Table 1.
Disease types and anatomical involvements of cerebellar patients.
Fig 1.
Experimental tasks and model framework.
(A) In the saccade trials, subjects executed a saccade to a 20° rightward target. In the pre-exposure phase, the target was extinguished at saccade onset. In the exposure and post-exposure phase, the target either stepped 6° inward (inward condition), 6° outward (outward condition) or stayed at its initial position (no step condition). In the pre-saccadic localization trials, subjects localized a 12 ms flash with a mouse cursor while holding gaze at the fixation point. In the post-saccadic localization trials, subjects performed a saccade to a 20° rightward target and then localized the 12 ms pre-saccadic flash with a mouse cursor. Please note that the stimuli are not drawn to scale. The mouse cursor was a blue line pointer. The yellow circle illustrates gaze location but was not present at the stimulus display. (B) The target with the physical distance P1 is represented at the location V1 on the visuospatial map. An inverse model maps V1 onto a motor command M. Before saccade start, a forward dynamics model transforms a copy of the motor command CDM into visuospatial coordinates, i.e. into the computed displacement of visual space CDV. A forward outcome model then shifts retinal coordinates by CDV to predict the visual location of the post-saccadic target . For saccade execution, the motor command is transposed to saccade peak velocity κ and saccade duration λ, producing the saccade vector PM. The actual post-saccadic target appears at retinal position V2. A backward outcome model then postdicts the visual post-saccadic target back to pre-saccadic space
. The visuomotor system evaluates the accuracy of the motor command with respect to the postdicted target position (Epost) in order to adapt its gains ωv, ωm and ωcd. A decrease of ωm (inward learning) is controlled by downregulating saccade peak velocity while an increase of ωm (outward learning) is controlled by upregulation of saccade duration. When saccades are performed repetitively to the same, non-stepping target, oculomotor fatigue occurs, i.e. peak velocity declines, which is usually compensated by an increase of saccade duration.
Fig 2.
Example subject data for the inward condition and within-subject saccade variability in the pre-exposure phase.
Saccade vectors, pre- and post-saccadic localizations for the inward condition of (A) an example control subject and (B) an example patient. The pre-exposure phase measured subjects’ baseline state without target step. The exposure phase induced saccadic learning and the post-exposure phase measured adaptation-induced changes to the saccade vector, pre- and post-saccadic localizations. Similar to the pattern that we found at group level, the patient shows less learning in the saccade vector and higher saccade endpoint variability compared to the control subject. In the model, the predicted post-saccadic target is derived from post-saccadic localization relative to saccade landing. (C) Within-subject standard error of saccade vectors in the pre-exposure phase (averaged across the three conditions per subject) compared between control subjects and patients, *** p <.001, ** p <.01, * p <.05 and n.s. p ≥.05.
Fig 3.
Individual saccade peak velocities in dependence on saccade vectors from early trials (blue) to late trials (yellow).
Saccade peak velocities and saccade vectors are shown separately for each subject and condition (controls C1-C8, patients P1-P8 including disease type and disease duration in years). During inward learning of control subjects, the decrease of the saccade vector encompasses a decrease of saccade peak velocity. This is in line with saccade shortening being mainly controlled by downregulating peak velocity. During outward learning, the saccade vector increases while peak velocity stays stable. This is in line with saccade lengthening being mainly controlled by upregulating saccade duration (see Fig 4). In the no step condition, saccade peak velocity encompasses a small but substantial decline that, however, is not accompanied by a decline of the saccade vector. This is a sign of oculomotor fatigue being successfully compensated by healthy subjects. As known from cerebellar patients, the patients’ saccade vectors and peak velocities are more variable than in control subjects. Moreover, overall learning effects on saccade vector and peak velocity are smaller. In the no step condition, patients show substantial oculomotor fatigue, i.e. a decline in peak velocity that is not fully compensated by saccade duration.
Fig 4.
Individual saccade durations in dependence on saccade vectors from early trials (blue) to late trials (yellow).
Saccade durations and saccade vectors are shown separately for each subject (controls C1-C8, patients P1-P8) and condition. During inward learning of control subjects, saccade duration declines in subjects C3, C5, C7 and C8 (yet not significantly across subjects when compared between the pre- and the post-expose phase, t7 = -1.01, p = .346). The decrease of the saccade vector rather stems from a decline of saccade peak velocity (see Fig 3). In the outward condition, saccade duration increases together with the saccade vector. This is consistent with saccade lengthening being mainly controlled by upregulation of saccade duration. In the no step condition, saccade duration increases, thereby compensating for the peak velocity loss seen in Fig 3. In patients, small learning effects can be seen but saccade vectors and durations are more noisy. In the no step condition, saccade duration is increased only in patient P4 and P7. Overall, duration cannot sufficiently counteract the peak velocity loss.
Fig 5.
Pre- and post-exposure mean ± standard error (dots with error bars), trial-by-trial saccade data of the exposure phase (jagged blue lines) and model fits to the data (smooth lines) for (A) control subjects and (B) cerebellar patients, separately for each condition (inward, no step, outward). (1) Visual pre-saccadic target V1 (fitted to pre-saccadic localizations), motor command M (fitted to saccade vectors), computed displacement of visual space CDV, postdicted pre-saccadic target . (2) Predicted post-saccadic target
(fitted to post-saccadic localizations with respect to saccade landing), visual post-saccadic target V2. (3) Visual gain ωv, motor gain ωm, CD gain ωcd. (4) Postdictive motor error Epost. (5) Saccade peak velocity κ. (6) Saccade duration λ. Asterisks indicate significant difference between the pre- and post-exposure phase with *** p <.001, ** p <.01, * p <.05 and n.s. p ≥.05.
Fig 6.
Baseline state and pre- to post-exposure changes.
(A) Baseline state of the visuomotor system averaged across the pre-exposure phases of the three conditions (mean ± standard error), separately for control subjects and patients. Group-centered asterisks indicate significant difference from 20° (V1, M, CDV), from 1 (ωv, ωm, ωcd) or from zero (Epost). (B) Pre- to post-exposure changes in the inward condition. (C) Pre- to post-exposure changes in the no step condition. (D) Pre- to post-exposure changes in the outward condition. For B-D group-centered asterisks indicate significant difference from zero. Panel-centered asterisks above a horizontal indicate significant difference between control subjects and patients with *** p <.001, ** p < .01, * p <. 05 and n.s. p ≥ .05.
Table 2.
Fitted parameters and residual standard errors.
Fig 7.
Correlation of motor command M and CDV signal across subjects at steady state.
At steady state, i.e. in the pre-exposure phase across all three conditions (baseline) and in the post-exposure phase of the inward condition, the no step condition and the outward condition, the motor command M and CDV signal highly correlate across control subjects and patients. This shows that the quantification of the CDV signal by the model based on the trans-saccadic target localization and saccade data is a valid estimate of the internal representation of the saccade.
Fig 8.
Simulation of long-term visuomotor behavior after disease onset.
(A) Oculomotor fatigue in the very early phase of the disease causes a loss of saccade peak velocity κ that can only be partially compensated by upregulation of saccade duration λ. Consequently, a decline of the saccadic motor command M leads to saccade hypometry, that, in turn, results in a rise of motor errors Epost. Preserved long-term learning at perceptual (αv) and motor level (αm)—that, yet, slowly decays throughout disease progression—counteracts to keep saccadic behavior calibrated. Hence, the visuomotor system stabilizes with an overestimation of the pre-saccadic target eccentricity (V1) and recovery from saccade hypometria (M), matching the baseline visuomotor gains measured in cerebellar patients (ωv and ωm; ωcd deviates; residual standard error RSEω = 0.05). Simulations started with the visuomotor gains ωv, ωm and ωcd, the learning rates αv, αm and αcd, the peak velocity decay rate γκ and the duration compensation rate γλ of healthy subjects; αv, αm, αcd, γκ and γλ change until they match the values of cerebellar patients. Progression rates were νκ = 0.012, νλ = 0.040 and να = 1.7*10−7. Please note that the different subplots show different timescales. (B) Residual standard error RSEω depending on how fast learning rates (scaled by να), peak velocity decay rate (scaled by νκ) and duration compensation rate (scaled by νλ) change towards patients’ values. Simulations with RSEω ≤ 0.05 are marked with a white dot.