**Additional Comments About fMRI Pre-Processing**

**Quality Assurance**Although all slices should be quickly assessed visually, the

*initial*slices of an fMRI acquisition should be especially scrutinized. This is the time when tissue magnetization may not have not yet reached a steady-state equilibrium and signal intensity may appear artificially high. Most scanners perform one or more “dummy scans” and discard the first 3-5 slices, but this is worth checking. For some experiments it may be desirable to censor even more initial slices (e.g., to allow a subject to acclimatize to loud scanner sounds). Graphical methods (illustrated below) permit rapid identification of outlier data. High-signal outliers result in false areas of activation; low-signal outliers create false areas of deactivation. Additional time series diagnostics include mean voxel intensity, variance of voxel intensity, and temporal signal-to-noise per slice.An option called "Mean Intensity Adjustment" (or one with similar wording) is available in most fMRI software. Its purpose is to remove global fluctuations in average background signal from slice to slice. Before the current era of fully digital RF multi-transmit and receiver chains, this option was more widely used, but is now largely unnecessary for modern scanners operating at 3T or below. Intensity normalization may still be needed for fMRI studies at 7T or higher where RF-inhomogeneities can be more problematic.

**Distortion Correction**__. Basic rapid field mapping is commonly performed as a normal part of automated prescan procedures. In the simplest case a low-resolution dual echo sequence with relatively short__

**Field mapping and unwarping***TE's*is first performed, with computation of magnitude and phase-difference images. The phase-difference images require

*as all phase measurements (however large) are "wrapped" (compressed) over the range of 0°−360°. After phase unwrapping field map values are used to calculate corrective pixel shifts in the phase-encode direction, a process known as*

**unwrapping***(not to be confused with unwrapping above!). Because field map artifacts and noise create problems, some spatial smoothing (often Gaussian) is typically performed as well as masking to exclude voxels outside of the brain. More sophisticated field mapping and unwarping techniques include those that continuously update during data acquisition.*

**unwarping**__. T2*-dephasing creates inhomogeneity in the__

*Z*-shimming*z-*(slice-select)-direction as well as in plane (

*xy*-direction). To restore the signal a compensating gradient along the

*z*-axis is applied to be sure the

*k*-space trajectory returns to the origin at time

*TE*. As commonly implemented, images are collected using 3-4 different positive and negative

*z*-gradients applied immediately after the RF-pulse and then combined using a square root sum of squares approach. The method may also be applied to reduce in-plane artifacts in the phase-encode direction, and a 3D-implementation has also been developed. A major disadvantage of

*z*-shimming is the time penalty, meaning a longer

*TR*with fewer slices and decreased temporal resolution. Additionally, portions of the original image not suffering from susceptibility-induced signal loss can be dephased by the z-shimming gradients and potentially made worse.

It should be noted that distortion correction techniques such as field mapping, unwarping, and

*z*-shimming cannot restore fMRI signals lost due to dephasing. These techniques merely attempt to reassign recorded signals to the proper points in space from which they arose.

**Slice-Timing Correction**Interpolation of the time-shifted data points may be performed by nearest neighbor, tri-linear, multipoint spline, or sinc approximations. Nearest neighbor and linear interpolation are the fastest, but introduce more smoothing artifacts; cubic/multipoint B-spline or (Hanning-windowed) sinc methods are generally preferred. These latter techniques tend to spread the artifact out over a wider range of nearby voxels. Whether to do slice time-correction as a pre-processing step vs post-processing HRF model shifting remains in dispute. Likewise, if the pre-processing option is chosen, whether to do slice-timing correction before or after motion correction is also not agreed upon, and may depend on the expected degree of motion as well as slice order.

**Motion Correction**The iterative minimization procedure used for fMRI motion correction schemes is typically a nonlinear least squares routine (e.g., Levenberg-Marquardt). Possible errors in this process may result from finding only a local (rather than global) minimum of the cost function, leading to suboptimal results. Once motion parameters for realignment have been determined, they are applied to create a new 3D motion-corrected data set. Creation of the corrected data set requires spatial interpolation, as the new data points typically fall in between the original uncorrected data points. This process may be computationally-intensive, so usually some combination of (fast) linear interpolation is used during the initial motion correction steps, followed by a more time-consuming interpolation method (such as windowed sinc) for the final spatial transformation.

Typically head motions are relatively small (<2 mm) during normal fMRI experiments, so the assumptions underlying this rigid body approach are justified. However, sudden abrupt head motion (as seen near volume 245 in the figure above) will violate these conditions and may not produce an appropriate correction for motion.

Rigid body transformations cannot compensate for non-linear effects. These include field inhomogeneity effects, motion during slice acquisition, interpolation artifacts, and spin-excitation history effects. Field inhomogeneity effects may be the most important. Even though rigid head motion can be corrected in image space, head displacements affect magnetic field homogeneity and shimming, so even with perfect realignment some motion-related errors persist. These additional sources of residual motion error are often referred to as the

Typically head motions are relatively small (<2 mm) during normal fMRI experiments, so the assumptions underlying this rigid body approach are justified. However, sudden abrupt head motion (as seen near volume 245 in the figure above) will violate these conditions and may not produce an appropriate correction for motion.

Rigid body transformations cannot compensate for non-linear effects. These include field inhomogeneity effects, motion during slice acquisition, interpolation artifacts, and spin-excitation history effects. Field inhomogeneity effects may be the most important. Even though rigid head motion can be corrected in image space, head displacements affect magnetic field homogeneity and shimming, so even with perfect realignment some motion-related errors persist. These additional sources of residual motion error are often referred to as the

*and may be addressed in part by unwarping (described above).***residual variance**

**Temporal Filtering**Low frequency drifts in fMRI data are very common, and if not accounted for, will severely reduce the power of the statistical analysis. They will also invalidate event-related averaging, which assumes a stationary level of signal over the course of an experiment. Accordingly, removing these drifts is a mandated step for every fMRI study. This must be done carefully, however, as true condition-related signal changes may be inadvertently removed by this process if improperly applied.

Typically, low frequency drifts are removed as part of the preprocessing pipeline. They may also be removed during the post-processing/statistical analysis phase by incorporating them as “nuisance predictors” in the

If the pre-processing route is chosen, then a Fourier frequency filtering method is typically employed. Here, the fMRI signal time course for a voxel is transformed into the frequency domain using a

Typically, low frequency drifts are removed as part of the preprocessing pipeline. They may also be removed during the post-processing/statistical analysis phase by incorporating them as “nuisance predictors” in the

*. Both approaches are commonly used (although not together) with generally similar results.***General Linear Model (GLM)**

If the pre-processing route is chosen, then a Fourier frequency filtering method is typically employed. Here, the fMRI signal time course for a voxel is transformed into the frequency domain using a

*. A certain group of low frequencies (say 1-3 cycles) is removed, and the filtered data retransformed back into the time domain.***Fast Fourier Transform (FFT)**
Because FFT frequency filtering does not work well with purely linear trends, several fMRI software packages first remove linear trends in the time domain with a simple regression tool before transforming into the frequency domain. Additionally Fourier-based filtering techniques may also introduce spurious autocorrelations into the data.
Accounting for low frequency drifts can also be done as a post-processing step, including them as confound predictors in the GLM. Some investigators prefer this approach. In brief, 3-5 additional columns are added to the GLM design matrix ( X) composed of low-frequency waves. These may be a low frequency Fourier basis set of sines and cosines plus a constant linear trend term or a slightly more sophisticated (but closely related) set.discrete cosine transform (DCT) |

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**References**