Assessment of the effect of tissue motion in diffusion MRI: Derivation of new apparent diffusion coefficient formula

Elie Bretin (1) , Imen Mekkaoui (1) , Jerome Pousin (2)

1 MMCS - Modélisation mathématique, calcul scientifique
2 ICJ - Institut Camille Jordan

We investigate in this paper the diffusion magnetic resonance imaging (MRI) in deformable organs such as the living heart. The difficulty comes from the hight sensitivity of diffusion measurement to tissue motion. Commonly in literature, the diffusion MRI signal is given by the complex magneti-zation of water molecules described by the Bloch-Torrey equation. When dealing with deformable organs, the Bloch-Torrey equation is no longer valid. Our main contribution is then to introduce a new mathematical description of the Bloch-Torrey equation in deforming media. In particular, some numerical simulations are presented to quantify the influence of cardiac motion on the estimation of diffusion. Moreover, based on a scaling argument and on an asymptotic model for the complex magnetization, we derive a new apparent diffusion coefficient formula. Finally, some numerical experiments illustrate the potential of this new version which gives a better reconstruction of the diffusion than using the classical one.

Mots clés: Diffusion magnetic resonance imaging; cardiac diffusion imaging; Bloch-Torrey equation; diffusion encoding gradient; apparent diffusion coefficient; asymptotic analysis

Domaines: Mathématiques [math]

Elie Bretin, Imen Mekkaoui, Jerome Pousin. Assessment of the effect of tissue motion in diffusion MRI: Derivation of new apparent diffusion coefficient formula. 2017. ⟨hal-01496331⟩