Variable density spiral fMRI

Introduction: In the original variable-density (VD) spiral trajectory[1], the sampling density varies throughout the k-space trajectory; i.e., k(τ) = λτe , where the parameter α controls the rate of density variation. Here, we propose a k-space trajectory consisting of an Archimedean spiral[2] from the origin out to a given radius k1, and extending beyond k1 with a variable-density spiral of α>1 (Eq.1, Fig.1). This design allows for a reduction in readout time at the expense of under-sampling only the high spatial frequencies, which may provide flexibility for improving the performance of either normalor high-resolution fMRI. We introduce the use of this trajectory in fMRI of the human brain, demonstrating that the VD spiral permits the use of a single-shot spiral-in/out[3] trajectory for high (128x128) resolution. To obtain high-resolution (128x128) functional images, a conventional (fully Archimedean) spiral takes 59.8 ms to traverse k-space; note that an EPI trajectory would take even longer (60.1 ms for partial k-space). Such a long readout exacerbates signal dropout, particularly in susceptibility regions. Thus, one typically uses an interleaved (2-shot) spiral-in/out acquisition in which half of the k-space trajectory is gathered in each interleave. However, the interleaved acquisition suffers a loss of temporal resolution and allows fewer time frames to be acquired within the same total scan time, and in addition may experience aliasing due to gradient imperfections. We therefore hypothesized that a spiral-in/out with our proposed VD trajectory, which would permit a shorter TE and more rapid readout without interleaving, might yield improved BOLD sensitivity and statistical power compared to both the conventional spiral-in/out and interleaved spiral-in/out acquisitions. Methods: The proposed VD spiral trajectory, parameterized by k1 and α, is given by