A total of 17 patients with cerebellar deficits and 14 age-matched controls were tested in one or more of the following experiments. Patients were excluded if they had any clinical or MRI evidence of damage to extra-cerebellar brain structures, or clinical evidence of dementia, aphasia, peripheral vestibular loss, or sensory neuropathy. The age-matched controls were clinically screened for any neurological impairments. Experiments 1–2 tested 11 cerebellar patients (seven male, four female) and 11 age-matched controls (four male, seven female). Patient and control ages were within +/- 3 years of age. The one exception is a pairing of a 78-year-old patient with a 71-year-old control. Experiment 3 tested 12 cerebellar patients (eight male, four female) and 12 age-matched controls (three male, nine female), and all patient and control ages were within +/- 3 years of age. Subjects gave informed consent according to the Declaration of Helsinki. The experimental protocols were approved by the Institutional Review Board at Johns Hopkins University School of Medicine. Each subject used his or her dominant arm for all tasks. The only exception was one unilaterally affected cerebellar patient who was instructed to use her affected, non-dominant, hand. We quantified each subject’s ataxia using the International Cooperative Ataxia Rating Scale (ICARS) (Trouillas et al., 1997). Because this study involves upper limb reaching behavior, we calculated an Upper Limb ICARS sub-score comprising the sum of the upper-limb kinetic function elements of the test. The results of the ICARS as well as demographic information for all patients are shown in Table 1.

For all experiments, subjects were seated in a KINARM exoskeleton robot (BKIN Technologies Ltd., Kingston, Ontario, Canada), shown in Figure 1A, which provided gravitational arm support while allowing movement in the horizontal plane. A black video screen occluded the subjects’ view of their arm movements. The shoulder position was fixed at a 75° angle, as shown in Figure 1C. The wrist joint was also fixed; therefore, the elbow joint was the only freely mobile joint. Data were recorded at 1 kHz. The KINARM system exhibits a cursor delay. Using a high-speed camera, we measured this delay (0.0458 s) and took the delay into account in modeling the human control system.

Figure 1

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A 1 cm diameter white dot (cursor) was projected onto the display to indicate the subject’s index fingertip position. The display was calibrated so that the projected dot position aligned with the subject’s fingertip position. Subjects performed three experiments:

• Experiment 1: sum-of-sines tracking task.

• Experiment 2: single-sines tracking task.

• Experiment 3: discrete reaches with acceleration-dependent feedback.

For Experiments 1 and 2 (tracking tasks), subjects were instructed to try to keep the cursor in the center of the target, a 1.5 cm diameter green dot (Figure 1C). The target angle followed a pseudorandom sum-of-sines (Figure 1D) or single-sine pattern. Each trial was 100 s long. We tested three different Feedback Gain conditions in the sum-of-sines (Experiment 1) task: 1.35 (cursor moves 35% farther than hand), 0.65 (cursor motion is attenuated by 35%), and 1.0 (veridical feedback; Figure 1B). Subjects were not informed that there was a gain change.

For Experiment 3 (discrete reaches), the robot moved the arm to align the cursor with the red dot start position (55° elbow angle) before each reach. After approximately 2 s, the red dot disappeared, and a green target dot (1.5 cm diameter, at 85° elbow angle) appeared elsewhere on the screen. Subjects were instructed to bring the white cursor dot to the center of the green target dot (a 30° flexion movement) as smoothly and accurately as possible without over or undershooting the target. If the fingertip did not reach within 1.75 cm of the target within 800 ms, the green dot changed to blue and subjects were instructed to complete the reach (trials were not repeated); the subjects were also asked to try to move faster on the next trial. The next trial started after the subject kept the fingertip in the target dot for two continuous seconds.

Healthy control subjects performed five practice trials and patients performed 10 practice trials to familiarize themselves with the procedure. If subjects were still confused about the procedure after the practice trials, they were given more practice trials until they were comfortable with the procedure.

Some subjects completed only a subset of the experiments due to time constraints (see Table 1). For every experiment, between trials, subjects were told to relax while the robot moved the subject's hand to bring the cursor to the start position.

The Parameter Estimation by Sequential Testing (PEST) algorithm was used to iteratively determine the best Acceleration-Dependent Feedback Gain values to apply in Experiment 3 by analyzing the history of the responses to different applied values (Taylor and Creelman, 1967). If the mode of the initial set of reaches was hypermetric, the Acceleration-Dependent Feedback Gain would be decreased. Likewise, it would be increased if the mode of the set was hypometric. The initial step size used for the PEST algorithm was 0.01. The maximum step size for the PEST algorithm was limited to 0.01 and the minimum step size was 0.0035. The maximum Acceleration-Dependent Feedback Gain was set to +/- 0.02. The PEST algorithm was terminated when two blocks of the same Acceleration-Dependent Feedback Gain yielded a mode of reaches classified as ‘on target.’ Alternatively, if this portion of the experiment took longer than approximately 20 min or the subject was experiencing fatigue, the most successful Acceleration-Dependent Feedback Gain was selected based on those which had already been tested.

To probe participants' ability to use visual feedback, we challenged cerebellar patients and age-matched controls to keep a cursor within a target dot that was following an unpredictable trajectory. The normalized Fourier spectrum (magnitude only) of the target trajectory is shown in Figure 1E and the spectrum of a single subject’s response is shown in Figure 1F. Note that this subject had clear peaks at all of the frequencies of target movement in the veridical condition (1x).

Subjects also were exposed to two Feedback Gain conditions where the cursor was presented at 0.65x or 1.35x. A phasor plot for each Feedback Gain condition is shown for a single cerebellar patient in Figure 3A. Points with the smallest phase lag (~30°) are responses from the lowest frequencies (0.1 Hz). Responses at the five lowest frequencies are marked with solid dots. As a function of increasing input frequency, the phase lag increases and the plotted points move progressively clockwise around the origin. Note in Figure 3A that the example subject scales his movement, especially at the lowest frequencies, in response to the Feedback Gain applied. For the 0.65 Feedback Gain condition, he increases the scaling of his movement in comparison to the veridical condition, as expected. Similarly, in the 1.35 Feedback Gain condition, he decreases the scaling of his movement in comparison to the veridical condition.

Figure 3

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For each patient, we computed a Scaling Factor that best scaled responses at the lowest five frequencies (Materials and methods); to visualize how well this Scaling Factor represents our data, the phasor data from an example cerebellar patient in the 1.35 Feedback Gain condition shown in Figure 3A is multiplied by its scaling factor to yield the corresponding line in Figure 3B. If the scaling factor is a good fit for the data, the data should rest on top of the veridical line. Note that the phase is not modified by this scaling computation, so we should not expect to see an improvement in phase alignment in this second plot.

Figure 3C shows the Scaling Factors for all subjects for each Feedback Gain condition. We conducted a one-sided t-test to determine whether patients scaled their gain in the hypothesized direction against the null hypothesis that patients’ scaling factors would be 1 (i.e. they would not respond to the applied feedback gain). Both groups scaled up (patients: p=0.03, t = −2.1, DOF = 10; controls: p=4×10⁻⁶, t = −8.3, DOF = 10) or scaled down (patients: p=0.005, t = 3.23, DOF = 10; controls p=0.0002, t = 5.3, DOF = 10) their movement, commensurate with the respective decrease or increase of the cursor Feedback Gain. We performed a two-way ANOVA, confirming that the effect of Feedback Gain (0.65 vs. 1.35) on Scaling Factor was significant (F(1,40)=59.7, p=2×10⁻⁹, η_p²=0.7), whereas the effect of group (patient vs. control) on Scaling Factor was not significant (F(1,40)=0.05, p=0.83), with no significant interaction between group and gain (F(1,40)=3.57, p=0.07). We accounted for the samples being dependent on one another because each subject was exposed to both the 0.65 and 1.35 gain conditions. The effect size was computed using the Hentschke and Stüttgen toolbox (Hentschke and Stüttgen, 2011).

Note that the subjects typically exhibited a Scaling Factor of around 1.2 in the 1.35 Feedback Gain condition. Intuitively, this indicates that subjects rescaled their movements as if to compensate perfectly for an experimentally applied Feedback Gain of 1.2; had they compensated perfectly, their scaling factor would have been 1.35. Likewise, for a Feedback Gain of 0.65, the Scaling Factor was typically approximately 0.8, again implying that subjects compensated, albeit not fully, for the visual rescaling (Figure 3). Critically, the patients’ responses to the feedback scaling were comparable to that of age-matched controls, suggesting that they were able to use visual feedback in a substantively similar manner.

In computational terms, one can interpret the data from Experiment one to mean that cerebellar patients had a functional feedback loop in their control system. Here we asked if they are using the same ‘control structure’ (i.e. a model of the interplay between sensory feedback, external sensory input, and motor output) as age-matched controls. Because the cerebellar and age-matched control groups scaled their movements similarly in Experiment 1, one might hypothesize that they were using a similar control structure. However, the scaling was measured relative to each subject’s baseline movement in the veridical condition and was not a measure of their overall error performance on the task; for example, issues of phase lag would not be captured by the scaling analysis. Thus, here we use our findings from Experiment 1 along with the model selection procedure described by Madhav et al., 2013 to determine any differences in control structures used by patients and age-matched controls.

Consider the hypothesized model depicted in Figure 4A. In this model, the brain calculates the error between perceived elbow angle and target angle, as shown in the subtraction calculation in the feedback diagram. The model merges the cascade of the subject's internal controller and mechanical plant (arm and robot dynamics); the combined plant and controller is treated as a classic McRuer gain-crossover model—a scaled integrator—a model based on the assumption that the subject is responding to an unpredictable stimulus (McRuer and Krendel, 1974). Our hypothesis is that all model parameters would be equivalent between patients and age-matched controls, except that patients would have a feedback delay commensurate with their visual processing time and controls would have a lower latency feedback delay commensurate with their proprioceptive feedback processing time (Bhanpuri et al., 2013; Cameron et al., 2014; Crevecoeur and Scott, 2013; Izawa and Shadmehr, 2008). This is because we expect that patients would rely more on (slower) visual feedback to compensate for their deficient estimation of limb state. Visuomotor delay during smooth pursuit tracking is generally much faster than the time required for movement initiation, and estimates for such visuomotor tracking delay vary, but would be expected in the range of 110 to 160 ms (Brenner and Smeets, 1997; Day and Lyon, 2000; Franklin and Wolpert, 2008; Haith et al., 2016; Pruszynski et al., 2016; Saunders and Knill, 2003).

Figure 4 with 2 supplements see all

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To test this hypothesized model, we performed model fitting and model selection on all possible model configurations (Figure 4—figure supplement 1A,B). Our hypothesized model was just one possibility and the parameter values of the models were not constrained a priori. The models were compared based on joint consideration of model consistency and model fit. Model fitting and selection produced five models, called Best 4 (Lowest Variance), Best 4 (Lowest Error), Best 5 (Lowest Variance), Best 5 (Lowest Error), and Best 6, that were nearly equivalent in their trade-off between model inconsistency and model fitting error (Figure 4—figure supplement 1C). Model Best 6 added one more free parameter compared to Best 5 (Lowest Variance) and was the only one of the top five models that allowed for variation in the feedback delay for controls; this addition yielded a small delay (~39 ms) and while only providing a small enhancement in model fit-error, shown in both frequency domain plot and time domain validation (Figure 4—figure supplement 1C and Figure 4—figure supplement 1D). Thus, out of parsimony, we eliminated model Best 6 considered both Best 4 and both Best 5 models as the top models. These top models were extremely similar in their structure and parameters (Figure 4—figure supplement 1B and Table 2). Indeed, in all four top models, the feedback delay was zero for control subjects, substantially shorter than cerebellar patients. This suggests that controls can rely on an internal model of their hand position and/or proprioceptive feedback to make corrections for their future movements while cerebellar patients must rely on delayed visual feedback (see Discussion).

Rather than picking up a single best model, we drew the following general conclusions from the modeling. The Final Model (Figure 4B) was distilled from the top four models to show the general features among them, together with the range of parameters derived from these models. In addition to the parameter values having consistent values across the top four models, they also have intuitively plausible values (Table 2). While the true parameters have biological limitations, we did not restrict their values during the fitting procedure. This provides a useful diagnostic tool, since unrealistic parameter fits would indicate inadequate model structure: parameter bias is a hallmark of model deficiency. In the four top models, Visual Delays for controls were found to be 141–147 ms, which is physiologically plausible. Interestingly, this delay was much shorter than for patients, whose Visual Delays were 181–211 ms. Critically, patients exhibited longer response delay both on the visual measurement of target motion and that of self-movement feedback, compared to controls. The top models also suggest that Feedback Delay is shorter than Visual Delay for both patients and controls, although for two of top models, the patients exhibited equivalent Visual and Feedback Delays. Visual Gain values are all approximately 0.40 which also seems reasonable given a visual inspection of the data: subjects do not appear to be attempting to replicate the full magnitude of the signal, but some smaller portion of the signal. We further examined the frequency responses of patients and controls (Figure 4—figure supplement 2A). Patients exhibited substantially greater phase lag at high frequencies than controls; at low frequencies, both populations exhibited very little phase lag, but, surprisingly, controls exhibited slightly more phase lag than patients in this frequency range. Thus, there was a phase ‘cross over’ frequency between patients and controls, which was also captured by our top models (Figure 4—figure supplement 2B).

As a final test of our modeling approach, we examined how our Best 4 (Lowest Err) Model's parameters changed when we applied variations in Feedback Gain as shown in Table 3. Recall that in the 1.35 Feedback Gain condition, the dot moves more than the person's hand position; therefore, we expect the subject to move slightly less than they do in the veridical feedback condition because they do not need to move as much to get the same visual output (i.e. we expect k to decrease). Similarly, we expect the subject to attempt to replicate a greater portion of the signal because it is easier to do so. Thus, we expect the Visual Gain (the amount of the input signal that the subject is trying to reproduce) to be greater in the 1.35 Feedback Gain Condition than in the veridical condition. Recall that the Visual Gain affects the input to the visual error computation. We expect the opposite trend for the 0.65 Feedback Gain condition, as is detailed in Table 3. Given that we believe the delays are biologically limited based on transmission time of visual information, we expect the delay magnitudes to stay the same between Feedback Gain conditions. Indeed, the model parameters change in the hypothesized manner when different Feedback Gains were applied. The results from fitting the Best 4 (Lowest Err) Model to the data from each of the different Feedback Gains yields the parameter values shown in Table 4. The visual feedback delays are nearly identical between Feedback Gain conditions, and the k and Visual Gain values increase and decrease as hypothesized in Table 3. The one difference between the hypothesis and these model values is in the lack of a feedback delay for the control subjects. This discrepancy is addressed in the Discussion section.

Lastly, we used bootstrapping to generate confidence intervals for the parameter values in our Best 4 (Lowest Err) Model. Confidence intervals (see Methods) for our best model to be: 2.1–3.4 for k_patient and k_control; 0.32–0.46 for Visual Gain_patient and Visual Gain_control; 174–261 ms for Visual Delay_patient; and 122–161 ms for Visual Delay_control, and Feedback Delay_patient.

We validated the sinusoidal tracking paradigm by quantifying a known behavioral deficit in cerebellar visuomotor control. In this predictable task, we expected healthy participants would be efficient, exerting less than or equal to the amount of effort required to minimize error for a given phase lag. Where subjects lie relative to this tradeoff can be visualized on a phasor plot; efficient tracking would yield points on or inside the effort/error tradeoff circle (Figure 2B, Materials and methods). We hypothesized that patients with impaired prediction may in some cases exert more effort than needed to minimize error, resulting in phasor points outside the effort/error tradeoff circle. We also hypothesized that patients would generate larger tracking errors.

At the five lowest frequencies tested, all control responses landed in/on the circle, whereas only 31% of patient responses landed in/on the circle (Figure 5). Additionally, patients generated larger tracking errors: 70% of patient responses exhibited larger error magnitude than the respective age-matched control responses. Furthermore, we created an aggregate tracking error for the single-sines experiment by calculating the sum of the tracking errors for the lowest five frequencies. We compared the aggregate tracking error between patients and age-matched controls by calculating the difference for each pair and testing those differences against 0 using a two-sided sign test. The null hypothesis for a two-sided sign test is that there was no difference between patients and their age-matched controls. The alternative hypothesis is that the controls may be either better or worse than patients. When we compared the difference between the aggregate tracking errors for each patient/control pair to 0, controls were significantly better than patients at single-sines tracking with 10 out of 11 controls performing better than their age-matched counterpart (p=0.012). These results illustrate cerebellar patients’ poor predictive ability. Importantly, note that this analysis does not distinguish what portion of their errors stemmed from poor prediction of the stimulus trajectory versus poor control of the arm.

Figure 5

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For comparison, we also included the results from the task where the stimulus was unpredictable (sum-of-sines from Experiment 1) in Figure 5. For this experiment, because neither group would be able to predict the target trajectory, we expected that patients would be less impaired relative to controls. Indeed, patient and control behaviors were more similar in this condition: for the five lowest frequencies tested in the sum-of-sines condition, 72% of control responses and 64% of patient responses were in/on the circle. Note, however, that there is an increased phase lag of the cerebellar patients (relative to controls), particularly as the frequency of the stimulus increases, which would be expected if the patients were dependent primarily on time-delayed visual feedback (a pure feedback delay introduces greater phase lag at higher frequencies). Specifically, 73% of individual patient frequency responses were more phase lagged than the responses of the age-matched control (as computed on an individual frequency basis).

As expected, we also observed a reduction in tracking error from the sum-of-sines task to the single-sines task. We calculated the magnitude of the tracking error for each subject for each frequency (i.e. for the frequencies that were tested in both conditions) and then compared the errors between the conditions. 93% of controls’ and 75% of patients’ tracking errors were reduced in the single-sine task in comparison to his or her performance in the sum-of-sines task. Again, we computed the aggregate tracking error for the sum-of-sines task, as described earlier, using the same five frequencies used in the single-sines aggregate tracking error calculation. We then used a two-sided sign test to determine that patients (p=9×10⁻⁴) and controls (p=9×10⁻⁴) were better at tracking single-sines than sum-of-sines, with all patients and all controls having less tracking error for single-sines than sum-of-sines.

To specifically look at phase lag between groups (patients vs. controls) and conditions (single- vs. sum-of-sines), we used a circular statistical approach. Figure 6 shows polar representations of the phase lags from the single-sine and sum-of-sines conditions (Figure 6A,C) and an example time series from a control and cerebellar subject tracking the 0.85 Hz sine wave (Figure 6B,D). The example control subject showed little phase lag suggesting that this individual could make use of an internal prediction of the dot movement and their arm movement. In contrast, the example cerebellar subject showed a systematic phase lag suggesting that their ability to use prediction is impaired. The pattern of lag can be visualized across frequencies in the polar plots. As a group, controls show a small increase in lag as the frequency increases in the single-sine condition, whereas the cerebellar group shows large lags (Figure 6A and C, compare purple vectors). Circular ANOVA for the single-sine condition showed that the cerebellar group had greater lags compared to controls (Group effect, p=1×10⁻⁸), that the lags increased with frequency (Frequency effect, p=7×10⁻¹¹) and an interaction such that the cerebellar group lags increased more than controls across frequency (Interaction effect, p=2×10⁻⁶). In the sum-of-sines condition, the difference in lags across frequency was qualitatively greater when comparing cerebellar and control groups (Figure 6A and C, compare black vectors). Overall the cerebellar group showed greater phase lags compared to controls (Group effect, p=0.02), and there was a statistically significant effect of Frequency (Frequency effect, p=7×10⁻³⁰). Group x Frequency interaction (Interaction effect, p=0.03), was less significant than that seen in the single-sine condition.

Figure 6

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The results from Experiment 1 indicated that cerebellar patients’ feedback control may be largely intact. In Experiment 3, we leveraged this intact element of their control system to reduce dysmetria. Our goal was to provide each cerebellar patient with customized visual position feedback information that took into account their controller’s mismatched feedforward model. This altered visual feedback would help them generate the correct motor command for a simple elbow movement (30° flexion) by accounting for their actual arm dynamics.

Here, we used a motor task that requires subjects make a discrete movement to a target that is stepped to a new position. This was chosen so that we could compare our data to previously published results using the same task with cerebellar patients. Subjects were asked to make a 30° elbow flexion movement from a home target to a stepped target. The task was completed with both veridical visual feedback and with altered visual feedback that was designed to reduce their dysmetria.

Bhanpuri et al. theorized that cerebellar patients have a static mismatch between their controller’s internal model of their limb inertia and the actual limb inertia for elbow flexion movements (Bhanpuri et al., 2014). Critically, for single-joint elbow flexion or extension, an inertial mismatch causes an acceleration-dependent error in the internal dynamic model because inertia and acceleration are kinematically yoked. Thus, we predicted that an Acceleration-Dependent Feedback Gain, $k_a$ (block diagram inset in Figure 7A) could provide corrective feedback to enhance reaching performance of cerebellar patients. Specifically, we took a subject’s estimated acceleration (see Materials and methods), multiplied this by the Feedback Gain, and then added it to the position of the subject’s cursor:

Figure 7

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We predicted that positive value for $k_a$ would make a subject more hypermetric and negative value would make a subject more hypometric. Thus, we expected hypometric patients would experience a reduction in dysmetria with a positive gain. Similarly, we expected hypermetric patients would experience a reduction in dysmetria when a negative gain was applied. For a given value for the gain for $k_a$, subjects completed 30° elbow flexion reaching movements in the Kinarm exoskeleton robot. Reaches were categorized as hypometric, hypermetric, or on-target based on the angle where they made their first correction to their movement. The Acceleration-Dependent Feedback Gain $k_a$ was applied to the visual feedback provided on the Kinarm screen. For more details on the implementation and instructions of this task, see Materials and methods.

When an appropriate Acceleration-Dependent Feedback Gain $k_a$ was applied, dysmetria was reduced. The effect of this gain on the displayed trajectory is shown in Figure 7A, where the dashed green line shows the altered visual feedback given to the subject and the solid green line shows the subject’s actual reach to the target for a single Feedback Gain condition. Increasing the magnitude of $k_a$ had a graded effect on the trajectory profile, as shown by the decreasing amplitude of the solid traces in Figure 7A. To find the 'best' $k_a$ we applied the PEST algorithm (see Materials and methods). Applying this gain shifted the angle of first correction in the way we predicted, as shown in both Figure 7B. Figure 7C shows all the data collected during the implementation of PEST as well as additional trials across a range of gains $k_a$ (see Materials and methods) that were collected for a subset of patients (and all control subjects; see Figure 8). Critically, positive Acceleration-Dependent Feedback Gain made patients more hypermetric and negative Acceleration-Dependent Feedback Gain made patients more hypometric; likewise for control subjects. Thus, subject-specific Acceleration-Dependent Feedback Gain was needed to best reduce dysmetria. In general, increased Acceleration-Dependent Feedback Gain magnitude was needed to ameliorate greater dysmetria.

Figure 8

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Cerebellar patients are thought to make faulty state estimates of arm motion due to a damaged internal model, which adversely affects their proprioceptive estimates during active movement (Bhanpuri et al., 2013). Thus, we expect them to increase their reliance on visual feedback, which is time delayed compared to proprioceptive feedback. Here we hypothesized that our patients’ feedback control system would have an increased delay in comparison to controls. This hypothesis is supported by work that showed that healthy subjects normally rely more on proprioception than vision for feedback control (Crevecoeur et al., 2016). Based on the Crevecoeur et al., 2016 model, increased variability of the proprioceptive information would lead to increased weighting of visual feedback (Crevecoeur et al., 2016; Weeks et al., 2017), which comes at the cost of increased delay for patients compared to controls.

Our modeling results reveal that patients have a delay in their feedback loop that approximates what one would expect from visual feedback, while controls appear to have negligible feedback delay. One interpretation of the control data is that controls are relying on a predictive internal model of their arm dynamics. This would allow them to make corrections even faster than they could using purely proprioceptive feedback. In other words, healthy controls can make corrections for current target movements based on a prediction of the present limb state from outdated measurements and known motor commands, rather than waiting on delayed sensory feedback.

We think that the cerebellar patients’ deficits are best explained by their dependence on time-delayed visual feedback, though it is theoretically possible that delays in motor execution could contribute. Previous studies have shown that some patients with cerebellar damage exhibit longer than usual reaction time delays when asked to make discrete, rapid movements (Beppu et al., 1987; Beppu et al., 1984; Day et al., 1998; Holmes, 1917; Vilis and Hore, 1980). These reaction time studies aimed to quantify a movement initiation delay as opposed to a feedback delay. Here, we specifically assessed the timing of the in-flight trajectory alterations made while tracking an unpredictable stimulus. While our feedback delay is a type of ‘reaction time’ because this task requires making corrections on the fly, the neural mechanisms underlying these corrections may differ from those responsible for planning and initiation of a rapid movement.

Cerebellar patients can also show a reduced feedback gain in situations where responses are driven by proprioception more than vision. Kurtzer et al., 2013 studied cerebellar patients’ ability to modulate long latency stretch responses (i.e. EMG responses within 45–100 ms of a muscle stretch) that depend on knowledge of intersegmental dynamics of the arm. This was assessed by mechanically perturbing the elbow joint and measuring long latency responses from elbow muscles and from shoulder muscles in anticipation of the passive shoulder motion induced by elbow movement. Cerebellar patient responses were found to have a lower gain and a slight delay in timing compared with controls. We interpret this in the context of the different task demands between studies-- in that study, proprioception drove the response; here vision appears to be more important to patients. These results combined suggest that cerebellar subjects can reweight which feedback modality to rely on (proprioception versus vision) depending on task demands, consistent with Block and Bastian, 2012, and may reduce the sensorimotor gain on either modality to minimize the negative effects of delay.

Lastly, while the confluence of data and modeling presented here seems to indicate that patients rely disproportionately on delayed feedback from vision for this visuomotor tracking task, two of our top models (Model Best 5, Lowest Err and Best 4, Lowest Err; see Table 2) actually exhibited shorter feedback delays than visual delays for patients. This suggests that the patients’ control systems in this task may include some reliance, albeit weaker, on prediction and proprioception.

Sensorimotor tasks are naturally analyzed using control systems theory and system identification (Roth et al., 2014), and because cerebellar patients’ dysmetria resembles a poorly tuned control system, many researchers have analyzed cerebellar behavior using control theory (Luque et al., 2011; Manto, 2009; Miall et al., 1993; Porrill et al., 2013).

Our modeling results indicate that control subjects make corrections based on prediction of a future limb state measurement. While there is some controversy on this (Pélisson et al., 1986; Wolpert et al., 1998), previous work has proposed that the cerebellum might function in a manner consistent with a Smith Predictor (Miall et al., 1993). Essentially, a Smith Predictor is a control architecture that compensates for self-movement feedback delay. To achieve this requires a simulation of the plant in order to predict sensory consequences of motor output, and a simulated delay that ‘stores’ the plant simulation for comparison with delayed feedback. In order to understand the consequences of incorporating a Smith Predictor, consider the generic feedback block diagram of sensorimotor control depicted in Figure 9 (top) and model the brain as either a controller with (Figure 9, left) or without (Figure 9, right) a Smith Predictor. Interestingly, upon simplification, we find the exact structures yielded by two of the top models (Best 5 Lowest Var and Best 4 Lowest Var): the patient model matches the simplified block diagram without a Smith Predictor and the age-matched control model matches the simplified block diagram which one. This suggests that an intact cerebellum may act in a manner qualitatively similar to a Smith Predictor and that patients ability to perform such prediction is impaired.1.

Figure 9

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Perhaps the increased feedback delay in the cerebellar patients is unavoidable if one assumes the patients' control systems lack the essential capabilities of a Smith Predictor (making and storing predictive plant simulations). Thus, the apparent increased reliance on visual feedback seen in cerebellar patients may not be a compensatory mechanism at all—perhaps all subjects rely on delayed visual feedback, but healthy subjects disguise the delay using predictions of future measurements of limb state. Patients may simply lack this capability and it is not that they compensate for their deficit by relying more on visual feedback but instead that the loss of the sensory prediction and storage reveals the visual feedback delay inescapably present in both groups. This would provide some clarity on how cerebellar patients could ‘learn’ to ‘compensate’ in this way even when their cerebellum was damaged.

At its core, the Smith Predictor has to do with simulating the mechanical plant (and appropriate delay) in order to mitigate the effect of feedback delay. But notice that in our model there is a large visuomotor delay on the reference input even with the Smith Predictor in place. In order to compensate for the delayed visual measurement of the stimulus, the brain would need to be able to predict reference motions. To avoid this confound of stimulus prediction, and focus on feedback delay compensation, we fit our models using responses to unpredictable (sum-of-sine) target motions.

But, what if the target motion were predictable? Previously, it was shown in another species (weakly electric fish) that target predictability can indeed improve tracking performance, and it was hypothesized that this was based on an internal model of predictable reference motion (Roth et al., 2011). Here, we extend this to healthy human subjects who show marked improvement in the single-sine (predictable) tracking task. Cerebellar patients exhibit much more modest improvement in tracking predictable stimuli, suggesting that they may have impairment in both their own plant model predictions and predictions of external sensory references (see Results, Experiment 2). Further data and experiments would be needed to better isolate the effects of cerebellar damage on these potentially disparate functions of the cerebellum.

Lastly, even if a healthy cerebellum helps ‘cancel’ expected cursor feedback, this does not imply that visual cursor feedback goes unused: any errors in visual feedback, i.e., cursor self-motion feedback that is not precisely anticipated by the cerebellum, could be highly informative, and recent evidence (Yon et al., 2018) suggests that a predictive model of action–perception could heighten perceptual sensitivity, making self-motion (in this case, cursor) feedback more nuanced and precise.

There are potential alterative modeling interpretations of the data presented in this paper. For example, a state predictor with optimal state feedback (Crevecoeur and Gevers, 2019) is consistent with our observation that healthy subjects compensate for delay and is an avenue for further investigation. Also, our observation that visual target delay was longer in the patient model than the control-subject could conceivably be due to a different source of phase lag that our simplified modeling structure was not able to capture. Future experiments and analysis will investigate this further.

In Experiment 3, we were successfully able to reduce the dysmetria of both the hypermetric and hypometric cerebellar patients in an elbow flexion task. Our visual feedback-control-based intervention was developed based on a control model which represented dysmetria as a mismatch between the patient’s internal model of their limb inertia and the actual limb inertia (Bhanpuri et al., 2014). Thus, the success of our intervention provides support to this inertial mismatch theory. However, recent evidence based on the application of limb weights suggest that the inertial mismatch theory may be insufficient to explain dysmetria in multi-joint movements (Zimmet et al., 2019). Thus, feedback enhancement of multi-joint movements will likely require modifications of the simple acceleration-based controller tested in this paper. Moreover, the ‘best’ acceleration-dependent feedback gain was patient specific even for the single-degree-of-freedom reaches tested for this study, suggesting that idiosyncrasies in each patient’s motor control system (Kuling et al., 2017; Rincon-Gonzalez et al., 2011) may mandate patient-specific tuning. Such tuning will be made more complex for 2D and 3D arm movements.

Though our intervention successfully reduces the initial over or undershooting component of the reach, our method does not attempt to correct all aspects of dysmetria. Patients with cerebellar ataxia also typically exhibit increased movement variability. Application of this visual feedback gain does not attempt to reduce the variability of patient reaches. Secondly, our intervention does not completely eliminate the oscillations experienced by the subject after this first correction is made. Moreover, our modeling work does not characterize or explain this increased variability directly. Mild oscillations after the first correction can be seen in Figure 7A. It is possible that adding a damping term to the feedback intervention might be able to address this oscillatory behavior.

Our results provide an encouraging foundation for future studies because they show that cerebellar patients are capable of using their own intact visual feedback control system to make accurate reaches. Further study is needed to determine whether this intact feedback control system could be leveraged therapeutically to reduce dysmetria without need for a virtual reality system. Alternatively, it is possible that wearable sensory augmentation (for example, tendon vibration or skin stretch) could be used as a surrogate for the vision-based sensory shift provided here. These alternatives are especially important because drug therapy for cerebellar ataxia is not currently viable, leaving rehabilitative and assistive therapies alone as the primary means of treatment for these patients. In any case, we hope that by identifying these intact movement control mechanisms we might help move treatment possibilities forward.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

National Institute of Child Health and Human Development HD040289 to AJB and NJC, Applied Physics Lab Graduate Fellowship FNACCCX19 to AMZ, National Science Foundation 1825489 to NJC and AJB. Thanks to James Freudenberg, Brent Gillespie, Adrian Haith, Matthew Statton, and Sarah Stamper for helpful comments and discussion. Thanks to Amanda Therrien for recruitment of patients, clinical assessments, and feedback throughout this process.

Human subjects: The experimental protocol was approved by the Institutional Review Board at Johns Hopkins University School of Medicine (protocol # IRB00182673) and all participants gave informed consent prior to joining this study, according to the Declaration of Helsinki.

© 2020, Zimmet et al.

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