Mathematical justification of macroscopic models for diffusion MRI through the periodic unfolding method

Article type: Research Article

Authors: Coatléven, Julien

Affiliations: IFPEN 1 et 4 Avenue de Bois-Préau, 92852 Rueil-Malmaison, France. E-mail: [email protected]

Abstract: Diffusion Magnetic Resonance Imaging (dMRI) is a promising tool to obtain useful information on cellular structure when applied to biological tissues. A coupled macroscopic model has been introduced recently through formal homogenization to model dMRI’s signal attenuation. This model was based on a particular scaling of the permeability condition modeling cellular membranes. In this article, we explore all the possible scalings and mathematically justify the corresponding limit models, using the periodic unfolding method. We also illustrate through numerical simulations the respective behavior of the limit models when compared to dMRI measurements.

Keywords: diffusion MRI, homogenization, Bloch–Torrey equation, periodic unfolding, imperfect transmission, trace jumps

DOI: 10.3233/ASY-151294

Journal: Asymptotic Analysis, vol. 93, no. 3, pp. 219-258, 2015