UC Santa Cruz

Diffusion MRI (dMRI) provides a sensitive measure of water molecule movement in biological tissues based on observed decay in magnetic resonance (MR) signal, enabling the detection of microstructural abnormalities as well as details. This thesis explores the artificial simulation of dMRI scans using dMRI simulators, focusing on two prominent methods: Monte-Carlo or particle-based simulations and the Bloch- Torrey partial differential equation (PDE) based simulation approach. The methodology involves a comparative analysis of these techniques, highlighting the theoretical and computational aspects of the Monte-Carlo and Bloch-Torrey PDE methods. Then, we reimplement the Bloch-Torrey PDE-based simulations in a differentiable manner. By implementing this approach in a differentiable manner, we enhance the simulation process’s flexibility and speed, facilitating the development of new dMRI acquisition, analysis, and reconstruction techniques. This work explains how differentiability can be achieved with the PDE-based method with Pytorch, providing a foundation for further research and application in medical imaging and reconstruction and tackling the inverse problem in dMRI to an extent.