This project is focused on developing improved insights into the functioning of the primary visual cortex of the brain. This is the first region of the cerebral cortex (the convoluted part of the brain responsible for higher cognitive function in primates) to receive and process visual information from the eyes. It can be viewed as a two-dimensional sheet of millions of brain cells (neurons) communicating with each other via electrical signals. The electrical activity patterns of these neurons encode information about a visual image, which is then processed by other regions of the brain, resulting in the visual perception of a dynamically changing three-dimensional world. Visual information is often represented by spatially structured or coherent activity patterns. Understanding the mechanisms that underpin the origin and maintenance of these dynamical patterns is not only important for understanding the normal functioning of the visual brain, but also the occurrence of pathological states during epileptic seizures and migraines. One of the major challenges in neuroscience is determining how the wiring of the visual brain contributes to the generation of cortical activity patterns. The investigator has developed mathematical models of the primary visual cortex based on models that describe the generation and spread of electrical activity across the two-dimensional cortical sheet. Recent experimental studies indicate, however, that the laminar or layered structure of the primary visual cortex plays a crucial role in the production of these activity patterns. This research project, which is part of a larger collaborative program with the Moran Eye Center at the University of Utah, aims to extend previous mathematical models in order to take into account the laminar structure and determine how it affects a range of spontaneous visual phenomena. The main focus of the collaboration is to use a combination of neurophysiology, anatomy, and computational modeling to understand the functional architecture of the primary visual cortex and its role in visual processing. The Moran group is currently developing the use of light to control genetically modified cells and virus labeling techniques in order to understand the fine-structure of the visual cortex, which will be used to refine the mathematical models. The underlying idea linking the two projects is that the neural circuits used in the mathematical models to understand spontaneous activity are the same as those used to explain observations of the normal response of the cortex to visual stimulations. This project promotes scientific progress in the interdisciplinary field of mathematical neuroscience and vision and contributes to the interdisciplinary training of graduate students and postdocs.
The modeling of the primary visual cortex involves the construction and analysis of continuum neural field models, in which the large-scale dynamics of spatially structured networks of neurons is described in terms of nonlinear, integro-differential equations. A major advantage of working with neural fields is that powerful methods from the mathematical theory of nonlinear partial differential equations can be adapted to analyze such models. Almost all previous studies of neural fields have ignored the fact that the cerebral cortex has a laminar structure, with neurons in distinct layers often having distinct stimulus response properties and participating in distinct circuits. There is also extensive coupling between layers via so-called vertical connections. In this project the laminar neural field models will be used study two important examples of spontaneous visual phenomena, namely, binocular rivalry waves and visual hallucinations. One possible mechanism for the latter is based on the idea that some chemical or physical disturbance can destabilize the visual part of the brain, inducing a spontaneous pattern of cortical activity. The geometry of the resulting hallucination thus reflects the intrinsic architecture and symmetry of the visual cortex. Analyzing such patterns can provide further insight in how the brain processes images in normal vision. Binocular rivalry is the phenomenon where perception switches back and forth between different images presented to the two eyes. The resulting fluctuations in perceptual dominance and suppression provide a basis for non-invasive studies of the human visual system and the identification of possible neural mechanisms underlying conscious visual awareness.
