Spatial statistical smoothing function to analytical data from cerebral blood flow imaging

Spatial statistics is widely used in fields where analysis of large-scale distributions is performed, such as synoptic meteorology and geostatistics. We constructed a smoothing function as part of a fundamental study aimed at introducing spatial statistics to the Z score map of cerebral blood flow-single photon emission tomography (CBF-SPET) and examined the applicability of spatial statistics to CBF-SPET imaging. The free statistical processing language R was chosen as the development language, and the smoothing function was constructed by use of a kernel function, a thin-plate spline function, and the Bayesian method. A Gaussian function was used as the kernel function, and three values for the smoothing parameters (0.25, 0.5, standard deviation (SD)) were used. Furthermore, the smoothing parameters of the thin-plate spline function were estimated by use of generalized cross validation (GCV), the Gibbs sampling method was adopted for the Bayesian method, and the number of iterations and the value for the burn-in were set to 500 and 250, respectively. In performing the visual assessment of the source image and the smoothed image, there were no differences caused by the smoothing process. However, there were discrepancies in the contour map at each step of the smoothing iteration. Comparing the residual sum of squares of the source image and the resulting image after each smoothing iteration, the minimum and maximum values for the image after processing with a kernel function were 1.329x10(-11) and 21.96 when the smoothing parameters were 0.25 and SD, respectively. The smoothing function, which was examined for the purpose of applying the spatial statistical method to CBF-SPET imaging, successfully performed a smoothing without generating visible discrepancies when compared with the source image. In conclusion, our research showed that spatial statistics as performed by us is applicable as an analytical method for better cerebral blood flow-SPET imaging.