A more accurate account of the effect of k-space sampling and signal decay on the effective spatial resolution in functional MRI

Abstract The effects of k-space sampling and signal decay on the effective spatial resolution of MRI and functional MRI (fMRI) are commonly assessed by means of the magnitude point-spread function (PSF), defined as the absolute values (magnitudes) of the complex MR imaging PSF. It is commonly assumed that this magnitude PSF signifies blurring, which can be quantified by its full-width at half-maximum (FWHM). Here we show that the magnitude PSF fails to accurately represent the true effects of k-space sampling and signal decay. Firstly, a substantial part of the width of the magnitude PSF is due to MRI sampling per se. This part is independent of any signal decay and its effect depends on the spatial frequency composition of the imaged object. Therefore, it cannot always be expected to introduce blurring. Secondly, MRI reconstruction is typically followed by taking the absolute values (magnitude image) of the reconstructed complex image. This introduces a non-linear stage into the process of image formation. The complex imaging PSF does not fully describe this process, since it does not reflect the stage of taking the magnitude image. Its corresponding magnitude PSF fails to correctly describe this process, since convolving the original pattern with the magnitude PSF is different from the true process of taking the absolute following a convolution with the complex imaging PSF. Lastly, signal decay can have not only a blurring, but also a high-pass filtering effect. This cannot be reflected by the strictly positive width of the magnitude PSF. As an alternative, we propose to first approximate the MRI process linearly. We then model the linear approximation by decomposing it into a signal decay-independent MR sampling part and an approximation of the signal decay effect. We approximate the latter as a convolution with a Gaussian PSF or, if the effect is that of high-pass filtering, as reversing the effect of a convolution with a Gaussian PSF. We show that for typical high-resolution fMRI at 7 Tesla, signal decay in Spin-Echo has a moderate blurring effect (FWHM = 0.89 voxels, corresponds to 0.44 mm for 0.5 mm wide voxels). In contrast, Gradient-Echo acts as a moderate high-pass filter that can be interpreted as reversing a Gaussian blurring with FWHM = 0.59 voxels (0.30 mm for 0.5 mm wide voxels). Our improved approximations and findings hold not only for Gradient-Echo and Spin-Echo fMRI but also for GRASE and VASO fMRI. Our findings support the correct planning, interpretation, and modeling of high-resolution fMRI.

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