Harrison L M, Penny W, Flandin G, Ruff C C, Weiskopf N, Friston K J
Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London, WC1N 3BG UK.
Neuroimage. 2008 Dec;43(4):694-707. doi: 10.1016/j.neuroimage.2008.08.012. Epub 2008 Aug 23.
Spatial models of functional magnetic resonance imaging (fMRI) data allow one to estimate the spatial smoothness of general linear model (GLM) parameters and eschew pre-process smoothing of data entailed by conventional mass-univariate analyses. Recently diffusion-based spatial priors [Harrison, L.M., Penny, W., Daunizeau, J., and Friston, K.J. (2008). Diffusion-based spatial priors for functional magnetic resonance images. NeuroImage.] were proposed, which provide a way to formulate an adaptive spatial basis, where the diffusion kernel of a weighted graph-Laplacian (WGL) is used as the prior covariance matrix over GLM parameters. An advantage of these is that they can be used to relax the assumption of isotropy and stationarity implicit in smoothing data with a fixed Gaussian kernel. The limitation of diffusion-based models is purely computational, due to the large number of voxels in a brain volume. One solution is to partition a brain volume into slices, using a spatial model for each slice. This reduces computational burden by approximating the full WGL with a block diagonal form, where each block can be analysed separately. While fMRI data are collected in slices, the functional structures exhibiting spatial coherence and continuity are generally three-dimensional, calling for a more informed partition. We address this using the graph-Laplacian to divide a brain volume into sub-graphs, whose shape can be arbitrary. Their shape depends crucially on edge weights of the graph, which can be based on the Euclidean distance between voxels (isotropic) or on GLM parameters (anisotropic) encoding functional responses. The result is an approximation the full WGL that retains its 3D form and also has potential for parallelism. We applied the method to high-resolution (1 mm(3)) fMRI data and compared models where a volume was divided into either slices or graph-partitions. Models were optimized using Expectation-Maximization and the approximate log-evidence computed to compare these different ways to partition a spatial prior. The high-resolution fMRI data presented here had greatest evidence for the graph partitioned anisotropic model, which was best able to preserve fine functional detail.
功能磁共振成像（fMRI）数据的空间模型能够估计一般线性模型（GLM）参数的空间平滑度，并且避免了传统的单变量分析对数据进行预处理时的平滑操作。最近，基于扩散的空间先验方法[哈里森，L.M.，彭尼，W.，道尼佐，J.，和弗里斯顿，K.J.（2008年）。基于扩散的功能磁共振图像空间先验。《神经影像学》]被提出，该方法提供了一种构建自适应空间基的方式，其中加权图拉普拉斯算子（WGL）的扩散核被用作GLM参数的先验协方差矩阵。这些方法的一个优点是，它们可用于放宽在使用固定高斯核对数据进行平滑时隐含的各向同性和平稳性假设。基于扩散的模型的局限性纯粹是计算方面的，这是由于脑体积中的体素数量众多。一种解决方案是将脑体积划分为切片，对每个切片使用空间模型。通过用块对角形式近似完整的WGL，这减少了计算负担，其中每个块可以单独分析。虽然fMRI数据是按切片采集的，但表现出空间连贯性和连续性的功能结构通常是三维的，这就需要更明智的划分。我们使用图拉普拉斯算子将脑体积划分为子图来解决这个问题，其子图的形状可以是任意的。它们的形状关键取决于图的边权重，边权重可以基于体素之间的欧几里得距离（各向同性）或基于编码功能响应的GLM参数（各向异性）。结果是对完整WGL的一种近似，它保留了其三维形式并且还具有并行处理的潜力。我们将该方法应用于高分辨率（1立方毫米）的fMRI数据，并比较了将体积划分为切片或图分区的模型。使用期望最大化算法对模型进行优化，并计算近似对数证据以比较这些划分空间先验的不同方法。这里呈现的高分辨率fMRI数据为图分区各向异性模型提供了最强的证据，该模型最能够保留精细的功能细节。
