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. Author manuscript; available in PMC: 2022 Jan 6.
Published in final edited form as: IEEE Int Conf Rehabil Robot. 2017 Jul;2017:658–663. doi: 10.1109/ICORR.2017.8009323

Customized Therapy Using Distributions of Reaching Errors

Moria F Bittmann 1, James L Patton 2, Felix C Huang 3
PMCID: PMC8734946  NIHMSID: NIHMS1744485  PMID: 28813895

Abstract

While there has been recent success with robotic therapy approaches, individual differences in motor impairments motivate the need for customized therapy. Our latest work with healthy participants considered the likelihood of one’s error to construct a customized force field training environment, which we termed an error field. We believe error statistics could characterize individual motor impairments for stroke survivors. Here we present preliminary results from a pilot study testing this therapy technique on individuals following stroke. We tracked the changes in error for three stroke survivors across multiple days using error field training, and found that participants’ errors reduced for all target directions across sessions. We also used a modeling approach to test whether the changes in error reflected the specific mathematical structure of the intervention. These results provide encouraging preliminary evidence that error field training can be valuable for both characterizing deficits and custom-tailoring therapy.

I. Introduction

Following a stroke, more than two-thirds of survivors have reduced arm function [1]. There are a great variety of motor deficits that occur following a stroke, and the severity of such impairments can vary quite widely [2-5]. Stroke survivors can develop abnormal contraction coupling, or “synergies,” that are based on the arm’s orientation [6]. Robotic therapy can offer many advantages to training beyond conventional therapy such as high repetition, applying assistance-as-needed or gradually increasing intensity [1, 7, 8]. Several studies have used adaptive control algorithms to account for individual differences where they adjust assistance for an individual on an as-needed basis, similar to a therapist [9, 10]. However, there have been limitations to their success to generalize or lead to long-term functional improvements [11, 12]. While these approaches ensure participants are able to complete the task, they do not address individual impairments.

Recent studies have shown training benefits using error augmentation (EA), where error is magnified via haptic or visual feedback. Error augmentation techniques have led to improved clinical measures and reduced errors in tasks ranging from reaching, walking, and stepping [13-16]. Researchers believe that by focusing the attention of the motor system to errors, for example, by applying perturbing forces, participants are more likely to correct their mistakes. The optimal method for applying EA, however, remains unknown. Studies suggest that the appropriate gain might differ based on individual abilities [15, 17]. In a recent study focusing on distributions of movements during motor exploration, Huang and Patton found that certain motor deficits were unique to each stroke survivor [18]. Likewise, we believe that such individual-specific qualities should affect success in reaching movements.

Our previous work with healthy participants has shown that force field training based on participants’ unique error statistics, or error fields, improved performance in a novel visual transformation [19]. Building upon traditional EA approaches, our current study considered an intervention scheme in which each participant’s error likelihood dictated the magnitude of augmented forces applied during training. This ensured that the intervention focused on errors made most frequently, and ignored spurious or random errors. We believe that such statistics of movement errors can also be used to customize the “motor relearning” of therapy for stroke survivors so that training can focus on the unique regions where frequent movement errors occur.

Here we present our preliminary results from a pilot feasibility study on such an error-defined customization of robotic therapy in three chronic stroke subjects. This investigation first tested whether there was a detectable improvement due to this customized training technique. Secondly, because our technique depended on error tendencies, we considered whether initial error statistics (probability distributions) might predict later errors. This study provides a proof-of-concept demonstration of how training with error fields is a promising way to reduce reaching errors following stroke.

II. Methods

A. Human subject experiment

Three stroke survivor subjects participated in this study at the Rehabilitation Institute of Chicago (Chicago, IL). The main inclusion criteria were 1) chronic stroke (8+ months post-stroke), 2) hemiparesis with moderate to severe arm impairment measured by the Fugl-Meyer Assessment UE (FMA-UE score of 15-50, [20], 3) primary cortex involvement. The exclusion criteria included 1) severe sensory deficits in the limb using the Two-Point Discrimination Test [21], 2) severe spasticity (Modified Ashworth of 4 preventing movement [22]) and, 3) aphasia, cognitive impairment or visual deficits that would influence their ability to perform the experiment tasks. All participants provided informed consent in accordance with Northwestern University Institutional Review Board. Participant information is summarized in the Table I, where clinical measures listed are from the affected arm.

TABLE I.

Summary of stroke survivor participants

Participant
1 2 3
Age (years) 62 60 60
Years past stroke 8 10 2.5
Lesion Type Hemorrhagic Ischemic Ischemic
Affected hand R R L
AMFM Pre 22 21 19
Post 23 22 19
ARAT Pre 17 16 20
Post 17 16 20
BBT Pre 6 7 8
Post 8 8 8
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B. Experimental conditions

Using the affected arm, each participant was asked to control a planar force feedback device, as described in previous work [23], see Fig. 1B. Real-time feedback of the handle position was provided to subjects using a large video display orientated upside-down and projected onto a mirror above the participant’s hand. The mirror height was positioned such that the visual feedback appeared to be co-incident with the hand. Participants were seated such that the shoulder of their affected arm was centered in the workspace, approximately 38 centimeters away from the robot. The wrist was secured in a brace connected to the robot handle so that only movement of the elbow and shoulder was possible. The brace was supported with a planar arm support. The robot control and instrumentation was mediated with a Simulink-based XPC Target computer, with a basic rate of 1 kHz. Data was collected at 200 Hz. The robot generated torques that compensated for some of inertial effects of the robot arm during all experiment phases.

Figure 1:

Figure 1:

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A) Experimental protocol showing the sequence of conditions for each session. B) Overhead view of planar manipulandum and arm support. Participants performed goal-directed movements to 10 targets (each target represents two directions).

Goal-directed reaching:

Participants reached to ten target locations arranged in a pentagram pattern 18 cm apart (Fig. 1B). After completing the reach, they received feedback of their movement time, where color indicated if the movement was too slow (yellow), too fast (red), or within the desired range (green). The ideal movement time was set at 750 milliseconds.

Motor exploration:

While the focus of this study was on reaching movements, we also included phases of motor exploration as a way to examine potential parallels in learning between the two movement paradigms. Participants were instructed to move the robot handle to various positions, speeds, and movement directions within the robot workspace (0.6 meters x 0.4 meters). They received continuous feedback of their cursor with real-time velocity represented as a “tail” trailing the cursor. A trial consisted of two cumulative minutes of movement with a speed greater than 0.04 meters/second. Following the trial, participants received a score that reflected the variety of movement patterns as previously described in [18, 24].

C. Experimental protocol

A total of 8 sessions were conducted over 4-weeks. Error field training was performed during sessions 3-7 (Fig. 1A). Each session lasted from 1 to 1.5 hours. Training sessions were spaced every other day from each other, while initial assessments were spaced one week prior and one week post training. Before interacting with the robot on Session 1, 2, and 8, a physical therapist evaluated each participant. The evaluation including the following stroke assessments: Fugl-Meyer Assessment (FMA), Action Research Arm Test (ARAT), Box and Blocks Test (BBT) and the Intrinsic Motivation Inventory (IMI) questionnaire. Once positioned in the robot, participants began by making goal-directed movements in a null field with interspersed epochs of motor exploration. On Session 2, participants continued to train in a null field for the duration of the session. Following characterization on Session 3-7, participants experienced Error Field training, which featured perturbing forces based on the most common errors exhibited during baseline of that day.

D. Force field customization

Baseline reaches at the beginning of each training day served as the basis for the design of the customized forces used for that session (see Fig. 2). Distributions of error were calculated using the perpendicular distance from the straight-line path (err) with respect to the distance, d, along the path. To formulate a customized error field based on this characterization of baseline data, we computed a continuous analytic function parameterized by movement state. In a previous study with healthy, we used time to parameterize error [19]. In contrast, for this study we chose path distance to parametrize error because we discovered that stroke subjects initiated and timed their movements inconsistently.

Figure 2:

Figure 2:

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Initial error trajectories during characterization (Session 1 - baseline) for each participant. Characteristic movement errors vary with target direction and are not the same in participant. Note we have re-aligned the origins of all reaches for illustration purposes.

Our overall approach for designing an intervention for reaching errors is to present an error augmentation scheme that is further modulated by the likelihood of error. For this purpose, we employ an assumption that the error distribution is normal but varying along the trajectory. The process for determining the error field function is described below, for every target direction independently:

  1. The mean and standard deviation of error across the trajectory were fit with seventh order polynomials, creating functions fμ (d) and fσ(d) for the mean and standard deviation respectively.

  2. The probability of the error occurring at each distance, d, along the trajectory was calculated in real-time by using a single Gaussian distribution:
    p(d,err→)=1fσ(d)∗2∗π⋅e−(err−fμ(t))22∗(fσ(d))2

  3. The presented forces were computed as a function of the error probability and real-time measured error. A scaling factor, λ, was determined using the 80% confidence interval bounds of the error and finding the value such that the maximum force does not exceed 15 N.

FEF→(d)=λ⋅err→⋅p(d,err→)

Forces initiated only at the instant the hand leaves the origin. Forces then smoothly diminished to zero once the hand was within 1 centimeter of the target.

E. Data Analysis

Performance error

We used the initial characterization phase at the beginning of each session to measure the change in error either due to null field training or error field training. We also measured the movement time and peak velocity for each movement.

Prediction of error change – models of improvement

Because our error field intervention depended on the subject’s error distributions, we suspected that we could predict error changes using the baseline statistics from each session. We entertained three candidate models to predict later errors, εf, based on the initial mean of error μi and initial standard deviation of error, σi:

εmodel1=μi−σIεmodel2=μiεmodel3=μi−mean(σi)

Model 1 was our best guess of what our approach was hoping to do – shift the individuals’ error closer to zero based on the distribution. Model 2 was a control, where no change was expected, and Model 3 was a hybrid, where the shift was best predicted by the error and the mean of the variance.

To evaluate the predictive success of each model, we determined the coefficient of determination R2 for the prediction. We inspected how error could be predicted between different sessions.

Generalization to motor exploration

To test the transfer of training to participants’ performance during the motor exploration condition, we calculated the change in velocity distribution across sessions (method is previously described in [24]). To gauge the expansion of reaching ability, we first calculated the 50th percentile contour of 2-D velocity and then found the coverage of data within the contour boundary. This value represents the estimated area of movement tendencies in the velocity domain.

Statistics

We performed a 2-way ANOVA for each participant using factors of target and session. Post-hoc t-tests were used to perform pairwise comparisons between sessions and corrected using the Bonferroni-Holm method. All analyses were considered significant at an alpha level of 0.05.

III. Results

Given the short duration of our intervention, we did not anticipate large changes in clinical evaluations. Accordingly, we found very limited evidence of improvement in clinical measures, see Table I. However, our analysis of reaching errors provides some evidence that customized training achieved their intended effects.

Initial errors were direction-dependent

Our ANOVA results indicated that reaching direction interacted with subject error across sessions (p<0.001). Further analysis of within subject target effects revealed that participants’ reaching errors in the first (baseline) session varied across target directions (1-way ANOVA on target direction; p<0.001 for Participant 1, p<0.001 for Participant 2, p=0.016 for Participant 3) – see initial trajectory errors in Fig. 2, Fig. 3. Each participant appeared to be unique in the manner in which these initial errors varied across direction. At the end of training, errors differed significantly by target for Participant 1 (p < 0.001) and Participant 3 (p<0.001). These subject- and direction-specific errors reduced across training. In fact, errors no longer differed across movement direction by the end (session 8) for Participant 2 (ANOVA session – target interaction, p>0.05).

Figure 3:

Figure 3:

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Customization of forces. Error field training is customized using each day’s initial baseline errors (Session 1). Top row shows the error trajectories across day for Participant 1, Target Direction 2. Bottom row shows the respective error distributions and resulting force field (red arrows) for the five error field training sessions.

Performance improved across training

We found that all subjects significantly improved (decreased reaching error) between the initial baseline reaching on session 2 (start of training) to the final evaluation session on session 8 (see Fig. 5). The error decreased an average of 2.8 cm for Participant 1 (40% error reduction, p=0.0152), 1.3 cm for Participant 2 (35% error reduction, p=0.0074), and 0.9 cm for Participant 3 (18% error reduction, p=0.0486).

Figure 5:

Figure 5:

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A) Error change across sessions. Mean initial error from the characterization phase of each training session, error bars represent the 95% confidence intervals for error change across all target directions. Gray bars represent the change in error between subsequent sessions. Significant overall change in session-to-session error is designated with a red asterisk. B) Change in movement time (green) and peak velocity (red) across sessions. Participant 1 and Participant 2 showed no overall change in movement time but decreased peak velocity (Δ=−0.1 m/s, p<0.001 and Δ=−0.2 m/s, p<0.001). Participant 3 decreased movement time by an average of 150 ms (p<0.001) and peak velocity increased by 0.1 m/s (p<0.001).

Note that while this preliminary study did not include a control group, our protocol design does allow us to examine whether there were sudden changes in learning due to error field training. We compared the change in error due to one session of null field training (session 2 to 3) with that of one session of error field training (session 3 to 4) to see if one type of training had a greater effect. We found all subjects significant reduced error for both these training conditions (p=0.001, p=0.027, p=0.043 for session 2-3 and p=0.001, p=0.037, p=0.025 for session 3-4), but there were no detectable differences in error reduction between these two conditions (p>0.05).

We also inspected two secondary metrics—movement time and peak velocity (Fig. 5)—in order to better understand any trade-off between speed and accuracy [25]. We expected that as error decreased, participants would reduce movement time and increase peak velocity. Participant 1 showed no change in movement time, but had an average change in peak velocity of 0.1 m/s (p< 0.001). Participant 2 showed significant session-to-session interactions for movement time, but no overall change. There was a significant decrease in peak velocity of 0.2 m/s (p<0.001). For Participant 3, movement time changed from session 1 to session 8 by 150 ms (p<0.001), while peak velocity increased by 0.1 m/s (p<0.001).

Generalization to another task -- free exploration

Participants also were asked to freely explore their available workspace, pre- and post-training. We used a velocity coverage metric and found that while no effect was detected for Participant 1, we found a significant increases for Participant 2 (average increase of 1 m/s; p=0.006) and Participant 3 (average increase of 3.7 m/s; p<0.001).

Predicting improvement

Our analysis also demonstrated how predictive models can be used to establish a relation between the initial and final error distributions. Comparing three candidate model predictions (Fig. 4), we found significant R2 values only for Model 1 (mean R2=0.39±0.1, 0.35±0.1, 0.31±0.1). Model 2 showed limited success, for Participants 1 and 2 (R2=0.09±0.7, 0.11±0.9).

Figure 4:

Figure 4:

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Model predictions (black line) where the initial distribution is used to predict the mean error from the following session (red dotted line). Model predictions were performed for error changes following one session of repetitive practice and error changes following one session of error field training.

Model predictions across all possible sessions revealed no predicative power (average R2 across target directions was negative). Model predictions were only observed (positive R2) for measuring error in sessions immediately following training (Fig. 6).

Figure 6:

Figure 6:

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Average coefficient of determination (R2) for model predictions (Model 1) across targets shown for all combinations of sessions. The model predicts the following session’s error distribution based on the mean and standard deviation. Colored squares indicate positive R2 values. Note that the prediction is only specific to the following session.

IV. Discussion

This study examined whether a customized training intervention that models error statistics can improve reaching for stroke survivors. We tested three participants across five training sessions in which we presented error field training—forces that augmented feedback based on error likelihood. We found that overall error significantly decreased for all participants from both error field and null field training. Our most important finding, however, was that the error field training caused changes in error that were predictable from the initial distribution of errors used for designing forces.

We found that errors significantly differed based on target directions, which further supports the idea that training should be customized to individual needs. Previous research has suggested that such differences in movement errors are due to abnormal synergies following stroke and that velocity profiles can be location specific [6]. Here we show possible manifestations of such synergies leading to large variations in error along the movement trajectory. Not only were errors different in magnitude and variance with and between participants, but also they varied daily, which suggests that customized therapies should adapt as the user trains over an extended period.

Our results here showed that error fields could reduce perpendicular error beyond what was achieved through repetitive practice alone (Fig. 5). Although the amount of reduction in error varied based on the magnitude of initial error (not surprisingly, participants with higher error had larger changes), participants averaged a 30% reduction in error. While null field training did decrease performance error for two participants, only error field training showed significant differences from the initial errors for all target directions. Even for participants beginning training with relatively low reaching errors (Participant 3), we could see a significant decrease in reaching errors.

We found that changes in error trajectories exhibited patterns that closely paralleled the structure of training forces. Given that the magnitude of training forces is governed by the participant’s proximity to their errors, we found evidence that participants moved one standard deviation from the mean (resulting in relatively low forces). In our previous study of healthy subjects training with error fields, we also found that subjects similarly changed their error patterns to align with one standard deviation away from their initial mean, corresponding to the location where forces would reduce to zero [19]. Here we provide further evidence of learning that appears to structured according to the error field intervention, where the error distribution predicted the mean error observed at the start of the next session. We entertained the same model predictions for null field training and found no such effect.

Thus, while error did change due to null field training, it did not do so in a systematic manner. Exploration of model predictions for alternate sessions indicated that the predictive power is only unique to the following session’s error profile (Fig. 6). Further, as training progressed and errors are closer to zero, the model results were no longer positive across all targets. This ability to predict error changes could be a valuable tool in assessing the performance of a participant during training.

While we were able to show evidence that error field training promoted learning according to their intended design, such results did not necessarily translate into large performance gains when we compare one session of null field training to one session of error field training (Fig. 6). Since we began error field training immediately after, it is unclear if improvements from null field training would be retained. Further we did not find differences in clinical measures (Table I), suggesting that we might need to provide additional training sessions until we are confident the error field method has plateaued.

In contrast, we believe the true benefit of error field training is to cause participants to adapt movement gradually from their original patterns. We were successful in demonstrating how participants changed based on their variance, reaching errors with high probability and low variance only incrementally decreased by one standard deviation. This result is consistent with recent findings by others who have shown that high motor variability promotes learning [26, 27].

This study revealed the need for therapy to adapt to the variation of errors seen in stroke survivor subjects. In our current approach, the error field is designed from the baseline trials characterized at the start of each session. While we believe this approach recognizes the specific training requirements of the stroke survivor, such daily changes in the design of training forces also poses a limitation to our analysis. To truly operate under the “challenge point framework” [28], where the greatest amount of learning is achieving by adjusting the task difficulty with the participant’s skill level, we would need to re-characterize multiple times within each training session.

In contrast to traditional clinical measures that evaluate task completion, here we showed a novel approach to training that makes use of the observed statistics of error exhibited by stroke survivors. This method ensured that training intervened on only the most relevant errors and adjusts to any day-to-day variation often seen in stroke survivors. Beyond the benefits of therapy for upper-extremity rehabilitation this approach could serve as a basis for a wide range of therapeutic approaches.

Acknowledgment

We would like to thank Emily Lazzaro for her help with recruitment and clinical evaluations, Zachary Wright for his technical assistance and advice on this project, and the Robotics Lab at RIC for insights and commentary.

*Research supported by NIH R01 NS053606 - 05A1.

Contributor Information

Moria F. Bittmann, University of Illinois at Chicago, Chicago, IL, 60607, Rehabilitation Institute of Chicago, Chicago, IL, 60611, National Institutes of Health, Bethesda, MD.

James L. Patton, University of Illinois at Chicago and the Rehabilitation Institute of Chicago..

Felix C. Huang, Rehabilitation Institute of Chicago and Northwestern University, Chicago, IL..

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