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Computation of linear acceleration through an internal model in the macaque cerebellum

Nature Neuroscience volume 16, pages 1701–1708 (2013)Cite this article

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Abstract

A combination of theory and behavioral findings support a role for internal models in the resolution of sensory ambiguities and sensorimotor processing. Although the cerebellum has been proposed as a candidate for implementation of internal models, concrete evidence from neural responses is lacking. Using unnatural motion stimuli, which induce incorrect self-motion perception and eye movements, we explored the neural correlates of an internal model that has been proposed to compensate for Einstein's equivalence principle and generate neural estimates of linear acceleration and gravity. We found that caudal cerebellar vermis Purkinje cells and cerebellar nuclei neurons selective for actual linear acceleration also encoded erroneous linear acceleration, as would be expected from the internal model hypothesis, even when no actual linear acceleration occurred. These findings provide strong evidence that the cerebellum might be involved in the implementation of internal models that mimic physical principles to interpret sensory signals, as previously hypothesized.

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Figure 1: Schematic illustrating the TWR stimulus.
Figure 2: Motion signals during TWR.
Figure 3: Model schematic and simulations.
Figure 4: Example cell response.
Figure 5: Quantification of firing rate changes during TWR at 45° s−1 in preferred and anti-preferred directions.
Figure 6: Population responses, eye movements and model simulations during steady-state TWR.
Figure 7: Comparison between initial and steady-state TWR.
Figure 8: Time dependence of normalized population responses as a function of the delay between the beginning of EVAR and the tilt movement.

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Acknowledgements

We would like to thank E. Klier, P. Blazquez and T. Yakusheva for critically reading the manuscript. This work was supported by a grant from the US National Institutes of Health (EY12814).

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Authors and Affiliations

  1. Department of Otolaryngology, Washington University School of Medicine, St. Louis, Missouri, USA

    Jean Laurens

  2. Department of Neuroscience, Baylor College of Medicine, Houston, Texas, USA

    Hui Meng & Dora E Angelaki

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Contributions

J.L. designed and performed the experiments, analyzed the data, and prepared the manuscript. H.M. performed experiments. D.E.A. designed the experiments and prepared the manuscript.

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Correspondence to Dora E Angelaki.

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The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Processing of vestibular information with a forward internal model.

(Alternative formulation to the model of Fig. 3) This schematic model is representative of the models of Borah et al. (1988), Merfeld (Merfeld et al. 1993a; Merfeld 1995) and Glasauer and Merfeld (1997).

Supplementary Figure 2 Reconstructed three-dimensional locations of the recorded cells in stereotaxic coordinates.

Shown separately for each animal. (a)-(c) Frontal views; (e)-(g) Saggital views. Each square corresponds to a single neuron, color-coded according to its type/location: Blue: cerebellar nuclei cells; Red: nodulus/uvula Purkinje cells, separated into “identified” (filled symbols, where each complex spike was followed by a pause in simple spike firing for at least 10ms) and "putative" (open symbols). Black (cerebellar nuclei) and grey (nodulus/uvula) circles illustrate cells recorded from the same animals using different experimental protocols. Eye movement-sensitive cells in the cerebellar nuclei are shown with cyan crosses. In each animal, the position of the abducens nuclei was first identified and then used to reconstruct the stereotaxic coordinates of the recorded cells. Recording locations of cerebellar nuclei neurons include mostly the rostral fastigial, but potentially also the anterior interposed, nuclei. Most nodulus/uvula cells were recorded within a 6 mm region directly ventral to the rostral fastigial nuclei, which includes mostly the nodulus and to a lesser extent the ventral uvula. In (d) and (h), the boundaries of the corresponding anatomical structures were reconstructed based on the macaque brain atlas (Mikula et al. 2008; Paxinos et al. 2000). Int.: interposed nuclei, Med.: medial (fastigial) nuclei, Nod.: Nodulus. Note that all recorded Purkinje cells had coefficient of variation, CV2>0.4 and spontaneous firing rates larger than 30 spikes/s, criteria used to separate Purkinje cells from cerebellar interneurons (Heine et al. 2010). The combination of these properties and the presence of complex spikes recorded simultaneously with simple spikes provides strong support that we have recorded from Purkinje cells, rather than cerebellar interneurons.

Supplementary Figure 3 Example eye movements.

During (a-c) pitch and (d-f) roll TWR. (a), (d) EVAR velocity and pitch/roll tilt stimuli. (b), (e) Horizontal and (c), (f) vertical eye velocity. All runs were performed with the same EVAR direction (leftward), but initial tilt positions were opposite (a,d: red vs blue curves). The curves shown in (b,c) and (e,f) represent averages across 3 trials in animal V. Pitch TWR elicits an induced roll (torsional) aVOR and an induced horizontal tVOR, whose direction reverses with the pitch direction, and which is superimposed on the yaw aVOR (b, black). Roll TWR elicits an induced vertical aVOR (f), but no conjugate horizontal tVOR in darkness (e). (g, h) Average torsional VOR (red and blue curves) during pitch and roll TWR (n=73 and 77 trials, respectively) recorded in two additional animals implanted with a dual eye coil (details of implantation and analyses can be found in Klier et al. 2006) in order to measure three-dimensional (horizontal, vertical and torsional) eye movements. For comparison, the average induced aVOR and tilt aVOR curves obtained by measuring vertical eye movements are shown in grey. During pitch TWR (g), the induced aVOR is around the roll axis. During roll TWR, the tilt aVOR is around the roll axis. Thus, torsional and vertical aVOR mirror each other. This confirms that no additional torsional eye velocity beyond the expected aVORs occurred during steady-state TWR.

Supplementary Figure 4 Yaw velocity signals during steady-state TWR.

(a) Projection of the EVAR vector (red) on the yaw axis of the head (black arrow, the projection is shown as a dashed blue line). During each tilt movement, the projection of the EVAR vector on the yaw axis increases when the head nears upright and decreases when the head tilts away. The tilt angle used in this panel is 30°. (b-c) Same simulations as in Fig. 2d. The yaw signals following TWR in the steady-state (b, red rectangle) are detailed in (c). During tilt (grey band), a small yaw velocity component transiently activates the horizontal canals during each tilt (black, peak velocity 0.6°/s). This components is visible in the central yaw signal (blue). Due to central processing (Merfeld et al. 1993a,b; Merfeld 1995; Angelaki and Hess 1995; Laurens et al. 2010; Laurens and Angelaki 2011), a longer-lasting yaw signal develops after each tilt movement. This component doesn't reach zero between two successive tilts. (d): yaw aVOR measured during steady-state TWR, which matches the simulation accurately. Note the small amplitude. Importantly, by following the analysis of Merfeld et al. (1999), the tVOR and yaw aVOR components can be satisfactorily distinguished (see also Supplementary Fig. 3).

Supplementary Figure 5 Response profile of individual neurons and comparison between neuronal populations.

(a), (b) Average (±95% CI) steady-state responses of all 'confirmed' (red) and 'putative' (black) Purkinje cells and cerebellar nuclei neurons (blue) during TWR in the preferred direction (PD), anti-PD or during control. (c,d) Acceleration signals decoded from the populations of nodulus/uvula (n=27) and cerebellar nuclei (n=31) neurons (c) and 'putative' (n=13) and 'confirmed' (n=14) Purkinje cells in the nodulus/uvula (d), computed as follows: Decoded Acceleration = (FRPD-FRControl)/S, where FRPD is the average firing rate across the population during TWR in the PD (in spikes per s), FRControl is the average response during control (in spikes per s), and S is the gain to sinusoidal translation in (spikes per s)/(m.s-2). The black bands below the curves indicate the points in time at which the decoded signals are significantly different (t-test, with p < 0.01). Although cerebellar nuclei responses were generally more modest in amplitude, there were no significant differences in nodulus/uvula and cerebellar nuclei population responses, particularly during peak amplitude (c). There were no differences in population responses of 'confirmed' and 'putative' Purkinje cells (d). Thus, data have been presented together in the main text. Note that cerebellar neurons show a larger firing rate response in their "on direction" than firing rate decrease in their "off direction". This is not unexpected and often described in other cerebellar areas (e.g., the primate flocculus; Miles et al. 1980).

Supplementary Figure 6 Temporal relationships between various motion variables.

(a) During each tilt movement (grey band), the tilt aVOR (green) occurs in nearly perfect synchrony with stimulus velocity (black). The induced aVOR (cyan) grows steadily and peaks after the tilt aVOR peak. The neuronal response (red, decoded acceleration signal) follows the induced aVOR with roughly similar dynamics and reaches a peak ~200-250ms later. The tVOR (magenta) builds up even more slowly and peaks at ~3s, well after the neuronal response. Data shown represent normalized averages of all cells/sessions recorded (a.u.: arbitrary units). (b) Model simulations of the same variables. Note the striking match with actual response profiles in (a). Even while ignoring transmission delays of neuronal signals, this analysis demonstrates that temporal differences observed experimentally between tilt aVOR, induced aVOR, tVOR and neuronal responses can be explained by the dynamic relationships between motion variables in the model. (c) Schematic representation of the filtering relationships between various variables. The model in Fig. 3 can be approximated by filtering the tilt velocity though a series of leaky integrators, but it has been expanded to also simulate the tVOR under the assumption it is driven by a mixture of acceleration and velocity signals (Angelaki 1998). Though curve fitting, we estimated that the tVOR could be approximated by the equation: d(tVOR)/dt = 0.63 dA/dt + 0.32 A -1/12.5 tVOR, where A is the decoded acceleration signal. The corresponding transfer function is H(ω) = (4+8.4*j*ω)/(1+12.5*j*ω). These successive filters are responsible for the observed temporal differences in tilt aVOR, induced aVOR, tVOR and neuronal responses.

Supplementary information

Supplementary Text and Figures

Supplementary Modeling, Supplementary Table 1 and Supplementary Figures 1–6 (PDF 1442 kb)

Illustration of the TWR stimulus.Illustration of the TWR stimulus.

(a) Real stimulus (Rotator). Only the head of the subject is represented (the rail system onto which the rotator is mounted is not shown). The red and green arrows represent the rotation axis of the EVAR and tilt movement, respectively. For better visibility, this movie shows a tilt angle of 25° and one tilt movement every 5s. (b) Decomposition of the EVAR velocity in an egocentric frame of reference. This panel shows the head tilting back and forth relative to the EVAR velocity vector (red). The projection of this vector onto the yaw and roll axes (black arrows) are shown in blue and cyan. Note that the projection onto the yaw axis is approximately constant (but see Supplementary Fig. 4), whereas the projection onto the roll axis switches direction with each tilt movement (as in Fig. 2d,e; broken lines). (c) Rotation signals sensed by the semicircular canals: yaw (blue) and roll (cyan) (comparable to black lines in Fig. 2 d,e). The brain continuously reconstructs the net rotation by summing the yaw and roll velocity signals (red arrow). During 'initial' TWR, the yaw and roll velocity components are correctly sensed by the canals and, even though these signals decay with a time constant of 4s, the resulting net rotation signal (red) remains aligned with the earth-vertical. During 'steady-state' TWR, however, yaw velocity (blue) changes minimally and the net rotation signal (red) is closely aligned with the roll axis (cyan) following each pitch tilt. (MP4 5174 kb)

Perception during TWR.

(a) Real stimulus (Rotator) showing actual pitch tilt (10°). (b) Simulated motion perception generated by the internal model. During initial TWR, head tilt is perceived accurately, but the perception of rotation decreases over time. During steady-state TWR, each forward and backward tilt movement induces erroneous sideward tilt and translation signals. Note that the amplitude and duration of illusory motion shown in this movie were scaled for better visibility and are not accurate. (MP4 5554 kb)

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Laurens, J., Meng, H. & Angelaki, D. Computation of linear acceleration through an internal model in the macaque cerebellum. Nat Neurosci 16, 1701–1708 (2013). https://doi.org/10.1038/nn.3530

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