Synopsis

While diffusion MRI tractography has provided important insights on the human brain connectome, fibre-tracking through heterogeneous voxels has proven to be a challenging endeavour. Recently, we devised MRI acquisition- and processing methods to resolve sub-voxel heterogeneity with nonparametric 5D relaxation-diffusion distributions where contributions from distinct tissues are separated while circumventing the use of limiting assumptions. The separation between tissue-signals provides a clean mapping of nerve fibres that can then be used as an input in fibre-tracking algorithms. Additionally, values of relaxation rates and diffusivities are estimated for each distinct fibre bundle, potentially giving tract-specific information on chemical composition and microstructure.

Introduction

Methods

In vivo human brain data: A healthy volunteer was scanned on a 3T Siemens MAGNETOM Prisma equipped with a 32-channel receiver head-coil, using an EPI sequence customised for variable echo times (TE) and b-tensor diffusion encoding^5,7. Images with different b-tensors and TE were acquired, yielding a 5D acquisition space (Fig.1a) whose dimensions match those of the sought-for R₂-D distributions. Tensor-valued diffusion encoding was performed with numerically optimised waveforms⁸ that were both spectrally-matched⁹ and Maxwell-compensated¹⁰. All images were recorded using TR=4 s, FOV=234×234×60 mm³, voxel-size=3×3x3 mm³, partial-Fourier=6/8, and iPAT=2 (GRAPPA).

Phantom data: Data was acquired on a liquid crystalline sample featuring several microscopic domains wherein water diffusion is highly anisotropic¹¹. The sample was prepared so that different domains have different orientations relative to the laboratory frame of reference. The liquid crystal was measured on an 11.7T Bruker micro-imaging system, using a single-shot RARE sequence allowing for R₂ weighting, and diffusion encoding with arbitrary gradient waveforms¹². Remaining settings were: voxel-size 37.5x37.5x600 μm³, 5 slices, and TR=1s. The phantom data was used to showcase the effects of R₂-dispersion on the estimation of fibre-orientations, and to validate the proposed framework.

Relaxation-diffusion distributions: Spatially-resolved R₂-D distributions were retrieved from the 5D datasets using an unconstrained Monte-Carlo algorithm¹³. Avoiding common regularisation metrics¹⁴, we estimate for each imaging voxel an ensemble of 96 plausible solutions, each of which consists of 10 (R₂,D_A,D_R,θ,φ)_i=1:10 nodes and their respective P_i=1:10(R₂,D_A,D_R,θ,φ) weights.

ODF estimation: Binning the R₂-D space separates the contributions from anisotropic tissue components (Fig. 1b). The corresponding sets of bin-resolved P_i=1:10(R₂,D_A,D_R,θ,φ) weights were then convolved onto a sphere using a Watson distribution kernel¹⁵. Averaging the 96 sets of spherically convolved distributions results in smooth Orientation Distribution Functions (ODF), independently estimated for each voxel. Because each point of the smooth distributions is assigned to a specific (R₂,D_A,D_R,θ,φ) coordinate, we can assign any individual dimension of the R₂-D space to specific ODF-peaks. FiberNavigator¹⁶ was used to extract tracts connecting the three highest local maxima of the per-voxel ODFs.

Results & Discussion

Phantom experiments (Fig. 2a) show that diffusion-weighted data measured at a single TE may lead to an underestimation of signal fractions of high-R₂ components. Even though the phantom possesses a homogeneous chemical composition, ODF maps computed at higher TE seem to indicate a non-uniform spatial distribution of water. In this case, this is attributed to a R₂-dependency on domain orientation. Acquiring data at multiple TE and subsequent retrieval of R₂-D distributions not only yields more accurate ODFs, but also allows mapping of peak-specific R₂ contributions (Fig. 2b).

For human brain data, 5D R₂-D distributions allow the quantification of distinct cerebral tissues without relying on assumptions about the number or properties of individual components (Fig. 1b). The directionally-coloured ODFs from anisotropic tissue components are displayed in Fig. 3. Anatomically-plausible fibre tracks were reliably extracted from the ODF maps (Fig.4). Fig. 5 shows colouring of the ODF peaks according to the sub-voxel values of R₂, D_iso = (D_A+2D_R)/3, and D_Δ² = (D_A–D_R)²/9D_iso². Unlike the phantom-data, no R₂-orientational dependence was discernible in the in vivo data. Nevertheless, correlating R₂ with microscopic D leads to an improved mapping of anisotropic tissue-compartments, for example in the caudate nucleus (white arrows in Fig. 5).

Conclusion

Acknowledgements

This work was financially supported by the Swedish Foundation for Strategic Research (AM13-0090) and the Swedish Research Council (2009–6794, 2014–3910). In vivo data was acquired at the UK National Facility for In Vivo MR Imaging of Human Tissue Microstructure funded by the EPSRC (grant EP/M029778/1), and The Wolfson Foundation. The authors are also grateful to the Netherlands Organisation for Scientific Research (NWO) (680-50-1527), the Wellcome Trust, UK (grants 096646/Z/11/Z and 104943/Z/14/Z), the Whitaker Fellowship, and the Natural Sciences and Engineering Research Council of Canada (NSWERC) (PDF-502385-2017) for supporting this research.

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