A Mathematical Model for Understanding the STatistical effects of k-space (AMMUST-k) preprocessing on observed voxel measurements in fcMRI and fMRI

Image processing is common in functional magnetic resonance imaging (fMRI) and functional connectivity magnetic resonance imaging (fcMRI). Such processing may have deleterious effects on statistical maps computed from the processed images. In this manuscript, we describe a mathematical framework to evaluate the effects of image processing on observed voxel means, covariances and correlations resulting from linear processes on k-space and image-space data. We develop linear operators for common image processing operations, including: zero-filling, apodization, smoothing and partial Fourier reconstruction; and unmodeled physical processes, including: Fourier encoding anomalies caused by eddy currents, intra-acquisition decay and magnetic field inhomogeneities. With such operators, we theoretically compute the exact image-space means, covariances and correlations which result from their common implementation and verify their behavior in experimental phantom data. Thus, a very powerful framework is described to consider the effects of image processing on observed voxel means, covariances and correlations. With this framework, researchers can theoretically consider observed voxel correlations while understanding the extent of artifactual correlations resulting from image processing. Furthermore, this framework may be utilized in the future to theoretically optimize image acquisition parameters, and examine the order of image processing steps.

[1]  G H Glover,et al.  Image‐based method for retrospective correction of physiological motion effects in fMRI: RETROICOR , 2000, Magnetic resonance in medicine.

[2]  P. Bandettini,et al.  Single‐shot half k‐space high‐resolution gradient‐recalled EPI for fMRI at 3 tesla , 1998, Magnetic resonance in medicine.

[3]  Andrew S. Nencka,et al.  Improving robustness and reliability of phase-sensitive fMRI analysis using temporal off-resonance alignment of single-echo timeseries (TOAST) , 2009, NeuroImage.

[4]  J R Reichenbach,et al.  Commutator filter: A novel technique for the identification of structures producing significant susceptibility inhomogeneities and its application to functional MRI , 1996, Magnetic resonance in medicine.

[5]  B. Biswal,et al.  Functional connectivity in the motor cortex of resting human brain using echo‐planar mri , 1995, Magnetic resonance in medicine.

[6]  P. Jezzard,et al.  Correction for geometric distortion in echo planar images from B0 field variations , 1995, Magnetic resonance in medicine.

[7]  Daniel B. Rowe Modeling both the magnitude and phase of complex-valued fMRI data , 2005, NeuroImage.

[8]  Karl J. Friston,et al.  The slice-timing problem in event-related fMRI , 1999 .

[9]  Apodization and Smoothing Alter Voxel Time Series Correlations , 2008 .

[10]  G. Glover,et al.  Correction of physiologically induced global off‐resonance effects in dynamic echo‐planar and spiral functional imaging , 2002, Magnetic resonance in medicine.

[11]  E. Formisano,et al.  Functional connectivity as revealed by spatial independent component analysis of fMRI measurements during rest , 2004, Human brain mapping.

[12]  Daniel B. Rowe,et al.  A complex way to compute fMRI activation , 2004, NeuroImage.

[13]  Peter A. Bandettini,et al.  Separating respiratory-variation-related fluctuations from neuronal-activity-related fluctuations in fMRI , 2006, NeuroImage.

[14]  Stephen M. Smith,et al.  Improved Optimization for the Robust and Accurate Linear Registration and Motion Correction of Brain Images , 2002, NeuroImage.

[15]  Nikolaus Kriegeskorte,et al.  Artifactual time‐course correlations in echo‐planar fMRI with implications for studies of brain function , 2008, Int. J. Imaging Syst. Technol..

[16]  Jeff H. Duyn,et al.  Low-frequency fluctuations in the cardiac rate as a source of variance in the resting-state fMRI BOLD signal , 2007, NeuroImage.

[17]  D. Rowe,et al.  Image Space Correlations Induced by K-Space Processes , 2007 .

[18]  D. Rowe,et al.  Signal and noise of Fourier reconstructed fMRI data , 2007, Journal of Neuroscience Methods.

[19]  Michael Brady,et al.  Improved Optimization for the Robust and Accurate Linear Registration and Motion Correction of Brain Images , 2002, NeuroImage.

[20]  Jack Dongarra,et al.  Preface: Basic Linear Algebra Subprograms Technical (Blast) Forum Standard , 2002 .

[21]  Yu-Chung N. Cheng,et al.  Magnetic Resonance Imaging: Physical Principles and Sequence Design , 1999 .

[22]  Karl J. Friston,et al.  Functional Connectivity: The Principal-Component Analysis of Large (PET) Data Sets , 1993, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[23]  Daniel B. Rowe,et al.  Complex fMRI analysis with unrestricted phase is equivalent to a magnitude-only model , 2005, NeuroImage.

[24]  D. Rowe,et al.  The use of Three Navigator Echoes in Cartesian EPI Reconstruction Reduces Nyquist Ghosting , 2007 .

[25]  Wilson Fong Handbook of MRI Pulse Sequences , 2005 .