Automatic Evaluation of Strephenopodia Based on Plantar Pressure and Machine Learning: A Pilot Study

Purpose Stroke patients often suffer from strephenopodia because of high muscle tension or muscle spasms, which seriously affect their walking ability and rehabilitation. During the treatment of strephenopodia, there are practical demands for convenient, automatic, and quantitative assessments of the angle of strephenopodia. However, existing strephenopodia detection methods, including traditional clinical gait analysis, gait video analysis and plantar pressure systems, suffer from object obstruction or require complex setups. In this paper, we proposed a novel methodology for automatically predicting the angles of strephenopodia based on a gait analysis system using machine learning methods. Methods Plantar pressure distribution data from thirty healthy participants were recorded during walking on the Zebris FDM-THM instrumented treadmill and were processed to generate 15 gait features. The right ankle angles on the coronal plane were measured by the Vicon system to provide a detailed description and explanation of strephenopodia walking. Three machine learning methods were implemented to build stochastic function mapping from gait features to strephenopodia angles. Results This study showed good reliability and precision prediction of the angle of strephenopodia [determination coefficient (R2) ≥ 0.80]. Gaussian process regression (GPR) exhibited the best regression performance [R2=0.93, mean root-mean-square error (RMSE) = 0.67]. Conclusion The study results showed that this strephenopodia-detection method is not only convenient to implement but also has high accuracy and outperforms previous reports. Measurements derived from the gait analysis system are proper estimators of the angle of strephenopodia and should be considered to improve diagnosis and assessment of the stroke population.


Introduction
Stroke is one of the top leading causes of adult disability around the world [1], and 80% of the stroke patients tend to experience different degrees of walking obstacles [2].
Strephenopodia is one of the most common sequelae of stroke and is an adduction and supination varus posture.
Strephenopodia seriously affects the patient's daily life and rehabilitation and may also cause serious injury [2][3][4]. To obtain better rehabilitation, it is necessary for patients to train themselves to walk properly using their own muscles [5]. If the muscles are not exercised because the foot rests on top of a comfortable orthotic shape, they would lose strength, and consequently, protective shock absorption, efficient gait [6] and other complex functions [7] become impaired. This highlights the necessity to automatically monitor the angle of strephenopodia to warn patients to consciously correct varus using their own muscles to achieve effective rehabilitation. Typical approaches for the detection of strephenopodia include traditional clinical gait analysis, gait video analysis and plantar pressure systems [5].

Pressure and Machine Learning: A Pilot Study
In the clinic, traditional gait analysis method [8] is mostly used for monitoring and providing feedback about strephenopodia before and after rehabilitation to evaluate treatment. Visual examination and standard goniometry are common tools in clinical assessment and diagnosis conducted by clinicians [4]. The physician observes the patient's gait features by visual inspection using clinical scale evaluations, such as the Brunnstrom assessment [9] and Clinical Spasticity Index (CSI) scores [10], and uses a measuring tool [5] to measure the angle of inversion. The results of this observational method rely on the observer's skill and clinical experience, and it cannot be widely used by nonprofessionals. In addition, concern for privacy leads to unnatural action when faced with the doctor's inquiries.
Moreover, it is inconvenient to operate and cannot be recorded in real time in later stages. This method does not meet the requirements for clinical application [11,12].
Gait video analysis is another method for strephenopodia evaluation. Computer vision [13], 3D kinematic analysis in vivo [4,14], and optoelectronic stereophotogrammetry in vivo [15] were applied in patients with foot pathologies.
Radiographic measurement [16] is also used for pronation and supination evaluation through the position of the talofirst metatarsal angle and the calcaneal-second and fifth metatarsal angles. However, this method is expensive and complex, which makes timely adjustment of the method inconvenient.
Since the acquisition of plantar pressure is simple and noninvasive, it has been widely used in detecting and monitoring gait patterns and lower extremity movements [17][18][19]. In a previous report [3], smart textile socks with five integrated pressure sensors were used for pronation and supination detection. Another study [5] utilized a pressuresensitive insole to detect foot pronation in real time, and feedback provided to the user reduced pronation significantly. Smart footwear insoles are implemented for recognition of foot pronation and supination other reports as well [20]. These methods are proven to be effective in detecting pronation and are relatively low cost. However, they are only able to detect whether foot pronation exists and cannot quantitatively determine the angle of foot pronation. Therefore, it is critical to develop a simple, convenient, and noninvasive method to detect strephenopodia in clinical practice. The plantar pressure distribution can reflect lower limb movements [18,19] in stroke survivors and serve as a strephenopodia-detection method. The electronic mats of Zebris FDM-THM instrumented treadmills are matrices of piezoresistive effect-based sensors. The Zebris treadmill can generate quantified values for gait and balance components, thus enabling exposure of subtle variations usually invisible to the naked eye [21,22]. The "butterfly" diagram [21] from the instrumented treadmill reflects the variability of the center of the pressure trajectory during walking. Other parameters, such as the Center of Pressure (COP), double support phase (DSP), and cadence [23] for correlations and multiple classification analysis, were gathered with instrumented treadmills.
In this paper, we proposed a strephenopodia angle prediction method that can predict the foot supination angle based on the plantar pressure distribution. This method can be used to provide real-time feedback to the user to warn them about strephenopodia conditions. We collected a data set that consisted of plantar pressure distribution data and lower limb motion from 30 participants. Then, we fitted a Gaussian process regression (GPR) model to the data set.
Experimental results indicate that our method can predict the foot supination angle with high precision. We also provide a performance comparison between the GPR and other regression models.  Table 1 provides summary information about the participants.

Experimental Setup
The experimental setup included three parts: a Zebris FDM-THM Treadmill (Zebris Medical GmbH, Germany) for measuring the plantar pressure distribution, wedge- Platform systems embedded in a treadmill are considered the gold standard in plantar pressure measurement and have high measurement precision [24]. We utilized the Zebris FDM-THM Treadmill ( Figure 1) to obtain the gait features.
We designed three wedge-shaped blocks with different heights. In the experiment, the blocks were stuck under the forefoot to simulate different strephenopodia conditions.
The higher the block, the more severe the simulated foot supination. Participants walked at self-selected speeds on the treadmill under the 4 different conditions. In the first condition, the participants walked freely with no block; then, for the other three conditions, blocks with different heights were stuck to the first metatarsal area of the medial forefoot of the right foot. We asked the participants to keep the blocks close to the ground as much as possible but not touch the treadmill belt to ensure a certain angle when walking, which imitates the different degrees of strephenopodia conditions.
We attached 16 reflective markers to the subject, and details about the marker positions are described in reference [25]. The Vicon system measures the trajectories of these 16 reflective markers, which will be used to calculate joint kinematics later. Gait patterns are represented by lower limb joint trajectories: ankle adduction/abduction on the coronal plane, mainly referring to strephenopodia, and other joint rotations are not considered.

Measurement Procedure
First, we asked all participants to participate in an adaptation-familiarization trial to obtain a self-selected walking speed and adapt and maintain the inversion angle.

Preprocessing of Joint Trajectories
All the raw gait trajectories obtained by the Vicon system need to go through a series of processes. 1) We removed invalid gait patterns caused by marker occlusions. 2) We applied low-pass filtering using a Butterworth low-pass filter with a cutoff frequency of 6 Hz to reduce noise in raw signals. Figure 2 shows the filtered right ankle angle trajectory.
3) The gait sequence was split into gait cycles to obtain the average of the minimum value of each gait cycle for ankle flexion/extension because we found that in the support phase, the varus foot was relatively smaller throughout the gait cycle. 4) The average of the minimum right ankle value of each gait cycle was calculated, where is the number of gait cycles, is the minimum value of the right ankle angle throughout the -th gait cycle, and is considered to be the strephenopodia angle.    Stance phase the phase of a gait cycle in which the foot has contact with the ground.
3 Maximum force the average maximum values reached in N for the three zones: toes, mid-foot and heel.
3 Maximum pressure the average maximum values reached in N/cm² for the three zones: toes, mid-foot and heel.

Gait Feature Extraction
As shown in Figure 3, the plantar pressure distribution is a good description of the different severities of strephenopodia. The data dimensionality of plantar pressure is too large to be directly applied in machine learning algorithms. Therefore, we extracted 15 gait features from the raw plantar pressure data collected by the Zebris gait analysis system (Table 2).
"Butterfly" diagrams are presented in Figure 4. There are obvious differences between both foot asymmetries in gait phases that can be obtained [2] and have more asymmetrical stance times compared with healthy subjects. The shadow of the right footprint also decreased, indicating varus deepening in the foot.
These 15 gait features were extracted from the raw plantar pressure data and served as the input features of our dataset to train the different regression models.

Prediction of strephenopodia angles
We implemented three regression models Gaussian process regression (GPR), Support vector regression (SVR), and Stepwise linear regression (SLR), to evaluate their performance in predicting strephenopodia angles from gait features.

Definition of Training Set
The The regression models will be optimized to build mapping relationships between the input and the output .

Gaussian Process Regression
A Gaussian process (GP) [26][27][28] is a stochastic process specified by its mean function and its covariance function, ( ), ( , ′ ) : In our work, the mean function and covariance function are determined as follows: where 2 is the signal variance of the kernel function, is the shape parameter of the kernel function, and = ( −2 ) is a symmetric matrix of hyperparameters.

Support Vector Regression
The support vector regression (SVR) model is characterized by its kernels, sparse solution, and Vapnik-Chervonenkis (VC) control of the margin and the number of support vectors. SVR models are trained using a symmetrical loss function, which equally penalizes high and low misestimates. In ε-SV regression [29][30][31][32], our goal is to find a function, ( ), that has at most ε deviation from the actually obtained targets for all the training data and is as flat as possible. We construct a linear regression function: The optimization criterion penalizes data points whose yvalues differ from ( ) by more than ε. The slack variables, ξ and * , correspond to the size of this excess deviation for positive and negative deviations.

Stepwise Linear Regression
Stepwise linear regression [33-35] is a multivariate statistical data analysis method that studies the correlation between dependent variables and multiple influencing factors and is widely used in prediction and control. In the preliminary regression analysis, we first establish the total regression equation between the dependent variable y and the independent variable x and then perform hypothesis testing on the total equation and each independent variable.
If the regression equation reaches a satisfactory level, the algorithm terminates. Otherwise, some variables that are not significantly different will be eliminated using the interpreted information. This process is an iterative process to ensure that the final set of explanatory variables is optimal.

Results
The methods are tested with the five-fold cross-validation method. We randomly divide the collected data set into five groups. For each of the five iterations, four groups are used as the training set, and the other group is used as the test set.
The hyperparameters of these three algorithms are optimized by the grid search method. The results are aggregated to verify the models to find the average prediction accuracy of the system [36].
We selected the root-mean-square error (RMSE) and determination coefficient (R2) as model evaluation parameters. The correlation index R2 describes the fit of the regression model. The closer R2 is to 1, the better the fit of the model. The R2 for individual regressors reached 1, indicating that the models exhibited the desired prediction performance. R2 and RMSE were formulated as follows: where is the number of samples, is the right ankle angle, ̅ is the mean value of the right ankle angle and ̂ is the predicted angle.
The regression accuracies for the three machine learning regression methods are shown in Table 3 and Figure 5. The GPR method achieved the best prediction performance, with the highest R2 (0.93) and lowest RSME (0.67) among all regression algorithms. All regression algorithms had a higher R2 (≥0.80) in the walking tasks. These algorithms all showed relatively good ability to predict the angle.     The major limitation of our work is that our regression models are only tested on simulated data from healthy participants instead of data acquired from stroke survivors.
Although common strephenopodia walking movement patterns were simulated by healthy participants in this paper, strephenopodia walking patterns may be more variable in stroke survivors. Future research is needed to explore the regression performance in predicting the strephenopodia angles of stroke survivors.
In this paper, we proposed and tested the use of plantar pressure distribution for predicting strephenopodia angles.
This novel method can provide quantitative and unobtrusive monitoring of strephenopodia conditions. We  Right ankle angles on the coronal plane.

Figure 3
The plantar pressure distribution in the stance phase. (a) Healthy gait; the degree of strephenopodia increases from (b) to (d).

Figure 4
The "butter y" diagrams derived from the Zebris treadmill: (a) Normal gait. (b) Gait with mild pronation.
(c) Gait with severe pronation. R2 and RMSE metrics for the GPR, SVR and SLR.

Figure 6
Kernel density estimate (KDE) plots for the prediction errors of three regression models. The distributions of the prediction errors are demonstrated intuitively in these plots.

Figure 7
Actual angle and predicted angle of three regression models.