## Section: New Results

### Investigating water diffusion in biological tissue: with application to anatomical and functional neuroimaging

Participant : Jing Rebecca Li-Schlittgen.

Water diffusion in biological tissues is not free (Gaussian), as the signal attenuation is not monoexponential with diffusion-weighting (b value). Some groups have successfully characterized this attenuation with a biexponential model, which suggests the presence of 2 water pools in slow or intermediate exchange. However, this model is still controversial and the nature of the 2 pools (e.g., membrane-bound and intra/extracellular bulk water) remains elusive. We proposed a semi-analytical model of multiple-compartment diffusion. We consider the Bloch-Torrey partial differential equation model (PDE in time and space) for the magnetization and show that because the diffusion MRI signal is the integral of the magnetization, we can formulate an ordinary differential equation (ODE only in time) directly on the signal. This makes the inverse problem of determining biological parameters from the DMRI signal more numerically tractable, as the number of unknowns is vastly reduced. At the same time, the link between the biological properties of diffusion in the different compartments and the overall signal is made more direct and will aide in the more straightforward interpretation of the DMRI signals in terms of the underlying physical properties of water diffusion in tissue. This model is more general than the widely used Karger model because it takes into account the geometry of the cellular structure. This work is conducted in collaboration with D. Calhoun (CEA, Saclay), C-H. Yeh (National Yang-Ming University, Taiwan, CEA, Saclay), C. Poupon (CEA Neurospin, Saclay) and D. Le Bihan (CEA Neurospin, Saclay).