Cross-Leg Prediction of Running Kinematics across Various Running Conditions and Drawing from a Minimal Data Set Using a Single Wearable Sensor

Abstract

The feasibility of prediction of same-limb kinematics using a single inertial measurement unit attached to the same limb has been demonstrated using machine learning. This study was performed to see if a single inertial measurement unit attached to the tibia can predict the opposite leg’s kinematics (cross-leg prediction). It also investigated if there is a minimal or smaller data set in a convolutional neural network model to predict lower extremity running kinematics under other running conditions and with what accuracy for the intra- and inter-participant situations. Ten recreational runners completed running exercises under five conditions, including treadmill running at speeds of 2, 2.5, 3, and 3.5 m/s and level-ground running at their preferred speed. A one-predict-all scheme was adopted to determine which running condition could be used to best predict a participant’s overall running kinematics. Running kinematic predictions were performed for intra- and inter-participant scenarios. Among the tested running conditions, treadmill running at 3 m/s was found to be the optimal condition for accurately predicting running kinematics under other conditions, with R² values ranging from 0.880 to 0.958 and 0.784 to 0.936 for intra- and inter-participant scenarios, respectively. The feasibility of cross-leg prediction was demonstrated but with significantly lower accuracy than the same leg. The treadmill running condition at 3 m/s showed the highest intra-participant cross-leg prediction accuracy. This study proposes a novel, deep-learning method for predicting running kinematics under different conditions on a small training data set.

1. Introduction

Running is one of the most popular recreational sports worldwide and is associated with various types of injuries. The estimated incidence of injuries in the lower limbs ranges from 19% to 79% among recreational runners [1]. Although the knee, thigh, and calf muscles are the most predominant sites of such injuries [2], the knee joint is the most frequently injured joint while running [3]. As the prevalence of such injuries is high, understanding lower-limb kinematics while running is critical and researchers need to look for various means through which these can be predicted and prevented.

Three-dimensional video-based motion analysis systems are regarded as the gold standard in gait and running kinematics analysis [4]. However, these systems need to be installed in a large laboratory setting that requires highly sophisticated and expensive equipment [5,6]. Such a system cannot be used to analyze kinematics in outdoor settings. Wearable sensor devices that can provide real-time data on human running patterns in actual running events present a feasible and preferable alternative to the motion analysis systems [7]. Magneto-inertial measurement units (MIMUs), comprised of gyroscopes, accelerometers, and magnetometers, have been used to measure joint angles, acceleration, and angular velocity [8,9,10,11]. The use of MIMUs for joint angle measurement during sports events has become common [5,10]. Studies have reported high reliability and validity for joint kinematic measurements in gait and running analysis, prediction, and estimation [12,13,14,15]. Wearable devices have also been shown to be useful for monitoring diabetes-related parameters and physical activity assessment for people with knee osteoarthritis [16,17]. Current literature highlights the need for more research employing such sensors for standardization, better reporting, and inclusion of other vulnerable populations.

These sensors can be attached to the subjects by straps, and the three-dimensional orientation of their body segments can be monitored with good accuracy [18]. Their sampling rate is very high, making them suitable for research. MIMU systems are commercially available for gait analysis and to quantify lower-limb kinematics; however, the subjects are required to carry several sensors. This can cause some degree of restriction in performance which is certainly not desirable while investigating kinematics during distance running. With the aim of reducing the number of sensors and associated restrictions, this study investigated if we can use just one wearable MIMU sensor to predict lower-limb kinematics.

Various studies have investigated the reliability and validity of MIMU-based systems compared to the marker-based motion-capture systems [19,20,21,22,23]. These studies indicate that MIMU-based systems are useful for calculating ranges of motion and determining spatiotemporal variables. Previous studies showed excellent agreement between the MIMU and motion-capture systems. It was also reported that in the sagittal plane, the root-mean-squared error and range-of-motion error were less than 1 degree between the two systems and the motion-capture system [20]. A high level of agreement in the pelvis-related angles in the sagittal plane was also noted between the two systems [22]. Among others, MyoMotion and IMeasureU inertial measurement units have been shown to have good relative reliability and validity. They are a practical and economical tool for assessing most of the body’s joints, especially for running-based team sports [24,25,26,27,28]. IMeasureU inertial measurement units have been reported to be a valid tool for analyzing peak velocity and average split velocities for sprint [29].

Several studies have used machine learning to augment sensor-data information [13,14,15,30]. Gholami et al. [5] formulated an innovative convolutional neural network (CNN) method to process data from a shoe-mounted sensor to predict lower limb running kinematics in the sagittal plane during treadmill running. Rhudy and Mahoney [31] showed that gyroscopes were more accurate than accelerometers in counting steps when placed on ankle-mounted wearable sensors. Similarly, Chow et al. [10] have reported that using a gyroscope is more effective than using an accelerometer when collecting data for use in a CNN model to predict lower extremity running kinematics. The feasibility of prediction of right-limb kinematics using a single MIMU attached to the right tibia using machine learning has also been demonstrated [10]. However, the feasibility of predicting opposite-limb kinematics using a single MIMU attached to another limb is unknown. The use of am MIMU attached to the right tibia to predict the kinematics of the left limb, that is, the opposite limb is known as cross-leg prediction. In addition to reducing the redundancy and cost, using a small number of sensors in joint kinematics measurement can increase the convenience provided by wearable sensors [30]. However, available data are less informative.

A complete understanding of the optimal and minimal training data sets for running kinematic predictions has yet to be attained. Therefore, this study aimed to (1) determine the optimal running condition for use as a minimal training data set to be processed by a CNN model to predict running kinematics in other running conditions and (2) investigate cross-leg predictions using a single MIMU with only using gyroscope measurements. This study’s results shall help develop a reliable prediction model using a smaller number of MIMUs and provide researchers with a more convenient, economical, and user-friendly method of studying kinematics in outdoor running and other sports.

2. Materials and Methods

2.1. Study Design

An observational study design for a cross-sectional study was used in this study.

2.2. Setting

This study was conducted in a university laboratory setting.

2.3. Participants

Ten recreational runners (five men and women, average age 22.7 ± 1.3 years, average height 168 ± 6.3 cm) were recruited for this study through a poster posted on the university campus. All the participants were injury-free at the time of the study and had no reported history of injury in the past six months. Each participant signed a written informed consent approved by the Human Research Ethics Committee of the university before data collection. The ethical approval number for the study is Ref. no. 2018-2019-0119.

2.4. Instrumentation

Two sets of MIMUs were attached to each participant, seven MyoMotion sensors for the lower extremities (Model 680, Noraxon Scottsdale, Arizona, USA Inc.) and a single IMeasureU sensor (Vicon IMeasureU Limited, Oxford, UK). The set of MyoMotion sensors was used to measure targeted joint kinematics in the sagittal plane, and the single IMeasureU sensor was used to capture gyroscope measurements, which were then processed by a deep-learning model. According to the manufacturers’ recommendations, the MyoMotion sensors were attached to the participants’ lower extremities with a belt or elastic straps on the pelvis, bilateral thighs, shanks, and feet (Figure 1). Angular displacements in the sagittal plane for the knees and hips were determined at 100 Hz. A single IMeasureU sensor was attached to the anteromedial side of the right tibia (Figure 1). The raw data were acquired at 500 Hz from the gyroscope built into the IMeasureU sensor. Three vertical foot strikes on each leg were performed at the beginning of each trial to synchronize the two systems [32].

2.5. Data Collection and Experimental Protocol

A written Physical Activity Readiness Questionnaire (PARQ-Q; Canadian Society for Exercise Physiology, 2002) was completed by all participants. Any participant who had any known anatomical abnormality was excluded from this study. Their age and anthropometric data (height and weight) were recorded. All the running trials were conducted on a treadmill in the laboratory or an indoor squash court. All the participants were instructed to wear self-selected attire and running shoes and not to participate in any rigorous physical activity for at least a day before each test. The sensors were then instrumented, calibrated, and synchronized.

For treadmill running trials, the participants were advised to warm up by jogging on the treadmill for 30 s at 1.5 m/s. After the warm-up, the treadmill speed was increased every 3 min at increments of 0.5 m/s from 2 to 3 m/s [5,10,33]. For the level-ground running trial, the participants were instructed to run at their preferred speed on an indoor squash court for 3 min (average speed 2.4 ± 0.3 m/s). The speeds of all the participants were measured using a timing system (Brower Timing Systems, Draper, UT, USA). The data acquired from the IMeasureU sensor were down-sampled to 100 Hz for data analysis.

2.6. Deep-Learning Regression

The deep-learning CNN model proposed by Gholami et al. [5] was used in this study. The target variable array Y, including values for the flexion and extension of the hip, knee, and ankle, was modeled by four one-dimensional convolutional (Conv 1D) layers. The first two layers had 50 filters followed by a pooling layer with 2:1 sub-sampling. The other two layers had 100 filters. Before being consolidated into Y with only three neurons, the outputs were flattened and fed into a dense layer with 100 neurons. A kernel size of 3 with a rectified linear unit and a stride value of 1 [34] was used to activate all layers except the regression output. The stochastic method stipulated by Adam [35] was used for optimization, with a batch size of 512 and a learning rate of 0.001 at 50 epochs to reach stable convergence. A Glorot normal initializer (Xavier normal initialize) [36] was used for weight initialization. A Python program with the Keras and Tensor flow packages was used for implementation.

The gyroscope measurements were used as the regressor as they were shown to be more accurate than the accelerometer measurements [10]. The resultant of the x- and z-components of the gyroscope that reflected the angular movements in the sagittal plane was used.

2.7. Evaluation

A CNN model was adopted to evaluate intra- and inter-participant scenarios in this study. Each participant’s full running data set comprised five data subsets, each collected under one of five conditions: treadmill running at 2.0 (C1), 2.5 (C2), 3.0 (C3), and 3.5 (C4) m/s and level-ground running (C5). In the intra-participant scenario, the data obtained under one of the five conditions for a single participant were used as training data. The data obtained under the remaining four conditions for the same participant were used as testing data.

In the inter-participant scenario, a leave-one-out scheme was used [5,10]. The data of nine participants were utilized for training the model. We then used the data of the tenth to test the model. These processes were repeated ten times, and each participant was assigned as the left-out participant once. The data set for each condition covered a period of 3 min. The data collected during the first and the last 15 s of running under each condition were disregarded as an ingress buffer to analyze the data in the steady-state. The data sets comprising data collected during the remaining 2.5 min of running under each condition were segmented into three data subsets, each covering 60, 60, or 30 s. The data collected during the first 60 s of running under each condition were extracted and concentrated as the training and testing data sets in data analysis.

2.8. Variables

To contrast the running data arrays (X) and the target variable (Y), five of the following parameters were calculated: the coefficient of determination (R²), root-mean-square error (RMSE), normalized-root-mean-square error (NRMSE), standard deviation (STD), and normalized standard deviation (NSTD). All the parameters were calculated in Python 3.7. R² was applied to all points of actual and predicted joint angles in the sagittal plane. RMSE was applied to data points at specific gait events, i.e., for peak flexion during stance for knee and peak flexion for hip. NRMSE normalized the RMSE with the overall range of data values. STD was calculated at points of specific gait events, i.e., for peak flexion during stance for knee and peak flexion for hip. NSTD was applied to all points of actual and predicted data values.

The average R² was used as an indicator to determine the goodness-of-fit of the model. The average RMSE and NRMSE indicated the differences between the predicted and actual values. The STD and NSTD indicated the amount of variation of the model. Figure 2 illustrates the peak angles used to evaluate the prediction’s accuracy.

2.9. Statistical Analysis

The average R² was calculated to determine the goodness-of-fit between the predicted and actual values. The average RMSE, NRMSE, STD, and NSTD were also calculated and compared. The coefficient of determination was calculated according to the formula of Schober et al. [37]. The normality of data was confirmed by the Shapiro–Wilk test. The effects of side (left and right) and condition (C1 to C5) on each parameter were investigated using a two-way repeated-measures analysis of variance (ANOVA). When there was a significant interaction between the side and condition factors, a one-way repeated-measures ANOVA test was conducted to compare the differences among the five conditions for each side, and a paired t-test was performed to compare the difference between the right and left sides for each running condition. The level of significance was set at p < 0.05. The Bonferroni correction was adopted for post-hoc comparisons.

3. Results

3.1. Intra-Participant Scenario

The results of various parameters for evaluating the intra-participant model for predicting bilateral hip- and knee-joint kinematics using a single MIMU attached to the right tibia using the data set of one of the running conditions are summarized in

Table 1. The various parameters for evaluating the accuracy of intra-participant predictions. * denotes significant differences between left and right sides with p < 0.05.

Intra-Participant Model							Pairwise Comparisons with p < 0.05
Running Condition		C1	C2	C3	C4	C5
		Mean (SD)	Mean (SD)	Mean (SD)	Mean (SD)	Mean (SD)
R2	Left hip	0.847 (0.093)	0.851 (0.166)	0.880 (0.076)	0.867 (0.111)	0.651 (0.252)	2–5, 3–5, 4–5
	Right hip	0.909 (0.049)	0.905 (0.081)	0.902 (0.043)	0.894 (0.058)	0.824 (0.095)	1–5
	Left knee	0.893 (0.034)	* 0.934 (0.032)	0.935 (0.033)	0.879 (0.088)	* 0.824 (0.122)	1–2, 1–3
	Right knee	0.927 (0.036)	* 0.961 (0.018)	0.958 (0.020)	0.938 (0.044)	* 0.923 (0.041)	1–2, 2–5, 3–5
RMSE (°)	Left hip	* 5.4 (2.1)	5.8 (2.6)	* 6.1 (1.9)	* 6.9 (2.8)	* 11.3 (4.0)	1–5, 2–5, 3–5
	Right hip	* 3.6 (1.2)	4.6 (2.5)	* 4.7 (1.2)	* 5.4 (1.8)	* 6.7 (2.1)	1–5
	Left knee	6.6 (1.7)	* 5.8 (2.3)	* 6.9 (2.8)	* 10.9 (6.8)	* 8.0 (2.2)	2–3, 2–5
	Right knee	5.3 (1.8)	* 3.8 (1.2)	* 4.1 (1.2)	* 4.6 (1.5)	* 5.3 (1.5)	1–2
NRMSE (%)	Left hip	* 10.2 (3.6)	9.9 (4.8)	9.2 (3.0)	* 9.2 (4.1)	* 16.7 (6.4)	1–5, 2–5, 3–5, 4–5
	Right hip	* 6.7 (2.0)	7.5 (3.5)	7.1 (1.9)	* 7.3 (2.5)	* 10.2 (2.4)	1–5
	Left knee	8.5 (1.7)	6.9 (2.5)	* 7.2 (2.9)	* 10.5 (5.9)	* 8.9 (3.5)	3–5
	Right knee	7.0 (2.8)	4.6 (1.7)	* 4.4 (1.6)	* 4.6 (1.4)	* 6.1 (2.1)	1–2, 1–3
STD (°)	Left hip	2.3 (0.8)	2.3 (1.3)	2.4 (1.2)	2.1 (0.5)	4.2 (1.3)	1–5, 3–5, 4–5
	Right hip	1.9 (0.5)	2.5 (2.3)	2.0 (0.4)	2.1 (0.3)	4.2 (1.3)	1–5, 3–5, 4–5
	Left knee	* 2.6 (0.8)	* 2.1 (0.4)	* 2.4 (0.6)	* 2.7 (1.1)	* 3.9 (1.1)	2–5, 3–5
	Right knee	* 1.9 (0.4)	* 1.4 (0.2)	* 1.5 (0.4)	* 1.7 (0.4)	* 2.8 (0.6)	1–5, 2–5, 3–5, 4–5
NSTD (%)	Left hip	4.3 (1.5)	3.8 (2.0)	3.6 (1.7)	2.7 (0.6)	6.1 (1.1)	1–5, 3–5, 4–5
	Right hip	3.5 (0.7)	4.1 (3.4)	3.0 (0.6)	2.9 (0.5)	6.5 (1.4)	1–5, 3–5, 4–5
	Left knee	3.4 (1.5)	* 2.5 (0.5)	* 2.5 (0.8)	* 2.7 (1.2)	* 4.2 (1.4)	2–5, 3–5
	Right knee	2.5 (0.6)	* 1.8 (0.4)	* 1.6 (0.5)	* 1.7 (0.5)	* 3.3 (1.0)	1–2, 1–3, 1–4, 2–5, 3–5, 4–5

. The data for determining ankle joint kinematics were corrupted and excluded from the data analysis.

The accuracy of the intra-participant predictions (R²) had a range of 82.4% to 96.1%, except for the cross-leg prediction of the left hip using the data under the level-ground running condition (C5). (Table 1) The RMSE for predicting peak hip and knee flexion during stance had a range of 3.6 to 11.3 degrees. The accuracy of the predictions of the left leg (i.e., cross-leg) kinematics, denoted by R², RMSE, and NRMSE, was consistently lower than those of the right leg, and most of the differences between the left- and right-side predictions were statistically significant (Table 1). The variability of cross-leg prediction of the peak flexion of the left knee during stance, denoted by STD and NSTD, was significantly larger than that of the right knee.

The main effects of the running condition were statistically significant for all the evaluation parameters with p < 0.05. Post-hoc pairwise comparisons among the five running conditions showed that using data collected under C3 (treadmill running at 3.0 m/s) as the training data had the largest R² values for cross-leg intra-participant predictions (Table 1).

3.2. Inter-Participant Scenario

The results of various parameters for evaluating the inter-participant model for predicting bilateral hip and knee kinematics using a single MIMU attached to the right tibia using the data set of one of the running conditions are summarized in

Table 2. The various parameters for evaluating the accuracy of inter-participant predictions. * denotes significant differences between left and right sides with p < 0.05.

Inter-Participant Model							Pairwise Comparisons with p < 0.05
Running Condition		C1	C2	C3	C4	C5
		Mean (SD)	Mean (SD)	Mean (SD)	Mean (SD)	Mean (SD)
R2	Left hip	0.744 (0.141)	* 0.754 (0.145)	* 0.784 (0.132)	0.741 (0.187)	0.677 (0.404)	NS
	Right hip	0.805 (0.151)	* 0.855 (0.117)	* 0.856 (0.111)	0.798 (0.187)	0.813 (0.165)	NS
	Left knee	* 0.819 (0.143)	* 0.824 (0.161)	* 0.865 (0.091)	0.865 (0.083)	0.882 (0.079)	NS
	Right knee	* 0.908 (0.086)	* 0.933 (0.032)	* 0.936 (0.031)	0.915 (0.040)	0.935 (0.042)	NS
RMSE (°)	Left hip	7.3 (1.6)	* 8.3 (1.9)	* 7.1 (1.9)	7.6 (3.9)	8.8 (5.7)	NS
	Right hip	6.2 (3.3)	* 5.3 (2.1)	* 5.2 (2.0)	6.6 (3.9)	6.2 (2.1)	NS
	Left knee	8.4 (5.5)	8.1 (4.6)	8.9 (5.3)	8.2 (3.8)	8.4 (4.8)	NS
	Right knee	5.7 (2.8)	6.5 (2.3)	6.0 (2.3)	6.4 (2.5)	5.4 (1.8)	NS
NRMSE (%)	Left hip	11.3 (2.7)	* 12.9 (3.0)	* 11.0 (3.2)	12.0 (7.0)	14.1 (10.2)	NS
	Right hip	9.9 (5.7)	* 8.3 (3.1)	* 8.1 (3.1)	10.5 (6.6)	9.8 (3.5)	NS
	Left knee	9.6 (7.8)	9.3 (6.4)	10.3 (7.7)	9.2 (4.7)	9.3 (5.7)	NS
	Right knee	6.5 (3.5)	7.4 (2.7)	6.8 (2.8)	7.3 (3.0)	6.1 (2.1)	NS
STD (°)	Left hip	3.2 (1.0)	* 3.5 (1.1)	3.0 (0.7)	3.0 (0.7)	2.8 (0.5)	NS
	Right hip	2.7 (0.6)	* 2.8 (0.6)	2.8 (0.7)	2.7 (0.6)	2.6 (0.6)	NS
	Left knee	* 3.0 (1.0)	* 3.0 (0.9)	* 2.9 (1.0)	* 2.9 (1.1)	* 3.0 (1.1)	NS
	Right knee	* 2.2 (0.7)	* 2.0 (0.4)	* 2.0 (0.6)	* 1.8 (0.3)	* 1.9 (0.5)	NS
NSTD (%)	Left hip	4.9 (1.3)	* 5.3 (1.4)	4.6 (0.9)	4.6 (0.8)	4.3 (0.7)	NS
	Right hip	4.2 (0.9)	* 4.4 (0.8)	4.3 (1.0)	4.3 (0.8)	4.1 (0.8)	NS
	Left knee	3.4 (1.6)	* 3.3 (1.3)	3.3 (1.6)	* 3.2 (1.6)	* 3.4 (1.6)	NS
	Right knee	2.4 (0.8)	* 2.3 (0.5)	2.2 (0.7)	* 2.1 (0.4)	* 2.1 (0.6)	NS

NS = Not significant.

.

The main effects of running conditions were not significant for all the evaluation parameters. The accuracy of the inter-participant predictions (R²) had a range of 74.1% to 93.6%, except for the cross-leg prediction of the left hip using the data under the level-ground running condition (C5) (Table 2). The RMSE for predicting peak hip and knee flexion during stance had a range of 5.2 to 8.9 degrees. The accuracy of the inter-participant predictions of the left leg (i.e., cross-leg) kinematics, denoted by R², RMSE, and NRMSE, was consistently lower than that of the right leg but with only a few of the significant differences between the left- and right-side predictions (Table 2). The variability of cross-leg prediction of the peak flexion of the left knee during stance, denoted by STD ad NSTD, was significantly larger than that of the right knee (Table 2).

4. Discussion

This study investigated which of the five running conditions, i.e., treadmill running at 2.0, 2.5, 3.0, and 3.5 m/s and level-ground running, may be used for the most accurate prediction of overall running kinematics using only gyroscope measurements. Gyroscope measurement was used as a regressor in the running kinematic predictions, and a CNN model was applied to predict the hip and knee-joint angles in the sagittal plane. This study proposed a novel method for predicting running kinematics using a deep-learning method with the minimal regressor measurements and the data collected under the optimal running condition as the training data set. We computed the running kinematic predictions in intra- and inter-participant scenarios. We adopted the one predict-all scheme in this study by using kinematic data collected under one running condition to predict kinematics under other running conditions.

Intra-participant means how good the prediction would be if the subjects’ own MIMU signals are used to predict their own kinematics. Inter-participant prediction means how good the prediction would be when the model developed by the data of a number of subjects is used to predict the kinematics of a new subject. Except for the cross-leg prediction of the left hip using the data under the level-ground running condition (C5), the accuracy of the predictions (R²) was larger than 82% and 74%, respectively, for intra- and inter-participant predictions. This study demonstrated the feasibility of using gyroscope data measured by a single MIMU attached to the right tibia to predict running kinematics using a deep-learning method. The feasibility of cross-leg predictions using a single MIMU was also demonstrated.

For both intra- and inter-participant scenarios, it was consistently found that the predictions of the running kinematics of the leg with the single MIMU attached were more accurate than that of cross-leg prediction. Moreover, the accuracy for knee-joint angle prediction in the sagittal plane was higher than that for the hip joint. The accuracy of cross-leg prediction might depend on the level of symmetry and complexity of the running pattern. As we developed our model using only healthy recreational runners with relatively symmetrical running patterns, it would be worthwhile to study the validity of the model in runners with asymmetric patterns.

This study investigated the differences in running kinematics among different running conditions and speeds. Four low to moderate speeds were selected for the treadmill running conditions. Overall, using running kinematics data under treadmill running at 3.0 m/s (C3) as the training data set provided the most accurate cross-leg predictions in the intra-participant scenario. The accuracy of prediction using data under the level-ground running condition (C5) was the lowest. Future studies should investigate running kinematics at other speeds as well as under different running surface conditions for cross-field prediction.

This is one of the first few studies to use a CNN model to predict kinematics from treadmill running data while level-ground running. This provides new insight and inspiration for future techniques used to predict kinematics during level-ground running. Previous studies were limited to predicting kinematics only while treadmill running [5,38,39,40]. More similar studies are required to further investigate such predictions while running on different surfaces. This will enhance understanding of the kinematics of real-world running.

It would be better if one single MIMU system could capture both the lower-limb kinematics and the tibia movement. As the MyoMotion system did not allow this option, two separate MIMU systems were used in the current study. Additionally, the data of the ankle joint angles were corrupted with offset errors and abnormalities in waveforms. The cause of interference might have been due to the magnetic field in the laboratory. The interference was greater when closest to the ground, and the sensors on the feet were primarily affected [41]. The possibility of using a single MIMU system should be considered, and the accuracy of our model in predicting ankle joint kinematics should be further investigated.

This study was conducted on a very small sample comprising recreational runners running at their comfortable speed. The validity of these models should be studied among a large group of runners while running at extreme speeds, including those with injury or after fatigue who shall present large asymmetries. The validity of the model for other IMU systems should be confirmed in further study. Improvement of the placement and fixation of the sensors at the ankle joint should be the goal of future studies. Future studies should also compare methods used in this study with gold standard motion-capture systems, which would further strengthen the study design. It would be worthwhile to develop a model for running on different surfaces as well as running uphill or downhill, as these are more common in real marathon races.

5. Conclusions

This study proposes a novel, deep-learning method for predicting running kinematics under different conditions on a small training data set; the optimal regressor and the minimal data set for running kinematics prediction were determined. The predictions of bilateral hip- and knee-joint angles in the sagittal plane were analyzed using a single MIMU sensor attached to the anteromedial side of the right tibia. The cross-leg predictions for the left leg kinematics using a single MIMU attached to the right tibia were shown to be feasible. However, the predictions exhibited lower accuracy compared to those of the right leg. The treadmill running condition at 3.0 m/s demonstrated the highest accuracy in intra-participant cross-leg prediction.