Movement drift is the result of optimal sensory combination Jeroen B.J. Smeets, John J. van den Dobbelsteen, Robert J. van Beers, Eli Brenner Afdeling Neurowetenschappen, Erasmus MC, Rotterdam, The Netherlands It is well known that if you move your hand repetitively between several targets, the endpoints of your hand’s movements gradually drift away from the target positions1. This phenomenon has either been explained as being caused by drift in sensory alignment 2 or as the result of the accumulation of execution errors1. We here show that this drift can be understood as being caused by optimally combining3 discrepant visual and proprioceptive information. Our hypothesis is that the visual estimate of hand position does not disappear when the hand disappears from view. It persists and is updated with visual and/or efferent information about the hand’s intended movements. However, each movement of the unseen hand adds uncertainty to this visual estimate, because the actual movement might differ from the intended one (execution variance " ex2 ). The optimal combination of visual (v) and proprioceptive (p) information leads to an estimated position of the hand:

xˆ h =

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" 2p " 2p " v2 + n" ex2 x h, p + 2 x h,v = x h, p + 2 (x h,v # x h, p ) " 2p + " v2 + n" ex2 " p + " v2 + n" ex2 " p + " v2 + n" ex2

(1)

A similar reasoning holds for the target (for which we assume that an estimate in proprioceptive terms exists). If proprioception and vision differ systematically4, 5 (xp ≠ xv), the perceived locations of hand and target will drift apart; after n movements the difference will be:

$ 1 # 2p + # v2 '"1 # v2 + # 2p xˆ h " xˆ t = (x p " x v ) " 2 (x p " x v ) = & + 1) (x p " x v ) 2 # p + # v2 + n# ex2 % n # ex (

(2)

We tested equation (2) by asking subjects to move 50 times between four targets in a virtual environment without seeing their hand. This first block yielded an experimental estimate for the sensory mismatch (xp - xv) and precision ( " v2 + " 2p ). We subsequently gave subjects 20 trials with veridical feedback. The measured variance in this second block ( " ex2 ) is the last parameter needed to predict the drift after removing visual feedback (curves in the figure 1). The actual drift that we observed matched the theoretically ! predicted drift rather well, both in amplitude and time-course (see figure 1). !

The mismatch between vision and proprioception differed considerably (in amplitude and direction) between subjects. However, individual subjects’ drift was reproducible across blocks of trials both within sessions and over days. As predicted, the drift after 50 trials was in the same direction and slightly smaller than the systematic error in the first block (figure 2). The predictions of our model of optimal sensory integration for the drift of movement endpoints does not only describe our data very well, it is also compatible with various other experimental reports on movement drift. For instance, our model predicts that the amount of drift depends on the number of movements made, and not on the time the hand is out of view. This is in line with the results of Desmurget el al.6. The well-established finding that faster movements are more variable than slow 2 ones7 leads to another prediction of our model. The larger variance in execution ( " ex ) of fast 8 movements should lead to faster drift. This has indeed been observed . The important conclusion that follows from this model is that one can see drift in motor performance without any drift in the underlying perceptual estimates.

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Figure 1: The absolute error during the experiment, averaged over all subjects and repetitions. The two curves are the (identical) predictions of equation (2) for the two blocks after feedback based on the errors in the first two blocks.

Figure 2: The three components of the systematic error for individual subjects. The dashed lines are the model predictions. A: The drift in 50 trials after feedback as a function of the systematic error before feedback. B: The errors in the second sessions as a function of the errors in the first one.

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