Spatio-temporal autoregressive models defined over brain manifolds
Spatio-temporal autoregressive models defined over brain manifolds
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DOI：
10.1385/ni:2:2:239
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发表时间：
2004-06-01
期刊：
影响因子：
3
通讯作者：
Valdes-Sosa, PA
中科院分区：
文献类型：
--
作者：
Valdes-Sosa, PA
多变量自回归时间序列模型（MAR）是神经影像学中越来越多地用于探索功能连接的工具。它们为分析特定大脑区域对其他区域的格兰杰因果关系提供了框架。在本文中，我们将把注意力限制在线性MAR模型上，其中一组自回归系数矩阵a (k) (k = 1，…p)描述图像的现值对其过去的滞后值的依赖。估算A(k)和确定哪些元素为零的方法是众所周知的，并且是直接衡量影响的基础。然而，到目前为止，MAR模型所能处理的时间序列数量有限，这迫使它只能先验地选择（少量）感兴趣的体素或区域进行分析。这忽略了大脑功能数据的完整时空本质，事实上，这些数据是在一个潜在的连续空间流形——大脑上采样的时间序列的集合。在功能数据分析的框架内建立了一个完整的时空MAR模型（ST-MAR）。对于空间数据，矩阵a (k)的每一行是给定体素的影响场。指定了一个贝叶斯ST-MAR模型，其中要求所有体素的影响场在空间上平滑变化。这一要求是通过惩罚影响场的空间粗糙度来实现的。这种粗糙度是用空间拉普拉斯算子的离散版本来计算的。通过奇异值分解实现了计算维数的大量降低，使模型的交互式探索成为可能。为了分析静息脑节律的起源，使用与EEG同时收集的fMRI时间序列来说明该模型的使用。
Multivariate Autoregressive time series models (MAR) are an increasingly used tool for exploring functional connectivity in Neuroimaging. They provide the framework for analyzing the Granger Causality of a given brain region on others. In this article, we shall limit our attention to linear MAR models, in which a set of matrices of autoregressive coefficients A(k) (k = 1, ..., p) describe the dependence of present values of the image on lagged values of its past. Methods for estimating the A(k) and determining which elements that are zero are well-known and are the basis for directed measures of influence. However, to date, MAR models are limited in the number of time series they can handle, forcing the a priori selection of a (small) number of voxels or regions of interest for analysis. This ignores the full spatio-temporal nature of functional brain data which are, in fact, collections of time series sampled over an underlying continuous spatial manifold-the brain. A fully spatio-temporal MAR model (ST-MAR) is developed within the framework of functional data analysis. For spatial data, each row of a matrix A(k) is the influence field of a given voxel. A Bayesian ST-MAR model is specified in which the influence fields for all voxels are required to vary smoothly over space. This requirement is enforced by penalizing the spatial roughness of the influence fields. This roughness is calculated with a discrete version of the spatial Laplacian operator. A massive reduction in dimensionality of computations is achieved via the singular value decomposition, making an interactive exploration of the model feasible. Use of the model is illustrated with an fMRI time series that was gathered concurrently with EEG in order to analyze the origin of resting brain rhythms.