Synopsis

Double diffusion encoding (DDE) allows the estimation of microscopic fractional anisotropy (μFA), which is a promising metric for studying microstructural properties of brain tissue independent of orientation dispersion. However, a large number of acquisitions is needed to obtain a rotationally invariant measurement of μFA, which poses a problem in clinical settings. A DDE protocol with a reduced number of acquisitions has recently been proposed as a solution. In this study, we assessed the accuracy of this approach and its potential for reporting μFA accurately. Our results show that a reduced number of acquisitions is sufficient for characterizing μFA.

Introduction

Theory

μFA can be calculated as

$$\mu FA=\sqrt{\frac{3}{2}} \sqrt{\frac{\varepsilon}{\varepsilon+\frac{3}{5}\text{MD}^2}},\,\,\,\,\,\,\,\,\,\,(1)$$

where $$$\varepsilon=\text{ln}(S^{PA}_{||}/S^{PA}_{\perp})b^{-2}$$$ is quantified from the powder averaged data acquired with parallel and orthogonal gradient pulse pairs, and MD stands for mean diffusivity ². The DDE 5-design holds up to the fifth order of the cumulant expansion and requires 12 parallel and 60 orthogonal gradient pulse pairs for powder-averaging the data (Figure 1A) ². In case of Gaussian diffusion, some of the orthogonal gradient pulse pairs measure the same in-plane diffusion tensor trace, and are thus redundant. We sought to test Yang’s hypothesis that 6 parallel and 6 orthogonal gradient pulse pair directions can closely approximate $$$\varepsilon$$$ ³ (Figure 1B).

Methods

All experiments were approved by the local competent authority.

Specimen preparation. A rat brain (N=1) was extracted through standard transcardial perfusion. The rat brain was inserted into a fluorinert filled tubed and placed in the scanner at 23 ° C.

Data acquisition. All experiments were performed on a 9.4 T Bruker BioSpec scanner harnessing an 86 mm volume coil for transmission and 4-element array cryocoil for reception. An in-house DDE-EPI pulse sequence was used with b = 0, 1000, 2000, 3000 s/mm², δ = 5 ms, ∆ = t_m = 15 ms, TE = 69 ms, TR = 1 s, voxel size = 0.2 x 0.2 x 0.8 mm, FOV = 20 mm x 20 mm, partial Fourier = 1.25, and double sampling.Three slices were acquired with a slice gap of 0.5 mm.

We compared the five-design (A) and the clinical directional scheme (B), which are shown in figure 1. To maximize SNR and to match acquisition number in both, acquisitions in A were averaged 30 times and acquisitions in B were averaged 90 times. We used 12 symmetric acquisitions in B instead of 6 to eliminate possible artifacts arising from cross-terms between the imaging and diffusion gradients.

Image analysis. Data was denoised using a Marchenko-Pastur-PCA denoising procedure ⁵, and Gibbs ringing artifacts were reduced using a sub-voxel shift algorithm ⁶. Voxel-specific SNR was quantified as the standard deviation divided by the mean signal over 39 b0-images. Registration was done with single-step DFT algorithm ⁷. Mean diffusivity was estimated by fitting a diffusion tensor to the parallel data at b = 1000 s/mm². $$$\varepsilon$$$ was fit to multi-shell data. μFA was calculated using equation 1. Synthetic Rician noise was added to the data to artificially lower SNR.

Results and discussion

The high quality of pre-processed data is highlighted in figure 2.

When comparing the two sets of directions using multi-shell data, we find similar µFA values for the studied b-values (Figure 3). Voxel-wise comparison of the two µFA maps reveals excellent agreement between the two methods: Pearson’s correlation coefficient = 0.91, mean difference = 0.015, std = 0.07 (Figure 4). Similar variance (Pearson's correlation coefficient = 0.92, mean difference = 0.002, std = 0.06) was observed when the 5-design experiment was repeated. The cost of reducing the number of orthogonal gradient pulse pairs is small.

After confirming that the reduced directions are sufficient for accurately quantifying μFA using multi-shell data, we studied the minimum SNR for obtaining acceptable μFA maps with just 24 acquisitions. Clinically acceptable protocol duration is less than ten minutes, which limits SNR. The effect of noise on the minimal acquisition protocol’s single-shell μFA estimates at b = 3000 s/mm² are shown in figure 5. An SNR of 40 in non-diffusion-weighted images appears to be the very minimum for measuring μFA at b = 3000 s/mm².

Conclusion

We have shown that the accuracy of the clinical directional scheme is comparable to that of the 5-design, and that, given sufficient SNR, μFA can be precisely estimated with just 24 acquisitions rather than the 72 required for using the 5-design. This study thus encourages the use of DDE in the clinic for microstructural imaging.

Acknowledgements

References

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