Mathematical Modeling of the Visual Cortex

这个项目涉及哺乳动物如何处理视觉场景的一些最基本的特征，如方向和空间频率的数学描述。 这个过程发生在初级视觉皮层（V1）。 特别是，将描述和分析的粗粒度的神经元模型的帮助下，V1的猕猴观察屏幕与漂移，站立，或随机闪烁的正弦光栅，测量V1的神经元的反应的实验。 该模型是一个非线性积分方程，其性质将被研究分析以及计算。粗粒度模型结合了重要的解剖信息，包括V1的方向和空间频率偏好神经元映射的架构，皮质-皮质神经元连接的大小和强度，以及V1的神经输入的详细布局。将计算V1神经元的方向和空间频率调谐作为时间的函数，并与实验数据进行比较，着眼于确定哪种皮层结构更好地描述了真正的生物学：前馈（假设皮质-皮质相互作用不重要）或反馈（假设皮质-皮质相互作用对神经元调谐曲线的时空演变至关重要）。 这项工作将与纽约大学神经科学中心的神经科学家Robert Shapley和应用数学家大卫麦克劳克林（David McLaughlin）和迈克尔雪莱（Michael Shelley）合作，在PI Gregor Kovacic为期一年的访问框架内进行。该IGMS项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）共同支持。

This project concerns a mathematical description of how mammals process some of the most elementary characteristics of the visual scene, such as orientation and spatial frequency. This processing takes place in the primary visual cortex (V1). In particular, experiments, which measure the response of neurons in V1 of a macaque monkey observing a screen with a drifting, standing, or randomly-flashed sinusoidal grating, will be described and analyzed with the aid of a coarse-grained neuronal model of V1. This model is a nonlinear integral equation, whose properties will be studied analytically as well as computationally. The coarse-grained model incorporates vital anatomical information, including the architecture of the orientation- and spatial-frequency-preference neuronal maps of V1, the sizes and strengths of the cortico-cortical neuronal connections, and the detailed layout of the neural input into V1. The orientation andspatial-frequency tuning of V1 neurons as functions of time will be computed and compared with the experimental data, with an eye on determining which cortical achitecture better describes the true biology:feed-forward (which assumes no importance of the cortico-cortical interactions), or feed-back (which assumes that cortico-cortical interactions contribute crucially to the spatio-temporal evolution of theneuronal tuning curves). The work will be performed in collaboration with neuroscientist Robert Shapley and applied mathematicians David McLaughlin and Michael Shelley at New York University's Center for Neural Science, in the framework of a year-long visit by the PI, Gregor Kovacic.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).