Lipschitz-Killing curvature based expected Euler characteristics for p-value correction in 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 a 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, in which measurements are densely sampled on a regular lattice and Gaussian smoothing makes the resulting random field homogeneous, the random fields from fNIRS are inhomogeneous 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 cannot be used for general random fields such as F-statistics. To overcome these difficulties, we employ the expected Euler characteristic approach based on Lipschitz-Killing curvature (LKC) to control the family-wise error rate. We compared this correction method with Sun's tube formula for t-statistics to confirm the existing method. Based on this comparison, we show that covariance estimation should be modified to consider channel-wise least-square residual correlation. These new results supplement the existing tool of statistical parameter mapping for fNIRS.

► General formulae for p-value corrected t- and F-statistics are derived for fNIRS. ► Equivalence between Sun's tube formula and LKC-based expected EC method has been demonstrated using real data. ► We showed that spatial correlation between different channel residuals should be incorporated into the channel residual covariance estimation. This modification makes the tube formula and LKC-based expected EC methods equivalent. Furthermore, this modification removes the artifact for individual t map.