TOPOLOGICAL SINGULARITIES IN CORTICAL ORIENTATION MAPS - THE SIGN THEOREM CORRECTLY PREDICTS ORIENTATION COLUMN PATTERNS IN PRIMATE STRIATECORTEX

Optical imaging methods have revealed the spatial arrangement of orien tation columns across striate cortex, usually summarized in terms of t wo measurements at each cortical location: (i) a 'best' stimulus orien tation, corresponding to the stimulus orientation that elicits a maxim al response, and (ii) the magnitude of the response to the best orient ation. This mapping has been described as continuous except at a set o f singular points (also termed 'vortices' or 'pinwheels'. Although pri or work has shown that vortex patterns qualitatively similar to those observed in visual area 17 of the Macaque cortex can be produced by ei ther band-pass or low-pass filtering of random vector fields, there ha s been to date little further topological characterization of the stru cture of cortical vortex patterns. Nevertheless, much theoretical work has been done in other disciplines on mappings analogous to the corti cal orientation map. In particular, a recent theorem in the optics lit erature, termed the sign principle, states that adjacent vortices on z ero crossings of a phase (orientation) mapping must always alternate i n sign. Using digitized samples of recently published optical recordin g data in monkey striate cortex, we show that the cortical orientation data does indeed possess 100% anti-correlation in vortex sign for nea rest-neighbour vortices, as predicted by the sign theorem. This provid es strong experimental support for the assumptions of continuity of co rtical vortex maps which underly the sign theorem. Similar analysis pr edicts a lack of 'higher-order' vortices in the cortical orientation m ap, which is also found to be in agreement with optical imaging observ ations. It also follows from this work that cortical vortices must be created simultaneously in clockwise-anti-clockwise pairs. This suggest s a possible basis for a modular (hyper-columnar) relationship among p airs of cortical vortices that originate at the same developmental tim e. In summary, this work indicates that primate visual cortex orientat ion column structure is best understood in the context of other 'order ed continuous media' (e.g. liquid He-3, cholesteric liquid crystals, r andom optical phase maps, to name only a few) in which an order parame ter (orientation in this case) is mapped to a physical space, and in w hich the topological properties of the mapping determine the observabl e regularities of the system. We also point out that these methods may well be applied to a variety of other cortical map systems which admi t an 'order parameter', i.e. for which each cortical position is assig ned a continuous stimulus value.