frontal and transverse joint rotations.

The results of the SPM analysis revealed that joint angle waveforms before and after offset correction exhibited significant differences in specific phases of the gait cycle. This suggests that offset correction meaningfully altered joint kinematics in certain gait phases, which may be attributed to sensor misalignment or soft tissue artifacts before correction.

In this study, we found that the systematic error (SE) ranged from 4.4° to 10.3° before offset correction and decreased to 4.1° to 7.9° after correction. Although most previous studies [32] suggest that an acceptable error range is approximately 5°, our findings align with other studies reporting slightly higher residual errors for IMUs, even after offset correction. For instance, Blanco-Coloma et al. [14] reported post-correction RMSEs of 6.28° for the hip joint and 4.26° for the ankle joint, highlighting persistent discrepancies despite corrections. A 7.9° error in joint kinematics may appear substantial in the context of a full gait cycle. However, it is important to note that this level of discrepancy falls within the range reported in previous IMUs validation studies and is likely influenced by soft tissue artifacts, sensor placement variability, and individual movement characteristics. These factors contribute to misalignment between the IMUs sensor axes and the anatomical reference frames, leading to measurement discrepancies, as also noted by Park and Yoon [33]. Additionally, the assumption of a neutral posture during static calibration can introduce residual errors if participants deviate from the assumed posture.

Despite these challenges, it is crucial to consider the clinical significance of such errors. Moderate discrepancies may still be acceptable for assessing broader gait characteristics in clinical and real-world settings, where optical motion capture is often impractical. For example, Ferrari et al. [17], while validating the Outwalk protocol, observed that post-correction errors in hip, knee, and ankle joint flexion-extension angles decreased substantially, with CMC values exceeding 0.88, aligning with the reduction trend seen in our SE values. Similarly, Nüesch et al. [34], comparing the RehaGait system with the Vicon optical system, reported post-correction RMSEs below 5° for walking and below 8° for running, confirming the clinical validity of IMUs. Thus, while a 7.9 ° error in joint angles is larger than the ideal threshold, it remains within an acceptable range for IMUs-based gait analysis, particularly when considering fall risk assessment, real-world applications, and the trade-off between practicality and precision. IMUs continue to be valuable tools for capturing overall gait patterns and detecting deviations associated with fall risk, especially in scenarios where gold-standard optical motion capture is not feasible.

Additionally, we observed an interesting phenomenon: older adults at a high risk of falling tend to exhibit slightly higher CMC and lower SE values, particularly in the sagittal plane, when comparing joint angle curves measured by IMUs to those from an OMC system. We believe this trend may reflect the fact that individuals at a higher risk of falling often walk at slower speeds compared to their lower-risk counterparts. This reduced speed could potentially lead to more precise joint angle measurements, as slower movements might allow for finer control and less variability in movement paths. However, it is important to note that the differences in CMC and SE between the two groups are relatively small. Given these subtle differences, whether they carry clinical significance remains uncertain and requires further investigation.

As for discrete parameters, IMUs demonstrated generally strong correlations and relatively low RMSE values with the OMC system for sagittal plane ROM during the stance, swing, and entire gait cycle after offset correction. However, the validity of IMUs varied depending on the type of discrete parameter. Consistent with Zeng et al. [15], our findings confirmed that sagittal plane ROM parameters showed significantly smaller differences between IMU-based and optical motion capture (OMC) systems than other discrete parameters. This suggests that IMUs can effectively capture joint ROM in the sagittal plane, supporting their potential for real-world clinical applications.

In contrast, the correlations between IMUs and the OMC system were generally weaker (ranging from weak to moderate) for foot strike and peak joint angles, especially during the swing phase. This discrepancy may be due to the challenges IMUs face in capturing rapid motion changes, particularly at critical turning points where joint velocity and acceleration fluctuate sharply [35]. Since IMUs rely on sensor fusion algorithms to estimate angular changes, these rapid transitions may introduce inaccuracies. Additionally, the weaker performance during the swing phase compared to the stance phase can be attributed to sensor stability. During stance, IMUs remain relatively stationary, enabling more reliable gravity-based angle estimations. Conversely, the swing phase involves more dynamic and complex accelerations, increasing noise and measurement errors [33].

Beyond the sagittal plane, IMUs exhibited only weak to moderate correlations with the OMC system in the frontal and transverse planes, aligning with previous studies [15, 36]. This may be due to larger errors in IMUs-based estimations of rotational movements. Notably, IMUs showed higher correlations with the OMC system during slow walking compared to normal and fast walking. Slow walking involves more stable gait patterns, reducing measurement noise and improving IMU accuracy. This trend is consistent with prior research [16, 36], which also observed better IMU performance at lower gait speeds.

Reliability

As for reliability analysis, the consistency of joint waveforms was found to vary across different planes. In the sagittal plane, both within-raters and between-raters assessments demonstrated good to excellent consistency in both groups. For the frontal plane, the within-raters consistency was weak to moderate in both groups, while the between-raters consistency ranged from weak to good in both groups. In the transverse plane, moderate to good consistency was observed for both between-raters and within-raters comparisons. The good reliability reported in the sagittal plane confirmed that the STT system was quite robust for the measurement of joint kinematics in the sagittal plane of the lower extremity during gait for older adults [15]. In addition, The RMSE between joint angle waveforms was less than 5° under mostly conditions in all planes, which was supported by previous studies which demonstrated that within-session reliability of IMUs-measured gait angles was clinically acceptable (standard error of measurement [SEM] < 5°) [16].

Additionally, the reliability of discrete joint parameters assessed using ICCs and RMSEs demonstrated consistent trends across within-rater and between-rater comparisons. Specifically, both comparisons showed moderate to excellent reliability in the sagittal plane (Hip: ICC = 0.741–0.942; Knee: ICC = 0.719–0.925; Ankle: ICC = 0.669–0.936). Correspondingly, the RMSE values for the sagittal plane were generally lower, ranging from 2.1° to 8.4°, indicating that IMUs can capture joint angles and range of motion with relatively high accuracy. These results are consistent with the findings of [16], which reported strong sagittal plane reliability (ICC ≥ 0.90) during gait task. The predominance of flexion-extension in the sagittal plane likely reduces the complexity of the motion, making it less sensitive to sensor misalignment and noise interference.

However, reliability was notably lower in the frontal and transverse planes, where ICCs ranged from poor to good, and RMSE values were higher, particularly for the knee and ankle joints. Similar limitations were observed in previous research [15, 16], where greater errors occurred in non-sagittal planes due to smaller range of motion and higher susceptibility to soft tissue artifacts, sensor placement variability, and complex multi-directional accelerations. Collectively, our findings highlight that while IMUs offer robust and reliable measurements in the sagittal plane, challenges persist in the frontal and transverse planes due to complex motion patterns, sensor limitations, and artifacts. Nonetheless, the absence of significant differences in SPM analysis and the strong CMC values in the sagittal plane underscore the utility of IMUs for gait assessment in older adults, particularly for applications where sagittal plane kinematics are of primary interest.

The present study demonstrates that IMUs provide valid and reliable measurements for sagittal plane joint kinematics across walking velocities, making them suitable for real-world gait analysis and clinical settings. Given their portability, cost-effectiveness, and ease of use, IMUs hold significant potential for large-scale gait assessments, particularly in community-dwelling older adults. These systems can facilitate longitudinal monitoring of gait patterns, early detection of gait impairments, and targeted interventions to reduce fall risks. However, caution should be exercised when interpreting measurements in the frontal and transverse planes. Future advancements in sensor fusion algorithms, calibration techniques, and real-time motion correction may further improve the accuracy and reliability of IMUs in these planes.

Comparisons among fall risk and walking speeds

This study provides novel insights by evaluating gait kinematics across different fall risk groups and walking speeds through IMUs system. By highlighting these distinct gait kinematics characteristics, our study provides perspective on how IMUs-based assessments can be used to detect subtle gait deviations that may contribute to fall risk, paving the way for early fall risk measurement. Consistent with hypothesis, significant fall risk and walking speed main effects were found in lower extremity joint angles. Compared with low fall risk individuals, high fall risk elderly exhibited smaller joint angles in sagittal plane during specific gait cycles. Compared with slow walking speed, fast walking speed exhibited lager joint angles in sagittal plane. The observed differences in joint kinematics suggest that individuals at higher fall risk exhibit altered movement strategies, potentially as compensatory adaptations to maintain balance. These interesting findings align with existing theories on fall mechanisms, which propose that gait modifications—such as reduced hip extension, altered step timing, and increased variability—may contribute to fall susceptibility [37, 38].

Despite the promising results, several limitations should be acknowledged. First, the study relied on static calibration, which may have introduced alignment errors. Future studies should explore dynamic calibration protocols to enhance measurement accuracy. Second, the sample consisted of older adults, and the generalizability of the findings to other populations, such as individuals with gait disorders, remains unclear. Finally, the use of different walking velocities provides valuable insights, but additional functional tasks (e.g., stair climbing or turning) should be included to comprehensively evaluate IMUs’ performance in capturing complex motion patterns. Future research should also investigate the integration of machine learning algorithms to improve IMUs-based kinematic estimations, particularly in the frontal and transverse planes. Additionally, combining IMUs with other sensor modalities, such as force plates or electromyography (EMG), may provide a more holistic understanding of gait biomechanics in clinical populations.

Conclusions

Overall, this study demonstrates that IMUs are an accurate and reliable tool for assessing lower extremity kinematics in both low- and high-fall risk older adults across various walking speeds. However, caution is needed when interpreting data from the frontal and transverse planes. High fall risk individuals exhibited reduced joint angles in specific gait cycles, while faster walking speeds were associated with increased joint angles.