Magn Reson Imaging
Department of Biophysics, Medical College of Wisconsin, Milwaukee, WI 53226, USA.
Published: December 2009
In functional magnetic resonance imaging (fMRI), the process of determining statistically significant brain activation is commonly performed in terms of voxel time series measurements after image reconstruction and magnitude-only time series formation. The image reconstruction and statistical activation processes are treated separately. In this manuscript, a framework is developed so that statistical analysis is performed in terms of the original, prereconstruction, complex-valued k-space measurements. First, the relationship between complex-valued (Fourier) encoded k-space measurements and complex-valued image measurements from (Fourier) reconstructed images is reviewed. Second, the voxel time series measurements are written in terms of the original spatiotemporal k-space measurements utilizing this k-space and image relationship. Finally, voxelwise fMRI activation can be determined in image space in terms of the original k-space measurements. Additionally, the spatiotemporal covariance between reconstructed complex-valued voxel time series can be written in terms of the spatiotemporal covariance between complex-valued k-space measurements. This allows one to utilize the originally measured data in its more natural, acquired state rather than in a transformed state. The effects of modeling preprocessing in k-space on voxel activation and correlation can then be examined.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2783194 | PMC |
http://dx.doi.org/10.1016/j.mri.2009.05.048 | DOI Listing |
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