How does dMRI signal evolve during diffusion encoding: theoretical analysis and numerical simulations for Gaussian diffusion

Motivation: Until now, most attention has been focused on the final dMRI signals acquired, ignoring the signal evolution during diffusion encoding. However, the methods, which incorporated water exchange between compartments into modelling to extract more comprehensive tissue information, need to consider the signal evolution within the different compartments, as described in Karger model. Goal(s): Figure out the dMRI signal evolution in the simplest case: Gaussian diffusion. Approach: Theoretical analysis, Monte-Carlo and finite difference simulations. Results: Signal-evolution curves provided by analytical expressions and numerical simulations are consistent. An “observation-size” effect emerges, the signal-evolution curve depends on the spatial size of the observation area. Impact: Clarifying the actual dMRI signal evolution during diffusion encoding will inspire us to revisit the theoretical framework of Karger model. The results show that it is necessary to revise the current Karger-model-based methods for the “observation-size” effect.