Synopsis

We describe a new approach that enables in vivo whole brain diffusion MRI with simultaneously high spatial resolution (660 µm isotropic voxels) and high angular diffusion encoding resolution (64 orientations at b=1500 s/mm² and 4 b=0 s/mm² images) in only 15 minutes. This is achieved by combining the gSlider-SMS acquisition strategy with constrained image reconstruction techniques that enable denoising (exploiting the fact that the diffusion images are smooth with correlated edge locations) and interlaced data subsampling (achieved by exploiting the same correlated edge constraints used for denoising, as well as through the use of q-space smoothness constraints).

Purpose

Recent progress has shown that in vivo whole-brain diffusion MRI can be acquired with simultaneously high spatial resolution (660 µm isotropic voxels) and high angular diffusion encoding resolution (64 orientations at b=1500 s/mm² and 7 b=0 s/mm² images) in as short as 25 minutes on the 3T CONNECTOM system¹. This was achieved by combining the generalized SLIce Dithered Enhanced Resolution Simultaneous MultiSlice (gSlider-SMS) technique² for SNR-efficient data acquisition with the SNR-enhancing joint reconstruction (SER)^3,4 approach. Other recent work has shown that it possible to accelerate multi-encoding diffusion techniques like reversed-gradient field inhomogeneity correction⁵, gSlider-SMS⁶, and super-resolution reconstruction^7,8 using the concept of “interlaced subsampling.” In this approach, each point in q-space is acquired with only a portion of its nominal set of spatial encodings to save time in data acquisition. While this would normally lead to poor image quality, it has been shown that high-quality image reconstruction is still possible by incorporating spatial and q-space smoothness constraints into the reconstruction^5-8.

In this work, we show that gSlider-SMS, SER, and interlaced subsampling can all be combined together to provide substantial additional acceleration, and demonstrate in vivo human brain images with matching spatial coverage, spatial resolution, and diffusion encoding resolution to that described previously¹, but reducing the acquisition time from 25 minutes to 15 minutes.

Methods

The proposed approach was tested by retrospectively undersampling the same 25 minutes of gSlider-SMS data described previously¹. The conventional gSlider-SMS technique acquires simultaneous multislice diffusion data with slices that are 5x thicker than the nominal resolution, and uses 5 different RF encodings (that apply different phase modulations) to resolve the thinner slices that contribute signal to the thick slice. To simulate interlaced subsampling, we randomly discarded 2 out of 5 RF encodings for each of the 64 diffusion weighted images. We also discarded 3 out of the 7 images acquired without diffusion weighting (b=0 s/mm²), though retained the full set of encodings for the remaining unweighted images. This corresponds to keeping only 213 (58%) of the original 369 image volumes.

For simplicity, thick slices were first reconstructed using standard parallel imaging and simultaneous multislice reconstruction¹. Subsequently, thin slices were estimated by solving the optimization problem: $$\hat{\mathbf{p}} = \arg\min_{\mathbf{p}} \|\mathbf{b} - \mathbf{E} \mathbf{p}\|_2^2 + \lambda_1 J(\mathbf{p}) + \lambda_2 R(\mathbf{p}).$$ The first two terms of this equation correspond to a data consistency constraint ($$$\mathbf{b}$$$ is the vector of acquired data measurements for all voxels, all diffusion encodings, and all RF encodings; $$$\mathbf{E}$$$ is the matrix representing the gSlider mapping from thin slices to subsampled phase modulated thick slices, and also includes the effects of shot-to-shot phase variations induced by the diffusion encoding; and $$$\mathbf{p}$$$ is the vector of high-resolution images to be reconstructed) and a spatial-smoothness regularization constraint for SER^3,4 ($$$J(\cdot)$$$ is constructed based on a shared compound Markov Random Field edge model³, that encourages that image edges should be sparse, with correlation between the edge locations of different images). These two terms are very similar to what was used in previous work that combined gSlider-SMS with SER¹. The third term $$$R(\cdot)$$$ is a regularization penalty that encourages smoothness of the signal in q-space, following previous approaches for interlaced subsampling^5-8. For simplicity and consistent with some of the previous interlaced subsampling work⁵, we choose $$$R(\cdot)$$$ as simply the squared $$$\ell_2$$$-norm of the Laplace-Beltrami smoothness operator applied to the spherical harmonic representation of the q-space signal variations of each voxel⁹. Variables $$$\lambda_1$$$ and $$$\lambda_2$$$ correspond to regularization parameters that were adjusted manually to achieve the desired trade-off between spatial resolution and signal-to-noise ratio.

Our proposed new approach was compared against traditional gSlider-SMS from 25 minutes of data acquisition (without SER and without interlaced subsampling) and gSlider-SMS from 25 minutes of data acquisition with SER (without interlaced subsampling). After images were reconstructed, we computed orientation distribution functions (ODFs) using the Funk-Radon and Cosine Transform¹⁰ (using BrainSuite software, http://brainsuite.org/) and also estimated diffusion tensors.

Results

Discussion and Conclusions

Acknowledgements

References

1. Haldar JP, Fan Q, Setsompop K. “Whole-brain quantitative diffusion MRI at 660 µm resolution in 25 minutes using gSlider-SMS and SNR-enhancing joint reconstruction.” Proc. ISMRM 2016, p. 102.

2. Setsompop K, Stockmann J, Fan Q, Witzel T, Wald LL. “Generalized SLIce Dithered Enhanced Resolution Simultaneous MultiSlice (gSlider-SMS) to increase volume encoding, SNR and partition profile fidelity in high-resolution diffusion imaging.” Proc. ISMRM 2016, p. 607.

3. Haldar JP, Wedeen VJ, Nezamzadeh M, Dai G, Weiner MW, Schuff N, Liang Z-P. “Improved diffusion imaging through SNR-enhancing joint reconstruction.” Magn Reson Med 69:277-289, 2013.

4. Kim JH, Song S-K, Haldar JP. “Signal-to-noise ratio-enhancing joint reconstruction for improved diffusion imaging of mouse spinal cord white matter injury.” Magn Reson Med 75:1499-1514, 2016.

5. Bhushan C, Joshi AA, Leahy RM, Haldar JP. “Improved B0-distortion correction in diffusion MRI using interlaced q-space sampling and constrained reconstruction.” Magn Reson Med 72:128-1232, 2014.

6. Ning L, Setsompop K, Rathi Y. “A combined compressed sensing super-resolution diffusion and gSlider-SMS acquisition/reconstruction for rapid sub-millimeter whole-brain diffusion imaging.” Proc ISMRM 2016, p. 4212.

7. Ning L, Setsompop K, Michailovich O, Makris N, Shenton ME, Westin C-F, Rathi Y. “A joint compressed-sensing and super-resolution approach for very high-resolution diffusion imaging.” NeuroImage 125:386-400, 2016.

8. Van Steenkiste G, Jeurissen B, Veraart J, den Dekker AJ, Parizel PM, Poot DH, Sijbers J. “Super-resolution reconstruction of diffusion parameters from diffusion-weighted images with different slice orientations.” Magn Reson Med 75:181-195, 2016.

9. Descoteaux M, Angelino E, Fitzgibbons S, Deriche R. “Regularized, fast, and robust analytical Q-ball imaging. Magn Reson Med 58:497-510, 2007.

10. Haldar JP, Leahy RM. “Linear transforms for Fourier data on the sphere: Application to high angular resolution diffusion MRI of the brain.” NeuroImage 71:233-247, 2013.

11. Shattuck DW, Chiang MC, Barysheva M, McMahon KL, de Zubicaray GI, Meredith M, Wright MJ, Toga AW, Thompson PM. “Visualization tools for high angular resolution diffusion imaging.” Proc MICCAI 2008, pp. 298-305.