Worsley K J, Evans A C, Marrett S, Neelin P
Department of Mathematics and Statistics, McGill University, Quebec, Canada.
J Cereb Blood Flow Metab. 1992 Nov;12(6):900-18. doi: 10.1038/jcbfm.1992.127.
Many studies of brain function with positron emission tomography (PET) involve the interpretation of a subtracted PET image, usually the difference between two images under baseline and stimulation conditions. The purpose of these studies is to see which areas of the brain are activated by the stimulation condition. In many cognitive studies, the activation is so slight that the experiment must be repeated on several subjects and the subtracted images are averaged to improve the signal-to-noise ratio. The averaged image is then standardized to have unit variance and then searched for local maxima. The main problem facing investigators is which of these local maxima are statistically significant. We describe a simple method for determining an approximate p value for the global maximum based on the theory of Gaussian random fields. The p value is proportional to the volume searched divided by the product of the full widths at half-maximum of the image reconstruction process or number of resolution elements. Rather than working with local maxima, our method focuses on the Euler characteristic of the set of voxels with a value larger than a given threshold. The Euler characteristic depends only on the topology of the regions of high activation, irrespective of their shape. For large threshold values this is approximately the same as the number of isolated regions of activation above the threshold. We can thus not only determine if any activation has taken place, but we can also estimate how many isolated regions of activation are present.
许多利用正电子发射断层扫描（PET）进行的脑功能研究都涉及对相减后的PET图像的解读，通常是基线条件和刺激条件下两幅图像的差值。这些研究的目的是观察大脑的哪些区域在刺激条件下被激活。在许多认知研究中，激活程度非常轻微，以至于必须在多个受试者身上重复实验，并对相减后的图像进行平均以提高信噪比。然后将平均后的图像标准化为单位方差，接着搜索局部最大值。研究人员面临的主要问题是这些局部最大值中哪些在统计上是显著的。我们基于高斯随机场理论描述了一种确定全局最大值近似p值的简单方法。p值与搜索的体积除以图像重建过程的半高全宽的乘积或分辨率元素的数量成正比。我们的方法不是关注局部最大值，而是关注值大于给定阈值的体素集的欧拉特征。欧拉特征仅取决于高激活区域的拓扑结构，而与它们的形状无关。对于较大的阈值，这大致与阈值以上孤立激活区域的数量相同。因此，我们不仅可以确定是否发生了任何激活，还可以估计存在多少个孤立的激活区域。
