Modeling the Interactions of Stimuli and Ongoing Activity in Cortical Networks

我们感知世界的方式既受我们不断受到轰炸的感官输入的支配，也受我们大脑中正在进行的活动和我们以前的经验的支配。这种活动以及神经系统的自然连接塑造了我们大脑的自发行为，这种自发活动强烈地调节了感觉输入。在这个项目中，神经元(组成大脑的细胞)的计算和数学模型被用来理解哪些类型的自发行为是可能的，这如何依赖于线路，以及这种活动如何与感觉输入相互作用。正在进行的和诱发的行为受到积极(兴奋)和消极(抑制)影响的平衡控制。这种平衡的丧失可能会扰乱正常行为，并导致癫痫和精神分裂症等疾病。神经系统的数学模型提供了一种方法来检验实验者提出的假设，并根据这些模型的预测提出新的实验建议。神经系统中正在进行的活动以及它如何影响感觉和其他输入是最近许多实验活动的主题。特别是，很明显，在没有输入的情况下，神经元电路之间的内在相互作用可以对系统如何对传入的刺激做出反应产生强烈的影响，即使在大规模认知水平上也是如此。因此，非线性动力学方法将被应用于理论神经科学中处理这一问题的问题。在实验中观察到了各种形式的时空活动，包括空间局域活动、振荡和传播波。微扰和数值方法将被用来分析这些图案在受到各种刺激时的动力学，例如闪烁的光、局部或运动的刺激以及空间周期图案。均匀闪烁刺激导致对运动几何图案的感知，这可以通过对视皮层平均场模型的分析来解释。在与一个实验小组的合作中，我们将使用建模来预测这种感知如何随着闪烁参数的变化而改变。与此相关的是，当呈现高对比度的空间周期图案时，出现闪烁。将研究稳态周期状态的稳定性，以确定振荡的出现是否是Hopf分叉的结果。这一效应也可以解释为什么一些图像(如OP艺术)会导致视觉不适。本课题还将研究非局部连通网络中行波的存在性和性质。

How we perceive the world is governed both by the sensory inputs with which we are constantly bombarded, by ongoing activity in the brain, and by our previous experience. This activity as well as the natural wiring of the nervous system shapes the spontaneous behavior of our brains and this spontaneous activity strongly modulates the sensory inputs. In this project, computational and mathematical models of neurons (the cells that make up the brain) are used to understand what kinds of spontaneous behavior are possible, how this depends on the wiring and how this activity interacts with sensory inputs. The ongoing and evoked behavior is carefully controlled by a balance of positive (excitatory) and negative (inhibitory) influences. The loss of this balance can disrupt normal behavior and lead to diseases such as epilepsy and schizophrenia. Mathematical models of the nervous system provide a way to test hypotheses put forth by experimenalists and to also suggest new experiments based on the predictions of these models. Ongoing activity in the nervous system and how it impacts sensory and other inputs is the subject of much recent experimental activity. In particular, it is clear that the intrinsic interactions between neuronal circuits in absence of inputs can have a strong impact on how the system responds to incoming stimuli even at the large scale cognitive level. Thus, nonlinear dynamics methods will be applied to problems in theoretical neuroscience dealing with this question. Various forms of spatiotemporal activity are observed in experiments which include spatially localized activity, oscillations, and propagating waves. Perturbation and numerical methods will be used to analyze the dynamics of these patterns when subjected to various stimuli such as flickering light, localized or moving stimuli, and spatially periodic patterns. Uniform flickering stimuli lead to the perception of moving geometric patterns and these can be explained by the analysis of mean field models of visual cortex. In collaboration with an experimental group we will use the modeling to make predictions about how this percept is altered as parameters of the flicker vary. Related to this is the appearance of flicker when presented with high contrast spatially periodic patterns. Stability of the steady periodic state will be studied in order to see if the appearance of oscillations is the result of a Hopf bifurcation. This effect may also offer an explanation for why some images (such as op art) can induce visual discomfort. The existence an properties of traveling waves in nonlocally connected networks will also be studied in this project.