Fig. 5. Avoiding “heavy tails” in ACF via acquisition strategy.
Simulations depict two strategies to achieve the same final spatial resolution (4 mm). We generated synthetic time-series noise consisting of a thermal noise component and a physiological noise component. The synthetic thermal noise component was white-noise by design and therefore its spatial autocorrelation function is a Gaussian with a one-pixel FWHM. The physiological noise component was synthesized to have strong spatial autocorrelation out to 40 mm FWHM. These two sources were combined with weightings reflecting the σp/σ0 ratios seen in common fMRI acquisitions. The two strategies toward achieving the same final spatial resolution fMRI map were compared. (A) Acquire small voxels (1 mm isotropic) and spatially smooth to 4 mm. For 3T 32-channel coil acquisitions this is expected to be firmly thermal noise-dominated at acquisition. A thermal/physiological ratio of σp/σ0 = 0.75 and Gaussian smoothing kernel of 3.87 mm were used. (B) Acquire conventionally-sized voxels (3 mm isotropic) and smooth to 4 mm. In this case the acquisition is firmly physiologically noise dominated for the 32-channel coil at 3T. The measured thermal/physiological ratio σp/σ0 = 3.0 and Gaussian smoothing kernel of 2.65 mm were used.
Even though both acquisition/smoothing strategies were chosen to result in the same final spatial resolution (4 mm), only the strategy used in A (high spatial resolution, thermal noise dominated acquisition) results in a final ACF (solid red line) that is well described by a Gaussian function (best-fit Gaussian is shown in dashed red line). The strategy used in B (conventional resolution acquisition dominated by physiological noise) results in an ACF that deviates strongly from Gaussian, especially in the tails of the distribution, due to the long-range spatial correlations seen in physiological noise.