Stephan Klaas Enno, Kasper Lars, Harrison Lee M, Daunizeau Jean, den Ouden Hanneke E M, Breakspear Michael, Friston Karl J
Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK.
Neuroimage. 2008 Aug 15;42(2):649-62. doi: 10.1016/j.neuroimage.2008.04.262. Epub 2008 May 11.
Models of effective connectivity characterize the influence that neuronal populations exert over each other. Additionally, some approaches, for example Dynamic Causal Modelling (DCM) and variants of Structural Equation Modelling, describe how effective connectivity is modulated by experimental manipulations. Mathematically, both are based on bilinear equations, where the bilinear term models the effect of experimental manipulations on neuronal interactions. The bilinear framework, however, precludes an important aspect of neuronal interactions that has been established with invasive electrophysiological recording studies; i.e., how the connection between two neuronal units is enabled or gated by activity in other units. These gating processes are critical for controlling the gain of neuronal populations and are mediated through interactions between synaptic inputs (e.g. by means of voltage-sensitive ion channels). They represent a key mechanism for various neurobiological processes, including top-down (e.g. attentional) modulation, learning and neuromodulation. This paper presents a nonlinear extension of DCM that models such processes (to second order) at the neuronal population level. In this way, the modulation of network interactions can be assigned to an explicit neuronal population. We present simulations and empirical results that demonstrate the validity and usefulness of this model. Analyses of synthetic data showed that nonlinear and bilinear mechanisms can be distinguished by our extended DCM. When applying the model to empirical fMRI data from a blocked attention to motion paradigm, we found that attention-induced increases in V5 responses could be best explained as a gating of the V1-->V5 connection by activity in posterior parietal cortex. Furthermore, we analysed fMRI data from an event-related binocular rivalry paradigm and found that interactions amongst percept-selective visual areas were modulated by activity in the middle frontal gyrus. In both practical examples, Bayesian model selection favoured the nonlinear models over corresponding bilinear ones.
有效连接模型描述了神经元群体之间相互施加的影响。此外，一些方法，例如动态因果模型（DCM）和结构方程模型的变体，描述了实验操作如何调节有效连接。在数学上，两者都基于双线性方程，其中双线性项模拟了实验操作对神经元相互作用的影响。然而，双线性框架排除了通过侵入性电生理记录研究已确立的神经元相互作用的一个重要方面；即，两个神经元单元之间的连接如何由其他单元的活动启用或门控。这些门控过程对于控制神经元群体的增益至关重要，并通过突触输入之间的相互作用介导（例如通过电压敏感离子通道）。它们代表了各种神经生物学过程的关键机制，包括自上而下（例如注意力）调制、学习和神经调节。本文提出了一种DCM的非线性扩展，该扩展在神经元群体水平上对这些过程进行建模（到二阶）。通过这种方式，可以将网络相互作用的调制分配给一个明确的神经元群体。我们展示了模拟和实证结果，证明了该模型的有效性和实用性。对合成数据的分析表明，我们扩展的DCM可以区分非线性和双线性机制。当将该模型应用于来自对运动范式的阻断注意力的实证功能磁共振成像（fMRI）数据时，我们发现注意力诱导的V5反应增加可以最好地解释为后顶叶皮层活动对V1-->V5连接的门控。此外，我们分析了来自事件相关双眼竞争范式的fMRI数据，发现感知选择性视觉区域之间的相互作用受到额中回活动的调制。在这两个实际例子中，贝叶斯模型选择都更倾向于非线性模型而非相应的双线性模型。
