Figure 2. Simulations on accuracy and precision of MR-based axon radius mapping.

First, the left and middle panel show the difference between the estimated, ${\displaystyle \hat{r}}$, and theoretical, ${\displaystyle r}$, effective MR radius associated with various realistic axon caliber distributions (solid dots with different color for different distributions) for the clinical and preclinical setups, respectively. Axon caliber distributions were adopted from Aboitiz et al. (1992) and Innocenti et al. (2015) for the clinical simulations (see Figure 7), whereas various axon distributions (see Figure 4) derived from our own histology were used for the preclinical simulation. The average radii, $\overline{r}$, of the axon caliber distribution are shown for comparison (open dots). Additionally, the accuracy of the framework for a system with single cylinder with radius ${\displaystyle r}$ is shown (black line). Second (right figure), the feasibility to measure $D_a^{⟂}$ with statistical significance in case of scan settings and SNR for the Connectom (300 mT/m; blue), Aeon (1500 mT/m; green) protocol, respectively. For comparison, we also assessed the feasibility for the Prisma protocol as described in Veraart et al. (2019) (80mT/m; red). The shaded areas illustrate the 95% confidence intervals derived from Cramér-Rao lower bound analysis of model, Equation 2 with $f_{\mathrm{im}}=0$. The corresponding minimal cylinder radius $r$ that allows for the observation of significant $D_a^{⟂}(r)$, $r=0.76\mu \mathrm{m}$, 1.41 µm and 3.24 µm for Aeon, Connectom, and Prisma, respectively, is indicated by the vertical lines. In all plots, diffusivities and radii are expressed in ${\displaystyle \mu {\mathrm{m}}^2/\mathrm{m}\mathrm{s}}$ and ${\displaystyle \mu \mathrm{m}}$, respectively.