The impact of gradient strength on in vivo diffusion MRI estimates of axon diameter

Abstract

Diffusion magnetic resonance imaging (MRI) methods for axon diameter mapping benefit from higher maximum gradient strengths than are currently available on commercial human scanners. Using a dedicated high-gradient 3T human MRI scanner with a maximum gradient strength of 300 mT/m, we systematically studied the effect of gradient strength on in vivo axon diameter and density estimates in the human corpus callosum. Pulsed gradient spin echo experiments were performed in a single scan session lasting approximately 2h on each of three human subjects. The data were then divided into subsets with maximum gradient strengths of 77, 145, 212, and 293 mT/m and diffusion times encompassing short (16 and 25 ms) and long (60 and 94 ms) diffusion time regimes. A three-compartment model of intra-axonal diffusion, extra-axonal diffusion, and free diffusion in cerebrospinal fluid was fitted to the data using a Markov chain Monte Carlo approach. For the acquisition parameters, model, and fitting routine used in our study, it was found that higher maximum gradient strengths decreased the mean axon diameter estimates by two to three fold and decreased the uncertainty in axon diameter estimates by more than half across the corpus callosum. The exclusive use of longer diffusion times resulted in axon diameter estimates that were up to two times larger than those obtained with shorter diffusion times. Axon diameter and density maps appeared less noisy and showed improved contrast between different regions of the corpus callosum with higher maximum gradient strength. Known differences in axon diameter and density between the genu, body, and splenium of the corpus callosum were preserved and became more reproducible at higher maximum gradient strengths. Our results suggest that an optimal q-space sampling scheme for estimating in vivo axon diameters should incorporate the highest possible gradient strength. The improvement in axon diameter and density estimates that we demonstrate from increasing maximum gradient strength will inform protocol development and encourage the adoption of higher maximum gradient strengths for use in commercial human scanners.

Figure 1

Posterior distributions on (a–f) axon diameter a, (g–l) restricted fraction f_r, (m–r) CSF fraction f_csf, and (s–x) hindered diffusion coefficient D_h from a representative voxel in the body of the corpus callosum for data from subject 1 acquired at different G_max and q: (a, g, m, s) data set 1 (G_max = 77 mT/m); (b, h, n, t) data set 2 (G_max = 145 mT/m); (c, i, o, u) data set 3 (G_max = 212 mT/m); (d, j, p, v) data set 4 (G_max = 293 mT/m); (e, k, q, w) data set 5 (high q values); and (f, l, r, x) data set 8 (all data). The mean axon diameter, restricted fraction, CSF fraction, and hindered diffusion coefficient for each histogram is indicated by the green x along the x-axis and numerical value at the top right of each histogram. The bin size was set to 2 µm for the axon diameter estimates in (a) and (b) and 0.8 µm for the axon diameter estimates in (c), (d), and (e); 0.05 for the restricted fraction estimates in (g–l); 0.02 for the CSF fraction estimates in (m–r); and 0.025 µm²/ms for the hindered diffusion coefficient estimates in (s–x).

Figure 2

Effect of G_max and q on mean axon diameter estimates in all three subjects. Mean and standard deviation of axon diameter estimates for data sets 1–5 and 8 within the genu, body, and splenium ROIs in the midline sagittal slice of the corpus callosum for (a) subject 1, (b) subject 2, and (c) subject 3. (Insets) Delineation of ROIs placed in the genu, body, and splenium of the midline sagittal slice of the corpus callosum overlaid on representative b = 0 images for each subject.

Figure 3

Effect of diffusion time Δ on mean axon diameter estimates in all three subjects. Mean and standard deviation of axon diameter estimates for data sets 6–8 within the genu, body, and splenium ROIs in the midline sagittal slice of the corpus callosum for (a) subject 1, (b) subject 2, and (c) subject 3.

Figure 4

Voxel-wise estimates in the midline sagittal slice of the corpus callosum of subject 1 for (a–f) axon diameter, (g–l) restricted fraction, (m–r) CSF fraction, and (s–x) axon density for different G_max, high q and all data (data sets 1–5 and 8). The voxel-wise axon diameter a, restricted fraction f_r, and CSF fraction f_csf values represent the means of the posterior distribution on a, f_r, and f_csf, respectively. The axon density represents the restricted fraction weighted by the cross-sectional area calculated from the mean axon diameter (23).

Figure 5

Plots of the ROI-averaged signal in the genu, body, and splenium from the midline sagittal corpus callosum in subject 1 for different q and Δ listed in the legend. The solid lines represent the predicted signals from the fitted model. All measurements were normalized by the corresponding estimate of S₀ obtained at b = 0.