A novel evaluation system for arthrokinematic ankle motion using a rotary encoder

doi:10.21203/rs.3.rs-2985794/v1

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A novel evaluation system for arthrokinematic ankle motion using a rotary encoder

https://doi.org/10.21203/rs.3.rs-2985794/v1

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Ankle joint control is considered important for walking. The relationship between the kinematic indices and neurophysiological indices that reflect neuromuscular control of the lower extremity by upper motor centres must be evaluated to capture the essence of ankle joint control and construct rehabilitation. Herein, we developed the articulation motion assessments system (AMAS) to measure both these indices synchronously. The aim of this study was to validate the validity and reliability of the AMAS’ ankle kinematics analysis. This study included 14 heathy adults. AMAS, a reflective marker and inertial sensor was attached to their right foot, and they performed different ankle joint tasks, such as dorsiflexion, plantarflexion, inversion, and eversion with subjective maximum and mild angular movements. Each task was performed randomly under two conditions; comfortable and slow speeds.

Two-dimensional motion analysis and the AMAS had moderate-to-high correlation. The mean root mean square error (RMSE) was significantly lower than those of inertial sensor. The repeatability of the AMAS was better than 0.76 for intraclass correlation coefficients (3,1) and (3,k). However, the Bland-Altman analysis showed fixed errors.

Errors should be considered when comparing measurement methods. Synchronised kinematic and neurophysiological measurements should elucidate ankle joint control mechanisms and improve rehabilitation.

Health sciences/Health occupations

Health sciences/Medical research

Physical sciences/Engineering

Human walking is a uniquely acquired upright bipedal gait utilised in daily activities [1]. Walking maintains functional independence [2] and quality of life [3]. Walking speed is a gait performance index, and the clinical evaluation includes walking symmetry and stride length [4, 5]. Ankle joint control regulates walking speed [6–8]. This ankle joint coordinates the relative timing of ankle joint torque exertion and angular displacement in changes in walking velocity [9]. It encompasses the multifaceted elements of "the so-called movement itself" in kinematics and "its underlying neural mechanisms" in neurophysiology. However, the evaluation of ankle joint control has been limited to one aspect of kinesiology and kinetics [10, 11] and neurophysiology [12] using electroencephalography and electromyography. Muscle synergies [13], which involve cooperative muscle activities of multiple muscles, degrade and control movement.

Additionally, neuromuscular control of lower extremity by the upper motor centre (hereafter referred to as ‘lower-extremity muscle control’)[12, 14] influences muscle synergies. Understanding that lower-extremity muscle is being controlled by a nervous system-based motor control mechanism [15, 16], clarifies the neural mechanisms of movement disorders to capture the control mechanisms of various motor components [17, 18, 19]. Cortical-muscular coherence, a neurophysiological index for capturing neural mechanisms in lower-extremity muscle control, correlates brain activity with muscle activity [14]. It is a biomarker for movement disorders that may be used in rehabilitation therapy [20]. However, in clinical application, cortical-muscular coherence on the affected side must be accurately classified by determining its relationship to movements hampered by ageing or disability and to better understand its impact on movement disorders [21]. Therefore, neurorehabilitation for ankle joint control requires elucidating human walking ability using neurophysiological indices of lower-extremity muscle control. Due to its anatomical structure, foot motion is a simultaneous and complex multi-axis movement [22]. Large individual differences exist with some resulting in altered motion on the forefoot plane [23, 24]. Therefore, we hypothesised that a new lower-extremity muscle control evaluation method might combine kinematic and neurophysiological indices to capture ankle joint control, which is important for gait.

This hypothesis requires synchronous joint motion, activity, and brain activity measurements. A new system is required to measure ankle joint control kinematic and neurophysiological indices and determine the relationship between each index. Electroencephalography (EEG) and electromyography (EMG) use noninvasive scalp or skin electrodes for neurophysiological analysis that can be monitored remotely [25]. Three-dimensional motion analysis (3DMA) using optical motion capture with markers is the gold standard for kinematic analysis of walking and lower limb motion [26]; despite being expensive and requiring dedicated space [27]. It is also time-consuming and highly dependent on the evaluator’s skill and experience, as it requires manual identification of specific anatomical indicators captured by multiple videos [28]. The accuracy of joint angle measurements is affected by the measurement technique, environment, and specifications and number of cameras.[29]. Two-dimensional motion analysis (2DMA) that shows moderate correlation and high concordance with 3DMA [30] can identify kinematic features caused by disease [31] and is used in foot kinematic analysis [32]. However, capturing of optical motions using these markers requires video cameras and a restricted measurement environment.

Additionally, inertial sensor-based 3D motion analysers offer a simple method for outdoor measurement without a video camera. However, they have measurement errors due to magnetic field effects [33, 34]. A measurement method without magnetic sensors has been proposed; however, the magnetic sensor information is required during initial calibration [35], and an environment free from magnetic field effects is required. Therefore, establishing an evaluation method that integrates both kinematic and neurophysiological indices remains a challenge in terms of convenience and versatility in clinical applications. Even if evaluation of a walking prognosis is required, it is expected to be difficult for disabled persons with severe motor dysfunction sequelae due to brain function diseases.

We developed a rotary encoder-based ankle joint angle measurement system articulation motion assessment system (AMAS) to address the above clinical problems. This rotary encoder converts the mechanical displacement of rotation into an electrical signal and processes it to detect position, speed, and angle. It measures motor displacement in patients with Parkinson’s disease [36] and in wearable exoskeleton robots that support human movement [37]. This system can analyse the kinematics of dorsiflexion, plantar flexion, inversion, and eversion of the foot, without video camera image captures or magnetic sensors. Additionally, the system can synchronise with biological signal-processing equipment. Synchronised foot kinematic and neurophysiological analysis makes it possible to search for indices related to the results of these measurements. It may help to elucidate the ankle joint control mechanism, which is important for walking.

This study aimed to establish the foot motion task as a simple method of motion analysis using the newly developed AMAS and to confirm the validity, reliability, and reproducibility of this system by conducting a comparative validation with existing evaluations.

Fourteen healthy adults (two females) participated in the study, and none pulled out.

The time taken for each condition in the measurement task was 9.22±2.99 seconds (AVE±SD) in the comfortable condition and 13.64±6.60 seconds (AVE±SD) in the slow condition, with a significant difference (t=-8.28, p<0.001) and 95% confidence interval (CI): ([-5.49)- [-3.35]). It was confirmed that the joint angle data per measurement task extracted by each measuring device were non-normal using a normality test,(p<0.01).

１.Validity

１.１.Criterion Validity

Spearman's correlation analysis was used to compute the correlation coefficients between 2DMA, AMAS, and inertial measurement unit (IMU). In the sagittal plane angle, the correlation coefficient for the AMAS was ρ=0.53-0.77 (p<0.01). In the frontal plane angle, the correlation coefficient with 2DMA taken from the front was ρ=0.46-0.72 (p<0.01), and that with 2DMA taken from the back was ρ=-0.05-0.49 (p<0.01). However, in the sagittal plane angle the correlation coefficient for IMU was ρ=0.16-0.51 (p<0.01). In the frontal plane angle, the correlation coefficient for 2DMA taken from the front was ρ = -0.06 to 0.06 (p<0.01), and for 2DMA taken from the back, was ρ = 0.18 to 0.31 (p<0.01).

１.２．Root Mean Squared Error (RMSE)

The RMSEs of the AMAS and IMU for 2DMA were calculated. The mean RMSE in AMAS was 10.90 ± 2.93°[AVE± SD] for the sagittal plane angles. Of these, 10.41 ± 2.20° [AVE ± SD] were for the comfortable condition and 11.18 ± 3.38° [AVE ± SD] for the slow condition. However, in IMU, the RMSE was 17.30 ± 3.61° [AVE± SD]. Of these, 18.31±3.89° [AVE±SD] were for the comfortable condition and 16.34±4.37° [AVE±SD] for the slow condition. Thus, the RMSE of the AMAS in the sagittal plane angle was lower than that of the IMU.

In the frontal plane ankle joint inversion/eversion task, the mean RMSE with each measurement device for 2DMA viewed from the front was 13.44 ± 1.09° [AVE ± SD] for the AMAS. Of these, 13.43 ± 1.28° [AVE ± SD] for the comfortable condition and 13.43 ± 1.02° [AVE ± SD] for the slow condition. However, the RMSE for IMU was 32.00 ± 3.11° [AVE ± SD]. Of these, 34.49 ± 5.30° [AVE ± SD] were for the comfortable condition and 29.91 ± 1.93° [AVE ± SD] for the slow condition. The RMSE with each instrument for 2DMA viewed from behind was 13.68 ± 2.00° [AVE± SD]. Of these, 14.00 ± 1.92° [AVE ± SD] for the comfortable condition and 13.39 ± 2.07° [AVE ± SD] for the slow condition. However, the RMSE was 26.70 ± 2.54° [AVE ± SD] in IMU, 28.05 ± 3.62° [AVE ± SD] in the comfortable condition, and 25.39 ± 1.16° [AVE ± SD] in the slow condition. Thus, the RMSE of the AMAS at the frontal plane angle was lower than that of the IMU (Table. 1).

The RMSEs of the AMAS and IMU were significantly different in the t-test (p<0.01).

Table 2 shows the correlation coefficients ρ between 2DMA and AMAS, IMU, and RMSE for each motor task for each participant.

In the sagittal plane angle, the correlation coefficients between the AMAS and 2DMA ranged from ρ=0.54 to 0.96 (p<0.01) and RMSE ranged from 4.37°to 15.88°, indicating a more than moderate correlation in all participants. However, the correlation coefficients between IMU and 2DMA ranged from 0.20 to 0.94 (p<0.01), RMSE ranged from 6.28°to 31.23°. Participants I, M, and N were uncorrelated with 2DMA. Participant E showed a weak correlation, while participants J and L showed a negative correlation.

The correlation coefficient of the frontal plane angle with the 2DMA taken from the front with a high correlation coefficient was calculated for each participant. The correlation coefficients between the AMAS and 2DMA were ρ=0.26-0.95 (p<0.01). RMSE ranged from 13.07°-20.97°for the frontal plane angle, showing a weak correlation with 2DMA only for participant N and a moderate-to-high correlation for the others. However, the IMU ranged from ρ=0.06 to 0.80 (p<0.01) and the RMSE ranged from 9.89°to 52.64°, showing no correlation between participants E and I and a negative correlation between participants A and N.

２. Reliability

The intraclass correlation coefficient (ICC) (3,1)(3,k)[38] was used to evaluate repeatability. Five repetitions were treated as a fixed effect, and the ICC (3,1) was used to measure how consistently the same evaluator was able to measure the participant’s foot movement angle under the same conditions. The measured angle per foot movement task by the AMAS was above the ICC of 0.76 under all conditions (Table 3).

３. Consistency

Bland-Altman plots were constructed between the AMAS and IMU against 2DMA taken from the front with high values for the lateral and correlation coefficients in the foot dorsiflexion/plantarflexion and inversion/eversion tasks. The vertical axis (DIFF) is the difference between the 2DMA and AMAS or IMU, and the horizontal axis (MMEAN) is the mean between the 2DMA and AMAS or IMU. LOA is represents the range within which the difference between two measurements is acceptable as an error. Bland-Altman plots of sagittal plane angles in the dorsiflexion/plantarflexion task did not converge within the LOA for both instruments (Fig. 1-a).

The AMAS had a mean value of 1.26, and the LOA ranged from 23.58 to -21.07. However, the IMU had a mean of -1.82 and LOAs ranging from 30.00 to -36.54. The Bland-Altman plots of the frontal plane angle in the inversion/eversion task did not converge within the LOA for either instrument (Fig. 1-b).

For the AMAS, the mean difference between the two systems was 0.18, and the LOA ranged from 26.70 to -26.33. However, the IMU had a mean of -9.54 for the difference between the two systems, and the LOA ranged from 50.48 to -69.56. T-tests were used to confirm the presence of fixed errors. For each task, the AMAS and IMU for 2DMA were significantly different, with a two-tailed test with a probability of significance of <1% and 95% CI: (1.02 -1.49) for the AMAS and ([-2.19] –[-1.46]) for IMU for the sagittal plane angle, and ([-0.09] –[0.46]) for the AMAS and ([-10.16] –[-8.91]) for IMU for the frontal plane angle. A fixed error was suggested by the absence of 0 in the 95% CI, except for the angle of the frontal plane by the AMAS. Regression analysis was performed to confirm the presence of proportional errors. The probability of significance of the regression equation, with DIFF as the dependent variable and MMEAN as the independent variable, was <1% for all tasks for both measurement methods, indicating no proportional error.

We compared the reliability and validity of the AMAS, which uses kinematic and neurophysiological indices to capture ankle joint control important for walking, to existing kinematic analysis assessment systems.

Criterion validation showed a significantly greater than moderate correlation between the AMAS and 2DMA from the sagittal and anterior planes in all motor tasks and conditions without affecting joint angles and movement speed. The correlation coefficient values of 0-0.3 represent a weak correlation, 0.3–0.7 a moderate correlation, and 0.7-1.0 a strong correlation [39]. Therefore the present results revealed a more than moderate correlation. However, the IMU had no or a significantly low correlation with 2DMA. This suggests that the AMAS is more valid than the IMU for measuring the forefoot’s sagittal and forehead angles. Outliers and fixation errors are possible reasons for the lower measurement validity of the IMU over the AMAS, which may be due to magnetic effects. Biases exist in measurement systems, such as IMU, with an improved agreement with marker-based optical motion capture in the sagittal plane but larger errors in non-sagittal planes [40], and the differences vary among participants [41]. The position, calibration method, and measurement algorithm of common wearable sensors affect accuracy [42]. Electromagnetic interference makes IMUs unreliable indoors [43]. Therefore, measurements should be taken in a magnetically neutral environment [44]. This study was conducted in a laboratory, and the results are consistent with previous studies. The AMAS proved to be a highly versatile system for clinical use.

Regarding the regression model performance index validation results, the mean RMSE of the AMAS based on 2DMA was significantly lower than that of the IMU. However, the mean RMSE of the AMAS for the sagittal angle was 10.90° ± 2.93° (AVE ± SD) and 13.44 ± 1.09° (AVE ± SD) for the frontal angle. Each participant’s RMSE ranged from 4.37° to 15.88 for the sagittal angle and from 13.07° to 20.97°for the frontal angle, suggesting that large differences in measurement angles were observed and errors were introduced. Previous studies have advocated that IMU kinematics should be interpreted cautiously [40, 41] since the IMU must improve consistency and accuracy to replace marker-based optical 3D motion analysers, which are considered the gold standard. These results confirm the limitations of joint kinematics analysis using IMUs owing to the magnetic effects.

Regarding the results of the reliability validation, the AMAS’ repeatability of sagittal and forehead angles had an ICC value of ≥ 0.76 for all motor tasks and conditions. This suggests that the repeatability of measurements by the AMAS is better than that of the conventional method [38]. Because obtaining kinematic data from individuals using 3DMA with markers, the gold standard method, is costly and difficult, there is growing interest in a simple, inexpensive system with no local limitations [45]. The joint angles of foot motion measured by this system are comparable to those obtained using previous measurement methods. The system has been verified to be a highly convenient measurement device because it solves the problem of environmental restrictions. The system’s rotary encoder is a reliable and accurate sensor for measuring limb angles [46, 47]; however, it is often attached to a rigid mechanical attachment on the exoskeleton and is, therefore, unsuitable as a wearable device [48]. Therefore, the external dimensions of this system were designed to be compact enough to be worn on foot, increasing its versatility as a wearable device.

However, regarding the results of the agreement validation, the results of the Bland-Altman analysis showed that the differences between 2DMA and each of the measurement devices compared to 2DMA did not converge within the LOA, and no proportional error was found, but a fixed error was found; the differences between the 2DMA and AMAS were plotted upward in both the sagittal and forehead planes, indicating that 2DMA tends to measure at lower values than those associated with the AMAS. However, the difference between 2DMA and IMU was plotted downward in both the sagittal and forehead planes, suggesting that IMU measurements tend to be higher than 2DMA measurements. The clinically acceptable joint angle error in gait motion analysis is < 5° RMSE [49]. In this study’s measurements, the RMSE exceeded the clinically significant limit, although it differed from gait motion. This raises the concern that while this system’s ankle joint angles measurement can be used as a primary indicator, there may be some errors when comparing the foot motion analysis data from other motion analysis devices.

In rehabilitation, kinematic and kinetic quantification is necessary to measure sensory-motor recovery, and recovery of post-stroke patients requires assessment of motor quality using kinematic and kinetic measures to allow interpretation of neuroimaging results, rehabilitation, and recovery. A multidisciplinary team in collaboration with clinicians in the field is necessary to provide a diverse perspective [50]. The AMAS developed in this study measures foot motion from two aspects: the sagittal plane and the anterior frontal plane, and its high validity and good repeatability have been verified using the measurement results from 2DMA. Additionally, the velocity of ankle motion did not affect the system’s angular measurement. Poor joint angle changes, decreased velocity in various movements, and abnormal compensatory movements accompany movement in post-stroke patients. Kinematic movement analysis results are essential for distinguishing between motor recovery and compensatory movement patterns [50, 51]. Therefore, the results of this study suggest that this system has the potential to provide a clinical kinematic assessment of participants with various motor impairments, ranging from mild to severe, in the rehabilitation field.

In the future, a wired external output will allow the system can be connected to commercially available biological signal-processing equipment. This will enable the synchronous measurement of joint angle changes expressed through the body as ankle joint control and biological signals such as EEG and myopotentials as neuromuscular control. In recent years, combining neurophysiological methods with kinematic analysis alone has provided new insights into the treatment of disorders [52]. Therefore, this system contributed to developing a new evaluation method for neurorehabilitation by establishing itself as a more detailed evaluation method in clinical practice, implementing multifaceted kinematic, kinetic, and neurophysiological aspects of ankle joint control.

Because of convenience, versatility, and the ability of synchronous measurement with various biological signals, The AMAS was developed to provide a kinematic and neurophysiological assessment of ankle joint control, which is important for walking in rehabilitation settings and real-life environments. The fact that a fixation error occurred suggests room for improvement in this system. It is expected that, with future improvements against errors, clinical evaluation using this system will contribute to elucidating the mechanism of ankle joint control and developing individualised and optimised rehabilitation.

Participants

There were 14 participants (12 men and two women, age 22 ± 1 years, height 1.70 ± 0.06 m, weight 65.07 ± 14.81 kg). The inclusion criteria were an absence of cognitive problems, motor sensory dysfunction in the lower extremities, and visual impairment. The study was explained verbally and in writing, and the participants provided written informed consent before participating in the study. This study was approved by the Research Ethics Committee of Kyoto Tachibana University (Approval No. 22-13) and conducted in accordance with the Declaration of Helsinki.

Protocol

Herein, each measurement device was first attached to the patient before any measurement was taken. All tasks were performed sitting on a chair with a backrest one step above the floor. The measurement tasks consisted of automatic voluntary movements of dorsiflexion, plantar flexion, inversion, and eversion of the foot on one side. They were performed in two ranges of motion, the maximum range of motion, and mild range of motion, according to the participant’s subjective judgement. For each automatic voluntary movement, two conditions were set according to the participant's subjective movement speed: "movement at a comfortable speed (comfortable speed condition)" and "movement at a slow speed (slow speed condition). These conditions were set to verify whether it is possible to measure a wide range of participants with mild to severe disabilities since the range of joint motion is assumed to be narrow and patients with motor dysfunction have slow movement. Each participant was required to complete five consecutives measurement tasks. The measurement task sequence was randomised using a random number table. The chair-sitting position with both hands on the knees was comfortable. Each measuring device was calibrated simultaneously in the midfoot position. The foot position was kept distal to the heel, away from the step, to maintain freedom of foot motion. Because biomechanical and neurophysiological studies have shown that foot motion is not lateralised [53,54], the kicking foot was determined to be the dominant foot in the measurement and was used as the measurement limb. Each participant’s dominant foot was the right foot. Measurements were taken using a video camera. The centre of the video camera lens was positioned at the centre of the foot; therefore, the height was adjusted using a tripod, and the camera was positioned 1 cm from the front and rear and 1 m from the right side (Fig. 2-a).

Instrumentation

On one of the participant’s legs, an AMAS, reflective marker, and IMU sensor was attached (Fig. 2-b).

１．AMAS

This system is a joint angle measurement device that simultaneously measures the plantarflexion/dorsiflexion and inversion/eversion angles during ankle joint motion and consists of an ankle joint orthosis, controller, and operation application (Fig. 3-a).

The Ankle Joint Unit (Fig. 3-b) consists of two units with a built-in rotary encoder (manufactured by Supertech Electronic). One unit was attached to the outer lower leg, which served as the basic axis, and the other was to the dorsal foot (metatarsal head), which served as the moving axis.

A pipe connects both units, and plantar dorsiflexion movement is transmitted to the basic axis-side unit via the connecting pipe, causing the rotary encoder to rotate. Similarly, the basic shaft-side unit supported the connecting pipe, and the inversion/eversion motion of the foot was transmitted to the rotary encoder of the mobile shaft-side unit. The controller transmits the signal from the rotary encoder resulting from foot joint motion to the application (tablet). The application converts the signals into angles and displays in real time the changes in plantarflexion/dorsiflexion and inversion/eversion angles over time. The angle data were saved as a CSV file.

The system simultaneously extracts the dorsiflexion/plantarflexion and inversion/eversion angles (degrees) of the foot. The sampling rate was 50 Hz.

２． 2DMA

The reference motion capture was performed using the free 2DMA software Image J (NIH, USA) for 2DMA with reflective markers. Nine anatomical landmarks were selected according to the methods of previous studies: the fibular head, tibial tuberosity, posterior medial surface of the lower leg, medial anterior surface of the medial and lateral phalanges, lateral malleolus, first and fifth metatarsal heads, posterior calcaneus (CAL), and directly above it [55]. Reflective markers were attached to the skin using double-sided tape at selected landmarks. Two 30 bps digital high-definition video cameras (Panasonic, Japan) were used to capture images from the anterior and posterior sides for the frontal plane task and the right lateral side for the sagittal plane task during the measurement task. The video captured by the video camera was clipped at 30 Hz using the free video playback software GOM Player (Gretech, Korea). Each data point was then extracted and corrected every 0.14 seconds. Capture data were used to calculate joint angles from 2D coordinates using the free 2D motion analysis software ImageJ. The dorsiflexion/plantarflexion angle of the foot in the sagittal plane is the angle between the straight line connecting the fibular head and the external capsule and the straight line connecting the fifth metatarsal head and the external capsule. The inversion/eversion angle of the foot viewed from the anterior is the angle between the lower leg axis consisting of the centre of the medial and lateral phalanges and the tibial coarse surface and the plantar axis consisting of the first and fifth metatarsal heads, based on the "Methods for Indication and Measurement of Range of Motion of Joints.” The angle of inversion/eversion of the foot viewed from the posterior is the angle between the line passing from the centre of the lower leg through the centre of the Achilles tendon and the line connecting the two markers at the rear of the heel.

From the 2DMA with sagittal plane videos, joint angles (degrees) were extracted with the dorsiflexion direction as positive and the plantar flexion direction as negative. From the 2DMA of the frontal plane video, the joint angles (degrees) were extracted, with the inversion direction as positive and the eversion direction as negative.

３．Inertial Measurement Unit(IMU)

Two MyoMotion sensors (Noraxon USA Inc., Scottsdale, AZ, USA) were used as inertial measurement units (IMU). The tibial sensor was wrapped around the lower leg using an attached belt, and the dorsal foot sensor was attached to double-sided tape. The sampling rate was 100 Hz.

From the IMU, dorsiflexion/plantarflexion and internal/external return angles (degrees) of the foot were extracted using sensors placed across the ankle joint.

Data analysis

The synchro light at the start of the IMU measurement and the sensor mat light input to the AMAS were used to synchronise the data. After the beginning of the video recording, the synchro light at the start of the IMU measurement was used to synchronise the video camera and IMU. The starting point of all the data was then temporally synchronised by the sensor mat signal input after the start of the AMAS measurement, and the sensor mat light was captured by the video camera. Synchronously measured data were corrected to align the data points. The data to be analysed were the time (s) taken for each measurement task extracted by each measurement device, the maximum angle (°) per frequency, and the angle (°) five consecutive times.

The statistical software SPSS (version 27.0; IBM Corporation, Armonk, NY, USA) was used for statistical analysis. Corresponding t-tests were used to test the difference in time between comfortable and slow conditions in the measurement task. All data were subjected to the Kolmogorov–Smirnov test of normality. The feature extraction of the AMAS was statistically validated for validity, the performance of the regression model, and repeatability and agreement of the measurement method [56]. For validity, the correlation coefficients between the AMAS and IMU were calculated from the results of the two-dimensional motion analysis. RMSE (1) was calculated as the performance index of the regression model [57].

$$RMSE=\sqrt{\frac{\sum {\left(X\left(t\right)-Y\left(t\right)\right)}^{2}}{n}}\text{⑴}$$

The maximum value of each of the five repeatedly extracted angular data was used in the analysis to evaluate repeatability. A two-way mixed model by a single examiner of the ICC was used [58]. Bland-Altman analysis was used to confirm the presence of systematic errors in the overall data to evaluate the agreement between the measurement methods and the characteristics of the measurement methods using the margin of error (LOA)(2)[59].

$$LOA=mean of difference \pm 1.96 x standard deviation of difference \left(2\right)$$

The significance level was set at 5%.

Acknowledgements

This work was supported by JSPS KAKENHI Grant Number JP 22H03445.

Author contributions

H.I. and T.K. conceived the study. T.K. and H.Y. collected the data. H.I. designed and performed the statistical analysis. H.I. contributed to the interpretation of the results. H.I. prepared the original manuscript. T.K. oversaw the conduct of the study. H.Y. and T.K. were responsible for the development of the study. All authors reviewed the manuscript and revised it critically for intellectual content. All authors approved the final version of the manuscript for publication.

Competing interests

The authors declare no competing interests.

Data availability statement

All the relevant data are presented in the manuscript. All data are available from the authors upon request.

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Tables 1 to 3 are available in the Supplementary Files section.

No competing interests reported.

Table1.tif
Table 1. Spearman’s correlation coefficients, RMSE values for each assignment condition The table shows the correlation coefficient (ρ) and RMSE (°) for all assignment conditions for the AMAS and IMU with respect to the 2DMA.
Table2.tif
Table 2. Spearman’s correlation coefficient, RMSE values per participant The table shows the correlation coefficient (ρ) and RMSE (°) for each participant from A to N.
Table3.tif
Table 3. Reliability results The table shows the repeatability of measurement repetitions for all task conditions by AMAS by ICC (3,1) (3,5).

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A novel evaluation system for arthrokinematic ankle motion using a rotary encoder

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