Functional near-infrared spectroscopy (fNIRS) is a non-invasive imaging approach for measuring brain activities based on changes in the cerebral concentrations of hemoglobin. Recently, statistical analysis based on general linear model (GLM) has become popular. Here, to impose statistical significance on the activation detected by fNIRS, family-wise error (FWE) rate control is important. However, unlike fMRI, where measurements are densely sampled on a regular lattice and Gaussian smoothing makes the resulting random field isotropic, the random fields from fNIRS are non-isotropic due to the interpolation from sparsely and irregularly distributed optode locations. Thus, tube formula based correction has been proposed to address this issue. However, Sun’s tube formula is only suitable for Gaussian random field, so it cannot be used for general t- and F- statistics from either individual or group analysis. To overcome these difficulties, we employ the expected Euler characteristic approach based on Lipschitz-Killing curvature (LKC), which has been widely used to address the brain shape analysis. We compared this correction method with Sun’s tube formula for individual t random field to confirm the existing method. Based on this comparison, we discovered an important distinction of fNIRS and fMRI such that mass-univariate approach should be modified to consider channel-wise least-square residual correlation. Moreover, by applying this for group level p-value correction, we observe that the ordinary least square estimation is effective for second level analysis due to sensitivity, reduced complexity, and the consistency with individual analysis for the case of precoloring. The new results supplements existing tool of statistical parameter mapping for fNIRS.
Functional near-infrared spectroscopy (fNIRS) is a non-invasive imaging approach for measuring brain activities based on changes in the cerebral concentrations of hemoglobin. Recently, statistical analysis based on general linear model (GLM) has become popular. Here, to impose statistical significance on the activation detected by fNIRS, family-wise error (FWE) rate control is important. However, unlike fMRI, where measurements are densely sampled on a regular lattice and Gaussian smoothing makes the resulting random field isotropic, the random fields from fNIRS are non-isotropic due to the interpolation from sparsely and irregularly distributed optode locations. Thus, tube formula based correction has been proposed to address this issue. However, Sun’s tube formula is only suitable for Gaussian random field, so it cannot be used for general t- and F- statistics from either individual or group analysis. To overcome these difficulties, we employ the expected Euler characteristic approach based on Lipschitz-Killing curvature (LKC), which has been widely used to address the brain shape analysis. We compared this correction method with Sun’s tube formula for individual t random field to confirm the existing method. Based on this comparison, we discovered an important distinction of fNIRS and fMRI such that mass-univariate approach should be modified to consider channel-wise least-square residual correlation. Moreover, by applying this for group level p-value correction, we observe that the ordinary least square estimation is effective for second level analysis due to sensitivity, reduced complexity, and the consistency with individual analysis for the case of precoloring. The new results supplements existing tool of statistical parameter mapping for fNIRS.
