Neurogeometry of vision.

Explorations of visual hallucinations, and in particular those of Billock and Tsou [Neural interactions between flicker-induced self-organized visual hallucinations and physical stimuli. Proceedings of the National Academy of Sciences, 104(20):8490-8495, 2007], show that annular rings with a background flicker can induce visual hallucinations in humans that take the form of radial fan shapes and vice versa. The well-known retino-cortical map tells us that the corresponding patterns of neural activity in the primary visual cortex (V1) for rings and arms in the retina are orthogonal stripe patterns. The implication is that cortical forcing by spatially periodic input can excite orthogonal modes of neural activity. In this thesis I will show that a simple scalar neural field model of primary visual cortex with state-dependent spatial forcing is capable of modelling this phenomenon. Moreover, I will show that this occurs most robustly when the spatial forcing has a 2:1 resonance with modes that would otherwise be excited by a Turing instability. By utilising a weakly nonlinear multiple-scales analysis I will determine the relevant amplitude equations for uncovering the parameter regimes which favour the excitation of patterns orthogonal to sensory drive. In combination with direct numerical simulations I will use this approach to shed further light on the original psycho-physical observations of Billock and Tsou, making extensive use of realistic retino-cortical maps.

The work described above will be further extended to include known orientation selectivity of cells in V1, with a generalisation of the non-local neural field model to include an orientation preference map (OPM) (with V1 now modelled as a fiber bundle that associates to every point of the cortex, or retina by the retino-cortical map, a copy of the unit circle). As well as probing further the role of OPMs in generating visual illusions (such as migraine aura), we will introduce plasticity to explore how these maps evolve under persistent visual stimulation.