Estimating Diffusion Tensor Distributions With Neural Networks

Abstract: Magnetic Resonance Imaging (MRI) is an essential healthcare technology, with diffusion MRI being a specialized technique. Diffusion MRI exploits the inherent diffusion of water molecules within the human body to produce a high-resolution tissue image. An MRI image contains information about a 3D volume in space, composed of 3D units called voxels. This thesis assumes the existence of a probability distribution for the diffusivity within a voxel, the diffusion tensor distribution (DTD), with the diffusivity described by a family of diffusion tensors. In 2D, these tensors can be described by 2x2 symmetric positive semidefinite matrices. The objective is to estimate the DTD of a voxel with neural networks for both 1D and 2D diffusion tensors. We assume the DTD to be a discrete distribution, with a finite set of diffusion tensors. The MRI signal is influenced by several experimental parameters, which for diffusion measurements are summarized in the measurement tensor B. To determine the diffusivity of a voxel, multiple measurement tensors are utilized, producing various MRI signals. From these signals, the network estimates the corresponding DTD of the voxel. The network seeks to employ the earth mover's distance (EMD) as its loss function, given the established use of EMD as a distance between probability distributions. Due to the difficulty of expressing the EMD as a differentiable loss function, the Sinkhorn distance, an entropic regularized approximation of the EMD, is used instead. Different network configurations are explored through simulations to identify optimal settings, assessed by the EMD loss and the closeness of the Sinkhorn loss to the EMD. The results indicate that the network achieves satisfactory accuracy when approximating DTDs with a small number of diffusivities, but struggles when the number increases. Future work could explore alternative loss functions and advanced neural network architectures. Despite the challenges encountered, this thesis offers relevant insight into the estimation of diffusion tensor distributions.