MÉTODO VOLUMÉTRICO

Discrete experiment

To examine whether this ordering effect was due to weighting of information by its recency or due to the CNS modelling how the context evolves over time, I explored

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phase of the perturbation cycle

Figure 4.4: Tracking performance (grey) and ideal tracking performance (heavy black). The data are averaged over subjects ± 95% confidence limits for each of the four conditions and each half of the perturbation cycle. The grey bar indicates the duration of a half cycle. Note th at the discon­ tinuities between half cycles in the Finger hidden conditions (b /d ), are due to the fact that the immediately preceding half cycle in the experi­ ment was always a Finger seen condition, not a Finger hidden condition.

the way in which the context estimate evolved in the absence of visual feedback. Subjects pointed in a situation where the context varied with equal likelihood back and forth between two possibilities. When feedback had been turned off, subjects gradually adopted a behaviour intermediate to th a t for either context. This be­ haviour is consistent with the CNS modelling how the context is likely to evolve, but cannot be explained by just weighting visual feedback according to its recency

(Figure 4.2a-c).

Continuous experiment

My results show th at subjects actively compensate for a time-varying sinusoidal perturbation in the absence of visual feedback without being aware of the pertur­ bation. The compensation strategy used suggests th at the CNS is able to extract the rate of change of the context. Furthermore, the CNS may be able to estimate higher order derivatives of the rate of change in context or be sensitive to the mean context. To investigate whether this behaviour is due to extrapolation of the current context estimate or due to learning driven by the difference in perturbation ampli­ tude between when feedback is extinguished and when it is turned back on again, I conducted a second continuous experiment, in which the perturbation at feedback removal and reappearance were identical. Since subjects still updated their context estimate similarly, this indicates th a t performance is based on extrapolation rather than error-driven learning.

In both the discrete and the continuous experiments, subjects were not aware of (and did not guess) either the purpose of the experiment or the fact th a t discrep­ ancies between their actual and displayed finger position had been introduced (see Methods).

Relation to model

Our results can be interpreted in terms of the context estim ation framework of Fig­ ure 3.2. The CNS uses feedback to generate its own estimate of the context Q . It also generates an estimate of how the context is likely to evolve over time P{Ct\Ct-i).

Our experiments suggest th at the CNS’ model of this transition probability incor­ porates the rate of change of the context. Additionally it may be sensitive to higher order derivatives of the context and/or the average context. The statem ent th at the CNS has an a estimate of how the context evolves over tim e implies th a t it can construct and use an internal model— a brain process simulating the behaviour of both the body and the outside world (Ito 1984; Kawato et al. 1987; Wolpert et al. 1995; Wolpert 1997; Merfeld et al. 1999). Previous studies have shown th a t inter­ nal models play a role in maintaining accurate control in the presence of sensory feedback delays (Ito 1984), generating anticipatory responses (Forssberg et al. 1992; Gordon et al. 1993; Jenmalm and Johansson 1997) and in distinguishing our own actions from externally produced stimuli (Jeannerod 1997; Blakemore et al. 1998). Here I propose th at an internal model exists to predict how the context is likely to evolve over time.

Conditt and Mussa-Ivaldi (1999) exposed subjects to time-dependent force fields. From the lack of generalisation, they concluded th at the CNS has no explicit repre­ sentation of time. These findings are not necessarily incompatible with ours. First, their experiment manipulated dynamic aspects of the context, while I used kinematic perturbations. It has been shown th a t internal models for dynamics and kinematics can be learned independently (Krakauer J.W. and Chez 1999). Secondly, Conditt et al. used bell-shaped force perturbations th at lasted 333 ms, while an equivalent half-cycle perturbation in our experiments was roughly twelve times slower.

emerges th at compensatory tracking (as in our experiment) is more difficult than pursuit tracking, and is also more difficult to extrapolate in the absence of visual feedback (for a review, see Poulton 1974). It is therefore quite surprising th a t sub­ je c t’s performance was so good, given that they were unaware of the perturbation,

and tracking was in three dimensions.

Extrapolation of context estimates has also been explored in smooth pursuit eye movements, which interestingly cannot be elicited voluntarily. Barnes et al. (1995) showed th at subjects can sustain sinusoidal smooth pursuit eye movements in the absence of target motion, by stabilising the target on the fovea and giving subjects appropriate attentional cues. While the authors interpret this as evidence for an short term memory trace of eye movements, the results are equally compatible with the framework of Figure 3.2.

I have shown that the CNS may explicitly represent time — in the sense th at extrapolation requires time estimation — in order to actively update its context estimate. This process does not require awareness, suggesting th a t the CNS may be continuously adapting motor behaviour to changing contexts without tapping attentional resources.

5 Imaging uncertainty and