Centre for Theoretical and Computational Neuroscience, University of Plymouth, Drake Circus, PL4 8AA, UK,
Cogn Neurodyn. 2008 Jun;2(2):137-46. doi: 10.1007/s11571-008-9045-1. Epub 2008 Apr 18.
The most prominent functional property of cortical neurons in sensory areas are their tuned receptive fields which provide specific responses of the neurons to external stimuli. Tuned neural firing indeed reflects the most basic and best worked out level of cognitive representations. Tuning properties can be dynamic on a short time-scale of fractions of a second. Such dynamic effects have been modeled by localised solutions (also called "bumps" or "peaks") in dynamic neural fields. In the present work we develop an approximation method to reduce the dynamics of localised activation peaks in systems of n coupled nonlinear d-dimensional neural fields with transmission delays to a small set of delay differential equations for the peak amplitudes and widths only. The method considerably simplifies the analysis of peaked solutions as demonstrated for a two-dimensional example model of neural feature selectivity in the brain. The reduced equations describe the effective interaction between pools of local neurons of several (n) classes that participate in shaping the dynamic receptive field responses. To lowest order they resemble neural mass models as they often form the base of EEG-models. Thereby they provide a link between functional small-scale receptive field models and more coarse-grained EEG-models. More specifically, they connect the dynamics in feature-selective cortical microcircuits to the more abstract local elements used in coarse-grained models. However, beside amplitudes the reduced equations also reflect the sharpness of tuning of the activity in a d-dimensional feature space in response to localised stimuli.
皮质神经元在感觉区域最突出的功能特性是其调谐的感受野，它们为神经元对外界刺激提供特定的反应。调谐的神经放电确实反映了认知表现的最基本和最完善的水平。调谐特性可以在几分之一秒的短时间尺度上动态变化。这种动态效应已通过动态神经场中的局部解（也称为“峰”或“峰值”）进行建模。在目前的工作中，我们开发了一种近似方法，将 n 个耦合的非线性 d 维神经场中局部激活峰的动力学（具有传输延迟）简化为仅用于峰值幅度和宽度的小一组时滞微分方程。该方法大大简化了对峰值解的分析，如在大脑中二维神经特征选择性的示例模型中所示。简化方程描述了参与形成动态感受野反应的几个（n）类局部神经元池之间的有效相互作用。在最低阶次，它们类似于神经质量模型，因为它们通常是 EEG 模型的基础。由此，它们在功能上的小规模感受野模型和更粗糙的 EEG 模型之间建立了联系。更具体地说，它们将特征选择性皮质微循环中的动力学与在更粗糙的模型中使用的更抽象的局部元素联系起来。然而，除了幅度之外，简化方程还反映了在响应局部刺激时，d 维特征空间中活动的调谐锐度。
