The Effect of Detrending When Computing Regression Coefficients

Detrending is a method used when applying linear re- gression to determine functional brain activation. It is performed to eliminate an overall mean and linear time drift in the signal. However, the resulting regression coefficients are not identical to those computed using a multiple linear regression method. In this study, these two methods are compared in a simulation and in a real fMRI bilateral finger tapping experiment. The result is that the correct determination of the regression coefficients crucially depends upon the chosen reference function. Introduction: When fitting the fMRI signal to an idealized ref- erence function such as a square wave, the method of detrending plus simple linear regression is often used where an estimated linear trend is subtracted and the difference fit to the reference function. The multiple linear regression alternative (l), (2) takes no such step. Mathematics: The determination of whether functional activation has occurred is based upon the regression coefficients from the fit of the BOLD signal to an idealized reference hnction (3), (4). The equation to be fit for the multiple regression technique for each voxel is g2.d = {(~~~~)~1~~~(~2( ~~)~1~~~~~(~~~~~ )~1~~~}~. (41