{"id":878,"date":"2018-01-11T12:17:59","date_gmt":"2018-01-11T02:17:59","guid":{"rendered":"https:\/\/www.cognav.net\/?p=878"},"modified":"2018-01-14T16:20:48","modified_gmt":"2018-01-14T06:20:48","slug":"neuronal-population-coding-of-movement-direction-2","status":"publish","type":"post","link":"https:\/\/braininspirednavigation.com\/?p=878","title":{"rendered":"\u3010Excerpt Note\u3011Neuronal Population Coding of Movement Direction"},"content":{"rendered":"<p><span style=\"color: #222222; font-family: Arial; font-size: 10pt; background-color: white;\">Georgopoulos, Apostolos P., Andrew B. Schwartz, and Ronald E. Kettner. &#8220;Neuronal population coding of movement direction.&#8221;\u00a0<em>Science<\/em>\u00a0(1986): 1416-1419. <\/span><\/p>\n<p><span style=\"color: #222222; font-family: Arial; font-size: 10pt; background-color: white;\">The blog is a brief summary of the neuronal population coding model for movement direction.<\/span><\/p>\n<p><strong>Brief Summary <\/strong><\/p>\n<ul>\n<li>\n<div style=\"text-align: justify;\">Although individual neurons in the arm area of the primate motor cortex are only broadly tuned to a particular direction in three-dimensional space, the animal can very precisely control the movement of its arm.<\/div>\n<\/li>\n<li>\n<div style=\"text-align: justify;\">The direction of movement was found to be uniquely predicted by the action of a population of motor cortical neurons.<\/div>\n<\/li>\n<li>\n<div style=\"text-align: justify;\">When individual cells were represented as vectors that make weighted contributions along the axis of their preferred direction (according to changes in their activity during the movement under consideration) the resulting vector sum of all cell vectors (population vector) was in a direction congruent with the direction of movement.<\/div>\n<\/li>\n<li>\n<div style=\"text-align: justify;\">This population vector can be monitored during various tasks, and similar measures in other neuronal populations could be of heuristic value where there is a neural representation of variables with vectorial attributes.<\/div>\n<\/li>\n<\/ul>\n<p><strong>The Neuronal Population Coding Model <\/strong><\/p>\n<p style=\"text-align: justify;\">We used the following model to describe the relations between the activity of each directionally tuned neuron (Fig.1)and the direction of movement in 3D space. Let x, y, z be the positive axes of a Cartesian coordinate system with center at the origin of the movement. Consider a movement vector <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop1.png\" alt=\"\" \/>of unit length that makes angles<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop2.png\" alt=\"\" \/> ,<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop3.png\" alt=\"\" \/>, <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop4.png\" alt=\"\" \/> with the x, y, and z coordinate axes, respectively. The direction of vector <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop5.png\" alt=\"\" \/>in 3-D space is specified by its direction cosines <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop6.png\" alt=\"\" \/> where <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop7.png\" alt=\"\" \/> , <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop8.png\" alt=\"\" \/>,<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop9.png\" alt=\"\" \/>, and where <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop10.png\" alt=\"\" \/> .<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop11.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: center;\">Fig. 1. Impulse activity of a single cell with movements in eight different directions indicated in the center drawing. Each line represents activity in one trial; eight trials for each movement direction are shown.<\/p>\n<p style=\"text-align: justify;\">We used the following model to relate cell activity to movement direction.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop12.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">Where <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop13.png\" alt=\"\" \/> is the frequency of discharge of a particular neuron during movement in direction<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop14.png\" alt=\"\" \/> , and <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop15.png\" alt=\"\" \/> are coefficients that vary from neuron to neuron. The values of these coefficients and their standard errors were estimated with multiple regression techniques.<\/p>\n<p style=\"text-align: justify;\">The model of Eq.1 implies that there is a particular movement vector <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop16.png\" alt=\"\" \/> for which the cell&#8217;s activity will be highest. The direction of this vector is the cell&#8217;s preferred direction, which can be determined by estimating the direction cosines <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop17.png\" alt=\"\" \/> of the vector<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop18.png\" alt=\"\" \/>from Eq.1 as follws.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop19.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">Where<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop20.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">The preferred directions observed for the 224 neurons that fit the model ranged over the whole 3D directional continuum about the origin of the movement.<\/p>\n<p style=\"text-align: justify;\">An equivalent expression of the model of Eq.1 is<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop21.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">Where <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop22.png\" alt=\"\" \/> is the angle formed by the cell&#8217;s preferred direction<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop23.png\" alt=\"\" \/>and the direction of a particular movement<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop24.png\" alt=\"\" \/>(Fig.2). It follows that the discharge rate, <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop25.png\" alt=\"\" \/> , will be highest with movements in the cell&#8217;s preferred direction, that is , when <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop26.png\" alt=\"\" \/>and <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop27.png\" alt=\"\" \/>coincide (<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop28.png\" alt=\"\" \/>degrees, <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop29.png\" alt=\"\" \/> ); lowest with movements in the opposite direction (<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop30.png\" alt=\"\" \/>degrees, <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop31.png\" alt=\"\" \/>); and in between with movements in intermediate directions (<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop32.png\" alt=\"\" \/>degrees, <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop33.png\" alt=\"\" \/>). Equation 2 indicates that motor cortical cells are broadly tuned in the sense that they change their activity with movements in any direction.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop34.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: center;\">Fig.2. Schematic diagram to show the preferred direction () of the cell illustrated in Fig.1.<\/p>\n<p style=\"text-align: justify;\">The direction of movement may be coded in a unique fashion by the neuronal ensemble. Consider a movement in an arbitrary direction<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop35.png\" alt=\"\" \/>. We want to find a way by which the neuronal population of the 224 directionally tuned cells with yield information about the direction of the movement<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop36.png\" alt=\"\" \/>. For that purpose we made three assumptions. (i) Each cell (indexed by i) makes a vectorial contribution along its preferred direction, <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop37.png\" alt=\"\" \/>. (II) The magnitude of the contribution (or length of the vector) <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop38.png\" alt=\"\" \/> of the <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop39.png\" alt=\"\" \/>th cell is a function of the movement direction and is taken to be equal to the change in cell activity from an offset level.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop40.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">Where, from Eq.2, <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop41.png\" alt=\"\" \/> is a constant and <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop42.png\" alt=\"\" \/> is the frequency of discharge of the ith cell for movement in direction <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop43.png\" alt=\"\" \/>. From assumptions (i) and (ii), it follows that the weighted vectorial contribution of the ith cell is<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop44.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">The vector <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop45.png\" alt=\"\" \/>will point toward the ith cell&#8217;s preferred direction if the weight <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop46.png\" alt=\"\" \/>is positive or in the opposite direction if the weight is negative. (iii) Finally, we sum vectorially these cell vectors to obtain the neuronal population vector <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop47.png\" alt=\"\" \/> corresponding to movement direction <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop48.png\" alt=\"\" \/>.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop49.png\" alt=\"\" \/>=<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop50.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">The outcome for one of the movement directions tested is shown in Fig. 3. The yellow line indicates the movement direction <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop51.png\" alt=\"\" \/>. The cluster of light purple lines represents 224 cell vectors (that is, the vectors <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop52.png\" alt=\"\" \/>, <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop53.png\" alt=\"\" \/> = 1 to 224) for movement direction <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop54.png\" alt=\"\" \/>. The direction of the population vector <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop55.png\" alt=\"\" \/>yielded by the vectorial summation of these cell vectors is orange. The direction of the population vector is very close to the direction of the movement vector(Fig.4). Therefore, the population vector predicts accurately the direction of the movement.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop56.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">Fig3. Cluster of 224 single cell vectorial contributions (light purple lines) for one movement direction (yellow). The population vector is orange.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop57.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">Fig. 4 Schematic diagram to show the directions of the population (<strong>P<\/strong>) and movement (<strong>M<\/strong>) vectors for the data in Fig.3. For illustration purposes, the population vector has been normalized so that both <strong>P <\/strong>and <strong>M <\/strong>are of unit length. Therefore, the direction cosines of these vectors equal their projections onto coordinate axes x, y, and z. These projections are shown as<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop58.png\" alt=\"\" \/> , <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop59.png\" alt=\"\" \/>,<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop60.png\" alt=\"\" \/>and<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop61.png\" alt=\"\" \/>,<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop62.png\" alt=\"\" \/>,<img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop63.png\" alt=\"\" \/>, for <strong>P<\/strong> and <strong>M<\/strong>, respectively. Also shown is the angle <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011118_0220_NeuronalPop64.png\" alt=\"\" \/> formed between the two vectors.<\/p>\n<p style=\"text-align: justify;\"><strong>Conclusion <\/strong><\/p>\n<p style=\"text-align: justify;\">The population vector computed for the motor cortex during the waiting period is in a direction congruent with that of the upcoming movement.<\/p>\n<p style=\"text-align: justify;\">The population vector can serve to monitor brain events during the spatial planning of the movement in space, in the absence of overt movement.<\/p>\n<p style=\"text-align: justify;\">Single cells were broadly tuned to the direction of the stimulus in the visual field but the population vector predicted accurately the direction of the stimulus.<\/p>\n<p style=\"text-align: justify;\">This result suggests that the population coding of motion direction proposed in the study may be of general significance to the problem of how directional information might be uniquely coded by neuronal ensembles.<\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Georgopoulos, Apostolos P., Andrew B. Schwartz, and Ronald E. Kettner. &#8220;Neuronal population coding of movement direction.&#8221;\u00a0Science\u00a0(1986): 1416-1419. The blog is a brief summary of the neuronal population coding model for movement direction. Brief Summary Although individual neurons in the arm area of the primate motor cortex are only broadly tuned to a particular direction in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[114,96],"tags":[241,239,240,235,242],"_links":{"self":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/878"}],"collection":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=878"}],"version-history":[{"count":4,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/878\/revisions"}],"predecessor-version":[{"id":959,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/878\/revisions\/959"}],"wp:attachment":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=878"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=878"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}