A New Approximation Technique for Maxwell's Equations

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Bressloff0209824 The long term goal of this project is to develop a dynamicaltheory of how neurons in primary visual cortex (V1) generate atuned response to multiple (rather than single) features of avisual stimulus, and how these responses are spatially integratedacross the cortex to generate more global information about avisual scene. A primary focus of the work is to extend currentnetwork models of orientation tuning to incorporate the fact thatV1 cells are also selective for spatial frequency. This ismotivated by the considerable physiological and psychophysicalevidence suggesting that cortical circuits carry out a localizedtwo-dimensional Fourier decomposition of a stimulus rather thansimply performing local edge detection. Optical imaging of thesurface of cortex has revealed an intricate relationship betweenthe distribution of orientation and spatial frequency preferencesacross cortex. How correlations between these two featurepreference maps is manifested by the local and long-rangecircuitry of V1, and the consequences for the large-scaledynamics of V1 is also investigated. The primary visual cortex (V1) located at the back of thebrain is the first cortical area to process visual informationreceived from the eyes. One of the classical results regardingthe function of neurons (brain cells) in V1 is that they analyzevery local features of a visual image, that is, they carry outimage decomposition. (For example, V1 cells are sensitive to theorientation of an edge representing the boundary between a lightand dark region of the image. This discovery by Hubel and Wieselled to the Nobel prize in medicine). A very important questionthat follows from this is how our coherent perception of theworld is reconstructed. Until recently, it was thought that thelocal information from cells in V1 was passed through higherorder processing stages in the brain where cognition occurs.However, it is becoming clear that long-range circuitry within V1could itself contribute to the process of reconstruction. Thebasic aim of the proposal is to investigate this process bydeveloping a large-scale mathematical model of primary visualcortex that incorporates the latest anatomical data regarding itsinternal circuitry. Understanding how early stages in the visualbrain encode images has important applications to informationtechnology (such as the development of artificial vision systems)and biotechnology (such as the development of an artificialprosthesis for the visually impaired). In the latter case itmight be possible one day to artificially stimulate primaryvisual cortex to induce a visual sensation, rather like acontrolled visual hallucination.