Imaging diffusional variance by MRI [public] : The role of tensor-valued diffusion encoding and tissue heterogeneity

Diffusion MRI provides a non-invasive probe of tissue microstructure. We recently proposed a novel method for diffusion-weighted imaging, so-called q-space trajectory encoding, that facilitates tensor-valued diffusion encoding. This method grants access to b-tensors with multiple shapes and enables us to probe previously unexplored aspects of the tissue microstructure. Specifically, we can disentangle diffusional heterogeneity that originates from isotropic and anisotropic tissue structures; we call this diffusional variance decomposition (DIVIDE).In Paper I, we investigated the statistical uncertainty of the total diffusional variance in the healthy brain. We found that the statistical power was heterogeneous between brain regions which needs to be taken into account when interpreting results.In Paper II, we showed how spherical tensor encoding can be used to separate the total diffusional variance into its isotropic and anisotropic components. We also performed initial validation of the parameters in phantoms, and demonstrated that the imaging sequence could be implemented on a high-performance clinical MRI system. In Paper III and V, we explored DIVIDE parameters in healthy brain tissue and tumor tissue. In healthy tissue, we found that diffusion anisotropy can be probed on the microscopic scale, and that metrics of anisotropy on the voxel scale are confounded by the orientation coherence of the microscopic structures. In meningioma and glioma tumors, we found a strong association between anisotropic variance and cell eccentricity, and between isotropic variance and variable cell density. In Paper IV, we developed a method to optimize waveforms for tensor-valued diffusion encoding, and in Paper VI we demonstrated that whole-brain DIVIDE is technically feasible at most MRI systems in clinically feasible scan times

Voxelwise spectral diffusional connectivity and its applications to Alzheimer's disease and intelligence prediction.

Human brain connectivity can be studied using graph theory. Many connectivity studies parcellate the brain into regions and count fibres extracted between them. The resulting network analyses require validation of the tractography, as well as region and parameter selection. Here we investigate whole brain connectivity from a different perspective. We propose a mathematical formulation based on studying the eigenvalues of the Laplacian matrix of the diffusion tensor field at the voxel level. This voxelwise matrix has over a million parameters, but we derive the Kirchhoff complexity and eigen-spectrum through elegant mathematical theorems, without heavy computation. We use these novel measures to accurately estimate the voxelwise connectivity in multiple biomedical applications such as Alzheimer's disease and intelligence prediction

Voxelwise spectral diffusional connectivity and its applications to Alzheimer's disease and intelligence prediction.

Human brain connectivity can be studied using graph theory. Many connectivity studies parcellate the brain into regions and count fibres extracted between them. The resulting network analyses require validation of the tractography, as well as region and parameter selection. Here we investigate whole brain connectivity from a different perspective. We propose a mathematical formulation based on studying the eigenvalues of the Laplacian matrix of the diffusion tensor field at the voxel level. This voxelwise matrix has over a million parameters, but we derive the Kirchhoff complexity and eigen-spectrum through elegant mathematical theorems, without heavy computation. We use these novel measures to accurately estimate the voxelwise connectivity in multiple biomedical applications such as Alzheimer's disease and intelligence prediction