Linear multi‐scale modeling of diffusion MRI data: A framework for characterization of oriented structures across length scales

Diffusion‐weighted magnetic resonance imaging (DW‐MRI) has evolved to provide increasingly sophisticated investigations of the human brain's structural connectome in vivo. Restriction spectrum imaging (RSI) is a method that reconstructs the orientation distribution of diffusion within tissues over a range of length scales. In its original formulation, RSI represented the signal as consisting of a spectrum of Gaussian diffusion response functions. Recent technological advances have enabled the use of ultra‐high b‐values on human MRI scanners, providing higher sensitivity to intracellular water diffusion in the living human brain. To capture the complex diffusion time dependence of the signal within restricted water compartments, we expand upon the RSI approach to represent restricted water compartments with non‐Gaussian response functions, in an extended analysis framework called linear multi‐scale modeling (LMM). The LMM approach is designed to resolve length scale and orientation‐specific information with greater specificity to tissue microstructure in the restricted and hindered compartments, while retaining the advantages of the RSI approach in its implementation as a linear inverse problem. Using multi‐shell, multi‐diffusion time DW‐MRI data acquired with a state‐of‐the‐art 3 T MRI scanner equipped with 300 mT/m gradients, we demonstrate the ability of the LMM approach to distinguish different anatomical structures in the human brain and the potential to advance mapping of the human connectome through joint estimation of the fiber orientation distributions and compartment size characteristics. Linear Multi‐scale Modeling (LMM) for diffusion weighted MRI enables a detailed microstructural tissue characterization by separating orientation distributions of restricted and hindered diffusion water compartments over a range of length scales. We demonstrate the ability of LMM to estimate volume fractions, compartment sizes and orientation distributions utilizing both simulations as well as empirical data from healthy subjects using a human 3T MRI scanner equipped with a 300 mT/m gradient system.