{"title": "Unifying the Sensory and Motor Components of Sensorimotor Adaptation", "book": "Advances in Neural Information Processing Systems", "page_first": 593, "page_last": 600, "abstract": "Adaptation of visually guided reaching movements in novel visuomotor environments (e.g. wearing prism goggles) comprises not only motor adaptation but also substantial sensory adaptation, corresponding to shifts in the perceived spatial location of visual and proprioceptive cues. Previous computational models of the sensory component of visuomotor adaptation have assumed that it is driven purely by the discrepancy introduced between visual and proprioceptive estimates of hand position and is independent of any motor component of adaptation. We instead propose a unified model in which sensory and motor adaptation are jointly driven by optimal Bayesian estimation of the sensory and motor contributions to perceived errors. Our model is able to account for patterns of performance errors during visuomotor adaptation as well as the subsequent perceptual aftereffects. This unified model also makes the surprising prediction that force field adaptation will elicit similar perceptual shifts, even though there is never any discrepancy between visual and proprioceptive observations. We confirm this prediction with an experiment.", "full_text": "Unifying the Sensory and Motor Components\n\nof Sensorimotor Adaptation\n\nAdrian Haith\n\nSchool of Informatics\n\nUniversity of Edinburgh, UK\n\nadrian.haith@ed.ac.uk\n\nCarl Jackson\n\nSchool of Psychology\n\nUniversity of Birmingham, UK\nc.p.jackson.1@bham.ac.uk\n\nChris Miall\n\nSchool of Psychology\n\nSethu Vijayakumar\nSchool of Informatics\n\nUniversity of Birmingham, UK\n\nr.c.miall@bham.ac.uk\n\nUniversity of Edinburgh, UK\nsethu.vijayakumar@ed.ac.uk\n\nAbstract\n\nAdaptation of visually guided reaching movements in novel visuomotor en-\nvironments (e.g. wearing prism goggles) comprises not only motor adapta-\ntion but also substantial sensory adaptation, corresponding to shifts in the\nperceived spatial location of visual and proprioceptive cues. Previous com-\nputational models of the sensory component of visuomotor adaptation have\nassumed that it is driven purely by the discrepancy introduced between vi-\nsual and proprioceptive estimates of hand position and is independent of\nany motor component of adaptation. We instead propose a uni\ufb01ed model in\nwhich sensory and motor adaptation are jointly driven by optimal Bayesian\nestimation of the sensory and motor contributions to perceived errors. Our\nmodel is able to account for patterns of performance errors during visuo-\nmotor adaptation as well as the subsequent perceptual aftere\ufb00ects. This\nuni\ufb01ed model also makes the surprising prediction that force \ufb01eld adap-\ntation will elicit similar perceptual shifts, even though there is never any\ndiscrepancy between visual and proprioceptive observations. We con\ufb01rm\nthis prediction with an experiment.\n\n1 Introduction\n\nWhen exposed to a novel visuomotor environment, for instance while wearing prism goggles,\nsubjects initially exhibit large directional errors during reaching movements but are able to\nrapidly adapt their movement patterns and approach baseline performance levels within\naround 30-50 reach trials. Such visuomotor adaptation is multifaceted, comprising both\nsensory and motor components [5]. The sensory components of adaptation can be measured\nthrough alignment tests in which subjects are asked to localize either a visual target or their\nunseen \ufb01ngertip, with their other (also unseen) \ufb01ngertip (without being able to make contact\nbetween hands). These tests reveal substantial shifts in the perceived spatial location of both\nvisual and proprioceptive cues, following adaptation to shifted visual feedback [7].\n\nWhile a shift in visual spatial perception will be partially re\ufb02ected in reaches towards visual\ntargets, sensory adaptation alone cannot fully account for the completenes of visuomo-\ntor adaptation, since the shifts in visual perception are always substantially less than the\nexperimentally-imposed shift. There must therefore be some additional motor component\nof adaptation, i.e. some change in the relationship between the planned movement and the\n\n\fv\nr\nt\n\ndisturbances}\n\ny\nr\nt\n\np\nr\nt\n\nut\n\nyt\n\nmotor command\n\nhand position\n\nvt\n\npt\n\nproprioceptive\nobservation\n\nvisual observation\n\nFigure 1: Graphical model of a single reach\nin a motor adaptation experiment. Motor\ncommand ut, and visual and proprioceptive\nobservations of hand position, vt and pt, are\navailable to the subject. Three distinct dis-\nturbances a\ufb00ect observations: A motor dis-\ny\nturbance r\nt may a\ufb00ect the hand position yt\ngiven the motor command ut. Visual and\np\nproprioceptive disturbances, r\nt , may\na\ufb00ect the respective observations given hand\nposition.\n\nv\nt and r\n\nissued motor command. This argument is reinforced by the \ufb01nding that patterns of reach\naftere\ufb00ects following visuomotor adaptation depend strongly on the motor task performed\nduring adaptation [5].\n\nFrom a modelling point of view, the sensory and motor components of adaptation have\npreviously only been addressed in isolation of one another. Previously proposed models of\nsensory adaptation have assumed that it is driven purely by discrepancies between hand\nposition estimates from di\ufb00erent sensory modalities. Ghahramani et al.\n[2] proposed a\ncomputational model based on a maximum likelihood principle, details of which we give in\nSection 3. On its own, this sensory adaptation model cannot provide a complete description\nof visuomotor adaptation since it does not fully account for improvements in performance\nfrom trial to trial. It can, however, be plausibly combined with a conventional error-driven\nmotor adaptation model in which the performance error is calculated using the maximum\nlikelihood estimate of hand position. The resulting composite model could plausibly account\nfor both performance improvements and perceptual shifts during visuomotor adaptation.\nAccording to this view, sensory and motor adaptation are very much independent processes,\none driven by sensory discrepancy and the other driven by (estimated) task performance\nerror.\n\nIn Section 4, we argue for a more uni\ufb01ed view of sensory and motor adaptation in which\nall three components of adaptation are jointly guided by optimal Bayesian inference of the\ncorresponding potential sources of error experienced on each trial, given noisy visual and\nproprioceptive observations of performance and noisy motor execution. This uni\ufb01ed sensory\nand motor adaptation model is also able to account for both performance improvements and\nperceptual shifts during visuomotor adaptation. However, our uni\ufb01ed model also makes the\nsurprising prediction that a motor disturbance, e.g. an external force applied to hand via\na manipulandum, will also elicit sensory adaptation. The MLE-based model predicts no\nsuch sensory adaptation, since there is never any discrepancy between sensory modalities.\nWe test this prediction directly with an experiment (Section 5) and \ufb01nd that force \ufb01eld\nadaptation does indeed lead to sensory as well as motor adaptation.\n\n2 Modelling framework\n\nBefore describing the details of the models, we \ufb01rst outline a basic mathematical frame-\nwork for describing reaching movements in the context of a motor adaptation experiment,\nrepresenting the assumptions common to both the MLE-based and the Bayesian adapta-\ntion models. Figure 1 illustrates a graphical model of a single reaching movement during\nan adaptation experiment, from the subject\u2019s point of view. The multiple components of\nvisuomotor adaptation described above correspond to three distinct potential sources of\nobserved outcome error (across both observation) modalities in a single reaching trial.\n\nOn trial t, the subject generates a (known) motor command ut. This motor command ut\nleads to a \ufb01nal hand position yt, which also depends on some (unknown) motor disturbance\n\n\fv\n\nr\n\np\n\nr\n\nyt\n\nvt\n\npt\n\nFigure 2: MLE-based sensor adaptation model.\np are\nVisual and proprioceptive disturbances r\nv\ntreated as parameters of the model. Estimates \u02c6r\nt\np\nand \u02c6r\nt of these parameters are maintained via an\nonline EM-like procedure.\n\nv, r\n\ny\nt (e.g. an external force applied to the hand) and motor noise \u01eb\nr\nhand position yt is given by\n\nu\nt . We assume the \ufb01nal\n\nu\nt \u223c N (0, \u03c3\n\n(1)\nwhere \u01eb\nu). Although this is a highly simpli\ufb01ed description of the forward dynam-\nics of the reaching movement, it can be regarded as a \ufb01rst-order approximation to the true\ndynamics. Similar assumptions have proved very successful elsewhere in models of force\n\ufb01eld adaptation, e.g. [1]\n\nyt = ut + r\n\n2\n\ny\nt + \u01eb\n\nu\nt ,\n\nThe experimenter ultimately measures the hand position yt, however this is not directly\nobserved by the subject. Instead, noisy and potentially shifted observations are available\nthrough visual and proprioceptive modalities,\n\nvt = yt + r\npt = yt + r\n\nv\nv\nt + \u01eb\nt ,\np\np\nt + \u01eb\nt ,\n\n(2)\n(3)\n\n2\n\nwhere the observation noises \u01eb\np, respectively.\n\u03c3\nWe denote the full set of potential disturbances on trial t by\n\nv\nt and \u01eb\n\np\nt are zero-mean and Gaussian with variances \u03c3\n\n2\n\nv and\n\nrt = (r\n\nv\nt , r\n\np\nt , r\n\ny\n\nt )T\n\n.\n\n(4)\n\ny\np\nt )T of the total\nv\nWe assume that the subject maintains an internal estimate \u02c6rt = (\u02c6r\nt , \u02c6r\nt , \u02c6r\ndisturbance rt and selects his motor commands on each trial accordingly. For reaches to a\nvisual target located at v\n\nt , the appropriate motor command is given by\n\n\u2217\n\nut = v\n\n\u2217\n\ny\nv\nt \u2212 \u02c6r\nt \u2212 \u02c6r\nt .\n\n(5)\n\nAdaptation can be viewed as a process of iteratively updating the disturbance estimate, \u02c6rt,\nfollowing each trial given the new (noisy) observations vt and pt and the motor command\nut. Exactly how the subject uses the information available to infer the current disturbances\nis the subject of subsequent sections of this paper.\n\n3 Existing sensory adaptation models\n\nThe prevailing view of sensory adaptation centres around the principle of maximum likeli-\nhood estimation and was \ufb01rst proposed by Ghahramani et al. [2] in the context of combining\ndiscrepant visual and auditory cues in a target location task. It has nevertheless been wide-\nley accepted as a model of how the nervous system deals with visual and proprioceptive\ncues. Van Beers et al.\n[7], for instance, based an analysis of the relative uncertainty of\nvisual and proprioceptive estimates of hand location on this principle.\n\nWe suppose that, given the subject\u2019s current estimate of the visual and proprioceptive\np\nv\nt , the visual and proprioceptive estimates of hand position are given\ndisturbance, \u02c6r\nt and \u02c6r\nby\n\nv\nv\n\u02c6y\nt = vt \u2212 \u02c6r\nt ,\np\np\nt = pt \u2212 \u02c6r\n\u02c6y\nt\n\n(6)\n(7)\n\nrespectively. These distinct estimates of hand position are combined via maximum likelihood\nestimation [7] into a single fused estimate of hand position.The maximum likelihood estimate\n(MLE) of the true hand position yt is given by\n\nM LE\n\u02c6y\nt\n\n=\n\n2\np\n\n\u03c3\n\n2\n\n2\nv + \u03c3\n\u03c3\np\n\nv\n\u02c6y\nt +\n\n2\nv\n\n\u03c3\n\n2\n\n2\nv + \u03c3\n\u03c3\np\n\np\n\u02c6y\nt .\n\n(8)\n\n\fv\nr\nt\n\nv\nt+1\n\nr\n\np\nr\nt\n\ny\nr\nt\n\nut\n\nyt\n\np\nt+1\n\nr\n\ny\nt+1\n\nr\n\nut+1\n\nyt+1\n\nvt\n\npt\n\nvt+1\n\npt+1\n\nFigure 3: Bayesian com-\nbined sensory and motor\nadaptation model.\nThe\nsubject assumes that dis-\nturbances vary randomly,\nbut smoothly, from trial to\ntrial.\n\nThe MLE-based sensory adaptation model states that subjects adapt their future visual and\nproprioceptive estimates of hand location towards the MLE in such a way that the MLE\nitself remains unchanged. The corresponding updates are given by\n\np\nv\nv\nv\n\u02c6r\nt+1 = \u02c6r\nt \u2212 \u02c6y\nt + \u03b7wp [\u02c6y\nt ] ,\np\np\np\nv\n\u02c6r\nt+1 = \u02c6r\nt + \u03b7wv [\u02c6y\nt \u2212 \u02c6y\nt ] ,\n\n(9)\n\n(10)\n\nwhere \u03b7 is some \ufb01xed adaptation rate. This adaptation principle can be interpreted as an\nonline expectation-maximization (EM) procedure in the graphical model shown in Figure\np are treated as parameters of the model. The E-step of the EM\n2. In this model, r\nprocedure corresponds to \ufb01nding the MLE of yt and the M-step corresponds to gradient\nascent on the likelihood of \u02c6r\n\nv and \u02c6r\n\nv and r\n\np.\n\n3.1 Extending the MLE model to account for motor component of adaptation\n\nAs it stands, the MLE-based model described above only accounts for sensory adaptation\nand does not provide a complete description of sensorimotor adaptation. Visual adaptation\nwill a\ufb00ect the estimated location of a visual target, and therefore also the planned movement,\nbut the e\ufb00ect on performance will not be enough to account for complete (or nearly complete)\nadaptation. The performance gain from this component of adaptation will be equal to the\ndiscrepancy between the initial visual setimate of hand posion and the MLE - which will be\nsubstantially less than the experimentally imposed shift.\n\nThis sensory adaptation model can, however, be plausibly combined with a conventional\nerror-driven state space model [6, 1] of motor adaptation to yield an additional motor\ny\ncomponent of adaptation \u02c6r\nt . The hand position MLE \u02c6yt can be used in place of the usual\nuni-modal observation assumed in these models when calculating the endpoint error. The\ny\nt on trial t is given by\nresulting update for the estimated motor disturbance \u02c6r\n\ny\n\u02c6r\nt+1 = \u02c6r\n\ny\nt + \u03b3(\u02c6y\n\n\u2217\n\nM LE\nt \u2212 \u02c6y\nt\n\n),\n\n(11)\n\nwhere \u02c6y\nrate.\n\n\u2217\n\nt = (v\n\nv\n\u2217 \u2212 \u02c6r\nt ) is the estimated desired hand location, and \u03b3 is some \ufb01xed adaptation\n\nThis combined model re\ufb02ects the view that sensory and motor adaptation are distinct\nprocesses. The sensory adaptation component is driven purely by discrepancy between the\nsenses, while the motor adaptation component only has access to a single, fused estimate of\nhand position and is driven purely by estimated performance error.\n\n4 Uni\ufb01ed Bayesian sensory and motor adapatation model\n\nWe propose an alternative approach to solving the sensorimotor adaptation problem. Rather\np as parameters, we consider all the disturbances (in-\nthan treat the visual shifts r\ny\nt ) as dynamic random variables. We assume that the subject\u2019s beliefs about how\ncluding r\n\nv and r\n\n\f30\n\n20\n\n10\n\no\n\n/\nr\no\nr\nr\n\nE\n\n \nl\n\na\nn\no\n\ni\nt\nc\ne\nr\ni\n\nD\n\n0\n\n \n0\n\n \n\nData\nBayesian Model\nMLE Model\n\n5\n\n10\n\n15\n\n20\nTrial Number\n\n25\n\n30\n\nFigure 4: Model comparison with visuomo-\ntor adaptation data. The Bayesian model\n(solid blue line) and MLE-based model\n(dashed red line) were \ufb01tted to performance\ndata (\ufb01lled circles) from a visuomotor adap-\ntation experiment [4]. Both models made\nqualitatively similar predictions about how\nadaptation was distributed across compo-\nnents.\n\nthese disturbances evolve over time are characterised by a trial-to-trial disturbance dynamics\nmodel given by\n\n(12)\nwhere A is some diagonal matrix and \u03b7t is a random drift term with zero mean and diagonal\ncovariance matrix Q, i.e.\n\nrt+1 = Art + \u03b7t,\n\nv\n\np\n\n, q\n\n\u03b7t \u223c N (0, Q).\n\n(13)\nA and Q are both diagonal to re\ufb02ect the fact that each disturbance evolves independently.\nu) and the diagonal of Q by q =\nWe denote the diagonal elements of A by a = (a\nu). The vector a describes the timescales over which each disturbance persists,\n(q\nwhile q describes the amount of random variation from trial to trial, or volatility of each\ndisturbance. These parameters re\ufb02ect the statistics of the usual \ufb02uctuations in sensory\ncalibration errors and motor plant dynamics, which the sensorimotor system must adapt to\non an ongoing basis. (Similar assumptions have previously been made elsewhere [3, 4]).\n\n, a\n\n, a\n\n, q\n\np\n\nv\n\nCombining these assumptions with the statistical model of each individual trial described\nin Section 2 (and Figure 1), gives rise to a dynamical model of the disturbances and their\nimpact on reaching movements, across all trials. This model, representing the subjects\nbeliefs about how his sensorimotor performance is liable to vary over time, is illustrated in\nFigure 4. We propose that the patterns of adaptation and the sensory aftere\ufb00ects exhibited\nby subjects correspond to optimal inference of the disturbances rt within this model, given\nthe observations on each trial.\n\nThe linear dynamics and Gaussian noise of the observer\u2019s model mean that exact inference is\nstraightforward and equivalent to a Kalman \ufb01lter. The latent state tracked by the Kalman\nt )T , with state dynamics given by (12). The\n\ufb01lter is the vector of disturbances rt = (r\nobservations vt and pt are related to the disturbances via\n\np\nt , r\n\nv\nt , r\n\ny\n\n(cid:18) vt\n\npt (cid:19) = (cid:18) ut\n\nut (cid:19) +(cid:18) 1 0\n\n0 1\n\n1\n\n1 (cid:19) (rt + \u01ebt) ,\n\nwhere \u01ebt = (\u01eb\n\nv\nt , \u01eb\n\np\nt , \u01eb\n\nu\n\nt )T . We can write this in a more conventional form as\n\nzt = Hrt + H \u01ebt,\n\n(14)\n\n(15)\n\nwhere zt = (vt \u2212 ut, pt \u2212 ut)T and H is the matrix of 1\u2019s and 0\u2019s in equation (14). The\nobservation noise covariance is given by\n\nR = E(cid:2)(H \u01ebt)(H \u01ebt)T(cid:3) = (cid:18) \u03c3\n\n2\n\n2\nv + \u03c3\nu\n\n2\nu\n\n\u03c3\n\n2\nu\n\n\u03c3\n\n2\n\np + \u03c3\n\u03c3\n\nu (cid:19) .\n\n2\n\n(16)\n\nThe standard Kalman \ufb01lter update equations can be used to predict how a subject will\nupdate estimates of the disturbances following each trial and therefore how he will select\nhis actions on the next trial, leading to a full prediction of performance from the \ufb01rst trial\nonwards.\n\n5 Model comparison and experiments\n\nWe have described two alternative models of visuomotor adaptation which we have claimed\ncan account for both the motor and sensory components of adaptation. We \ufb01tted both\n\n\f(a)\n\ny\n\nx\n\nError\n\n(b)\n\nTarget\n\nAdapted\ntrajectory\n\nCatch trial\ntrajectory\n\nStart\n\nFigure 5: (a) Experimental Setup, (b) Sample trajectories and performance error measure\n\nmodels to performance data from a visuomotor adaptation experiment [4] to validate this\nclaim. In this study in which this data was taken from, subjects performed visually guided\nreaching movements to a number of targets. Visual feedback of hand position (given via a\ncursor on a screen) was rotated by 30o relative to the starting position of each movement.\nThe mean directional error (averaged over targets and over subjects) over trials is plotted in\nFigure 4. The Matlab function lsqnonlin was used to \ufb01nd the parameters for each model\nwhich minimized the sum of the error between the data and the predictions of each model.\nu, \u03b7, \u03b3). For the Bayesian\nThere were 5 free parameters for the MLE-based model (\u03c3\nmodel we assumed that all disturbances had the same timescale, i.e. all elements of a were\nthe same, leaving 7 free parameters (\u03c3\n, a). The results of the \ufb01ts are shown\nin Figure 4. The spread of adaptation across components of the model was qualitatively\nsimilar between the two models, although no data on perceptual aftere\ufb00ects was available\nfrom this study for quantitative comparison. The Bayesian model clearly displays a closer \ufb01t\nto the data and the Akaike information criterion (AIC) con\ufb01rmed that this was not simply\ndue to extra parameters (AI C = 126.7 for the Bayesian model vs AI C = 159.6 for the\nMLE-based model).\n\n2\np , \u03c3\n\n2\nv , \u03c3\n\n2\nv , \u03c3\n\n2\np , \u03c3\n\nv\n\n2\nu, q\n\n, q\n\n, q\n\n2\n\np\n\nu\n\nAlthough the Bayesian model appears to describe the data better, this analysis is by no\nmeans conclusive. Furthermore, the similar scope of predictions between the two models\nmeans that gathering additional data from alignment tests may not provide any further\nleverage to distinguish between the two models. There is, however, a more striking di\ufb00erence\nin predictions between the two models. While the MLE-based model predicts there will be\nsensory adaptation only when there is a discrepancy between the senses, the Bayesian model\npredicts that there will also be sensory adaptation in response to a motor disturbance such\nas an external force applied to the hand). Just as a purely visual disturbance can lead\nto a multifaceted adaptive response, so can a purely motor disturbance, with both motor\nand sensory components predicted, even though there is never any discrepancy between the\nsenses. This prediction enables us to distinguish decisively between the two models.\n\n5.1 Experimental Methods\n\nWe experimentally tested the hypothesis that force \ufb01eld adaptation would lead to sensory\nadaptation. We tested 11 subjects who performed a series of trials consisting of reaching\nmovements interleaved with perceptual alignment tests.\n\nSubjects grasped the handle of a robotic manipulandum with their right hand. The hand\nwas not visible directly, but a cursor displayed via a mirror/\ufb02at screen monitor setup (Fig-\nure 5.1(a)) was exactly co-planar and aligned with the handle of the manipulandum. In\nthe movement phase, subjects made an out-and-back reaching movement towards a visual\ntarget with their right hand. In the visual localization phase, a visual target was displayed\npseudorandomly in one of 5 positions and the subjects moved their left \ufb01ngertip to the\nperceived location of the target. In the proprioceptive localization phase, the right hand\nwas passively moved to a random target location, with no visual cue of its position, and\nsubjects moved their left \ufb01ngertip to the perceived location of the right hand. Left \ufb01ngertip\n\n\fMean Localization Error \u2212 x\n\nMean Localization Error \u2212 y\n\nm\nc\n \n/\n \nr\no\nr\nr\n\n \n\nE\nn\na\ne\nM\n\n4\n\n3.5\n\n3\n\n2.5\n\n2\n\n1.5\n\n1\n\n0.5\n\n0\n\n\u22120.5\n\n\u22121\n\n \n\n \n\nPre\u2212Adaptation\nPost\u2212Adaptation\n\nVision\n\nProprioception\n\nModality\n\nm\nc\n \n/\n \nr\no\nr\nr\n\n \n\nE\nn\na\ne\nM\n\n11\n\n10.5\n\n10\n\n9.5\n\n9\n\n8.5\n\n8\n\n7.5\n\n7\n\n6.5\n\n6\n\n \n\n \n\nPre\u2212Adaptation\nPost\u2212Adaptation\n\nVision\n\nProprioception\n\nModality\n\nFigure 6: (a) Average lateral (in direction of the perturbation) localization error across\nsubjects before vs after adaptation, for vision and proprioception. Error bars indicate\nstandard errors. (b) Same plots for y-direction\n\npositions were recorded using a Polhemus motion tracker. Neither hand was directly visible\nat any time during the experiment.\n\nSubjects were given 25 baseline trials with zero external force, after which a force \ufb01eld was\ngradually introduced. A leftward lateral force Fx was applied to the right hand during the\nreaching phase. The magnitude of the force was proportional to the forward velocity \u02d9y of\nthe hand, i.e.\n\nFx = \u2212a \u02d9y.\n\n(17)\n\nThe force was applied only on the outward part of the movement (i.e. only when \u02d9y > 0).\nAfter steadily incrementing a during 50 adaptation trials, the force \ufb01eld was then kept\n\u22121) for a further 25 post-adaptation test trials. All subjects\nconstant at a = 0.3 N/(cms\nreceived a catch trial at the very end in which the force \ufb01eld was turned o\ufb00.\n\nThe particular force \ufb01eld used was chosen so that the cursor trajectories (and motor com-\nmands required to counter the perturbation) would be as close as possible to those used\nto generate the linear trajectories required when exposed to a visuomotor shift (such as\nthat described in [7]). Figure 5.1(b) shows two trajectories from a typical subject, one from\nthe post-adaptation test phase and one from the catch trial after adaptation. The initial\noutward part of the catch trial trajectory, the initial movement is very straight, implying\nthat similar motor commands were used to those required by a visuomotor shift.\n\n5.2 Results\n\nWe compared the average performance in the visual and proprioceptive alignment tests\nbefore and after adaptation in the velocity-dependent force \ufb01eld. The results are summarized\nin Figure 6(a). Most subjects exhibited small but signi\ufb01cant shifts in performance in both\nthe visual and proprioceptive alignment tests. Two subjects exhibited shifts which were\nmore than two standard deviations away from the average shift and were excluded from the\nanalysis. We found signi\ufb01cant lateral shifts in both visual and proprioceptive localization\nerror in the direction of the perturbation (both p < .05, one-tailed paired t-test). Figure\n6(b) shows the same data for the direction perpendicular to the perturbation. Although the\ninitial localization bias was high, there was no signi\ufb01cant shift in this direction following\nadaptation.\n\nWe quanti\ufb01ed each subject\u2019s performance on each trial as the perpendicular distance of the\nfurthest point in the trajectory from the straight line between the starting point and the\ntarget (Fig. 5.1(b)). We \ufb01tted the Bayesian and MLE-based models to the data following the\nsame procedure as before, only this time penalizing the disagreement between the model\nand the data for the alignment tests, in addition to the reaching performance. Figure 7\nillustrates the averaged data along with the model \ufb01ts. Both models were able to account\nreasonably well for the trends in reaching performance across trials (7(a)). Figures 7(b) and\n7(c) show the model \ufb01ts for the perceptual localization task. The Bayesian model is able to\naccount for both the extent of the shift and the timecourse of this shift during adaptation.\n\n\fm\nc\n \n/\n \nr\no\nr\nr\n\n \n\nE\ne\nc\nn\na\nm\nr\no\n\nf\nr\ne\nP\n\n3\n\n2\n\n1\n\n0\n\n\u22121\n\n\u22122\n\n\u22123\n\n \n0\n\n(a) Reaching Performance\n\n \n\nData\nBayesian Model\nMLE Model\n\n20\n\n40\n60\nTrial Number\n\n80\n\n100\n\nm\nc\n \n/\n \nr\no\nr\nr\n\nE\n\n \nt\n\nn\ne\nm\nn\ng\n\ni\nl\n\nA\n\n4\n\n2\n\n0\n\n\u22122\n\n0\n\n(b) Visual Alignment\n\n(c) Proprioceptive Alignment\n\nm\nc\n \n/\n \nr\no\nr\nr\n\nE\n\n \nt\n\nn\ne\nm\nn\ng\n\ni\nl\n\nA\n\n4\n\n2\n\n0\n\n\u22122\n\n0\n\n20\n\n40\n60\nTrial Number\n\n80\n\n100\n\n20\n\n40\n60\nTrial Number\n\n80\n\n100\n\nFigure 7: Trial-by-trial data and model \ufb01ts. (a) Reaching error, (b) Visual alignment test\nerror, (c) Proprioceptive alignment test error. The Bayesian (solid blue lines) and MLE-\nbased (dashed red lines) were \ufb01tted to averaged data across subjects (circles).\n\nSince there was never any sensory discrepancy, the MLE-based model predicted no change\nin the localization task.\n\n6 Conclusions and discussion\n\nOur experimental results demonstrate that adaptation of reaching movements in a force\n\ufb01eld results in shifts in visual and proprioceptive spatial perception. This novel \ufb01nding\nstrongly supports the Bayesian model, which predicted such adaptation, and refutes the\nMLE-based model, which did not. The Bayesian model was able to account for the trends\nin both reaching performance and alignment test errors on a trial-to-trial basis.\n\nSeveral recent models have similarly described motor adaptation as a process of Bayesian\ninference of the potential causes of observed error. K\u00a8ording et al. [3] proposed a model of\nsaccade adaptation and Krakauer et al. [4] modelled visuomotor adaptation based on this\nprinciple. Our work extends the framework of these models to include multiple observation\nmodalities instead of just one, and multiple classes of disturbances which a\ufb00ect the di\ufb00erent\nobservation modalities in di\ufb00erent, experimentally measurable ways.\n\nOverall, our results suggest that the nervous system solves the problems of sensory and\nmotor adaptation in a principled and uni\ufb01ed manner, supporting the view that sensorimotor\nadaptation proceeds according to optimal estimation of encountered disturbances.\n\nReferences\n\n[1] Opher Donchin, Joseph T Francis, and Reza Shadmehr. Quantifying generalization from\ntrial-by-trial behavior of adaptive systems that learn with basis functions: theory and\nexperiments in human motor control. J Neurosci, 23(27):9032\u20139045, Oct 2003.\n\n[2] Z. Ghahramani, D.M. Wolpert, and M.I. Jordan. Computational models for sensorimotor\nintegration. In P.G. Morasso and V. Sanguineti, editors, Self-Organization, Computa-\ntional Maps and Motor Control, pages 117\u2013147. North-Holland, Amsterdam, 1997.\n\n[3] Konrad P. K\u00a8ording, Joshua B. Tenenbaum, and Reza Shadmehr. The dynamics of\nmemory as a consequence of optimal adaptation to a changing body. Nat Neurosci,\n10(6):779\u2013786, June 2007.\n\n[4] John W Krakauer, Pietro Mazzoni, Ali Ghazizadeh, Roshni Ravindran, and Reza Shad-\nmehr. Generalization of motor learning depends on the history of prior action. PLoS\nBiol, 4(10):e316, Sep 2006.\n\n[5] M.C. Simani, L.M. McGuire, and P.N. Sabes. Visual-shift adaptation is composed of\nseparable sensory and task-dependent e\ufb00ects. J Neurophysiol, 98:2827\u20132841, Nov 2007.\n[6] K A Thoroughman and R Shadmehr. Learning of action through adaptive combination\n\nof motor primitives. Nature, 407(6805):742\u2013747, Oct 2000.\n\n[7] Robert J van Beers, Daniel M Wolpert, and Patrick Haggard. When feeling is more\nimportant than seeing in sensorimotor adaptation. Curr Biol, 12(10):834\u2013837, May\n2002.\n\n\f", "award": [], "sourceid": 689, "authors": [{"given_name": "Adrian", "family_name": "Haith", "institution": null}, {"given_name": "Carl", "family_name": "Jackson", "institution": null}, {"given_name": "R.", "family_name": "Miall", "institution": null}, {"given_name": "Sethu", "family_name": "Vijayakumar", "institution": null}]}