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，如方位和空间频率的数学描述。这一过程发生在初级视觉皮质(V1)。特别是，将描述和分析用漂移、站立或随机闪烁的正弦光栅观察屏幕的猕猴V1区神经元反应的实验，并借助于V1的粗粒度神经元模型进行分析。该模型是一个非线性积分方程，其性质将通过解析和计算来研究。粗粒度模型结合了重要的解剖学信息，包括V1的方位和空间频率偏好神经元地图的结构，皮质-皮质神经元连接的大小和强度，以及神经输入到V1的详细布局。将计算V1神经元的方位和空间频率随时间变化的函数，并与实验数据进行比较，以确定哪种皮质结构更好地描述真实生物学：前馈(假设皮质-皮质相互作用不重要)，还是反馈(假设皮质-皮质相互作用对神经元调节曲线的时空演变起关键作用)。这项工作将与纽约大学神经科学中心的神经学家罗伯特·沙普利、应用数学家大卫·麦克劳克林和迈克尔·雪莱合作进行，在PI格雷戈尔·科瓦奇为期一年的访问框架内。这个IGMS项目由MPS多学科活动办公室(OMA)和数学科学部(DMS)联合支持。

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).