Effective Diffusion Tensor Computed by Homogenization

Dang Van Nguyen¹, Denis Grebenkov², Cyril Poupon³, Denis Le Bihan³, Jing-Rebecca Li⁴

Diffusion MRI can give useful information on cellular structure and structural change. We show that the effective diffusion tensor obtained by mathematical homogenization theory is a good approximation to the long time apparent diffusion tensor under realistic DMR scanning conditions for both isotropic and anisotropic diffusion and general geometries. The homogenized diffusion tensor is obtained by solving three steady-state Laplace equations, which is a more computationally efficient approach than long time simulation in the time domain, either via Monte-Carlo simulation or numerical solution of the time-dependent Bloch-Torrey PDE.