Optimizing RetroICor and RetroKCor corrections for multi-shot 3D FMRI acquisitions

Abstract

Physiological noise, if unaccounted for, can drastically reduce the statistical significance of detected activation in FMRI. In this paper, we systematically optimize physiological noise regressions for multi-shot 3D FMRI data. First, we investigate whether 3D FMRI data are best corrected in image space (RetroICor) or k-space (RetroKCor), in which each k-space segment can be assigned its unique physiological phase. In addition, the optimal regressor set is determined using the Bayesian Information Criterion (BIC) for a variety of 3D acquisitions corresponding to different image contrasts and k-space readouts. Our simulations and experiments indicate that: (a) k-space corrections are more robust when performed on real/imaginary than magnitude/phase data; (b) k-space corrections do not outperform image-space corrections, despite the ability to synchronize physiological phase to acquisition time more accurately; and (c) the optimal model varied considerably between the various acquisition techniques. These results suggest the use of a tailored set of volume-wide regressors, determined by BIC or other selection criteria, that achieves optimal balance between variance reduction and potential over-fitting.

Keywords: 3D EPI; Brainstem; Functional MRI; GRE; Physiological noise; SPGR; SSFP.

Fig. 1

Reconstruction flowchart for RetroKCor and RetroICor. a: RetroICor corrections take place at the end of the reconstruction pipeline. The physiological noise regression can be included in the FMRI GLM analysis and is (typically) only performed on the magnitude data. b: RetroKCor corrections are performed on the complex k-space data. The residuals are the corrected data, which are further reconstructed to produce the eventual corrected images. Thick arrows represent multi-channel, complex, data, whereas the thin arrows represent combined, magnitude-only, data.

Fig. 2

Simulation experiments. a: the simulation pipeline showing the addition of thermal noise (globally) and physiological fluctuations (within the mask shown on the right). b: example time courses of the simulated noise (SNR = 100, pCNR = 10). c–g: the difference in tSNR after correction with RetroICor (panel c) compared to various optimizations of RetroKCor (panel d–g). Red and blue denote increase and decrease in tSNR after noise correction, respectively.

Fig. 3

2D in-vivo results comparing RetroKCor and RetroICor. a: the change in complex temporal standard deviation (tSD) after RetroKCor regressions on the M/P (left) and R/I channels (right). Here, we show absolute tSD to provide a depiction of the signal power (since percent change in tSNR at outer k-space is misleading). b: RetroKCor vs. RetroICor. Performing the regressions on the R/I channels has a clear advantage for RetroKCor, although small reductions in tSNR (up to 0.5%) can still be observed (denoted by the red arrow). For both cases, red (blue) indicates increased (decreased) temporal stability.

Fig. 4

3D simulation results showing the tSNR within the simulated noise region after regression. a: the effect of regressor resolution. b: the effect of temporal shift. The tSNR when only thermal noise is simulated is 37.8 whereas the tSNR with simulated physiological fluctuations is 19.5 denoted by the striped and dotted line in (b), respectively. The best results are achieved when 64 regressors are used (segment-specific regression). The tSNR drops with decreasing temporal resolution, although the effect is small. When only 1 time-point is used per volume, the optimal reference time-point is the time at which the center k_z-plane is acquired. A shift in either positive or negative direction causes the regression to become less affective.

Fig. 5

The residual variance after single regressor regressions for 2D GRE-EPI (a), 3D GRE-EPI (b), non-synchronized SPGR (c), synchronized SPGR (d), non-synchronized bSSFP (e), and synchronized bSSFP (f). RetroICor results are shown in red and RetroKCor results are shown in black. The mean across subjects is plotted with the error bars representing the standard deviation. The dashed gray line represents the expected residual variance obtained by a regression with a randomly constructed regressor.

Fig. 6

a–c: the residual variance after each model expansion step for 3D GRE-EPI, conventional bSSFP, and cardiac-synchronized bSSFP, respectively. d–f: The corresponding BIC values for each model expansion. The minimum BIC value for each sequence is marked by the red arrow. All plots represent the group mean with error bars representing standard deviation.

Fig. 7

RetroICor BIC results for non-synchronized 3D bSSFP. a: Example image for anatomical reference. b: The number of BIC selected regressors calculated voxelwise. Inferior brain regions and regions of CSF show the largest number of selected voxels. c: the amount of variance reduction when the full set of 22 regressors is used for the regression and d: when the BIC determined model containing four regressors is used. Even with only a few regressors a large amount of variance can be removed.

Fig. 8

Demonstration of the dominance of central k-space in the manifestation of physiological noise in 3D multi-shot volumes. a: Absolute deviation of the simulated multi-shot 3D volume from the instantaneous magnetization during each segment acquisition. The multi-shot volume deviates strongly from the instantaneous magnetization corresponding to outer k-space volumes, but closely matches the instantaneous magnetization at central k-space. This result demonstrates that physiological noise in the multi-shot 3D volume is dominated by the state of magnetization when central k-space is acquired, which is most likely the reason for the success of volume specific regressors like those used in RetroICor. b: the mean signal difference in the area of injected physiological noise averaged across all 150 simulated volumes. Error bars denote one standard deviation.