Embed Size (px)
Citation preview
Self-organizing maps
Cortical maps
(from Penfield & Rasmussen, 1950)
Somatosensorycortex
Visual cortex
V1topgraphic
map
Orientation selectivity changes in a regular manner across the surface of V1
Hubel & Wiesel’s“ice cube tray model”
Orientation maps in V1
(Blasdel 1992)
Direction selective cells in cat area 18 (Ca++ imaging - Ohki, Chung, Ch’ng, Kara, Reid, 2005)
Cortical maps are Plastic
(monkey auditory cortex - Recanzone,
Schreiner & Merzenich, 1993)
input
output
horizontalconnections
Self-organizing maps
Kohonen’s algorithm
Kohonen’s algorithm applied to a 2D input array
Map conforms to topology of input data
Energy function:
Kohonen’s algorithm
Gradient descent:
|x(µ) �wi|2
(x(µ) �wi)
Traveling salesman problem(‘Elastic net’ - Durbin & Willshaw 1987)
�wi = ⌘
X
µ
⇤µ(i) (⇠µ �wi) + (wi+1 � 2wi +wi�1)
!
<latexit sha1_base64="RA6hNB8aYnJAwhU1b6LrNYzqiPA=">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</latexit><latexit sha1_base64="RA6hNB8aYnJAwhU1b6LrNYzqiPA=">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</latexit><latexit sha1_base64="RA6hNB8aYnJAwhU1b6LrNYzqiPA=">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</latexit><latexit sha1_base64="RA6hNB8aYnJAwhU1b6LrNYzqiPA=">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</latexit>
E{wi} = ��X
µ
log
"X
i
exp(�|⇠µ �wi|2/2�2)
#+
2
X
i
|wi+1 �wi|2<latexit sha1_base64="ULwZ5+31p98xnv5aSyiqcwKUe9w=">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</latexit><latexit sha1_base64="ULwZ5+31p98xnv5aSyiqcwKUe9w=">AAACi3icbVFda9swFJW9j2Zpu2br417EQqGlS2p7g5bRQlkp9LGDpS1EjpEV2RGRbCHJW4PiP9OftLf9m8lJHrJ0FwSHc3SPrs5NJWfaBMEfz3/x8tXrrdab9vbO7tu9zrv3d7qsFKEDUvJSPaRYU84KOjDMcPogFcUi5fQ+nV41+v1PqjQrix9mJmkscF6wjBFsHJV0nq6RRQKbSZrZX3XCUA0vYA9plguMPiFdiQSJCiJe5ojTzAwXFEP0UR725uiRjZzcW3eYj6KTaGkwio6QYvnExPAYokxhYtEUS4lrG9VLo/laq2XHYb3p1W4nnW7QDxYFn4NwBbpgVbdJ5zcal6QStDCEY62HYSBNbLEyjHBat1GlqcRkinM6dLDAgurYLrKs4YFjxjArlTuFgQt2vcNiofVMpO5mM6je1Bryf9qwMtlZbFkhK0MLsnwoqzg0JWwWA8dMUWL4zAFMFHOzQjLBLjPj1teEEG5++Tm4i/qhw9+/dC+/reJogQ/gIzgEITgFl+AG3IIBIF7L63un3pm/63/2v/rny6u+t+rZB/+Uf/0XxGLHBQ==</latexit><latexit sha1_base64="ULwZ5+31p98xnv5aSyiqcwKUe9w=">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</latexit><latexit sha1_base64="ULwZ5+31p98xnv5aSyiqcwKUe9w=">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</latexit>
⇤µ(i) =exp(�|⇠µ �wi|2/2�2)Pj exp(�|⇠µ �wj |2/2�2)
<latexit sha1_base64="rnaDjPS+xcGS6PH+NsXiz0af8+Y=">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</latexit><latexit sha1_base64="rnaDjPS+xcGS6PH+NsXiz0af8+Y=">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</latexit><latexit sha1_base64="rnaDjPS+xcGS6PH+NsXiz0af8+Y=">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</latexit><latexit sha1_base64="rnaDjPS+xcGS6PH+NsXiz0af8+Y=">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</latexit>
Ocular dominance columns(Horton)
Model of ocular dominance column development(Miller, Keller & Stryker, 1989)
Results
cortical map receptive fields
Simulation of monocular deprivation
Elastic net model of position and orientation map(Durbin & Mitchison, 1990)
orientation mapposition map
Joint map of orientation and ocular dominance demonstrates tradeoff between feature diversity vs. smoothness within each feature dimension(from Blasdel 1992)
The cortical column: a structure withouta function
Jonathan C. Horton* and Daniel L. Adams
Beckman Vision Center, 10 Koret Way, University of California, San Francisco, CA 94143-0730, USA
This year, the field of neuroscience celebrates the 50th anniversary of Mountcastle’s discovery of thecortical column. In this review, we summarize half a century of research and come to the disappointingrealization that the column may have no function. Originally, it was described as a discrete structure,spanning the layers of the somatosensory cortex, which contains cells responsive to only a singlemodality, such as deep joint receptors or cutaneous receptors. Subsequently, examples of columnshave been uncovered in numerous cortical areas, expanding the original concept to embrace a varietyof different structures and principles. A ‘column’ now refers to cells in any vertical cluster that sharethe same tuning for any given receptive field attribute. In striate cortex, for example, cells with thesame eye preference are grouped into ocular dominance columns. Unaccountably, ocular dominancecolumns are present in some species, but not others. In principle, it should be possible to determinetheir function by searching for species differences in visual performance that correlate with theirpresence or absence. Unfortunately, this approach has been to no avail; no visual faculty has emergedthat appears to require ocular dominance columns. Moreover, recent evidence has shown that theexpression of ocular dominance columns can be highly variable among members of the same species,or even in different portions of the visual cortex in the same individual. These observations deal a fatalblow to the idea that ocular dominance columns serve a purpose. More broadly, the term ‘column’also denotes the periodic termination of anatomical projections within or between cortical areas. Inmany instances, periodic projections have a consistent relationship with some architectural feature,such as the cytochrome oxidase patches in V1 or the stripes in V2. These tissue compartments appearto divide cells with different receptive field properties into distinct processing streams. However, it isunclear what advantage, if any, is conveyed by this form of columnar segregation. Although thecolumn is an attractive concept, it has failed as a unifying principle for understanding corticalfunction. Unravelling the organization of the cerebral cortex will require a painstaking description ofthe circuits, projections and response properties peculiar to cells in each of its various areas.
Keywords: spandrel; barrel; angioscotoma; retinal wave; pinwheel; macaque
1. INTRODUCTIONHalf a century ago, Mountcastle et al. (1955) made aseminal observation while recording from cat somato-sensory cortex.Theynoted that all cells in a given verticalelectrode penetration responded either to superficial(skin, hair) or deep (joint, fascia) stimulation (figure 1). Itappeared that for a common receptive field location (e.g.the cat’s foreleg), cells were segregated into domainsrepresenting different sensory modalities. This discoveryledMountcastle (1957, p. 430) tohypothesize ‘there is anelementary unit of organization in the somatic cortexmade up of a vertical group of cells extending through allthe cellular layers’. He termed this unit a ‘column’. Bymaking multiple, closely spaced penetrations, Mount-castle concluded that individual columns are no morethan 500 mm wide and ‘intermingled in a mosaic-likefashion’. These blocks of tissue contain neurons whosesalient physiological properties are identical. The identi-fication of the column has been considered a break-through in neuroscience because it seems to simplify the
daunting task of understanding one of the most intricatestructures in biology: the cerebral cortex.
Mountcastle’s concept of the cortical column hasendured as a fundamental principle of brain organiz-ation. Yet when one stops to ponder its significance, itbecomes apparent that neuroscience has no commonlyaccepted definition of ‘column’. The term has beenused loosely by subsequent investigators to refer tomany different entities, some bearing only a vagueanalogy to the modality-specific columns in the catsomatosensory cortex. Here, we trace the evolution ofideas about columns, challenge the notion that they areessential processing elements within the nervoussystem and review new insights regarding their for-mation. Our review deals principally with the visualcortex, where columns have been studied mostintensively, but draws freely upon examples fromother cortical areas to emphasize certain points.
2. MINICOLUMNS, COLUMNS ANDMACROCOLUMNSMountcastle proposed the cortical column based onobservations made by recording from single cells,but he was influenced strongly by new ideas about the
Phil. Trans. R. Soc. B (2005) 360, 837–862
doi:10.1098/rstb.2005.1623
Published online 29 April 2005
One contribution of 12 to a Theme Issue ‘Cerebral cartography1905–2005’.
*Author for correspondence ([email protected]).
837 q 2005 The Royal Society
Although the column is an attractive concept, it has failed as a unifying principle for understanding cortical function. Unravelling the organization of the cerebral cortex will require a painstaking description of the circuits, projections and response properties peculiar to cells in each of its various areas.
