Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI 53716, USA.
IEEE Trans Biomed Eng. 2010 Sep;57(9):2122-34. doi: 10.1109/TBME.2010.2050319. Epub 2010 May 24.
A state-space formulation is introduced for estimating multivariate autoregressive (MVAR) models of cortical connectivity from noisy, scalp-recorded EEG. A state equation represents the MVAR model of cortical dynamics, while an observation equation describes the physics relating the cortical signals to the measured EEG and the presence of spatially correlated noise. We assume that the cortical signals originate from known regions of cortex, but the spatial distribution of activity within each region is unknown. An expectation-maximization algorithm is developed to directly estimate the MVAR model parameters, the spatial activity distribution components, and the spatial covariance matrix of the noise from the measured EEG. Simulation and analysis demonstrate that this integrated approach is less sensitive to noise than two-stage approaches in which the cortical signals are first estimated from EEG measurements, and next, an MVAR model is fit to the estimated cortical signals. The method is further demonstrated by estimating conditional Granger causality using EEG data collected while subjects passively watch a movie.
引入了一种状态空间公式，用于从噪声较大的头皮记录脑电图中估计皮质连接的多元自回归 (MVAR) 模型。状态方程表示皮质动力学的 MVAR 模型，而观测方程描述了将皮质信号与测量的 EEG 以及存在空间相关噪声相关联的物理关系。我们假设皮质信号源自已知的皮质区域，但每个区域内活动的空间分布是未知的。开发了一种期望最大化算法，可直接从测量的 EEG 中估计 MVAR 模型参数、空间活动分布分量以及噪声的空间协方差矩阵。模拟和分析表明，与两步法相比，这种集成方法对噪声的敏感性较低，在两步法中，首先从 EEG 测量中估计皮质信号，然后拟合 MVAR 模型到估计的皮质信号。该方法还通过使用受试者被动观看电影时收集的 EEG 数据来估计条件格兰杰因果关系得到了进一步证明。
