Section: New Results

Diffusion MRI

J.R. Li, K. V. Nguyen and I. Mekkaoui

Diffusion Magnetic Resonance Imaging (DMRI) is a promising tool to obtain useful information on microscopic structure and has been extensively applied to biological tissues.

We obtained the following results.

• The Bloch-Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI and NMR. Microscopic heterogeneity inside the imaging voxel is modeled by interfaces in- side the simulation domain, where a discontinuity in the magnetization across the interfaces is produced via a permeability coefficient on the interfaces. To avoid having to simulate on a computational domain that is the size of an en- tire imaging voxel, which is often much larger than the scale of the microscopic heterogeneity as well as the mean spin diffusion displacement, smaller represen- tative volumes of the imaging medium can be used as the simulation domain. In this case, the exterior boundaries of a representative volume either must be far away from the initial positions of the spins or suitable boundary conditions must be found to allow the movement of spins across these exterior boundaries.

  Many approaches have been taken to solve the Bloch-Torrey equation but an efficient high performance computing framework is still missing. We present formulations of the interface as well as the exterior boundary conditions that are computationally efficient and suitable for arbitrary order finite elements and parallelization. In particular, the formulations use extended finite elements with weak enforcement of real (in the case of interior interfaces) and artificial (in the case of exterior boundaries) permeability conditions as well as operator splitting for the exterior boundary conditions. The method is straightforward to implement and it is available in the FEniCS for moderate- scale simulations and in the FEniCS-HPC for large-scale simulations.

• The nerve cells of the Aplysia are much larger than mammalian neurons. Using the Aplysia ganglia to study the relationship between the cellular structure and the diffusion MRI signal can potentially shed light on this relationship for more complex organisms. We measured the dMRI signal of chemically-fixed abdominal ganglia of the Aplysia at several diffusion times. At the diffusion times measured, the dMRI signal is mono-exponential and can be accurately represented by the parameter ADC.

  We analyzed the diffusion time-dependent ADC using a well-known analytical formula that is valid in the short diffusion time regime. We performed this analysis for the largest sized cells of the ganglia to satisfy the short diffusion time requirement. We noted that a naive application of the short time formula is not adequate because of the presence of the cell nucleus, making the effective cell size much smaller than the actual cell size.

  We went on to perform numerical simulation of the ADC for several cell types of the abdominal ganglia. To create the simulation geometries, for the largest cells, we segmented a high resolution T2-weighted images and incorporated a manually generated nucleus. For small cells and nerve cells, we created spherical and cylindrical geometrical domains that are consistent with known information about the cellular structures from the literature. Using the library of simulation results, we fitted for the intrinsic diffusivities of the small cells and the nerve cells.

• We participated in providing simulation results for the Parietal team in their work on sensing Spindle Neurons in the Insula with Multi-shell Diffusion MRI.

• We started a new direction in the simulation and modeling of heart diffusion MRI with the post-doc project of Imen Mekkaoui, funded by Inria-EPFL lab. The project is co-supervised with Jan Hesthaven, Chair of Computational Mathematics and Simulation Science (MCSS), EPFL.