Section: New Results

Diffusion MRI

Homogenized diffusion tensor and approximate analytical formulae for the long time ADC

Participants : Jing-Rebecca Li, Houssem Haddar.

We model the bulk magnetization in biological tissue due to a diffusion gradient at the voxel level by a two compartment Bloch-Torrey partial differential equation. The cell membranes are modelled as infinitely thin permeable interfaces. We show the simulated long time apparent diffusion tensor of the PGSE sequence is close to the effective diffusion tensor from homogeneization theory for both isotropic and anisotropic diffusion. For nearly isotropic diffusion we give analytical approximate formulae for the long time apparent diffusion coefficient in two and three dimensions. The approximate formulae allow us to robustly estimate the change in the cellular volume fraction from ADC measurements before and after cell swelling if the cells are approximately uniform in size. We can also use the formulae to estimate the average cell size.

General ODE model of diffusion MRI signal attenuation

Participants : Jing-Rebecca Li, Hang Tuan Nguyen.

We model the magnetization in biological tissue due to a diffusion gradient by a two compartment Bloch-Torrey partial differential equation with infinitely thin permeable membranes. We formulate a ODE model for the magnetization and show the simpler ODE model is a good approximation to the Bloch-Torrey PDE model for a variety of gradient shapes. Using the ODE model we determine of the change in the cellular volume fraction from the signal attenuation obtained before and after cell swelling. This method requires only the ADC and Kurtosis of the two signal attenuations and the numerical solution of an ODE system.