Optimizing diffusion imaging sequences for examining fiber integrity in the brain is a key issue in neuroscience and radiology research. Past studies based on mathematical theory and computer simulations suggested that around 18-21 gradients might suffice for accurate estimation of FA (Papadakis et al., 2000
), but different studies disagree somewhat on the number of gradients needed to reliably estimate anisotropy indices. Here we improved upon past studies, by studying SNR profiles empirically in a relatively large number of normal subjects. We found that the SNR profiles and tendency to saturate depended on the DTI parameter of interest, each having a different profile of dependency on the scan time. Even so, a direct comparison of different studies is not possible, because the studies by Papadakis and Hasan used simulated data, for which noise is defined mathematically, and we used empirical data instead. There are also differences in the SNR definitions across studies, in that we included the biological variability of the signal over the region of interest, when taking into account the overall profile of variance.
The current study has three main conclusions. The number of diffusion-sensitized gradients affects the signal-to-noise ratio in different ways, for various DTI-derived parameters. For FA and RA, near-optimal SNR was achieved with 62~66 diffusion-sensitized gradients; for MD, this number was 58 and for GA and tGA, this number was about 55, while for VR, SNR increased well beyond 94 gradients. Our SNR plots, for a range of common anisotropy indices, may be useful in designing future acquisition protocols. Very high numbers of gradients were more beneficial when estimating parameters based on high-order products of tensor eigenvalues, which tend to be noisier. Differences in robustness for different DTI-derived measures derive from the arithmetic canceling or boosting of noise in the formulae for each index. The generalized fractional anisotropy (GFA), for example, required very large numbers of gradients to estimate reliably, and its SNR plot had not stabilized even with 100 gradients. Although GFA has been advocated as a good replacement for FA when large numbers of gradients are available, it requires the fitting of a spherical harmonic series expansion to the diffusion profile, which can be unstable unless very high angular sampling is available. Third, we confirmed that there is a special ratio of non-diffusion sensitized images, N(bx)/N(b0), that should also be collected to optimize SNR. Interestingly, this optimal ratio is also parameter-dependent, with values around 26 for VR, 10.57 for FA, 9.17 for RA, 9.13 for GA and tGA. This ratio was higher for some anisotropy indices (VR), lower for others (FA, RA, GA and tGA), and was not relevant at all for measuring mean diffusivity (MD), which is a relatively robust measure, which tends to cancel noise somewhat as the average of the diffusion tensor eigenvalues. Compared to other parameters, MD had relative higher noise resistance, needing fewer gradients to estimate, and fewer baseline signals.
The saturation number of each index should not be considered as a measure of the quality of each index for assessing biological characteristics of the white matter, such as fiber integrity. In our past studies, we found that FA outperformed GFA in terms of its correlation with IQ scores, even in 94-gradient scans that were expected to be sufficient to allow an accurate measure of GF (Chiang et al., 2008
); we also found that genetic influences on fiber characteristics were marginally more evident with tGA than FA, perhaps partly because the geodesic anisotropy takes into account the manifold structure of the diffusion tensors, when comparing them (Lee et al., 2008
). Ultimately, even if over 100 gradients are insufficient to reliably estimate GFA, it may not be any more useful for certain time-limited applications, even if it carries potentially different information not provided by other anisotropy indices.
Furthermore, there are several caveats regarding this study. Past studies relied mainly on computer simulations, which may not fully reflect the true sources of noise in a human subject’s scan. Even so, the achievable SNR in empirical data will also inevitably depend on the scanner, the magnetic field strength (here 4 Tesla), the spatial resolution, and circumstantial factors such as the amount of subject motion in the scanner. The issue of subject-specific variations was somewhat alleviated in the current study, as we examined 50 subjects’ scans, deriving plots for the minimum and maximum SNR achieved, as well as its mean profile, in a representative group of subjects. Even so, care may be needed in extrapolating our results to other scanners and field strengths. Second, if a study is designed to detect group differences in DTI (e.g., comparing patients with Alzheimer’s disease to groups of normal subjects), the image SNR is not the only relevant source of variation to consider – biological variability may be very high or relatively low, or the available sample sizes may be very high, so other considerations may supervene, and outweigh the need for very high SNR in each scan. Although our current study focuses on SNR improvement, whether or not this increased SNR translates into smaller minimal sample sizes to detect clinically relevant effects depends on the biological variation in these measures across subjects. Landman et al. (2007)
also noted that the estimated orientation of the diffusion tensor (principal eigenvector) depends not just on the angular sampling, but also on patient motion, field inhomogeneity, and EPI-related distortions. Thus, further studies of scanner field strength, spatial resolution, tolerability, motion artifacts, test/re-test reliability, and clinical effect sizes are needed to evaluate the added benefit of HARDI’s SNR for radiologic and neuroscientific studies.
Finally, in considering the trade-off between SNR and scan time, alternative uses of the scan time must also be taken into account, such as acquiring other potentially interesting MRI sequences (e.g., spectroscopy or FLAIR scans), minimizing patient burden, and minimizing the risk of non-compliance with longer scan times (i.e., losing the scan altogether). High-angular resolution acquisitions are time-consuming to collect, but it must be conceded that they may provide new insight into fiber architecture and connectivity that cannot be achieved, even in principle, using smaller numbers of gradients. Tractography studies, for example, derive angular information on local fiber trajectories, and tend to benefit from higher angular resolution well beyond the sampling limits where the SNR profiles for scalar anisotropy measures are saturated. Even so, these calibration plots may be of interest in designing future DTI protocols for assessing fiber integrity in the living brain.