Section: New Results

Diffusion MRI

Participants : Jing-Rebecca Li, Houssem Haddar, Simona Schiavi, Khieu Van Nguyen, Gabrielle Fournet, Dang Van Nguyen.

Diffusion Magnetic Resonance Imaging (DMRI) is a promising tool to obtain useful information on microscopic structure and has been extensively applied to biological tissues. In particular, we would like to focus on two applications:

• Inferring from DMRI measurements changes in the cellular volume fraction occurring upon various physiological or pathological conditions. This application is one of the first to show the promise of DMRI because it can detect acute cerebral ischemia (cell swelling) on the basis of lower than normal apparent diffusion coefficient a few minutes after stroke;

• Estimating the average cell size in the case of tumor imaging This application is useful as a diagnostic tool as well as a tool for the evaluation of tumor treatments;

For both of the above applications we approach the problem via the following steps:

• Construct reduced models of the multiple-compartment Bloch-Torrey partial differential equation (PDE) using homogenization methods.

• Invert the resulting reduced models for the biological parameters of interest: the cellular volume fraction in the first case, and the average distance between neighboring cells in the second case.

We obtained the following results.

• We derived using homogenization techniques an asymptotic model of the diffusion MRI signal for finite pulse magnetic field gradient sequences in the long diffusion time regime and numerically verified it using a Finite Element method for both isotropic and anisotropic diffusion configurations in three dimensions. This resulted in 2 publications.

• We derived a new asymptotic model of the diffusion MRI signal for low gradient strengths that is valid for a wide range of diffusion time scales. An article describing our results is under preparation.

• We performed a numerical study of a cylinder model of the diffusion MRI signal for neuronal dendrite trees. This resulted in 1 publication.

• We implemented a compressed sensing method for obtaining T2-weighted images in shorter scanning time and this method was used to segment nerve cells of the Aplysia Californica at the MRI center Neurospin. An article describing our results is under preparation.

• We participated in the characterization of glioma microcirculation and tissue features in a rat brain model using diffusion-encoding magnetic field gradient pulses sequences, working along with collaborators at the high field brain MRI center Neurospin. This resulted in 1 publication.

• We performed Monte-Carlo simulation of blood flow in micro-vessels in the brain with the goal of using the results to explain the MRI signal drop due to incoherent flow in the micro-vessels. This is an ongoing project.