Background
Because of large differences in responsiveness to motor training post-stroke (e.g., [
1]), predicting response to a specific training program is needed to improve outcomes via personalized treatment [
2]. One possible approach is to observe the changes in motor performance during the early phase of training and adjust the training program accordingly, assuming that improvements in performance during training correlate with long-term improvements. However, because of activity-dependent fatigability – defined as a decline in strength during muscle groups’ use, fatigue, or reduced attention in long and repetitive training sessions [
3,
4] – individuals post-stroke could show no improvements or even worsening of performance during training, but improvements in delayed retention tests. On the contrary, because of short-term components of motor memory post-stroke (e.g., [
5]), motor performance could improve during training, but these improvements could be short-lived. Such learning-performance distinction has been extensively studied in motor learning (e.g., [
6,
7]), but despite its clinical importance, it has been little studied in individuals with motor impairments due to stroke.
In this study, we re-analysed arm movement time during reach training in sixteen participants with chronic stroke collected from our recent study [
8] and analysed new data in ten non-disabled age-matched participants. All participants performed two sessions of unassisted intensive training with 600 reaching movements per session to an array of five targets of fixed diameter. Our main objective was to determine whether changes in movement times during the first training session could predict changes in movement times between a pre-training test and a 1-month retention test in both participants post-stroke and non-disabled age-matched participants.
Our measure of performance was Movement Time (MT) for the following reasons. First, because we collected kinematic hand trajectory data, MT was available after every movement, allowing us to analyse a large number of repeated performance measurements. Second, we have recently shown [
8] that two sessions of intensive arm reach training resulted in a significantly decrease in MT up to one month following training in individuals with chronic stroke. Third, a number of studies have used MT to quantify training-induced improvement in motor impairment and activity of the upper limb post-stroke [
9‐
13]. Fourth, shorter movement times post-stroke are associated with better shoulder-elbow movement coordination during reach practice [
11,
14‐
18]. Fifth, and most important, previous studies of reaching post-stroke [
8,
19] showed that kinematic variables, including MT, can be linked to clinical scores such as the upper extremity Fugl-Meyer (FM). Note that here, we only used data from the first training session to predict long-term changes for two reasons. First, practically in the clinic, we want to determine if training will be effective as soon as possible for individual patients (to avoid “rehabilitation in vain”). Second, most of the changes in movement time due to training occurred in the first session (see Fig.
3C in Park et al. [
8]).
We developed nonlinear mixed-effects models to decompose changes of MT during training into both gradual improvements of performance attributed to motor learning, as modelled with an exponential term that decreased as a function of training trials, and into gradual worsening of performance attributed to learning-unrelated factors [
3], as modelled with a linear term that increased as a function of trials. The use of exponential term to model learning is motivated by the well-known negatively accelerated gains in performance as a function of training in most motor learning tasks [
20], and by a recent study showing that long-term (one month) retention gain following arm reach training was predicted using a simple exponential decay model in non-disabled individuals [
21]. The use of the linear term to model worsening in performance during training following an initial improvement is based on observing that many participants post-stroke complained about “being tired” during training. In addition, the experimenter (HP) noticed that the performance of several participants post-stroke appeared to worsen during training. Visual inspection of the MT data during training reinforced these observations, with several participants showing increases in MT during training. Although activity-dependent fatigability is a probable cause especially given our intensive training program, other factors such as fatigue, attention, and motivation, may influence performance during training [
4,
22].
The use of the mixed-effects in the nonlinear model in this study is motivated by the high variability in lesion, impairment, spontaneous recovery, and responsiveness to therapy post-stroke [
23,
24]. Such large variability in both initial performance and gains due to therapy was observed in our previous study [
8]. One way to capture this variability is to fit a single model for each subject and then test for group differences for each parameter but such an approach poorly captures the underlying phenomena, because the large variability in parameters results in low power. Moreover, the risk of over-fitting the data is very high, with N*k parameters, where N is the number of participants and k the number of parameters to estimate. In contrast, an equivalent mixed-effects has only 2*k parameters: a mean (fixed parameters) and a variance (random parameters) around this mean for each or the k parameters. Thus, a single mixed-effects model can account for the large between-individual variability in initial and final performance, in learning-related performance changes, and in learning-unrelated performance changes. The individual parameters (the random effects) can be estimated based on the data and the parameter distribution [
25]. Although such nonlinear mixed-effects models are commonly used to model repeated measures in pharmacokinetic analysis, for instance, to describe drug concentration in the bloodstream, [
26], such models have only been recently used to characterize motor learning [
27,
28].
We thus hypothesized that a nonlinear mixed-effects model with exponential and linear terms will: 1) capture the between-subject variability in initial performance, 2) capture the differences in rate of performance improvements with training, 3) capture worsening in performance during training that is presumably due to fatigue or activity-dependent fatigability [
3,
4], and 4) predict the long-term (1 month) retention due to training. We also hypothesized that the participants with stroke will show larger worsening of performance during training than the non-disabled age-matched participants as shown by a larger “fatigue” model parameter. Finally, to predict the long-term effect of training, we studied the relationship between the model parameters and baseline initial movement time and baseline upper extremity Fugl-Meyer (FM) scores.
Discussion
We proposed a novel nonlinear statistical model with mixed-effects that accounted for the immediate and delayed changes in performance due to intensive arm reach training in individuals with chronic stroke and non-disabled age-matched individuals. Performance was operationalized with MT, a performance variable available at each trial in our arm reach protocol. The model estimated improvement in MT due to motor learning via a decreasing exponential term, worsening of performance due to learning-unrelated factors via an increasing linear term, and asymptotic performance via target-dependent constant terms. Thanks to the mixed-effects, this single model, with only eight free fixed parameters, fit all data from post-stroke and non-disabled 26 participants simultaneously (see Figs.
3 and
4). The nonlinear mixed-effects model can be used in a variety of learning studies such as those with large variability across individuals, for instance [
35].
Notably, we found that the learning-related exponential term predicted long-term changes in MT in the stroke group, but not by the overall change in performance during training (Fig.
6). Therefore, the model containing both negatively accelerated improvement and linear worsening of performance during training, “unmasked” a learning-performance distinction in intensive reach training post-stroke. Although fatigability, defined as a decline in strength during muscle groups’ use, is a probable cause for the worsening effect in the stroke group, especially given our intensive training program, increase in fatigue, decrease in attention, motivation, and other factors may affect performance during training [
3,
4,
22]. In contrast, the control group showed no distinction between learning and performance, because the “fatigue” parameter was near zero.
All model parameters, i.e., the initial performance parameter
A, the decay rate parameter
tau, the “fatigue” parameter
C, and the asymptotic performance terms
D
k
, were significantly larger in the stroke group than in the control group. In contrast, the stroke group learned to decrease MT at a slower rate than the control group. The median half-life time of the exponential was 44 trials out of 120 trials for the stroke group versus 25 trials for the control group. As observed in Figs.
3 and
4, whereas the exponential term was still decreasing toward the end of the training for participants in the stroke group, the effect of training plateaued for the control group. This result shows that participants in the stroke group continued to benefit from motor practice even though “raw” performance often plateaus as early as mid-training (see for instance S1, S10, and S15 in Fig.
3).
A number of model parameters correlated with clinical measures. For instance, initial performance, asymptotic performance, and “fatigue” term in the stroke group were predicted by the baseline upper extremity FM scores and MT
Pre1. In contrast, the decay parameter
tau, which provides an estimate of the rate of motor learning, did not correlate with baseline performance or impairment levels, despite being larger in the control group. The rate of learning may correlate with measures of brain injury or cortical function. For instance, a recent study showed that smaller corticospinal tract injury and cortical greater ipsilesional motor cortex (M1) activation were better predictors of response to a robotic training program than baseline impairment predictors [
1]. In addition, psychological variables such as self-efficacy may be important predictors in the rate of improvements in motor learning [
36]. Finally, the integrity of short-term memory post-stroke may be useful in predicting both the rate of learning and final performance [
5]. Using the same dataset, we previously reported that the MT
Pre1 significantly correlated with the initial upper extremity FM scores (R
2 = 0.53,
p < 0.001) and that changes in the Box and Block tests between Pre1- and 1 month retention test significantly correlated with the changes in MT (R
2 = 0.56,
p = 0.001) [
8]. Another kinematic variable, the number of peaks in the velocity profile, is an indicator of movement smoothness and positively relates with stroke recovery [
8,
12,
37]. In our previous study, we found that MT
Pre1 significantly correlated with the number of peaks at Pre1-test (R
2 = 0.65,
p < 0.002) [
8]. In the present study, however, the initial number of peaks was small at the onset of training, especially in the control group, making the number of peaks unsuitable for fitting with a continuous regressor, such as exponential decay as a function of trials.
Because the present study was a retrospective analysis of existing data, the main limitation is that we did not measure factors that may account for the worsening in performance during training. Thus, it is not clear what the “fatigue” term in our proposed model represents. Although fatigability is a probable cause, especially given our intensive training program, fatigue, attention, motivation, and other factors may affect performance during training [
3,
4,
22]. Future studies should repeatedly measure fatigability with strength testing and fatigue with visual analog scales before, during, and after training. A second limitation is that our proposed model may or may not be generalized to the wider stroke population since the participants in this study were in chronic stage (i.e., the minimum duration post-stroke since stroke 12 months) and with mild to moderate impairments. A future larger study should include different chronic stage and/or impairment level. A third limitation is that the accuracy requirements were fixed: all participants (stroke and control groups) were instructed to reach the targets (disk of 3 cm in diameter) as quickly as possible. Reaching anywhere within the target within the 5 s time limit was sufficient to successfully terminate the trial: all participants completed all trials within the 5 s time limit. Thus, accuracy is a fixed value; the effect of training on speed accuracy trade-off will require future work.
Acknowledgments
We thank members of the Computational Neuro-Rehabilitation and Learning lab at USC for useful comments.