Adaptive Noise Removal IRF-RETROICOR

Introduction: It has become common to correct for physiologic noise by prior regression [1] or by inclusion in the fit model for BOLD-weighted functional connectivity (fcMRI) and in some cases, for fMRI[2-4]. The noise model is based on the RETROICOR model [5,1], which removes variance with the same quasiperiodicity as the cardiac and respiratory cycles. However, to model the noise accurately, a large number of regressors is needed. For example, RET-2 (hereafter RETROICOR will be referred to as RET-N where N is model order) requires 2 orders of sine and cosine for both cardiac and respiration, or 8 regressors. In some applications at 3 Tesla, orders up to RET-5 have been shown to be necessary, but 5 order requires 20 regressors. It is a known issue (but not always accounted for) that increasing the number of regressions in a correction reduces the statistical power of the corrected dataset (see Fig 1b for std dev versus correction with simulated phase and increasing RET model order). Furthermore, it is our hypothesis that a more parsimonious model based on the most-strongly fitted noise signatures can explain all of the cardiac and respiration noise variance. We show a modification to RETROICOR that removes the same significantly fitted variance as RET-5 but with only 6 regressors (4 for cardiac, 2 for respiration), less than RET-2. We show evidence in 34 subjects that the cardiac and respiratory noise signatures detected by our methods are very similar across subjects, implying these are the actual noise signatures, and recommend adaptive noise modeling when the model order is greater than 2. Adaptive RETROICOR: IRF-RET: The RETROICOR model is shown in Eqn 1, where thetac,r are physiologic phase, a,bc,r are fit coefficients and sc,r are the modeled noise signals as described in [1]. This is fitted at every voxel (see Fig 1a for phase and RET-2 fit to pulse plethysmograph signal) to obtain coupling coefficients a,b, and are also normalized by variance as tc,r as in Eqn 2,3 by performing a vector sum and dividing by the non-modeled standard deviation. Simulated coupling tsim is determined for each dataset using Monte Carlo method of inputting random phase for theta. This gives us the null distribution of coupling. These are both histogrammed as in Fig 1c and coupling power for card, resp in each model is assessed as the percentage of voxels with greater tc or tr than tsim.