## Abstract

Healthy adults employ one of three primary strategies to recover from stumble perturbations—elevating, lowering, or delayed lowering. The basis upon which each recovery strategy is selected is not known. Though strategy selection is often associated with swing percentage at which the perturbation occurs, swing percentage does not fully predict strategy selection; it is not a physical quantity; and it is not strictly a real-time measurement. The objective of this work is to better describe the basis of strategy selection in healthy individuals during stumble events, and in particular to identify a set of real-time measurable, physical quantities that better predict stumble recovery strategy selection, relative to swing percentage. To do this, data from a prior seven-participant stumble experiment were reanalyzed. A set of biomechanical measurements at/after the perturbation were taken and considered in a two-stage classification structure to find the set of measurements (i.e., features) that best explained the strategy selection process. For Stage 1 (decision between initially elevating or lowering of the leg), the proposed model correctly predicted 99.0% of the strategies used, compared to 93.6% with swing percentage. For Stage 2 (decision between elevating or delayed lowering of the leg), the model correctly predicted 94.0% of the strategies used, compared to 85.6% with swing percentage. This model uses dynamic factors of the human body to predict strategy with substantially improved accuracy relative to swing percentage, giving potential insight into human physiology as well as potentially better informing the design of fall-prevention interventions.

## 1 Introduction

People exhibit various balance recovery strategies in response to a stumble perturbation. The three primary responses to a perturbation in swing phase have been identified as (1) the elevating strategy, in which the foot lifts up and forward to clear the obstacle in the same step, (2) the lowering strategy, in which the foot lowers to the ground behind the obstacle and clears it in the following step, and (3) the delayed lowering strategy, in which the foot initially lifts up but subsequently lowers to the ground behind the obstacle before clearing it in the following step [1,2]. The causal factors that underlie the selection of these recovery strategies are not well known. Better understanding the factors associated with strategy selection (i.e., the process by which a perturbation results in one of the three aforementioned recovery strategies), and particularly the information upon which this selection is based, may improve the design of interventions intended to mitigate the effect of stumble perturbations, especially for individuals at heightened fall risk (e.g., elderly individuals, stroke patients, and lower-limb prosthesis users).

Over the past several decades, the majority of stumble-related research has focused on three topics: experimental apparatus design, fall prediction, and recovery characterization. Regarding the first, various methods of eliciting stumbles in a lab setting have been presented and validated in order to study stumbling and the subsequent recovery or fall of healthy and impaired individuals. Methods include overground floor-deployable obstacle perturbations (e.g., Ref. [2]), overground rope-blocking (e.g., Ref. [3]), treadmill-based belt-deployable obstacle perturbations (e.g., Refs. [4] and [5]), treadmill-based rope-blocking (e.g., Refs. [6] and [7]), and electrical stimulation (e.g., Ref. [8]). Using these techniques, researchers have explored the risk factors for falls in various populations. Some studies investigate the effect of dynamic factors such as trunk flexion angle on recovery success [914], while others consider demographics and physical characteristics such as age, sex, strength and gait pattern [1517]. Other studies characterize the nature of recovery in healthy individuals, namely, the elevating, lowering, and delayed lowering strategies. The focus of these studies includes: the kinematics of the tripped limb for each recovery strategy [2,4,18], the reflexes involved in each recovery strategy [1,2,1922], the role of the support limb [23,24], the role of arm movements [25], the mechanical modeling of recovery [26], and segmental energy changes in recovery strategies [27].

Although the kinematics and kinetics of the three primary recovery strategies have been characterized, the basis upon which each is selected is not well established. The convention in prior literature is to associate stumble recovery strategy selection with the swing percentage at which the perturbation occurs. For example, it has been observed that elevating strategies are typically used following early-swing perturbations, while lowering strategies are typically used following late-swing perturbations (e.g., Ref. [2]). However, there is evidence that healthy individuals do not select a recovery strategy during a stumble event based upon swing percentage.

First, the accuracy with which swing percentage predicts strategy selection is limited, particularly in the mid-swing regime (i.e., 40–70% swing phase). Schillings et al. [1] introduced stumble perturbations to eight healthy individuals, targeted at early, mid, and late swing phase. The authors found that there was no clear swing percentage threshold that separated elevating from lowering strategies, concluding that the final strategy used was not simply a function of the swing percentage of the perturbation. Similarly, Forner Cordero et al. [7] introduced stumble perturbations of various durations and at various points in swing phase to five healthy individuals and concluded that the factors that led to the selection of a specific recovery strategy were unknown. Shirota et al. [6] also reported that perturbations during mid-swing can result in various recovery strategies, suggesting that other factors (besides swing percentage of perturbation) affect strategy selection. This idea was also highlighted in Ref. [28].

Second, swing percentage is neither a real-time measurement nor a physical quantity. Swing percentage is defined relative to the entire swing phase (time duration), which cannot be exactly known until the entire swing phase has been completed. Furthermore, swing percentage is not a direct physical measurement of the body's dynamic state at perturbation. Rather, a person (or device) who has stumbled must make a strategy selection in real-time, presumably based on sensing of one or more measurable quantities. Note that swing percentage can be estimated in real-time via measurement of at least one measurable proxy (e.g., ground reaction force), where the accuracy of the estimate depends on the degree of stationarity (i.e., invariant periodicity) and structural invariance (i.e., invariance in relationships between states). The accuracy of this real-time estimation therefore decreases as individuals change cadence or vary movement patterns. Thus, there is ample motivation for exploring the extent to which real-time physical measurements (which do not require assumptions of stationarity or structural invariance) can provide improved accuracy relative to a phase variable (e.g., swing percentage).

A couple papers have investigated factors beyond swing percentage for strategy selection [6,9]. Shirota et al. [6] investigated the effect of perturbation duration and limb tripped (i.e., left versus right), in addition to swing percentage, on strategy selection. They found that swing percentage and perturbation duration significantly improved the prediction of their multinomial logistic regression model, and that limb tripped improved the prediction but not significantly. Pavol et al. [9] investigated the effect of forward hip velocity and speed and height of the swing ankle (in addition to swing percentage) on strategy selection. They found that the odds of employing a lowering strategy increased as swing ankle height decreased, and the odds increased as swing percentage increased, but recovery strategy was unrelated to the forward hip velocity or swing ankle speed. The delayed lowering strategy was not investigated.

This work builds upon this prior research, and specifically leverages a large experimental set of stumble data to offer insight into the nature of the strategy selection process, specifically by identifying a set (or sets) of factors that (i) are real-time measurable, physical quantities and (ii) predict strategy selection with better accuracy than using the traditional swing percentage input. The intent is to provide a better understanding of which physical factors may form the basis of strategy selection, giving potential insight into human physiology as well as informing the design of interventional devices such as prosthetic limbs.

## 2 Methods

In order to gain insight into which real-time measurable quantities best describe the outcomes observed in a prior study of healthy participant stumble perturbations, the problem was treated as a classification problem with a large number of possible measurable inputs, and with three output classes: Elevating, Lowering, and Delayed Lowering. The authors established a basic framework for the strategy selection process, based on foot trajectory timing. Next, a set of potential model inputs was identified. Data from the prior stumble experiment were then processed and organized in such a way that the classification problem could be tested (i.e., features were extracted from the potential inputs as predictors, and data were organized into a set of potential features and corresponding output class for each trial). After several feature exploration steps, a feature selection process was implemented to obtain the final feature sets. Finally, classification results using the final feature sets were compared to results using swing percentage of perturbation as the feature set (within the same selection framework). The following subsections enumerate: (i) the stumble recovery experiment, (ii) the strategy selection framework, (iii) the set of potential model inputs, (iv) the composition of datasets for each stage, (v) feature exploration, (vi) feature selection, and (vii) model comparison.

### 2.1 Stumble Perturbation Experiment.

In order to provide an extensive dataset upon which a stumble recovery strategy selection model could be constructed and tested, seven healthy participants (three female, four male, mean age: 23.6 yrs, mean height: 1.8 m, mean mass: 81.3 kg) were recruited in a prior study for a series of stumble perturbation experiments. The stumble perturbation system and protocol used are described in Ref. [5]. All experimental protocols were approved by the Vanderbilt Institutional Review Board, and all participants gave their written informed consent. Each participant experienced 14 unexpected obstacle perturbations to each limb, targeted between 10% and 75% swing phase in 5% increments, while walking on a treadmill at 1.1 m/s. Note that the obstacle perturbations were imperceptible to the participants prior to contact due to obstacle delivery apparatus design choices and sensory occlusion techniques, as detailed in Ref. [5]. This seven-participant, single-speed stumble experiment is hereafter referred to as Experiment A.

In order to better inform a potential dependence on walking speed, the experimental protocol was repeated for one of the seven participants (Participant 3) at two additional speeds. For these trials, the participant experienced a total of 13 obstacle perturbations at 0.8 m/s and 13 obstacle perturbations at 1.4 m/s, targeted between 10% and 75% swing phase. This single-participant, two-speed stumble experiment is hereafter referred to as Experiment B.

For all trials, ground reaction force (GRF) data were collected under each foot at 2 kHz via a force-instrumented split-belt treadmill (Bertec, Columbus, OH), in addition to full-body kinematic data (including foot, shank, thigh, pelvis, torso, upper arm, and forearm segments), which were recorded at 200 Hz via an infrared motion capture system (Vicon, Oxford, GBR). GRF and motion capture data were processed with a zero-phase, third-order, Butterworth low-pass filter at a cutoff frequency of 15 and 6 Hz, respectively. Inverse dynamics were computed using Visual3D (C-Motion, Germantown, MD) to estimate full-body kinematics and kinetics for each trial.

The swing percentage at which the stumble occurred was calculated as the time of perturbation relative to the preceding toe-off event divided by the average swing time of 25 strides prior to the perturbation. The perturbation event was determined as the instant at which the foot contacted the obstacle, which was identified via a transient peak in the anterior-posterior GRF measured by the treadmill.

The recovery strategy used for each stumble event was identified as Elevating, Lowering, or Delayed Lowering, as determined by the trajectory of the swing foot immediately after the perturbation as follows: in the Elevating strategy, the foot lifts up and over the obstacle after contact with the obstacle; in the Lowering strategy, the foot lowers to the ground behind the obstacle after contact with the obstacle; in the Delayed Lowering strategy, the foot initially elevates (i.e., shows some upward motion) before elevation is abandoned and the foot subsequently lowers to the ground without clearing the obstacle.

### 2.2 Strategy Selection Framework.

Strategy selection was modeled using a two-stage process. During initial exploration, the response to the stumble perturbation was modeled as a one-stage process, in which at the time of perturbation, one of the three responses (Elevating, Lowering, or Delayed Lowering) was selected. Upon further analysis of the data, however, it became clear that a two-stage process, as depicted in Fig. 1, is more representative of the observed stumble recovery strategy selection process. Figure 1(a) shows a representation of typical data for foot height immediately following the stumble perturbation. As observed in the trajectories, the data indicate two points of bifurcation that occur at two distinct points in time: at the instant of perturbation, and tens of milliseconds after the perturbation. The first time point corresponds to either Elevating versus Lowering, while the second time point corresponds to either continuing to Elevate versus abandoning the Elevating strategy in favor of Lowering (i.e., Delayed Lowering). As such, the selection process was modeled as a two-stage process, as diagrammed in Fig. 1(b). Existence of a two-stage decision process is also supported by Ref. [1], which reports that the electromyography signals during a Delayed Lowering strategy suggest that on-line afferent information during the recovery is incorporated into the response and may be used to alter the final stumble recovery strategy. Schillings et al. [19], Nieuwenhuijzen et al. [29], and Nieuwenhuijzen et al. [30] support the existence of a two-stage muscle activity response to perturbations, and Refs. [31] and [32] explore this concept further by introducing a secondary constraint during trip recovery. Thus, the Delayed Lowering strategy is modeled as a change in initial strategy rather than a strategy in itself. The authors note that the existence of a two-stage selection process, such as that proposed here, was further substantiated by improved accuracy of the models (see Table D1 available in the Supplemental Materials on the ASME Digital Collection for results from alternate one-stage selection frameworks as a comparison). As such, model formulation was separated into two sequential classification problems: a first between Initially Elevating versus Lowering, and a second between Elevating versus Delayed Lowering, each with a potentially distinct set of real-time inputs.

Fig. 1
Fig. 1
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Table 1

The final feature sets chosen for the model for each stage of the strategy selection process, with corresponding total classification accuracies from the cross-validation process for Datasets A1 and A2 (i.e., the average of the percentage of correctly predicted trials from each participant/fold)

DatasetFeature setClassification accuracy
A1 (Stage 1)CF-to-COM angle ($θ)$99.0%
Knee angular velocity ($γ˙)$
Body COM vertical velocity ( $z˙com)$
Foot angular acceleration ($λ¨$)
A2 (Stage 2)IF-to-COM angular acceleration ($ϕ¨$)94.0%
Shank angular acceleration ($δ¨$)
Knee angle+ ($γ+$)
Body COM vertical velocity $Δ$ ($z˙comΔ$)
DatasetFeature setClassification accuracy
A1 (Stage 1)CF-to-COM angle ($θ)$99.0%
Knee angular velocity ($γ˙)$
Body COM vertical velocity ( $z˙com)$
Foot angular acceleration ($λ¨$)
A2 (Stage 2)IF-to-COM angular acceleration ($ϕ¨$)94.0%
Shank angular acceleration ($δ¨$)
Knee angle+ ($γ+$)
Body COM vertical velocity $Δ$ ($z˙comΔ$)

Note that the “+” indicates that the feature is the measurement taken 60 ms after perturbation, and the “$Δ$” indicates that the feature is the change in value from the instant of perturbation to 60 ms after the perturbation. Refer to Fig. 2 for diagrams depicting each physical quantity.

There are numerous classification algorithms that can be used for each stage in this model. In initial processing, multiple classification schemes were compared and all performed similarly; logistic regression was chosen based on its straightforward ability to report probability of membership in a certain class, which provides insight into the weight/confidence of each prediction, and its relative computational simplicity, which lends itself well to real-time implementation within embedded systems (e.g., for eventual implementation in interventional devices such as robotic prostheses).

### 2.3 Potential Model Inputs.

To capture the body's configuration and body-mass-normalized kinetic state, the potential inputs included joint (internal) and segment (external) angles, joint and segment angular velocities, joint and segment angular accelerations, foot center-of-mass (COM) linear velocities and accelerations, body COM linear velocities and accelerations, as well as each foot's anterior-posterior position relative to the body center of mass (and corresponding derivatives). The quantities considered are illustrated in Fig. 2.

Fig. 2
Fig. 2
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### 2.4 Composition of Datasets.

Data from the stumble perturbation trials were treated as the classification problem discussed in Sec. 2.2. To start, two datasets were generated from Experiment A–one to test each stage.

To test Stage 1 (see Fig. 1), each of the potential inputs was extracted for each trial at the instant of perturbation (hereafter referred to as features), and each trial was given the class tag Initially Elevating or Lowering (i.e., Elevating and Delayed Lowering strategies were labeled Initially Elevating while Lowering strategies were labeled Lowering). This dataset is hereafter referred to as Dataset A1, comprised of 35 features for each of the 188 relevant experimental trials.

To test Stage 2 (see Fig. 1), each of the potential inputs was extracted for all Initially Elevating trials (1) at the instant of perturbation and (2) 60 ms after the perturbation (hereafter referred to as features), and each of these trials was given the class tag Elevating or Delayed Lowering. The difference in each potential input from the instant of perturbation to 60 ms after the perturbation was also recorded and used as a feature. This dataset is hereafter referred to as Dataset A2, comprised of 105 features for each of the 165 relevant experimental trials. The 60-ms post-perturbation delay was chosen because it is sooner than the time-to-peak of the foot height trajectories of all Delayed Lowering strategies recorded (minimum: 90 ms, maximum: 200 ms; average: 128.7±28.2 ms) but long enough after the perturbation to allow for the integration of a new physiological reflex [1,19].

As in Dataset A, all Experiment B trials were tagged as Initially Elevating or Lowering for Dataset B1, and all Initially Elevating trials were tagged as Elevating or Delayed Lowering for Dataset B2, and the corresponding set of features was generated for each trial. Features were standardized to zero-mean and unit-variance [33].

### 2.5 Feature Exploration.

To gain an initial (and unsupervised) understanding of the information provided by the features for each stage, a principal component analysis (PCA) was computed for the 35-feature set (Stage 1) and 105-feature set (Stage 2), which gives an estimate of the dimensionality of each feature set. Additionally, the Pearson's linear correlation coefficient was calculated for each feature against every other feature, which gives insight into the redundancy or interdependence of some features.

In order to understand the performance of each feature individually in explaining strategy selection, each feature was singularly considered as a feature subset. For Stage 1, each feature in Dataset A1 was fit to a logistic regression model with L2 (i.e., ridge) regularization and cross-validated by participant [33]. Specifically, a model was fit to six participants' data and then tested on the remaining participant; this step was repeated seven times (until all trials had been tested). Initially Elevating was set as the reference class, such that for each trial, if the logistic regression model output a probability greater than 0.5, the trial was predicted as Initially Elevating; otherwise, it was predicted as Lowering. The probability and prediction for each trial were recorded. The percentage of trials that were predicted correctly (classification accuracy) was computed for each fold (which consisted of one participant's trials). After the seven iterations, the average of each participant's classification accuracy was computed and recorded as total classification accuracy. This process was performed for each of the following regularization strength (hyperparameter) values: 0.001, 0.01, 0.1, 1, 10, 100, 1000; the value that produced the highest total classification accuracy was used. For Stage 2, each individual feature in Dataset A2 was fit to a logistic regression model with L2 regularization and cross-validated by participant. Elevating was set as the reference class, such that for each trial, if the logistic regression model output a probability greater than 0.5, the trial was predicted as Elevating; otherwise, it was predicted as Delayed Lowering. This process was performed for each of the following regularization strength values: 0.001, 0.01, 0.1, 1, 10, 100, 1000; the value that produced the highest total classification accuracy was used.

### 2.6 Feature Selection.

A wrapper method was used to find the subset of features that produced the highest total classification accuracy for each stage (i.e., the subset of features that best modeled the strategy selection process for Dataset A1, and then again for Dataset A2) [34]. Specifically, every combination of features for each stage (with a maximum number of features based on PCA results) was considered using the cross-validation procedure with hyperparameter tuning described in Sec. 2.5, and the subsets that produced the highest total classification accuracy were recorded for each stage.

In order to arrive at a final feature set for each stage, the feature subsets that best predicted strategy selection for 1.1 m/s trials (i.e., the feature subsets that resulted in the highest total classification accuracy from the wrapper method on Experiment A) were then tested to determine whether they also extended across walking speeds (i.e., also extended to Experiment B). Recall that Experiment B consisted of Participant 3 walking at two other walking speeds. In order to test the extent to which the feature sets identified in Experiment A also described Experiment B, each of the best performing subsets for Stage 1 was trained on Dataset A1, excluding data from Participant 3, and tested on Dataset B1 (Participant 3's data at other walking speeds related to Stage 1) for each of the regularization strength values. Likewise, each of the best performing subsets for Stage 2 was trained on Dataset A2, excluding data from Participant 3, and tested on Dataset B2 (Participant 3's data at other walking speeds related to the Stage 2) for each of the regularization strength values. Classification accuracy was recorded for each stage for each feature subset-hyperparameter combination, calculated as the percentage of correctly predicted trials in Datasets B1 and B2. The feature subsets for each stage that performed best on Datasets B1 and B2 were chosen as the final feature sets.

Logistic regression model fitting and testing using the wrapper method with cross-validation and hyperparameter tuning were all performed in python (Python 3.8, Amsterdam, NL) using the Scikit-learn module [35]. Preliminary data exploration was performed using the Orange Data Mining Toolbox [36].

### 2.7 Model Comparison.

The classification results for the final feature sets for Stage 1 and Stage 2 were compared to the classification results for the feature set of swing percentage (using the same selection framework, classification algorithm, cross-validation process, and hyperparameter tuning) for Experiment A. Likewise, the classification results for training on Dataset A and testing on Dataset B using the final feature sets were compared to results using swing percentage as the feature set.

## 3 Results

### 3.1 Stumble Perturbation Experiment Results.

In total, Experiment A elicited 126 Elevating strategies, 39 Delayed Lowering strategies, and 23 Lowering strategies. Note that six trials were excluded due to the participant stepping onto the obstacle (i.e., targeting error), and two trials were excluded due to anomalous recoveries (i.e., due to foot scuff and falling, which prevented these trials from being classified as one of the three defined recovery strategies). The breakdown of strategy used as a function of swing percentage of perturbation is depicted in Fig. 3.

Fig. 3
Fig. 3
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Experiment B elicited a total of eight Elevating, three Delayed Lowering, and two Lowering strategies at 0.8 m/s and six Elevating, six Delayed Lowering, and one Lowering strategy at 1.4 m/s. These results are expanded upon in Fig. C1 available in the Supplemental Materials on the ASME Digital Collection, which shows the breakdown of strategy used as a function of swing percentage of perturbation.

### 3.2 Feature Exploration Results.

The PCA results indicated that approximately 80% of the variance of the Stage 1 set of features can be accounted for with three principal components, and 80% of the variance of the Stage 2 set of features can be accounted for with four principal components. Thus, four was set as the maximum number of features in a subset for the wrapper method described in Methods. To elaborate on the results of the PCA, Scree plots are reported in Fig. A1 available in the Supplemental Materials. Correlation coefficients of every feature pair are given in Figs. A2 and A3 available in the Supplemental Materials for reference.

The feature that best predicted strategy selection alone for Stage 1 was hip angular velocity $(α˙$) with 96.3% classification accuracy, and for Stage 2 was ipsilateral foot to body COM (IF-to-COM) angle at perturbation ($ϕ$) with 88.3% classification accuracy. Notably, eight features individually outperformed swing percentage (93.7%) for Stage 1, and 13 features individually outperformed swing percentage (85.6%) for Stage 2. The classification accuracy of each individual feature for each stage is tabulated in Tables A1 and A2 available in the Supplemental Materials for reference.

Table 2

Classification accuracy for the RTMM and SPM for each stage of the strategy selection process as well as composite accuracy for Dataset A. Specifically, the first two rows give the total classification accuracy from the cross-validation process for Datasets A1 and A2 (i.e., the average of the percentage of correctly predicted trials from each participant/fold). The composite accuracy (third row) was calculated by combining the Stages 1 and 2 classification accuracies, weighted by the number of trials in each class.

DatasetRTMM classification accuracySPM classification accuracy
A1 (Stage 1)99.0%93.7%
A2 (Stage 2)94.0%85.6%
Composite93.8%81.3%
DatasetRTMM classification accuracySPM classification accuracy
A1 (Stage 1)99.0%93.7%
A2 (Stage 2)94.0%85.6%
Composite93.8%81.3%

### 3.3 Feature Selection Results.

For Stage 1, using the wrapper method, four subsets of features (out of 59,500 possible subsets) produced a classification accuracy of 99.0% or higher. For Stage 2, 28 subsets of features (out of 4,973,150 possible subsets) produced a classification accuracy of 94.0% or higher. The final feature sets (i.e., the feature subsets for each stage that performed best when also testing on Dataset B) are reported in Table 1. Figures 4 and 5 further delineate the results for each stage with (a) the confusion matrix of prediction results and (b) scatter plots of the datasets as a function of inputs used. For reference, the classification results from remaining top performing subsets are tabulated in Tables B1 and B2 available in the Supplemental Materials.

Fig. 4
Fig. 4
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Fig. 5
Fig. 5
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### 3.4 Model Comparison Results.

The results from the two-stage strategy selection framework with final feature sets of real-time measurable, physical quantities (i.e., the final feature sets chosen as explained in Methods and reported in Table 1) will hereafter be referred to as the real-time measurable model (RTMM). The results from the same framework using swing percentage of perturbation as the feature set will hereafter be referred to as the swing percentage model (SPM).

Table 2 reports the classification accuracy results of the RTMM versus the SPM for each stage, as well as a composite accuracy for Dataset A. Specifically, the first two rows give the total classification accuracy from the cross-validation process for Datasets A1 and A2 (i.e., the average of the percentage of correctly predicted trials from each participant/fold). The composite accuracy (third row) was calculated by combining the Stages 1 and 2 classification accuracies, weighted by the number of trials in each class. Table 3 reports the classification accuracy results of the RTMM versus the SPM for testing on Dataset B. Specifically, the first two rows give the percentage of trials from Datasets B1 and B2 that were predicted correctly (after training on Datasets A1 and A2 with the final feature sets, excluding data from Participant 3). The composite accuracy (third row) was calculated by combining the Stages 1 and 2 percentages, weighted by the number of trials in each class. Additional figures delineating the results of the model for testing on Experiment B (i.e., confusion matrices and scatter plots) are provided in Figs. C2 and C3 available in the Supplemental Materials on the ASME Digital Collection for reference. For comparison, Fig. 6 reports the confusion matrix for each stage when using swing percentage as the feature set.

Fig. 6
Fig. 6
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Table 3

Classification accuracy for the RTMM and SPM for each stage of the strategy selection process as well as composite accuracy for Dataset B. Specifically, the first two rows give the percentage of trials from Datasets B1 and B2 that were predicted correctly (after training on Datasets A1 and A2 with the final feature sets, excluding data from Participant 3). The composite accuracy (third row) was calculated by combining the Stage 1 and Stage 2 percentages, weighted by the number of trials in each class.

DatasetRTMM classification accuracySPM classification accuracy
B1 (Stage 1)100.0%92.3%
B2 (Stage 2)95.7%91.3%
Composite96.2%85.2%
DatasetRTMM classification accuracySPM classification accuracy
B1 (Stage 1)100.0%92.3%
B2 (Stage 2)95.7%91.3%
Composite96.2%85.2%

## 4 Discussion

Unlike using the conventional swing percentage criterion for describing stumble recovery strategy selection, the RTMM provides a physically implementable model (i.e., employs real-time measurable, physical quantities as inputs), and better accuracy.

For Stage 1 (Initially Elevating or Lowering), the model correctly predicts 99.0% of the strategy selection observed in Experiment A with the feature set of contralateral foot to body COM (CF-to-COM) angle ($θ$), knee angular velocity ($γ˙$), body COM vertical velocity ($z˙com$), and foot angular acceleration ($λ¨$) at the time of perturbation, compared to 93.7% when using swing percentage. Note that CF-to-COM angle captures how far the contralateral foot leads (anterior to) or trails (posterior to) the body's COM at the time of perturbation. As shown in Fig. 4(b), as the contralateral foot becomes more posterior to the COM at perturbation (i.e., more negative angle), the more likely a Lowering strategy is used (i.e., the incidence of Lowering strategies increases). Knee angular velocity captures the mass-normalized momentum of the perturbed limb at perturbation. The faster the knee is extending at perturbation (i.e., more positive angular velocity), the more likely a Lowering strategy is used. Body COM vertical velocity captures the mass-normalized momentum of the whole body. As the velocity becomes more positive at perturbation, the more likely an Elevating strategy is used. In effect, the body tends to initially opt for a strategy that allows it to continue in the direction it is moving (i.e., avoid a change in momentum). Finally, the foot angular acceleration captures the instantaneous change in the ipsilateral foot's angular velocity (i.e., change in mass-normalized angular momentum, or angular impulse). When coupled with the other features, a distinct region forms in which the Lowering strategy is more common. For example, the Lowering strategy has higher incidence when the contralateral foot is well behind the COM with lower foot accelerations.

For Stage 2 (Elevating or Delayed Lowering), the model correctly predicts 94.0% of the strategy selection observed in Experiment A with the feature set IF-to-COM angular acceleration $(ϕ¨$) and shank angular acceleration ($δ¨$) at the time of perturbation, knee angle 60 ms after the perturbation $(γ+$), and change in body COM vertical velocity $(z˙comΔ$), compared to 85.6% when using swing percentage. IF-to-COM angular acceleration captures the instantaneous change in the body's angular velocity (i.e., change in mass-normalized angular momentum, or angular impulse). Shank angular acceleration similarly captures the instantaneous change in the tripped limb's angular velocity at perturbation. As shown in Fig. 5(b), the body is more likely to abandon Elevating as the magnitudes of these angular impulses increase. Knee angle captures the tripped limb's configuration state 60 ms after the perturbation. Change in body COM vertical velocity captures the body's mass-normalized change in momentum in the vertical direction. Combinations of these four features create distinct regions in which the Delayed Lowering strategy is more likely; for example, regions of less knee flexion (less negative knee angle) and higher angular acceleration magnitude tend to produce Delayed Lowering strategies.

Overall, the classification accuracy of the RTMM for Stage 2 is lower than for Stage 1; this suggests that there is some piece of Stage 2 that is not captured with the physical quantities used (e.g., there may be something intrinsic to each participant that might influence the Stage 2 strategy selection that is not represented by this dynamic model). To investigate this, an additional feature set of participant-specific properties was generated, which included the following: height, mass, sex, average swing time, average stride time, limb tripped, and minimum foot height in swing phase. However, none of these features increased the classification accuracy for Stages 1 or 2 of the strategy selection process, suggesting that neither stage was dependent on these factors (or, at least, not any more than the other features used). Thus, in Stage 2, factors that have not been captured in the present dynamic model (or captured by the participant properties) may be contributing to the selection of Elevating or Delayed Lowering. Such factors might be psychological and/or based on physical fitness, coordination, or strength. Collectively, these findings suggest that the initial reaction (Stage 1) of the strategy selection process is dominated by the physics (i.e., the dynamic conditions at the moment of perturbation, which are the quantities that were extracted and tested in this work), whereas Stage 2 may additionally be influenced by a participant's ability or other factors (that were not tested in this work), which vary participant-to-participant.

It is notable that the feature sets used in the RTMM perform well on trials at different walking speeds (Experiment B), and again outperform swing percentage, as shown in Table 3. Figures C2 and C3 available in the Supplemental Materials on the ASME Digital Collection support and expand upon these results, showing that the features maintain the same trends as from Experiment A. Thus, the RTMM may be robust and not limited to just one speed or cadence.

Table 4 shows the RTMM classification accuracy results (using the final feature sets with the same cross validation and hyperparameter tuning procedures as discussed previously) for only trials that occurred between 40–70% swing phase (89 trials in total: 40 Elevating, 37 Delayed Lowering, 12 Lowering) versus SPM. The RTMM outperforms swing percentage in predicting strategies chosen, even in mid-swing, which was the region most in question (see Introduction, Fig. 3 [1,6,7]).

Table 4

Classification accuracy for the RTMM and SPM for each stage of the strategy selection process as well as composite accuracy for Dataset A for only perturbations that occurred between 40 and 70% swing phase. Specifically, the first two rows give the total classification accuracy from the cross-validation process (i.e., the average of the percentage of correctly predicted trials from each participant/fold). The composite accuracy (third row) was calculated by combining the Stages 1 and 2 classification accuracies, weighted by the number of trials in each class.

DatasetRTMM classification accuracySPM classification accuracy
A1 (Stage 1)97.8%88.8%
A2 (Stage 2)87.0%71.4%
Composite86.8%66.8%
DatasetRTMM classification accuracySPM classification accuracy
A1 (Stage 1)97.8%88.8%
A2 (Stage 2)87.0%71.4%
Composite86.8%66.8%

The authors note that if an individual is walking with a stationary (i.e., periodically invariant) gait, as was the case for the treadmill trials used in this analysis, the swing percentage of perturbation can be estimated in real-time using the average swing time of previous strides. The accuracy with which swing percentage can predict strategy selected is reported here, and such an approach may be suitable for predicting strategy selection, depending on (1) availability of biomechanical data, (2) walking conditions, and (3) level of accuracy desired. However, the results reported herein indicate that RTMM approaches offer improved accuracy. Such a model is important in order to provide: (1) physiological insight into the human body's responses to swing-phase perturbations and (2) a basis on which various applications/interventions requiring real-time stumble recovery strategy selection could be implemented, both of which are discussed below.

As previously explained, the feature set used in the RTMM includes measurements that are related to either the configuration or normalized kinetic state of the human body at and just after perturbation. Given their real-time nature, these signals (or neurophysiological proxies for these signals) could be what the body is utilizing to reflexively respond. Each feature can be thought of as a signal sensed in a physiologically relevant process, such as a sensory neuron involved in spinal and long-loop reflexes. For example, muscle spindles are sensory neurons that sense limb velocity via muscle length and rate of change; thus, knee angular velocity is information potentially captured by these biological sensors. Similarly, Golgi tendon organs sense load on a limb, and so foot angular acceleration could be accessed and used by these sensory neurons. And more broadly, the configuration states such as CF-to-COM angle are information perceived by the vestibular system along with fusion of various proprioceptors.

The real-time nature of these features is not only important with regard to a potential link to relevant physiological systems, but also in the capacity to be accessed from wearable sensors for various applications. For example, given that these signals are used in the strategy selection process to successfully recover from a stumble, it may be advantageous to monitor these values in a fall prevention program or study. Additionally, for individuals with a higher propensity for falling, such as the elderly, stroke patients, or lower-limb prosthesis users, these signals might be incorporated into fall prevention controllers in assistive devices. Tables B3 and B4 available in the Supplemental Materials on the ASME Digital Collection report classification accuracy results for feature sets that include only quantities measurable from a lower-limb knee prosthesis as an example.

Note that the goal here was to find the best feature sets considering all potential features, so the authors did not place any limits on which of the potential features could be used in the wrapper method; however, for various applications/research questions there may be constraints on what number or type of features can be used (e.g., only features that are measurable from the ipsilateral limb are available, or only two features can be measured at a time). Thus, various other scenarios were considered and results are tabulated in Tables B3 and B4 available in the Supplemental Materials for reference. The authors recognize that one approach could have been to initially filter out features with high correlation values to reduce the set of potential features and thus number of potential subsets; however, because the authors had the computational bandwidth to try all combinations (up to four features in a subset), and the focus was on finding a set with the best performance (and not with interpreting coefficients), all features were kept in order to maximize opportunities for highest model performance. This is likely why many feature sets performed similarly (as indicated in Results); the authors chose to report the best feature sets in the main text but tabulate other top-performing sets in Tables B1-B4 available in the Supplemental Materials to inform readers on which other features worked well for reference.

There are several limitations to this work. First, for classification problems it is ideal to have an even distribution of classes, which was not the case for this study; this issue is addressed in this work in several ways. Experimentally, it is possible to control the timing of perturbation [5], but not to control the recovery strategy employed by the participant. The goal was to elicit perturbations at a range of points in swing phase, which was accomplished (see Fig. 3). The authors contend that the class distribution is more representative of real-life occurrences (i.e., the natural response from perturbations at a range of points in swing phase), and thus building a model from this distribution may better reflect the expected instances of these strategies in daily life. The authors do note that the distribution of swing percentage at which the perturbation occurred was not perfectly even; approximately 20% more of the perturbations occurred in the earlier half of swing phase (10–47.5% swing), but given experimental constraints some imperfection is expected. Nevertheless, as explained above, the model was rerun for trials only between 40 and 70% swing phase, which removed 86 Elevating trials (the strategy with the most instances in the full dataset), and results still showed improved accuracy. Additionally, the authors report the overall confusion matrix for each stage in Figs. 4 and 5 so that supplementary performance metrics can be calculated [33]. Furthermore, Table 5 reports the balanced accuracy score for each stage for Datasets A and B, which accounts for the class imbalance by taking the average of the true positive rate (sensitivity/recall) and true negative rate (specificity); the RTMM still outperforms SPM using this metric. Regardless, for both the RTMM and SPM the same set of trials was used; thus, the comparison is fair and consistent, and it still holds that the RTMM outperforms the SPM. Finally, note that a simple majority classification strategy, consisting of always choosing the majority class (Initially Elevating) for Stage 1, would result in a classification accuracy of 87.8% for Experiment A and 88.5% for Experiment B, and always choosing the majority class (Elevating) for Stage 2 would be 76.4% for Experiment A and 60.9% for Experiment B, and the RTMM results show accuracies substantially higher than these values.

Table 5

Balanced accuracy for the RTMM and SPM for each stage of the strategy selection process for testing with Datasets A and B. Balanced accuracy is calculated as the average of the true positive rate (sensitivity/recall) and true negative rate (specificity). Specifically, the first two rows give the average of the balanced accuracies from each participant/fold in the cross-validation process for Datasets A1 and A2. The last two rows give the balanced accuracy from testing on Datasets B1 and B2 (after training on Datasets A1 and A2 with the final feature sets, excluding data from Participant 3).

DatasetRTMM balanced accuracySPM balanced accuracy
A1 (Stage 1)97.1%84.2%
A2 (Stage 2)92.1%82.3%
B1 (Stage 1)100%66.7%
B2 (Stage 2)96.4%88.9%
DatasetRTMM balanced accuracySPM balanced accuracy
A1 (Stage 1)97.1%84.2%
A2 (Stage 2)92.1%82.3%
B1 (Stage 1)100%66.7%
B2 (Stage 2)96.4%88.9%

Second, an argument could be made that the increased classification accuracy with the RTMM is expected considering multiple features are included, compared to just one feature with the SPM. The authors agree with this assertion, but point out that limiting to one feature was not in the scope of the overall objective of the work. However, it is worth noting there were several individual features that independently outperformed swing percentage, as indicated in Results and expanded upon in Tables A1 and A2 available in the Supplemental Materials.

Third, one could argue that limiting the number of features in the final set could limit the performance of the final model. However, the authors contend it was reasonable to use the dimension that accounts for 80% of the variance of the dataset. This not only reduces the computational intensity but also limits the complexity of the model which is important for moderating model variance and thus performance on new data.

Fourth, the authors recognize that Experiment B is a limited dataset and only represents a single participant. Proving that this model extends across speeds was not a main objective of this work; rather, these results provide an initial indication that the RTMM represents the strategy selection process at multiple walking speeds. Note that the authors took care to remove Participant 3's trials from the single-speed training set (Dataset A), and as such the test set is a good indicator of the model's performance on new trials. More trials with additional participants would be ideal to confirm this observation in a future experiment.

Finally, one could argue that the participants in this study are not representative of the general population. Recall that the objective of this work was to create a model for healthy stumble recovery. Now that such a model has been proposed, valuable future work would be to repeat this process with mobility-impaired populations, such as the elderly, stroke patients, or individuals with lower-limb amputation. Understanding how these feature sets and strategies might differ may give insight into the deficiencies of the recoveries of these populations, informing areas for intervention and improvement.

## 5 Conclusion

In order to better characterize the nature of the stumble recovery strategy selection process, a set of features that are physical and measurable in real-time were identified that predict observed strategy selection with better accuracy than the conventional swing percentage criterion. For Stage 1 (Initially Elevating or Lowering), the model correctly predicts 99.0% of the strategies used with the feature set of CF-to-COM angle, knee angular velocity, COM vertical velocity, and foot angular acceleration at the time of perturbation, compared to 93.7% when using swing percentage. For Stage 2 (Elevating or Delayed Lowering), the model correctly predicts 94.0% of the strategies selected using the feature set of IF-to-COM angular acceleration and shank angular acceleration at the time of perturbation, knee angle 60 ms after the perturbation, and change in body COM vertical velocity, compared to 85.6% when using swing percentage. For Stage 1, the body tends to choose a strategy that prevents a change in momentum, as evidenced by trends seen in knee angular velocity and body COM vertical velocity. For Stage 2, the body tends to abandon the Elevating strategy (Delayed Lowering) in situations of high angular impulse, as evidenced by trends in IF-to-COM angular acceleration and shank angular acceleration. These feature sets also perform better than swing percentage on a dataset of trials at additional speeds, suggesting that the model may be robust to multiple walking speeds. The increased accuracy of Stage 1 predictions compared to Stage 2 suggests that while the initial reaction (Stage 1) of the strategy selection process is dominated by the physics, Stage 2 may be additionally influenced by participant-specific factors that were not collected, which may be further informed by future studies. These new findings inform both physiological understanding of healthy stumble recovery and interventions for those at fall risk.

## Funding Data

• National Institutes of Health (Grant No. R01HD088959; Funder ID: 10.13039/100000002).

• National Science Foundation Graduate Research Fellowship Program (Fellow ID: 2019277768; Funder ID; 10.13039/100000001).

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