Stumble perturbation system
The stumble perturbation system consists of (i) an obstacle delivery apparatus that inconspicuously releases an obstacle onto a split-belt, force-instrumented treadmill, and (ii) a predictive targeting algorithm which controls the timing of the perturbation. The major components of the system are illustrated in Fig. 1.
Obstacle delivery apparatus design
As with the system described in [18–21], the essential mechanism of inducing a stumble is based on introducing a weighted obstacle onto a treadmill belt. The obstacle used in this study was a 16 kg (35 lb) block of steel, chosen to ensure minimal movement relative to the treadmill belt during a stumble compared to previous designs which used a 2.2 kg (5 lb) obstacle [18–21]. The obstacle measures 20 cm wide, 12.5 cm long, and 7.5 cm high (8.125” x 5” x 3”). Firm foam padding of 1.25 cm in thickness (0.5”) is adhered to the front and bottom of the obstacle to protect the subject’s toes and the treadmill belt, respectively. Note that while this specific weight and shape were used for this study, an obstacle of any given weight and various shapes could be used in its place depending on the objective of the experiment. The system’s functionality is independent of the obstacle’s weight and shape, within certain bounds of size and form-factor.
Additionally, deployment of the obstacle onto the belt without perception necessitates that the obstacle be transferred to the belt with minimal impulse, which requires that the obstacle be deployed with near-zero vertical velocity, and horizontal velocity that approximates the treadmill belt speed. Any substantial variation from these velocities will result in a noticeable force impulse on the treadmill due to the change in obstacle momentum, which will be perceptible to the user, as was the case in previous designs [19, 20] and evident in the authors’ pilot testing.
In order to deploy the 16 kg obstacle with minimal impulse, a ramp-based obstacle delivery apparatus (Fig. 2) was designed to deploy the obstacle onto the treadmill belt, as illustrated in Fig. 1, at near-zero vertical velocity and at a prescribed, adjustable horizontal velocity in order to match a given belt speed. The ramp consists of an acrylic track attached to an aluminum frame with adjustable, vibration-damping feet. The obstacle is held at a given point along the ramp via an electromagnet, which is held by a rod located by a pair of holes in the ramp (Fig. 2). When released via computer control (discussed subsequently), the obstacle rolls down the ramped track on a set of flanged roller bearings mounted on shoulder bolts threaded into each corner of the obstacle (Fig. 2) and then onto the front of the treadmill belt (Fig. 1). Note that a large, padded bin was used to catch the obstacle on the posterior end of the treadmill. The initial height of the center of mass of the obstacle determines the horizontal velocity at exit, and thus the ramp includes multiple starting points for the obstacle (i.e., multiple initial heights) in order to approximate a range of treadmill belt speeds. The starting height can additionally be fine-tuned via a threaded interface between the electromagnet and the rod to more precisely match a given belt speed. While any curve that is tangent to the treadmill belt at the exit could be employed, in order to simplify and improve the timing algorithm, a tautochrone curve [32] was implemented, which has been shown to have two desired features for this application. For a mass without friction in a constant gravitational field, a tautochrone curve: 1) provides the fastest path between two points, and 2) provides a constant time of travel, regardless of the starting point. These features respectively: 1) minimize the delay between obstacle release and the perturbation, which reduces associated predictive error, and 2) enable multiple belt speeds while considering only a single, fixed ramp travel time in the algorithm.
Predictive targeting algorithm
A predictive targeting algorithm was developed so the system could elicit precisely timed perturbations during a given stride, in order to: 1) reduce the proportion of mistrials (e.g., in [7, 19], where 23% and 39% of attempts failed to elicit a stumble, respectively), and 2) enable a more precise study of the variation in response mechanics as a function of when the perturbation occurs during swing phase. The targeting algorithm assumes the use of a lateral split-belt, force-instrumented treadmill. The control flow information is illustrated in Fig. 3. Note that both a left and right obstacle delivery apparatus were used for the human subject experiment described here, but each is independent (i.e., only requires kinetic signals from the side to be perturbed) and therefore the algorithm is described in the context of a single obstacle delivery apparatus. The predictive targeting algorithm is initialized with a desired percent swing at which the perturbation should occur. At the next toe-off event after the obstacle release is triggered by the experimenter, the algorithm calculates a time delay (trelease) such that the perturbation will occur at the desired percent of swing phase. The desired percent of swing phase corresponds to a point in space and time after toe-off, hereafter referred to as the targeted perturbation point and the targeted perturbation time, respectively. The algorithm requires real-time measurement of the two sagittal plane forces (vertical and anterior-posterior (AP) ground reaction forces (GRF)) and the one sagittal plane moment (mediolateral ground reaction moment (GRM)) from the instrumented treadmill. These kinetic signals are used to calculate the AP center of pressure (CoP) which is then used to detect gait events. The detected gait events are used to determine the timing of the release of the obstacle to achieve a perturbation at the desired percent of swing phase. The specific algorithm by which the appropriate time delay is calculated is described below. The key measurements and variables used in the algorithm are defined in Fig. 4. For the implementation described here, the force and moment signals were sampled at 1 kHz and filtered with a 1st order low-pass filter with a cut-off frequency of 30.5 Hz. Additionally, an experimentally determined 90 N threshold was used on the vertical GRF to reduce noise in the CoP signal near heel-strike and toe-off. Below this threshold the CoP signal was zeroed. Also note, as indicated in Fig. 4, the sagittal plane forces and moment are measured by the instrumented treadmill with respect to a coordinate frame, which is provided by the treadmill manufacturer (Bertec, Columbus, USA).
The targeting algorithm assumes a uniform periodic motion (i.e., treadmill velocity is constant and the subject’s position on the treadmill does not change substantially between time of release and time of perturbation). The time delay trelease signifies when the obstacle should be released by the electromagnet in order to perturb the subject at a desired percent of swing phase. The time delay trelease is calculated at a specified toe-off as a function of several component times, illustrated in Fig. 4, as:
$$\begin{array}{@{}rcl@{}} t_{release} = {nt}_{st} + t_{foot} - t_{obstacle} \end{array} $$
(1)
where tst is the average stride time, tfoot is the time required for the foot to travel from toe-off position to the targeted perturbation point, tobstacle is the time required for the obstacle to travel from its initial position on the ramp to the targeted perturbation point, and n is the smallest integer that makes trelease≥0. The component times in (1) are computed as follows. The time tobstacle is defined by:
$$\begin{array}{@{}rcl@{}} t_{obstacle} = t_{tm} + t_{ramp} \end{array} $$
(2)
where tramp is the time required for the obstacle to travel down the ramp to its point of entry on the treadmill belt and ttm is the time required for the obstacle to travel on the treadmill belt from its point of entry on the treadmill to the targeted perturbation point. The time tramp is a constant due to the nature of the tautochrone curve and thus is independent of the starting position of the obstacle on the ramp. Although this time can be estimated analytically, it was determined experimentally to account for frictional effects. The time ttm is given by:
$$\begin{array}{@{}rcl@{}} t_{tm} = \frac{d_{tm}}{v_{tm}} \end{array} $$
(3)
where vtm is the treadmill belt velocity, assumed to be constant, and dtm is the distance the obstacle must travel on the treadmill to the targeted perturbation point, which is calculated as:
$$\begin{array}{@{}rcl@{}} d_{tm} = d_{CoP,to} - p_{sw}l_{st} \end{array} $$
(4)
where dCoP,to is the computed distance from the obstacle’s point of entry on the treadmill to the CoP at the toe-off event, psw is the targeted percent of swing phase (converted to a decimal) which is provided as an experimenter input into the algorithm, and lst is the computed average stride length (see Fig. 4). In this equation, the computed distance dCoP,to is given by:
$$\begin{array}{@{}rcl@{}} d_{CoP,to} = d - y_{CoP,to} \end{array} $$
(5)
where d is the AP positional offset between the obstacle’s point of entry on the treadmill and the force plate origin (Fig. 4), and yCoP,to is the distance from the AP CoP of the ipsilateral foot at toe-off to the force plate origin, which is given by calculating yCoP at the time of toe-off using:
$$\begin{array}{@{}rcl@{}} y_{CoP} = \frac{F_{y}h+M_{x}}{F_{z}} \end{array} $$
(6)
where h is the vertical positional offset between the belt surface and force plate origin, Fy is the AP GRF, Fz is the vertical GRF, and Mx is the mediolateral GRM (Fig. 4).
The stride length in (4) is computed as a moving average of the previous 10 stride lengths, each of which is calculated as the difference of the AP CoP at heel-strike and the prior toe-off:
$$\begin{array}{@{}rcl@{}} l_{st} = y_{CoP,hs}(i) - y_{CoP,to}(i-1) \end{array} $$
(7)
where i is the stride index, and ycop,hs and yCoP,to are the distances from the AP CoP signal to the force plate origin at heel-strike and toe-off, respectively. The heel-strike event is detected as an increase in the vertical GRF beyond the 90 N threshold, and heel-strike position is computed as the average of the first 10 non-zero samples of the AP CoP signal after the heel-strike event. The toe-off event is detected as a decrease in the vertical GRF below the threshold, and toe-off position is computed as the last 10 non-zero samples of the AP CoP signal prior to toe-off. Both of these CoP values are calculated using (6) at the time of their respective events. Stride time in (1) is the measured time between each successive ipsilateral heel-strike:
$$\begin{array}{@{}rcl@{}} t_{st} = t_{hs}(i) - t_{hs}(i-1) \end{array} $$
(8)
which is computed as a moving average of the past 10 stride times. Heel-strike time (ths) is the time of the heel-strike event, which is detected at the first non-zero sample of the AP CoP signal after swing phase.
The time tfoot, which is the time within the periodic cycle required for the foot to advance from the toe-off position to the targeted perturbation point, is given by:
$$\begin{array}{@{}rcl@{}} t_{foot} = p_{sw}t_{sw} \end{array} $$
(9)
where tsw is the moving average of the previous 10 swing times, each of which is calculated as the time difference between heel-strike and the prior toe-off:
$$\begin{array}{@{}rcl@{}} t_{sw} = t_{hs}(i) - t_{to}(i-1) \end{array} $$
(10)
where toe-off time (tto) is detected at the time of the last non-zero sample of the AP CoP signal during stance phase. Note that the calculation of swing time (tsw) may be affected by the threshold set on the force signals, thus artificially increasing the value. In this implementation an experimentally determined scaling factor that was inversely proportional to the subject’s average stride length was used to account for this effect of thresholding the GRF. As illustrated in Fig. 3, the time delay value calculated in (1) is computed at the toe-off event, using (2)-(10), to enable the experimenter to specifically target a perturbation at a desired percent of the swing phase. The computer-aided design (CAD) files for the obstacle delivery apparatus and scripts implementing the targeting algorithm are included in the Additional files 2 and 3, respectively, of this paper. The following section provides a validation of the experimental setup and algorithm.
Experimental validation
A 7-subject study of stumble recovery responses in healthy subjects was conducted in order to validate the efficacy of the stumble perturbation system. The protocol for this study and data analysis methods are outlined respectively in the subsections below.
Experimental protocol & data collection
Seven subjects participated, three females and four males (age: 23.6 yrs, height: 1.8 m, mass: 81.3 kg). All experimental protocols were approved by the Vanderbilt Institutional Review Board, and all subjects gave their written informed consent. Subjects walked on the treadmill at 1.1 m/s [19]. The handrails were removed so they could not be used as a recovery aid; however, a full-body harness with slackened safety rope was worn to prevent a true fall. To prevent subjects from hearing or seeing the obstacle being deployed, each subject listened to white noise via earbuds, wore noise-canceling headphones, and wore dribble goggles that occluded the inferior visual field. Each subject watched on-screen visual feedback to ensure a centered position on the treadmill and avoid crossing over to the contralateral force plate. As a distraction technique, subjects were instructed to count backwards aloud from an arbitrary number by intervals of seven [33] (i.e., perform Serial Sevens). Subjects were given several minutes to walk on the treadmill prior to testing in order to acclimate to the setup.
Various data were recorded during each trial, including GRF data, which were recorded under each foot at a sampling rate of 2 kHz via a lateral split-belt, force-instrumented treadmill (Bertec, Columbus, USA). Full-body kinematic data were collected via infrared motion capture at a sampling rate of 200 Hz, which included feet, shanks, thighs, pelvis, torso, upper arms, and forearms (Vicon, Oxford, GBR). The experimental protocol consisted of two sub-experiments. First, a perception experiment (hereafter referred to as Perception Trials) was performed to determine the extent to which subjects could perceive the deployment of the obstacles due to the potential introduction of vibrations to the treadmill, as this perception would induce an anticipatory response. Second, a perturbation experiment (hereafter referred to as Perturbation Trials) was performed to assess the timing accuracy of perturbations and quantify the kinematics and kinetics of the stumble recovery responses. In the Perception Trials, for each of the two belts, an obstacle delivery apparatus was aligned laterally on the treadmill belt to ensure that when the obstacle was released it would not contact the subject’s foot (i.e., it would pass lateral to the foot path). Subjects walked for approximately 15 min while the obstacles were released 6 times per belt at approximately 20, 30, 40, 50, 60, and 70% of swing phase. The subjects were asked to raise their hand on the respective side if or when they perceived the obstacle entering the treadmill.
Following the Perception Trials, each obstacle delivery apparatus was repositioned such that the obstacles, when released, would be in the line of progression of the subject’s foot. During the Perturbation Trials, each subject was perturbed 14 times per lower limb, targeted from 10% to 75% of swing phase in 5% increments. The order of perturbations was randomized in terms of targeted percent swing, the number of strides prior to the perturbation (between 25 and 120) and the side perturbed (i.e., left vs. right). A video of representative stumbles from these trials is provided in the Additional file 1.
Note that prior to each trial the subjects were not informed when or on which side the obstacle would be released, and as such they did not know when or where to expect the perturbation. The instructions given to the subjects prior to the Perturbation Trials were as follows: 1) Watch the visual feedback on screen to ensure a centered position on the treadmill, 2) perform serial sevens out loud, and 3) when the perturbation occurs, try to recover and return to steady state walking. They were also informed that in the event of a fall (i.e., in which they were caught by the overhead harness), the treadmill would be stopped.
Additionally, 60 s of unperturbed walking data were collected before and after the set of 28 perturbations, and the Perception Trials were repeated after the Perturbation Trials to ensure subjects did not acclimate to the system.
Data processing
GRF and motion capture data were filtered with a zero-phase, 3rd order, low-pass Butterworth filter with a cut-off frequency of 15 and 6 Hz, respectively. Next, inverse dynamics were computed using Visual3D (C-Motion, Germantown, USA) to estimate joint-level kinematics and kinetics for each trial. Additionally, the kinetic signal profile of the obstacle (i.e., the GRF and GRM profiles due to the obstacle as it travels across the treadmill from entry to exit) was obtained prior to the testing session (i.e., without a subject on the treadmill) and subsequently subtracted from the kinetic signals recorded during the Perturbation Trials. This removed the obstacle’s contribution to the measured kinetic data.
Prior to analysis, unperturbed walking data were parsed by heel-strike into strides and normalized to 100% of the stride cycle. Perturbed strides were normalized such that the toe-off event matched that of the unperturbed walking strides (i.e., perturbed strides were normalized based strictly on the stance phase, which is devoid of the perturbation).
The percent swing at which the stumble actually occurred was calculated as:
$$\begin{array}{@{}rcl@{}} P_{sw} = \frac{t_{pto}}{t_{sw,avg}} \end{array} $$
(11)
where tpto is the time the perturbation occurred relative to the preceding toe-off event, and tsw,avg is 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 AP GRF measured by the treadmill. The actual percentage of swing phase of the perturbation, Psw, was then compared to the targeted percentage of swing phase of the perturbation, psw, to assess the accuracy of the system.
The responses of the subjects to each perturbation were divided into three stumble recovery strategies that have been defined in previous works: the elevating strategy [5, 15, 20, 24], lowering strategy [5, 20, 24], and delayed lowering strategy [20, 24]. The recovery strategy was determined by the trajectory of the perturbed foot after contact with the obstacle. For the elevating strategy, the perturbed foot lifts up and over the obstacle, landing anterior to the obstacle. For both the lowering and delayed lowering strategies, the perturbed foot lowers posterior to the obstacle. During the delayed lowering strategy, the perturbed foot lifts slightly before lowering posterior to the obstacle, while in the lowering strategy the perturbed foot shows no upward movement before lowering.
To demonstrate that the system enables calculation of joint-level kinematics and kinetics, hip, knee, and ankle angle and moment trajectories over the recovery period for each strategy were computed and shown for a single subject in Figs. 6 and 9. To briefly summarize group-level results, peak GRFs, trunk deflection and joint flexion angles, and joint flexion and extension moments were also computed and the inter-subject means of these metrics for each recovery strategy were determined.
These summary metrics served to 1) provide values with which to compare to previous overground studies as further validation that the system is able to provide realistic perturbations leading to authentic stumble recovery responses, and 2) present initial findings to show trends in magnitude and range of responses across different recovery strategies. Wilcoxon rank-sum tests (α=0.05) with a Holm-Bonferroni correction were used to determine statistical significance of these summary metrics for each recovery strategy compared to the unperturbed control values.