Brain Microstructure Mapping from diffusion MRI using Least Squares Variable Separation

We introduce a novel data fitting procedure of multicompartment models for diffusion MRI (dMRI) data of the brain white matter. These biophysical models aim to characterize important microstructure quantities like axonal radius, density and orientations. In order to describe the underlying tissue properties, a variety of models for intra-/extra-axonal diffusion signals have been proposed. Combinations of these analytic models are used to predict the diffusion MRI signal in multi-compartment settings. However, parameter estimation from these multi-compartment models is an ill-posed problem. Consequently, many existing fitting algorithms either rely on an initial brute force grid search to find a good start point, or have strong assumptions like single fiber orientation to estimate some of these parameters from simpler models like the diffusion tensor (DT). In both cases, there is a tradeoff between computational complexity and accuracy of the estimated parameters. Here, we describe a novel algorithm based on the separation of the Nonlinear Least Squares (NLLS) fitting problem, via Variable Projection Method, to search for nonlinearly and linearly entering parameters independently. We use stochastic global search algorithms to find a global minimum, while estimating nonlinearly entering parameters. The approach is independent of any starting point, and does not rely on estimates from simpler models. We show that the suggested algorithm is faster than algorithms involving grid search, and its greater accuracy and robustness are demonstrated on synthetic as well as real data.