C. Normalization

Kinetic and kinematic gait variables are often affected by height and weight of the subjects. Acceleration from the lower limb may also be affected by these same factors. To minimize the confounding effect of patient anthropometric differences, we normalized both biomechanical and inertial gait variables by relevant factors. In prior research, Moisio et al. found that normalization methods were highly effective in reducing individual differences [7]. To normalize personal differences, kinetic and kinematic gait signals were divided by weight, and acceleration data were divided by height.

D. Biomechanical Gait Variable Extraction

In this session, we present information on the processes to extract the biomechanical gait variables of interest from laboratory instruments. Biomechanical gait variables included kinetic and kinematic parameters such as knee moments and ground reaction forces. The process of feature extraction is detailed below. In this study, we focused on initial loading behavior-related inertial gait variables as important recovery indicators for the population. Loading characteristics during gait are important as they are correlated with OA progression [6].  To address the loading patterns, relevant kinetic biomechanical gait variables including maximum knee flexion moment (KFM), maximum knee adduction moment (KAM), the first peak of vertical ground reaction force (vGRF), and maximum anterior ground reaction force (aGRF) were selected [4, 8]. Each step was first recognized by using 20% maximum vertical ground reaction force [9]. Then, intended patterns (i.e., maximum or first peak maximum) were recognized to obtain targeted biomechanical gait variables (Figure 2). Since both the average and symmetry of biomechanical gait variables are important indicators for unilateral TKA [10, 11], the four biomechanical gait variables from each step were then summarized in average and symmetry across the one-minute trial.

E. Inertial Gait Variable Extraction

E1: Gait Event Detection

Anterior directional acceleration was selected for accurate gait event recognition since the anterior dimensional motion of lower limbs was dominant over two other dimensions from an ankle-worn sensor perspective. Each heel-strike action generated a dramatic peak in the anterior directional acceleration; this peak was a clear indicator of initial loading within a gait cycle (Figure 3-a). The identified peaks were compared to the vertical ground reaction force data to validate the accuracy of acceleration-based gait event detection (Figure 3-b). The described methodology was applied to each ankle sensor individually. Once individual step recognition was complete, the recognized peaks from the two sensors and raw acceleration data were merged together to obtain data on step cycles.

E2: Gait Variable Extraction

Eleven gait variables were extracted to estimate the magnitude, impulse, and angles of initial loading from 3D-acceleration data. Since the focus of this study was on the initial loading characteristics of TKA patients, the inertial motion of the lower limbs following heel strikes (HS) was analyzed. Characteristics from the initial 10% of the stance phase of the gait cycle, the initial 10% of the directional impulse of the gait cycle, and the maximum directional acceleration at HS were extracted. Additionally, whole step vector magnitude, ankle angle variation in lateral and anterior directions, and step time were computed to explain the whole step characteristics (Table III).

E3:     Average and Symmetry

The basic gait variables vector from each step were summarized in terms of the average and symmetry of each trial. The trial-averaged inertial gait variables were applied to estimate the biomechanical gait variables. Since bilateral gait symmetry has gained more attention, particularly in the unilateral TKA population [11, 12], the basic gait variables were fed to calculate symmetry. The Symmetry Index (SI) proposed by Robinson et al. was applied to assess the symmetry of inertial gait variables [13]. To apply the concept of SI for TKA patients, SI was defined in the study as the difference of non-surgical limb from surgical limb rather than the difference of left limb from right limb.

F. Data Analysis

To quantify the relationship between all independent (i.e., eleven inertial gait variables) and dependent variables (i.e., four biomechanical gait variables), a Pearson Correlation analysis was conducted. For statistical analysis, the eleven inertial gait variables were categorized by directional perspectives, i.e., lateral, anterior, vertical, and inclusive inertial gait variables. (Table IV).

F1: Inertial Gait Feature Selection

To avoid overfitting of estimation models, subsets of eleven inertial gait variables were carefully selected for each of four biomechanical gait variables as a pre-processing method. Stepwise regression was applied to systematically select relevant inertial gait variables for the four-biomechanical gait variables [14]. The automatic procedure of stepwise regression by feeding all useful inertial variables helped us to reduce mutual information (i.e., non-overlapping) among eleven independent variables with smaller subset sizes. Stepwise regression criteria for variable inclusion was an increase in adjusted R2 value. To improve the robustness of the model, k-fold cross-validation was applied with k = 10 [15]. In k-fold cross-validation, 18 participants were randomly partitioned into 10 subfolders. A single subfolder was retained as the validation data for testing the model, and the remaining nine subfolders were fed as training data. The cross-validation process was then repeated 10 times, with each subfolder used exactly once as the validation data. The procedure was intended to make estimation models robust for unseen TKA patients’ gait data and improve the overall validity of model predictions.

F2: Hierarchical Regression

To determine the directional contributions to biomechanical measures, hierarchical linear regressions were used [15]. Specifically, selected inertial variables in each directional category were added to the regression models in steps as discussed in [16]. This procedure provided information regarding which directional inertial variables have the most predictive power on biomechanical variable estimation models. Separate regressions were conducted for each of the four biomechanical gait variables. Primary axis inertial variables were entered into the regressions at the first step. For example, KFM was knee moment in the anterior-posterior direction, so the anterior direction inertial variables from feature selection outcomes were added to the KFM estimation regression model in the first step. Then, the vertical and lateral inertial variables were entered in the second and third steps, respectively. For all hierarchical regressions, the inclusive inertial variables were entered at the last step (Figure 5). The significance of each model and the significant change in R2 between each step were evaluated. The change in R2 provided increased predictive power by the addition of certain directional inertial variables at each regression step.  

Results

Overall, ten inertial variables were significantly correlated with KFM, aGRF, and vGRF (Table V). Only ST was not significantly correlated with any biomechanical variables. In particular, IMP-V was solely correlated with KAM. The selected inertial gait variable subsets for each of the four biomechanical gait variables are listed in Table VI and VII. For trial-averaged biomechanical variable prediction models, no lateral inertial variables were selected for KFM and aGRF, and none of the vertical inertial variables were selected for KAM and vGRF (Table VI). ST was selected for all four biomechanical variable estimations, although ST was not significantly correlated with them in the Pearson Correlation analysis results. For the trial symmetry of biomechanical variable prediction models, the lateral and vertical magnitude variables (i.e., MAG-L, and MAG-V) were selected except an anterior magnitude variable (i.e., MAG-A) (Table VII). The inclusive variables were relatively less frequently selected for symmetry prediction models. Robustness and generalizability of the estimation models were improved by reducing the dimensionality of inertial gait variables. Hierarchical linear regression results demonstrated a strong potential that the proposed wearable sensor-derived acceleration data can assist in quantifying biomechanical gait measures. In Table VIII, the average and symmetry of biomechanical variables were predicted using the selected inertial variables. Each individual table contains the prediction results for 17 subjects. One subject (71 year-old male, BMI 31.6) was excluded from the analysis due to a distinctly abnormal gait pattern characterized by heel strikes with overtly large vertical ground reaction force. The subject was identified as an outlier based on the median absolute deviation measure [17]. By removing the subject, the average and symmetry of vGRF prediction produced more reasonable prediction power. Regarding average prediction results, all four biomechanical variables were significantly predicted by using selected subsets of inertial variables. Directional contributions were identified. For instance, aGRF was primarily related to the anterior axis, and the anterior inertial gait variables predicted most of the outcome (i.e., 0.467 of 0.697 as adj. R2). Similar directional alignments were observed from KFM and KAM. Although vGRF was significantly predicted, there was no such directional alignment because none of the vertical inertial variables was selected. In the symmetry prediction outcomes, the symmetry of KFM explained more than 87% of the variance in the variable. The effect of the uncommon walking subject was also trivial, so the exclusion of the subject did not change the results. Specifically, the symmetry of vGRF was substantially affected by the uncommon walking subject. The subject caused strongly biased gait variables and abnormally increased adj. R2 up to 0.919.  By removing the subject, adj. R2 was adjusted by 0.547.

Discussion

The goal of this study was to estimate kinematic and kinetic gait metrics using two ankle-worn wearable sensors in individuals after unilateral TKA. Overall, we found that our novel method of extracting unique features from 3D accelerations is capable of predicting key biomechanical measure in a post-TKA population. Compared to previous studies focused on predicting knee loads post-TKA, our results demonstrate greater predictive power. Rivière et al. have focused on isolated clinical measures such as limb alignment (R2 < 0.13) [3], and Vahtrick et al. have investigated on limb strength (R2 < 0.32) [4]. The results of this study indicate that wearable sensors can be used to predict key knee loading [1, 2] variables important to recovery post-TKA with greater power than basic clinical measures. This may be due to the more direct nature of wearable accelerometry during gait, versus indirect measures of predisposition (limb alignment) or capacity (strength) that do not take into account an individual’s active movement and muscle coordination during the specific task of gait. Outcomes of the regression models indicated that inertial gait features significantly estimated all four biomechanical gait features. Interestingly, the temporal parameter of step time was not significantly correlated with any biomechanical variables of interest, whereas most of the inertial variables showed moderate to significant correlation with biomechanical variables. In particular, as anterior direction motion of ankle-worn sensors was predominant over other two directions, many inertial variables were significantly corrected with aGRF. Primary axes of biomechanical variables were related to selected inertial variables. However, it was difficult to explain the connection between response and predictor variables due to the complex nature of gait. Notably, lateral and vertical heel-strike magnitude and anterior stance phase angle variation were commonly selected for symmetry prediction models, and inclusive variables were considered less important predictor variables. Our results imply that wearable sensor-based data that explain overall step timing were not useful to estimate the symmetry of biomechanical variables. Knee flexion moment was primarily explained by vertical inertial gait variables. It is likely that vertical inertial variables are related to limb impact during heel strike. Impact may be partially controlled by knee flexion with an increase in knee flexion during weight acceptance, serving to soften impact but subsequently increase peak knee flexion moment. On the other hand, knee adduction moment was primarily explained by lateral inertial gait variables. Gait modifications including increased step width, increased trunk sway, and toe-in gait have been shown to be effective at reducing knee adduction moment in a healthy population [18]. It is likely that individuals post-TKA may adapt similar strategies to reduce knee adduction moment because of pain or functional compensations. It is reasonable to believe that such gait adaptations may be evidenced through lateral inertial gait variables, given the changes in side-to-side movement (i.e., swaying, wide steps).

Conclusion

The proposed models and biomechanical gait variables estimation results provided evidence that inertial measurements can be used to reasonably estimate conventional biomechanical metrics. Although cross-validation was applied, generalization to the TKA population could be limited due to the small sample size of this study. Future work will examine the relationship between additional kinematic and kinetic variables and inertial variables in characterizing changes over time, and expand to additional populations and biomechanical metrics.