The present work introduces the use of variable-density spiral k-space trajectories for fMRI, and specifically examines their utility in high resolution imaging, where the long readout duration of conventional trajectories often dictate multi-shot acquisitions. In the proposed design, k-space is critically sampled with an Archimedean spiral between the center and a user-defined radius, and extended to the desired spatial resolution with variable-density undersampling. fMRI experiments using sensory stimuli indicate that a single-shot spiral-in/out sequence with this variable-density trajectory is more efficient, and at least as effective, as a conventional 2-shot spiral-in/out sequence in detecting neural activation at high (128×128) resolution.
By reducing the readout duration, the variable-density trajectory allows for reduced sensitivity to motion and off-resonance, improved temporal resolution (and more time frames) for a given spatial coverage, and/or better spatial coverage for a given temporal resolution. Another key advantage of the shortened readout duration of the variable-density spiral is the feasibility of including a spiral-in
component with a reasonable TE for single-shot high resolution fMRI, which can substantially mitigate susceptibility dropout in brain regions near air-tissue interfaces (20
). Current single-shot spiral fMRI at higher resolutions is often performed using a spiral-out trajectory (35
) as a fully Archimedean spiral-in trajectory would necessitate a TE at or beyond the limit of optimal BOLD sensitivity, and an acquisition window of approximately twice that value.
With the variable-density trajectory, there is a tradeoff between the duration of the readout and the severity of high spatial-frequency undersampling. The incomplete sampling of high spatial frequencies raises concerns that aliased signal may obscure true activation or generate false positives. Such effects were not apparent in the current experiments (Figs. and ), perhaps due to the relatively conservative choice of variable-density parameters (r
, α) and because the energy in the high spatial frequencies is small. While it is not possible to gauge absolutely the accuracy of an activation map, the robust localization of activation to the sensory cortices, along with the relatively high correspondence between the maps obtained with the VD and AR2
sequences on a single-subject basis despite potential across-scan variability, suggest that the effect is minor. In addition, though we used a fixed-width convolution kernel for the gridding reconstruction, it has been shown that varying the kernel extent across k-space as a function of the sampling density can further reduce aliasing energy in variable-density trajectories (37
The measured SNR values agreed closely with the theoretical calculation; the SNR of the VD sequence was approximately 15% less than that of the AR2, and the single-shot Archimedean sequence had an SNR reduction of over 30%, primarily from the longer TE necessitated by the associated readout duration of the spiral-in component. Despite the ~15% reduction in uniform-brain SNR of the VD sequence compared to AR2, the fMRI activation results indicate that the contrast-to-noise ratio in fact improved in the SM-event task, likely because of the greater fidelity of the more rapid single-shot acquisition in sampling the hemodynamic response.
In Comparison 2, the VD sequence yielded equal or larger spatial activation volumes in 4 of the 5 subjects, but the advantage did not survive a group-level t-test. Mean t-scores within suprathreshold voxels were, however, significantly greater at the group level with the VD sequence. For some subjects, the two sequences paradoxically yielded comparable activation magnitudes and yet quite different activation volumes (e.g. Subjects 1 and 5; ). In interpreting this result, however, note that larger activation volumes (i.e. number of voxels exceeding a predefined statistical threshold) do not necessarily imply higher mean t-scores, and vice versa. For Subject 5, fewer voxels were detected as activated for VD compared to AR, but among those voxels that did surpass the threshold, the mean t-score value was actually higher than that of the AR scan. Beyond detecting whether a voxel is “activated”, the t-score magnitude is also important as it affects the outcome of group-level voxel-wise statistics.
The fMRI experiments herein used parameter values of r=0.5 and α=3.6 for the VD trajectory. In general, the selection of these parameters can be guided by the desired readout time/TE and minimum FOV, as well as by the PSFs of their associated trajectories. As seen in Fig. and and discussed above, varying (r, α) results in different distributions of aliased energy. The intermediate values (0.5, 3.6) were chosen here for demonstration purposes; however, preliminary experiments revealed that robust fMRI activation was achievable across a range of parameter settings. Allowing r to vary from 0.4 to 0.6 in studies of a small number of subjects did not produce results whose differences exceeded natural inter-session variability, though further studies with larger subject populations might indeed reveal an effect. Reducing the TE from 48 ms to 42 ms in one subject was also found to yield comparable results. Optimal values in this parameter space are likely to vary with the particular spatial and temporal resolution requirements, k-space characteristics of the imaged sample, and brain regions of interest in the fMRI study.
Here, the VD sequence was compared against a 2-shot fully-Archimedean spiral-in/out sequence; for the latter, multiple (2
) shots were used in order to attain acceptable image quality at the desired spatial resolution. Yet, whether it is the most appropriate sequence against which to compare the VD method is perhaps open to discussion. A single-shot fully Archimedean sequence with a spiral-out
readout (with TE=30ms) was included in preliminary experiments but was, as expected (20
), found to produce inferior results compared to the two-shot spiral-in/out, and with excessive signal dropout in air/tissue interfaces. An echo-planar imaging sequence with parallel imaging acceleration was also considered as a point of comparison, and preliminary studies were performed. However, this sequence was ultimately not included in the study due to the SNR disadvantages of accelerated methods at high spatial resolution where thermal noise dominates.
While the present study focused on the use of variable-density spiral for efficient high resolution fMRI, there are other potential applications and alternate implementations. The reduction in readout time may prove useful for signal recovery at higher field strengths (e.g. 7 Tesla) where T2* is severely reduced; at conventional field strengths and lower spatial resolutions, it may reduce signal dropout in brain regions that are compromised by susceptibility-induced field gradients. As an illustration of the latter, shows the SFNR of the spiral-out images for 2 slices acquired at 2.5 × 2.5 mm2
in-plane resolution with a single-shot Archimedean spiral-in/out trajectory (minimum TE=39 ms) and a single-shot variable-density spiral-in/out trajectory (minimum TE = 29 ms). Improved SNR recovery in the orbitofrontal region is observed with the variable-density sequence, due primarily to the shorter TE. In addition, the proposed variable-density design may be implemented in interleaved 2D sequences or in 3D fMRI sequences. 3D methods have been shown to be effective for high-resolution fMRI, where thermal noise dominates physiological noise (38
SFNR maps of spiral-out images for 2 slices (left, right) with a single-shot Archimedean spiral-in/out sequence (AR, above) and a single-shot variable-density spiral-in/out sequence (VD, below). FOV = 22 cm, N=88.