Estimation of Respiration-Induced Noise Fluctuations From Undersampled Multislice fMRI Data Lawrence R. Frank, 1,3 * Richard B. Buxton, 1 and Eric C. Wong 1,2 Functional MRI time series data are known to be contami- nated by highly structured noise due to physiological fluctu- ations. Significant components of this noise are at frequen- cies greater than those critically sampled in standard multi- slice imaging protocols and are therefore aliased into the activation spectrum, compromising the estimation of func- tional activations and the determination of their significance. However, in this work it is demonstrated that unaliased noise information is available in multislice data, and can be used to estimate and reduce noise due to high-frequency respirato- ry-related fluctuations. Magn Reson Med 45:635– 644, 2001. Published 2001 Wiley-Liss, Inc. † Key words: functional magnetic resonance imaging; physiolog- ical noise; data analysis; multislice imaging; physiological fluc- tuations The analysis of functional magnetic resonance imaging (fMRI) time series data is complicated by the fact that the noise is not Gaussian (1–5). This is a consequence of the fact that the dominant contributions to the noise in fMRI are signal variations produced by physiological processes, rather than by the thermal noise. These physiologically related signal fluctuations are generally quite complicated and can have significant power over a wide range of fre- quencies. Moreover, these fluctuations can be correlated with one another, producing sidebands with significant power. The dominant contributions appear to be high- frequency fluctuations related to the quasiperiodic pro- cesses of respiration and cardiac pulsations, and low-fre- quency fluctuations, which can result from slow drifts in the time series, but have also been hypothesized to be related to noise correlations produced by the hemody- namic response of the brain (1,6). In spite of the complexities of the spectrum of noise fluctuations, estimation of functional activation can still be relatively straightforward even in the presence of such fluctuations, provided that its spectrum is not overlapped by that of the noise fluctuations, and that the data sam- pling rate is sufficient to critically sample the spectrum of the noise. If these conditions hold, standard methods of filtering can be applied (7) to reduce unwanted noise com- ponents. Unfortunately, while it is possible to collect data in a single slice at a rate sufficient to critically sample high-frequency physiological fluctuations, virtually no fMRI experiments are actually done in this way. Rather, multislice acquisitions are performed in order to achieve adequate spatial coverage. With the typical imaging pa- rameters used in multislice studies, the sampling rate for each slice is not sufficient to critically sample the physio- logical fluctuations, and the resulting time series noise is contaminated by aliased spectral components from the high-frequency physiological fluctuations. This not only reduces both functional signal-to-noise ratio (SNR) and significance of the estimates, but makes improper the use of many well-developed standard estimation techniques based on Gaussian noise models. However, in this work we show that it is possible to obtain unaliased information about the noise structure directly from multislice echo-planar imaging (EPI) fMRI time series data. This is achieved by noting two impor- tant features of such fMRI data: 1) Some physiological fluctuations are relatively global in nature and are there- fore present in the central k-space components. 2) Sur- prisingly, physiological fluctuations are critically sam- pled and obtainable in most multislice EPI data acqui- sitions if the data is reordered into temporal, rather than spatial, order (8). EXPERIMENTAL METHODS A natural way to assess the problem of noise in multislice fMRI is to compare two data sets acquired during the same stimulation paradigm: one acquired in a multislice fash- ion, and one in a rapidly sampled acquisition in a single- slice location as one of the multislice locations. To make the data sets more easily comparable, the same imaging parameters (except those related to slice acquisition) are used and, for reasons that will become clear, the repetition time in the multislice acquisition is set to the repetition time of the single-slice acquisition times the number of slices, so that the time between each data acquisition step, which we term the “effective sampling rate,” is the same in both experiments. All images were acquired on a 1.5T GE Signa LX system using a single-shot EPI acquisition. Images in both data sets acquired in the sagittal plane with imaging parameters FOV = 24 cm, slice thickness = 7 mm, TE = 40 msec, 64 matrix. The stimulation in both data sets was a simple visual field stimulation study (8 Hz flashing checkerboard) presented in a block design paradigm in order to simplify the spectrum of the activation: the stimulus was presented at a rate of 1 per sec, with the stimulus on for 16 sec and off for 16 sec, and thus a stimulation period = .03125 Hz. In the first data set, data were collected on a single slice with a very short repetition time ( TR = .25 sec) in order to critically sample what we hypothesize to be the largest 1 Department of Radiology, University of California at San Diego, San Diego, California. 2 Department of Psychiatry, University of California at San Diego, San Diego, California. 3 San Diego VA Healthcare System, San Diego, California. Grant sponsor: VA Merit Review; Grant number: SA321. *Correspondence to: Lawrence R. Frank, Ph.D., VA Medical Center, 9114/ MRI, 3350 La Jolla Village Drive, San Diego, CA 92161. E-mail: lfrank@ucsd.edu Received 8 February 2000; revised 25 October 2000; accepted 26 October 2000. Magnetic Resonance in Medicine 45:635– 644 (2001) Published 2001 Wiley-Liss, Inc. † This article is a US Government work and, as such, is in the public domain in the United States of America. 635