The “recipe” to know the type of dynamics “before” applying the diffusion models: application in heterogeneous phantoms

We applied a “recipe” developed in our previous work (Costantini et al. Sci. Rep 2023) to understand the type of dynamics underlying the analyzed sample and then apply the right diffusion model. Water and PEG-1500 at 40% w/w in water stored in two 10mm NMR tubes were acquired at different Δ (10-600ms), δ (4,5ms), and different gradient strengths g using a PGSTE with TR=4s, n=16 at 9.4 T. Moreover, heterogeneous fibers-like phantoms in water were acquired using DTI protocols at different g, Δ (12-400ms) and δ (2,3 ms). The recipe consists of three steps: in the first step the signal is rescaled by g^2 function. If the rescaled signals collapse and the f(δ1,δ2) function is constant, the dynamics are Gaussian and the derivative (second step) can be performed to understand if it has anomalous diffusion. Otherwise, the signals decay as a function of the b-values are performed (third step) and if they collapse the sample has a Super Statistics behavior (SS). We differentiated the contribution of water and polymer in the PEG sample highlighting the different dynamics. The water sample has a Brownian Motion with a diffusion coefficient of D water =2.09E-09m^2 /s. The water in the PEG at low gradients didn’t pass the first check, but it passed the third one showing SS dynamics with D waterPEG =3.16E-10m^2/s. The PEG chain too showed the same dynamics with D app =3.7E-11m^2/s, whereas the PEG’s OH was found to have an unknown dynamic’s process since it didn’t pass any check. Water in fiber phantoms shows different dynamics.