Life Science Research Center, School of Life Science and Technology, Xidian University, Xi'an 710071, China; Engineering Research Center of Molecular and Neuro Imaging Ministry of Education, School of Life Science and Technology, Xidian University, Xi'an 710071, China.
The Mind Research Network and LBERI, Albuquerque, NM 87106, USA; University of New Mexico, Department of Electrical and Computer Engineering, Albuquerque, NM 87131, USA.
J Neurosci Methods. 2017 Nov 1;291:1-12. doi: 10.1016/j.jneumeth.2017.08.003. Epub 2017 Aug 5.
Pearson correlation (simply correlation) is a basic technique for neuroimage function analysis. It has been observed that the spatial smoothing may cause functional overestimation, which however remains a lack of complete understanding. Herein, we present a theoretical explanation from the perspective of correlation scale invariance.
For a task-evoked spatiotemporal functional dataset, we can extract the functional spatial map by calculating the temporal correlations (tcorr) of voxel timecourses against the task timecourse. From the relationship between image noise level (changed through spatial smoothing) and the tcorr map calculation, we show that the spatial smoothing causes a noise reduction, which in turn smooths the tcorr map and leads to a spatial expansion on neuroactivity blob estimation.
Through numerical simulations and subject experiments, we show that the spatial smoothing of fMRI data may overestimate activation spots in the correlation functional map. Our results suggest a small spatial smoothing (with a smoothing kernel with a full width at half maximum (FWHM) of no more than two voxels) on fMRI data processing for correlation-based functional mapping COMPARISON WITH EXISTING METHODS: In extreme noiselessness, the correlation of scale-invariance property defines a meaningless binary tcorr map. In reality, a functional activity blob in a tcorr map is shaped due to the spoilage of image noise on correlative responses. We may reduce data noise level by smoothing processing, which poses a smoothing effect on correlation. This logic allows us to understand the noise dependence and the smoothing effect of correlation-based fMRI data analysis.
皮尔逊相关（简单相关）是神经影像学功能分析的基本技术。已经观察到空间平滑可能导致功能高估，但这仍然缺乏全面的理解。在此，我们从相关尺度不变性的角度提出了一个理论解释。
对于任务诱发的时空功能数据集，我们可以通过计算体素时间序列与任务时间序列的时间相关（tcorr）来提取功能空间图。从图像噪声水平（通过空间平滑改变）与 tcorr 图计算之间的关系，我们表明空间平滑会降低噪声，从而平滑 tcorr 图，并导致神经活动团块估计的空间扩展。
通过数值模拟和受试者实验，我们表明 fMRI 数据的空间平滑可能会高估相关功能图中的激活点。我们的结果表明，在基于相关性的功能映射 fMRI 数据处理中，对数据进行小范围平滑（平滑核的全宽半最大值（FWHM）不超过两个体素）。
在极端无噪声的情况下，尺度不变性的相关性定义了一个无意义的二进制 tcorr 图。在现实中，由于相关响应中的图像噪声破坏，tcorr 图中的功能活动团块具有一定的形状。我们可以通过平滑处理来降低数据噪声水平，这对相关性产生平滑效应。这种逻辑使我们能够理解基于相关性的 fMRI 数据分析的噪声依赖性和平滑效应。
