A Filtered Subtraction Approach for the Reduction of Physiological Noise in Perfusion Based fMRI

K. Restom, Y. Behzadi, J. E. Perthen, T. T. Liu Center for Functional MRI, University of California, San Diego, La Jolla, CA, United States Introduction Physiological noise is a dominant source of noise in fMRI experiments, especially at higher field strengths. A previous study showed that the sensitivity of perfusion based fMRI could be significantly improved by removing physiological noise components from the tag and control images separately, using a modified version of a image based retrospective correction method (RETROICOR) [1,2]. However, this method was not directly comparable to the filtered subtraction schemes typically employed in the analysis of ASL data. In this work, we present a new model in which physiological noise is removed from the perfusion time series obtained from the filtered subtraction of the tag and control images. We then compare the statistical performance of the filtered approach to the previous unfiltered approach by using experimental data obtained from functional ASL studies of the visual cortex and hippocampal region. Theory In an arterial spin labeling (ASL) experiment, a series of control images and tag images in which arterial blood is either fully relaxed or magnetically inverted, respectively, is acquired. Typically, the control and tag images are acquired in an interleaved fashion and a perfusion time series is formed from the filtered subtraction of the images. By adding physiological noise terms for tag and control images [2] to the ASL signal model described in [3], the ASL data can be described in matrix form as: y = smM 0b + sqq o b +α exp(−TI /T1B )M q o b ( )+U cD cPc c +U tD tPc t + e where y is ASL time series consisting of interleaved tag and control images, b represents multiplicative BOLD weighting, q represents perfusion, e is an additive noise term, M is a NxN diagonal matrix consisting of alternating –1 and 1s along the diagonal, and q o b denotes the Hadamard product of two vectors (i.e. element-byelement multiplication). The terms sm , sq , α, TI, and T1B denote pulse sequence dependent terms and relaxation constants. Physiological noise terms are UcDcPc c +U tD tPc t where P is a Nxm matrix containing m physiological regressors and c c and c t are unknown regressor weights for the control and tag images, respectively. The calculation of these regressors follows the approach presented in [1] for the RETROICOR method. The term U cD cPc c represents physiological noise contributions to the control images where D c is a downsampling matrix that picks out every odd sample of Pc c and U c is an upsampling matrix that inserts zeros between samples of D cPc c . The matrices U t and D t are defined similarly, with D t picking out even samples of Pc t . Most perfusion estimates are based upon filtered subtraction methods that attenuate the un-modulated terms smM 0b + sqq o b in the GLM (corresponding to BOLD weighted static tissue and perfusion terms)