3.1 Participants

This study included 15 patients over 18 years of age with at least six months after a single stroke (ischemic or hemorrhagic), with the ability to walk independently for 50 meters with or without a single point stick and the ability to provide informed consent were selected for biofeedback training [7]. Patients were excluded if they had ankle orthosis, any other medical condition that prevented them from walking on a treadmill, or any visual problem and a weight greater than 158 kg (weight limit problems of the harness) [7]. The participants were carefully informed, and their consent was secured to ensure informed participation. Informed written consent was obtained as per protocol and witnessed by the project staff member. The project staff (physiotherapist) explained the protocol and what participants needed to do, answering any questions before they signed up. Participants also received a copy of the project protocol prior to coming in for testing to read, understand, think about any questions, and share with their family or doctor.

The study (registered in the Australian and New Zealand Clinical Trials Registry - trial ACTRN12617000250336) was approved by the Human Research Ethics Committees of Victoria University, Australia, and Austin Hospital, Melbourne, Australia. The recruitment of the participants commenced on November 18, 2016, and was completed on March 22, 2023. Table 1 provides detailed information about the participants.

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Table 1. The table summarizes the participants’ details, including the number of subjects, age, affected lower limb, and walking speed among 15 patients.

https://doi.org/10.1371/journal.pone.0336503.t001

3.2 Data collection

We employed a three-dimensional motion analysis system (Optotrak^®, NDI, Canada) to capture kinematic data at 100 Hz. Following a standardized protocol [25], participants were outfitted with a cluster of three active markers, including one affixed to the big toe. The forefoot’s imaginary position was digitized using an active digitizing probe. To ensure safety and adherence to the protocol, all participants were secured by a safety harness and instructed to walk on a motorized treadmill at their self-selected walking speed for up to 10 minutes, with intervals of rest and breaks, as needed.

During subsequent biofeedback gait training sessions, the real-time sagittal trajectory of the big toe marker was displayed on a screen in front of the treadmill (see Fig 1). This display featured clear visuals of toe clearance and associated MFC events. The display also included a target range of MFC (calculated from baseline MFC data) depicted as a horizontal line on the screen [7]. Participants were then tasked with adjusting their MFC height to match the monitored ranges.

Patients underwent ten biofeedback training sessions, with faded biofeedback introduced after six initial sessions. Detailed information about the biofeedback training sessions is available in [7].

3.3 Assessment

Gait assessment evaluations were scheduled at the baseline and directly after the last training session (with a minimum interval of 20 minutes). After training, the participants were categorized as improved or unimproved. This categorization was determined based on the post-training MFC change from the baseline MFC data.

3.4 Computation of distance and similarity metrics

To evaluate the effectiveness of a training intervention, the baseline data serves as a reference point representing the measurements before any training occurred. The goal is typically to observe improvements in the post-training data compared to the baseline. Differences between the MFC series of the baseline and the second training session are computed by four distance metrics, and two similarity metrics [22,26]. Distance metrics quantify dissimilarity and focus on how far apart or different two points are, while similarity metrics measure resemblance and focus on how similar or related two vectors are. The range of distance metrics is typically from 0 to infinity, indicating higher values for more significant dissimilarity. Here, normalization is performed to make the distance metrics within the range of 0 to 1. Similarity metrics range from -1 to 1, with higher values indicating more remarkable similarity or robust relationships. We applied amplitude normalization to reduce sensor noises and eliminate amplitude-related variations caused by subjective physiological differences. Additionally, we perform zero-padding on the MFC series data, extending each series to 200 points before computing the four distance and similarity metrics mentioned below.

3.5 Predicting the improvement of MFC

To predict the improvement in MFC data from baseline treadmill training, we employ five classifiers [32]: Support Vector Machine (SVM), Random Forest (RF), AdaBoost, Ensemble Decision Tree (EDT), and Artificial Neural Network (ANN).

Support Vector Machine (SVM) is a supervised machine learning method based on the structural risk minimization principle [33]. It handles classification and regression by finding an optimal hyperplane to separate data points into distinct classes with maximum margin. The weight vector, bias, feature vectors, labels, Lagrange multipliers, and a kernel function determine the decision function. The decision function is given by:

(5)

where f(x) represents the decision function, w is the weight vector perpendicular to the separating hyperplane, b serves as a bias determining the position of the hyperplane, x_i represents the i-th feature vector of dimension d, is the label (target output) of x_i, is the Lagrange multiplier of the i-th data point, K(x_i,x) is the kernel function, and M represents the number of support vectors—data points in the margin. The function returns the sign of the argument.

Kernels help separate classes by transforming data into higher dimensions when not separable in lower dimensions, offering options like polynomial and radial basis functions alongside linear kernels [33].

Decision Tree is a non-parametric supervised method for classification and regression [34], utilizing a tree-like structure for classification or prediction.

1. Random Forest (RF) uses multiple Decision Trees through bagging, training each tree on a random subset of the data and considering only a random subset of features at each split [35].
2. AdaBoost (Adaptive Boosting) is a boosting algorithm that sequentially combines weak learners (like shallow Decision Trees). It trains them on weighted data, emphasizing previously misclassified samples in subsequent iterations to enhance performance [36].
3. Ensemble Decision Tree (EDT) with bagging combines multiple Decision Trees trained on different bootstrap samples of the training data. This approach boosts stability and reduces variance by introducing randomness. The final prediction comes from merging individual tree predictions through majority voting or averaging methods [37].

Artificial Neural Networks (ANNs) consist of artificial neurons that mimic biological neurons of the human brain. They have interconnected layers, including an input layer receiving data and an output layer generating predictions. The output response is defined by a non-linear function applied to the weighted sum of hidden layer outputs. The output response is defined as:

(6)

where o_k is the produced response of the k-th node of the output layer, f_o is the non-linear function at the output layer node, m is the number of nodes in the hidden layer, w_k,j is the weight connecting the j-th hidden node and the k-th output node, and h₀ = 1 is the bias term.

ANNs are supervised classifiers where weights are set during training. Backpropagation and optimization methods adjust these weights between neurons to minimize output errors. Precise weight learning is crucial, with optimization algorithms fine-tuning weights through mathematical processes [38].

3.6 Model training and evaluation

Due to the imbalanced nature of our dataset, consisting of 4 samples in one class and 11 samples in the other, we have employed three approaches (i) 5-fold stratified cross-validation on the original dataset, (ii) the undersampling method, and (iii) the oversampling method.

In the 5-fold stratified cross-validation approach, the dataset is divided into five folds. The model is trained on four of these folds, while one fold is reserved for testing. This process is repeated five times, ensuring that each fold preserves the original class distribution. As a result, the training and testing sets maintain the same distribution as the original dataset. After completing the 5-fold cross-validation, we calculate the average performance metrics, which helps evaluate the model’s robustness and reliability across multiple iterations.

To further mitigate the impact of class imbalance on performance metrics, we have employed random undersampling [39,40] and Synthetic Minority Over-sampling Technique (SMOTE)-based oversampling techniques [41]. For random undersampling, we have randomly selected three samples from each class for training, with the rest being used for testing. This random selection has been repeated 200 times to obtain average performance metrics. Additionally, we have applied SMOTE [41–43] (utilizing two nearest neighbors) to the training folds during each iteration of 5-fold stratified cross-validation and calculated the average performance metrics.

To ensure generalization, performance metrics such as accuracy (ACC), sensitivity (SENS), specificity (SPEC), and F1 score (F1) are calculated [44]. These three approaches evaluate the model’s performance while accounting for variations between subjects and ensuring its ability to generalize to unseen data.

3.7 Feature selection based on ranking and majority voting

Selecting relevant and non-redundant features is crucial for the classifier’s performance [25]. We used the minimum redundancy maximum relevance (mRMR) feature selection method to rank four features based on their relevance to the target variable and the redundancy they introduce [45]. The mRMR method aims to maximize the relevance of selected features to the target variable while minimizing redundancy among them. Due to the limited sample size, separately we stratified the data into five and three folds for feature selection. Employing a majority voting approach across the folds, we selected features that consistently ranked at the top in most of the folds.

3.8 Real-time adherence assessment metric (RAAM)

This section introduces our proposed real-time adherence assessment metric (RAAM) for measuring adherence between consecutive training sessions.

The Gait Profile Score (GPS) is a single index measure that summarizes the overall deviation of kinematic gait data relative to normative data [46,47]. Similar to the notion of GPS variation computation in [47], we measure improvement in adherence from one training session to another. We used 200 points (i.e., MFCs) corresponding to 200 strides. Instead of a gait cycle and nine measurements in [47], we use one MFC value measurement across 200 gait strides. We denote the gait session E_p,d of a patient p at datetime d as

(7)

where, is the k-th gait cycle of a gait session and K is the total number of gait cycles. We modify this notation in our case with a vector of t = 200 lines representing 200 strides instead of a single stride and n = 1 column, representing the MFC values as:

(8)

Instead of using normative data as a reference point, we have used each patient’s baseline. This baseline serves as the starting point from which we assess improvement. Then, we will use m^th similarity and distance metrics (represented as SIMDIST) to compute the MFC Variation Score (MVS) as

(9)

Then, we use Eq (9) to compute MFC-based GPS as

(10)

where, N is the number of similarity and distance measures.

We hypothesize that choosing one or multiple similarity and distance measures that effectively differentiate between baseline and training sessions would be more advantageous in GPS_MFC computation.

For (i + 1)^th training session, GPS_MFC(i + 1) variation from the previous session can be computed using:

(11)

We get 9 as we have 10 training sessions. We need to be cautious in using these metrics as either similarity or distance measures during the calculation of . When we exclusively calculate similarity, if is negative, it indicates an enhancement in the patient’s adherence ability from i^th to session. In contrast, if positive, it signifies a decline from the previous session.

If there is a distance metric present in the feature set, it is better to convert other similarity values into distance values for calculating . Since CC and CS range from 0 to 1, we can obtain distance values by subtracting them from 1, i.e., 1–CC or 1–CS. When using these distance measures, a negative value for indicates a decrease in the patient’s adherence ability from the i^th to the session. Conversely, a positive value signifies an improvement from the previous session.

4.1 Analysis of selected features

Fig 2 illustrates six extracted features that capture the distance and similarity between the MFC series of the baseline and second training session. The figure shows that the distance metrics (Euclidean and Manhattan) have lower values between the baseline and the second training session for three out of four unimproved patients compared to the improved patients. In the case of cross-correlation distance and dynamic time warping distance, the unimproved class exhibits a lower distance compared to the improved class. However, for DTW, the difference between the two classes is not very pronounced. However, interpreting the correlation coefficient between the MFC series is more complex. The low correlation coefficient values (regardless of their positive or negative nature) reveal that the training has an impact, resulting in a weak linear relationship between the baseline MFC and the second training MFC. Regarding cosine similarity, the figure also indicates that the unimproved class patients exhibit higher similarity between the baseline and the second training session compared to the improved class.

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Fig 2. This figure shows the variations in features across the two classes, utilizing six metrics: Euclidean distance (ED), Manhattan distance (MD), correlation coefficient (CC), cosine similarity (CS), cross-correlation distance (XCRD) and dynamic time warping distance (DTW).

It highlights that distance metrics (ED, MD, XCRD and DTW) are comparatively lower between the baseline and the second training session for unimproved participants than for improved participants. Low CC value suggests training impact with a weak linear relationship (i.e., mean shift) between baseline and second training MFC. CS indicates higher similarity between baseline and second training for unimproved patients compared to improved ones.

https://doi.org/10.1371/journal.pone.0336503.g002

After applying the mRMR-based feature selection, CS, XCRD, CC, and DTW features are consistently selected as the top-ranked variables in most cases, while ED and MD have ranked the lowest. The performance of the selected feature subsets in the SVM classifier, is presented in Tables 2, 3 and 4. To determine the best-performing feature set, we focused on features that consistently delivered the best F1-scores across the majority of scenarios. The decision to use the F1-score was based on its robustness in scenarios with data imbalance [48,49]. We have analyzed all three tables to determine which combination of features performs best in most cases. In Table 2, the RBF kernel yields the best outcomes for the combinations CC + CS, CC + XCRD, and CC + XCRD + CS. Table 3 indicates that the combination CS + XCRD achieves the best results across nearly all kernels. Table 4 highlights that CC + CS, CS + XCRD, and CC + CS + XCRD mostly excel in the RBF kernel.

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Table 2. Performance comparison of the selected features with the SVM Classifier utilizing five-fold stratified cross validation.

Best performance for a C value among the kernel is presented. Highest performances are highlighted, along with the feature set and kernel that achieved it. Evaluation Metrics: Accuracy (ACC), Sensitivity (SENS), Specificity (SPEC), and F1-score (F1). Similarity Measures: cs: Cosine Similarity, cc: Correlation Coefficient, md: Manhattan Distance, ed: Euclidean Distance, xcrd: Cross-correlation Distance, dtw: Dynamic Time Warping Distance.

https://doi.org/10.1371/journal.pone.0336503.t002

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Table 3. Performance comparison of the selected features with the SVM Classifier utilizing undersampling method.

Best performance for a C value among the kernel is presented. Highest performances are highlighted, along with the feature set and kernel that achieved it. Evaluation Metrics: Accuracy (ACC), Sensitivity (SENS), Specificity (SPEC), and F1-score (F1). Similarity Measures: cs: Cosine Similarity, cc: Correlation Coefficient, md: Manhattan Distance, ed: Euclidean Distance, xcrd: Cross-correlation Distance, dtw: Dynamic Time Warping Distance.

https://doi.org/10.1371/journal.pone.0336503.t003

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Table 4. Performance comparison of the selected features with the SVM Classifier utilizing SMOTE method.

Best performance for a C value among the kernel is presented. Highest performances are highlighted, along with the feature set and kernel that achieved it. Evaluation Metrics: Accuracy (ACC), Sensitivity (SENS), Specificity (SPEC), and F1-score (F1). Similarity Measures: cs: Cosine Similarity, cc: Correlation Coefficient, md: Manhattan Distance, ed: Euclidean Distance, xcrd: Cross-correlation Distance, dtw: Dynamic Time Warping Distance.

https://doi.org/10.1371/journal.pone.0336503.t004

Notably, the features based on CS, CC, and XCRD have proven to be better performers across the three classification scenarios, surpassing others and achieving 100% correct predictions in some instances. As no single set of features consistently outperforms in all three scenarios, we opted to include each feature that enhances performance in at least two of the scenarios. We want to ensure that we do not overlook any feature that provides value in one of the scenarios. This highlights the significance of each feature, contributing to a more robust feature set. Based on these findings, we have determined that CC + CS + XCRD is the optimal combination. Fig 3 illustrates that the combined feature of CC, CS and XCRD exhibits superior separability between the improved and unimproved classes compared to individual measures in Fig 2.

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Fig 3. This scatter plot shows the discriminatory capability of features to separate unimproved and improved classes using the CS,CC and XCRD-based feature selection and majority voting across five folds.

https://doi.org/10.1371/journal.pone.0336503.g003

4.2 Performance comparison of selected feature subset in different classifiers

Table 5 summarizes the performance of five machine learning models after fine-tuning their respective hyperparameters. The models evaluated are Support Vector Machine (SVM) (https://www.csie.ntu.edu.tw/cjlin/libsvm/), Random Forest (RF), Ensemble Decision Trees (EDT), AdaBoost, and Artificial Neural Network (ANN).

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Table 5. Classification performance metrics of selected feature (CC + CS + XCRD) among five different classifiers utilizing five-fold cross validation.

Metrics: accuracy (ACC), sensitivity (SENS), specificity (SPEC), and F1-score (F1).

https://doi.org/10.1371/journal.pone.0336503.t005

For the SVM, we explored three kernels (Linear, RBF, and Polynomial of degree 3) and varied the c value from 0.1 to 10000. In the case of RF and EDT, we experimented with the minimum leaf size (1, 5, and 10) and the number of trees (randomly chosen between 5 and 100). The AdaBoost classifier was fine-tuned by adjusting the learning rate (0.001, 0.01, and 0.1) and the number of weak learners (15, 20, 25, and 30).

For the ANN, we varied the learning rate (0.1, 0.01, and 0.001) and the number of hidden nodes (10, 20, and 50) within a single hidden layer (i.e., Multilayer perceptron(MLP)). Additional hyperparameter optimization for the ANN included:

• Optimization functions: Gradient Descent Backpropagation, Fletcher-Reeves Conjugate Gradient Descent, and Polak-Ribiére Conjugate Gradient Descent
• Transfer functions: tansigmoid and log-sigmoid
• A fixed number of epochs (1000)
• A ridge regularization value of 0.01

Based on the results, both SVM and ANN achieved the highest performance 100% across all performance metrics when utilizing selected cosine similarity, correlation coefficient and cross-correlation distance features.

4.3 Performance of similarity measures evaluated from alternative MFC features

We employed three distinct approaches to analyze the baseline and second training data: wavelet-based multi-exponent features [24], statistical and tone-entropy features [23], and raw MFC series analysis. Also, we combined all three features to capture complimentary information of each of the feature. For the wavelet-based approach, we conducted wavelet decomposition at eight levels on both the baseline and second training MFC series, extracting six features from each decomposition. We then calculated the CC, CS and XCRD between the baseline and second training wavelet features to assess their similarity.

Our statistical and tone-entropy analysis involved computing various descriptive statistics for MFC series, including mean, median, standard deviation, quartiles, and interquartile range. Additionally, we evaluated tone and entropy estimates from the MFC Percentage Index (PI) series. We calculated CC, CS and XCRD between the baseline and second training statistical-tone-entropy features to quantify their similarity. For the raw MFC series analysis, we calculated CC, CS and XCRD between the baseline and second training MFC series without any feature extraction.

To evaluate the performance of these different approaches, we employed five classifiers. We compared their performance using similarity measures derived from each method: wavelet-based, statistical-tone-entropy-based, raw MFC series, and all three features together (i.e., combined). Our results showed in Fig 4 that the raw analysis of MFC series, which used similarity measures computed directly from the MFC values without feature extraction, consistently outperformed both wavelet-based methods, statistical tone entropy, and combined features. This superior performance was evident across all metrics except for sensitivity in the Adaboost classifier.

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Fig 4. The figure displays the performance of five classifiers: (a) SVM, (b) MLP, (c) RF, (d) AdaBoost, and (e) EDT.

The evaluation involves the utilization of correlation coefficient (CC), cosine similarity (CS) and cross-correlation distance (XCRD) measures for Wavelet features [24], Statistical Tone Entropy (statTE) features [23], and the raw MFC data points. The raw MFC data shows better performance compared to wavelet, statistical-tone-entropy and combined features.

https://doi.org/10.1371/journal.pone.0336503.g004

These findings demonstrate the effectiveness of using these measures (CC, CS and XCRD) computed directly from MFC values than those derived from extracted features. The results suggest that, in this context, the raw data contains valuable information that may be partially lost in the feature extraction process. It is observed that, despite combining all three features, this combination fails to capture any additional complementary information that would enhance performance compared to the raw one. However, the utility of the feature-based approaches should not be discounted, as they offer insights into specific aspects of the data that are not immediately apparent in the raw series.

4.4 Adherence indication via similarity and distance measures

Fig 5 displays the average values of CC (Fig 5-(a)), CS (Fig 5-(b)) and XCRD (Fig 5-(c)) -based measures across all the 10 training sessions for both improved and unimproved stroke patients.

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Fig 5. The figure shows the average (a) CC (b) CS and (c) XCRD-based measures over 10 training sessions for all patients in two groups, demonstrating the trend of the impact of targeted biofeedback between the baseline and each training session.

CC and CS represent similarity measures. A low CC suggests a weak linear relationship between the baseline and the training session, while a high value indicates a strong linear relationship. A low CS value indicates that the subjects show less similarity to the baseline in that training session, while a high value suggests greater similarity. In contrast, the XCRD-based measure indicates dissimilarity: a high value in a particular training session means the subjects are less similar to the baseline condition, whereas a low value indicates a higher similarity. In (a), the CC-based measure indicates that the biofeedback has resulted in a weak linear relationship between the baseline and the training sessions. On the other hand in (b), the CS-based measure and in (c) XCRD-based measure clearly illustrate that when a patient’s training data is more similar to the baseline, they are less likely to show improvement during the post-assessment, and vice versa.

https://doi.org/10.1371/journal.pone.0336503.g005

Correlation Coefficient (CC) Analysis: The CC-based measure indicates that a lower correlation value might portray the impact of biofeedback on the MFC values during training sessions, potentially causing them to shift in a weakly linear manner compared to the baseline. This suggests that the mean value of MFC during the training session has likely deviated from the mean value of the baseline MFC [26] for both classes of patients.

Cosine Similarity (CS) Analysis: The CS-based measure reveals an interesting pattern across training sessions. Patients who showed improvement in the post-assessment phase consistently exhibited less similarity to the baseline compared to those who did not improve. This difference in similarity scores between improved and unimproved patients is observed for each training session.

Cross-correlation Distance (XCRD) Analysis: The XCRD-based measure reveals that those who showed improvement in the post-assessment phase consistently exhibited more distance to the baseline compared to those who did not. This difference in distances between improved and unimproved is observed for all the training sessions.

4.5 Inter-session improvement assessment

Our investigation revealed that measures based on correlation coefficient (CC), cosine similarity (CS) and cross-correlation distance (XCRD) performed better in predicting improvements using only the second training dataset. In accordance with the methodology outlined in Sect 3.8 to perform inter-session improvement or decrement assessment, we conducted a statistical significance test of CC, CS and XCRD values in the improved and unimproved class categories. This analysis informed our decision on which similarity measure to utilize for calculating the .

Using a non-parametric Mann-Whitney U test, we found that CS and XCRD values were statistically significant (p<0.05) for all training sessions except the 4th, 6th and 8th. This suggests that the assessment is reliable for most sessions. It has been observed that this exception occurred because one subject in the 6th training session and another subject in the 8th training session both from the unimproved class exhibited less similarity with the baseline. This may suggest that these patients made a greater effort to adhere to the target more effectively during those training sessions. Additionally, some exhibit a higher similarity to the baseline during some training session while being in the improved class.

Fig 6 represents the mean value of GPS_MFC in all available training sessions of individual participants. It is observed that in most cases the mean GPS_MFC is lower for unimproved participants and higher for improved participants. Fig 7 illustrates the relationship between the GPS_MFC of the second training session and the mean GPS_MFC of all the training sessions. The correlation coefficient between the GPS_MFC value of the second training session and the mean GPS_MFC is 0.6453, indicating a moderate to strong correlation [50].

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Fig 6. Figure represents mean of the values across the 10 training sessions for all the participants.

It is observed that the mean GPS_MFC is higher (i.e., dissimilar to baseline ) in most of the cases of improved participants compared to unimproved ones.

https://doi.org/10.1371/journal.pone.0336503.g006

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Fig 7. Figure represents correlation between of second training session and mean of the values across the 10 training sessions for all the participants.

The mean GPS_MFC of the second training session shows a correlation coefficient of 0.6453 with the mean GPS_MFC. This indicates a moderate to strong relationship between the GPS_MFC of second training session and the mean GPS_MFC across all sessions [50].

https://doi.org/10.1371/journal.pone.0336503.g007

Fig 8 illustrates the improvement or decline in adherence ability to feedback between consecutive training sessions using the measurement , with CS and XCRD as dissimilarity measures. In Fig 8, the x-axis ranges from 1 to 9. The value y for x = 1 represents the difference in GPS_MFC between the second and first sessions, and similarly up to the value y for x = 9 corresponds to the difference in GPS_MFC between the tenth and ninth sessions. In some areas of Fig 8, is shown as zero. This is due to data loss during collection; although the participant completed those specific sessions, technical issues prevented the data from being captured. All calculations were made with this consideration including mean GPS_MFC and . Across the training sessions, we use dissimilarity measure to compute GPS_MFC, we observed (in Fig 8) (1) instances of improvement between consecutive sessions (indicated by positive values) and (2) cases where improvement was not evident (represented by negative values indicating decrement).

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Fig 8. Illustration of improvement or decline of 15 stroke patients (i.e., (i)-(xv) ) between consecutive training sessions using the proposed , with CS and XCRD employed as the dissimilarity measure from the baseline.

From the 10 training sessions, nine values are computed. The first value signifies the difference in adherence capability between the second and first sessions, the second value represents the difference in adherence capability between the third and second sessions, and so forth up to the tenth session. The negative values of (represented in blue) computed across training sessions can be used to predict potential decrement in following the biofeedback, whereas positive values (represented in red) indicate a increment from the previous session for a specific patient.

https://doi.org/10.1371/journal.pone.0336503.g008

Notably, among stroke patients who did not show significant improvement during post-assessment (Fig 8 (i), (ix), (xii), and (xiii)), some displayed progress in some instances during consecutive training sessions. This suggests that (1) the observed differences may have been insufficient to demonstrate significant improvement during post-assessment, and (2) additional training sessions could potentially lead to significant enhancements within this group.