Synopsis

Studying the diffusion MRI signal as a function of more experimental parameters allows to establish correlations between different chemical and physical properties and to disentangle different compartments. Such measurements are common in the field of physical chemistry to characterise heterogeneous media, but are rendered impractical on human scanners due to hardware limitations. Here, we leverage ultra-strong gradients to acquire a 5-dimensional in-vivo human brain correlation dataset, which allows the characterisation of microstructural features through unconstrained inversion.

Introduction & Background

The concept of studying the signal attenuation as a function of more than one experimental variable has been used extensively in NMR to characterise heterogeneous materials. Motivated by the possibility to distinguish between environments with different physical and chemical properties and to establish correlations between these properties, diffusion-T2-relaxometry varies both b-value and echo time (TE) in repeated spin-echo experiments^1-4. Subsequently, inversion techniques can transform these 2-dimensional signals into a joint diffusivity-T2 distribution⁵.

In the case of anisotropic diffusion, however, a single diffusion-dimension is insufficient to describe the process in each microenvironment. By adding a shape dimension, the medium can now be described by a distribution of diffusion tensors (DTD) with varying shape $$$D_{\Delta}$$$ and size $$$D_{iso}$$$ (i.e. average diffusivity)⁶. Previous work has obtained the full shape-size-DTD in liquid crystals from unconstrained inversion based on data averaged over directions⁷. Fundamentally, this inversion relies on the availability of data with not only different diffusion encoding directions and b-values, but also different encoding “shapes” $$$b_{\Delta}$$$, as characterised by the b-tensor $$$\mathbf{B}$$$^8,9. This approach was only recently further extended to obtain the full shape-size-orientation-DTD – adding another two dimensions $$$\theta$$$ and $$$\phi$$$ – in orientationally ordered liquid crystals¹⁰. The 5-dimensional T2-DTD $$$P$$$ provides a comprehensive description of the chemical composition, density, size, shape, and orientation of a heterogeneous medium:

$$S(TE,b,b_{\Delta},\Theta,\Phi)=S(0)\int^\inf_0\int^\inf_0\int^1_{-1/2}\int^\pi_0\int^{2\pi}_0K(TE,b,b_{\Delta},\Theta,\Phi,T2,D_{iso},D_{\Delta},\theta,\phi)\times P(T2,D_{iso},D_{\Delta},\theta,\phi)d\phi d\theta dD_{\Delta}dD_{iso}dT2.$$

Critically, such measurements have been made on small bore systems with field gradient strengths that outstrip those typically available for human brain imaging. In this work, we translate the multi-dimensional approach to the human brain, leveraging the ultra-strong gradients of a Connectom scanner, and obtain the full T2-DTD without imposing priors on the number of compartments and without fixing parameters. We perform tractography on the DTD, allowing for the visualisation of along-tract properties of the tensor that was used for tract-propagation.

Methods

Data: A healthy volunteer was scanned on a 3T 300mT/m-gradient Siemens Connectom system with a prototype spin-echo sequence that enables diffusion encoding with arbitrary gradient waveforms¹¹. Images with different b-tensors and TE were acquired, yielding a 5-dimensional parameter space (Fig.1). The waveforms were numerically optimized¹², compensated for Maxwell terms¹³ and matched to have similar diffusion times¹⁴. Remaining settings were: no in-plane acceleration, voxel size = 3x3x3 mm3, matrix=70x70, 15 slices, TR=2800ms, partial-Fourier=6/8, bandwidth=2100 Hz/pix

Processing: The data were corrected for misalignment due to subject motion and eddy currents^15,16. The T2-DTD was estimated using a non-negative least squares algorithm that doesn’t assume a fixed number of compartments⁷. Briefly, the inversion is performed via a directed iterative approach wherein randomly generated $$$[T2,\mathbf{D}]$$$ sets are successively fitted to the measured signal in order to find the ten most probable $$$[T2,\mathbf{D}]$$$ solutions. While this approach allows us to obtain a T2-DTD distribution that agrees well with the acquired data, such solutions are by no means unique. Tractography on DTD components with an FA>0.2 was performed using the FiberNavigator¹⁷.

Results

Discussion & Conclusion

The 5-dimensional acquisition protocol presented here results in the most comprehensive in-vivo human brain correlation dataset to-date. The richness of the data allows the characterisation of microstructural features through an unconstrained inversion. Because of the few assumptions, the approach could be invaluable in explorative neuroscience studies in health and disease where it is unclear what type of tissue constituents are present, and could be used together with biophysical or statistical modelling to find more suitable sets of constraints.

We have performed fibre tractography on the full DTD which resulted in bundles consistent with anatomy. The combination of b-tensor shape and T2 makes this protocol highly useful for free water mapping and the investigation of tract- and compartment-specific diffusion properties and T2. The method is flexible and can be scaled down to lower dimensional correlation protocols.

Acknowledgements

References

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