Friston K J, Harrison L, Penny W
The Wellcome Department of Imaging Neuroscience, Institute of Neurology, Queen Square, London WC1N 3BG, UK.
Neuroimage. 2003 Aug;19(4):1273-302. doi: 10.1016/s1053-8119(03)00202-7.
In this paper we present an approach to the identification of nonlinear input-state-output systems. By using a bilinear approximation to the dynamics of interactions among states, the parameters of the implicit causal model reduce to three sets. These comprise (1) parameters that mediate the influence of extrinsic inputs on the states, (2) parameters that mediate intrinsic coupling among the states, and (3) [bilinear] parameters that allow the inputs to modulate that coupling. Identification proceeds in a Bayesian framework given known, deterministic inputs and the observed responses of the system. We developed this approach for the analysis of effective connectivity using experimentally designed inputs and fMRI responses. In this context, the coupling parameters correspond to effective connectivity and the bilinear parameters reflect the changes in connectivity induced by inputs. The ensuing framework allows one to characterise fMRI experiments, conceptually, as an experimental manipulation of integration among brain regions (by contextual or trial-free inputs, like time or attentional set) that is revealed using evoked responses (to perturbations or trial-bound inputs, like stimuli). As with previous analyses of effective connectivity, the focus is on experimentally induced changes in coupling (cf., psychophysiologic interactions). However, unlike previous approaches in neuroimaging, the causal model ascribes responses to designed deterministic inputs, as opposed to treating inputs as unknown and stochastic.
在本文中，我们提出了一种识别非线性输入-状态-输出系统的方法。通过对状态间相互作用的动力学进行双线性近似，隐式因果模型的参数简化为三组。这些参数包括：（1）介导外部输入对状态影响的参数；（2）介导状态间内在耦合的参数；（3）允许输入调制该耦合的[双线性]参数。在已知确定性输入和系统观测响应的情况下，识别过程在贝叶斯框架内进行。我们开发这种方法用于使用实验设计的输入和功能磁共振成像（fMRI）响应来分析有效连接性。在此背景下，耦合参数对应于有效连接性，双线性参数反映由输入引起的连接性变化。由此产生的框架使人们能够从概念上将fMRI实验表征为对脑区之间整合的实验性操纵（通过情境或无试次输入，如时间或注意力集），这种操纵通过诱发响应（对扰动或试次相关输入，如刺激）得以揭示。与之前对有效连接性的分析一样，重点在于实验诱导的耦合变化（参见心理生理相互作用）。然而，与神经成像中的先前方法不同，因果模型将响应归因于设计的确定性输入，而不是将输入视为未知且随机的。
