Tandem internal models execute motor learning in the cerebellum

Abstract

In performing skillful movement, humans use predictions from internal models formed by repetition learning. However, the computational organization of internal models in the brain remains unknown. Here, we demonstrate that a computational architecture employing a tandem configuration of forward and inverse internal models enables efficient motor learning in the cerebellum. The model predicted learning adaptations observed in hand-reaching experiments in humans wearing a prism lens and explained the kinetic components of these behavioral adaptations. The tandem system also predicted a form of subliminal motor learning that was experimentally validated after training intentional misses of hand targets. Patients with cerebellar degeneration disease showed behavioral impairments consistent with tandemly arranged internal models. These findings validate computational tandemization of internal models in motor control and its potential uses in more complex forms of learning and cognition.

Keywords: cerebellar degeneration; forward model; inverse model; motor control; prism adaptation.

Fig. 1.

Stages of hand reaching and operations in the prism-adaptation experiment. (A) Experimental procedures of the AOF or NAOF tasks. (B) Experimental procedures of the NF task. (C) Prism adaptation in healthy subjects (n = 5) during the AOF task. The thick and thin lines represent the mean and mean ± SD, respectively. (D) There was no adaptation in healthy subjects wearing a Fresnel prism plate during the NF task (n = 10).

Fig. 2.

Task-dependent fast and slow adaptation and hidden learning in healthy subjects. (A) Adaptation curves obtained by alternations between AOF phase (black dots, 10 trials, fast adaptation) and NF phase (red dots, five trials, slow adaptation). The dashed line indicates the baseline for the adaptive decreases in the degree of horizontal displacements. Red and black lines show fitted exponential curves. (B) Mean and SD of decay time constant of fitted curves for fast and slow adaptations. (C) Fast (black dots) and slow (red dots) adaptations determined by calculating averages during each NF trial. (D) Mean and SD of decay time constant of fitted curves for fast and slow adaptations determined by calculating averages during each NF trial. (E) Alternations between NAOF (blue dots, 10 trials) and NF (red dots 5, trials) tasks. (F) Horizontal displacements in TEST blocks in A and E. (G) Thirty trials of the NAOF task (blue lines, TRAINING session) followed by 10 trials of the AOF task [black lines, TEST-A session (box)]. (H) Test using the AOF task immediately after wearing a prism [CONTROL session (box)]. (I) Horizontal displacements in the AOF task in G (TEST-A block) and H (CONTROL block). (J) As in G but for the NF task (red lines). *P < 0.05 and **P < 0.01 by Mann–Whitney U test.

Fig. 3.

Changes in internal model properties in cerebellar patients. (A and B) Averaged adaptation curves for cerebellar patients with spinocerebellar ataxia type 6 (SCA6) and spinocerebellar ataxia type 31 (SCA31) indicating I_slow <0.5 and I_fast ≥0.5 (Dis 1–5 in SI Appendix, Table S2) (A) or I_slow <0.5 and I_fast <0.5 (Dis 6–10 in SI Appendix, Table S2) (B). a, b, and c show the periods of 10 trials. (C) Scatter diagram of I_fast vs. I_slow for healthy subjects and cerebellar patients.

Fig. 4.

Three types of learning operation in prism adaptation. Control system models for AOF (A), NF (B), and NAOF (C). X indicates the blockade of connection. The switch is operated by Ins3 (on in A and off in B and C). Red lines represent the feedforward circuit including the inverse model. Green lines represent the internal feedback circuit including the forward model. Ce, control error.

Fig. 5.

Trial-based changes in strength of adaptation. (A) Strength of adaptation for each internal mode, derived from the inverse model [S_slow(t), red line], motor cortex [S_diff(t) = S_fast(t) − S_slow(t), green line], and total [S_fast(t), black line] (Fig. 4A). These curves are estimated from Fig. 2C. (B) Area graph showing trial-dependent changes in the relative strength of adaptation in forward and inverse models. The black line shows [1 − S_slow(t)/S_fast(t)] × 100 based on the experimental results shown in Fig. 2C. Green and red areas indicate the ratios of the strengths of adaptation in the inverse model [S_slow(t)] and the forward model [S_diff(t)], respectively. S_diff(t) is higher than S_slow(t) during the initial 40 trials and decreases during the later trials.