![Fig. 1 A dMRI-scale histological gold standard for r eff . (a) Human corpus callosum tissue samples with annotated regions of interest (ROIs) scanned via light microscopy. (b) Light microscopy image of an example ROI. (c) Magnified view of (b) showing myelin sheath (black) and axonal body (white) segmentation. (d-f ) Sampling statistics of human corpus callosum histology datasets [3, 31, 32]: (d) donors per dataset, (e) ROIs per donor (mean across donors) and (f ) mean sample area and axon count per ROI (double-logarithmic scale). The dashed line represents the cross-sectional area of in-vivo dMRI voxels used in our study. (g-h) Axon radius distribution for (g) a light microscopy ROI and (h) a random subsample of the distribution in (g) including 10 3 axons, mimicking a ROI as presented by Aboitiz et al. [31]. Vertical dotted lines denote r eff ; insets highlight tails of axon radius distributions. (i) Sampling distribution of r eff as a function of ROI size (axon count) for the ROI in (g). The blue marker and dashed line represent r eff computed from all axons within the ROI, while boxplots show simulated sampling distributions for smaller ROI sizes, indicating the median (line), interquartile range (IQR, box), whiskers (1.5 IQR), and outliers (dots). Box colors reflect datasets, categorized by ROI size (see legend over d-g). Note that we do not explicitly mark the dataset of Caminiti et al. [3] as the ROI size roughly coincides with the ROI size used by Aboitiz et al. [31]. (j-k) Bias and coefficient of variation as a function of the ROI size based on sampling distributions as shown in (i). Markers showing mean ± standard deviation across ROIs. Color encoding follows definitions in (i).](https://www.researchgate.net/publication/389550229/figure/fig1/AS:11431281313624219@1741105997467/A-dMRI-scale-histological-gold-standard-for-r-eff-a-Human-corpus-callosum-tissue_Q320.jpg)
![Fig. 2 Comparison of r eff across modalities. (a-b) Histological spatial patterns of r eff across the corpus callosum, shown in mid-sagittal MNI slice with subregions indicated (dashed lines). (c-f ) Ex-vivo comparison of spatial patterns: (c) histology, (d) dMRI experiments, (e) experiment-like dMRI simulations (experimental SNR), and (f ) idealized dMRI simulations (SNR = ∞). Patterns in (c,e-f) show the group-average across donors, whereas the pattern in (d) covers the 15 ROIs of CC-01 scanned with ex-vivo dMRI (void area indicates ROI not scanned with ex-vivo dMRI; see Fig. 5b,e). For experiment-like simulations in (e), the pattern reflects the median across 1000 noise realizations. (h-k) In-vivo comparison of spatial patterns analogously to (c-f) with the following exceptions: spatial patterns in (h,j-k) are based on histological axon radii scaled by 1.3 to compensate for tissue shrinkage [31, 38] and pattern in (i) reflects the group-average across in-vivo subjects (see Section SI3 for per-subject patterns). (l-n) Quantitative comparisons of r eff from dMRI experiments/simulation scenarios in (d-f,i-k) against histology. Markers represent histological ROIs in Fig. 1a, with colors encoding experimental conditions (in-vivo vs. ex-vivo, see legend). For dMRI experiments in (l), exvivo markers include the 15 ROIs of CC-01 scanned with ex-vivo dMRI (see Fig. 5b,e), whereas in-vivo markers denote group-average r eff values (see Section SI3 for per-subject analyses). Note that r eff from in-vivo dMRI experiments exhibited some variability due to non-deterministic processing (across 10 iterations: R = 0.414 ± 0.03, all p < 0.05; see Section SI2). The simulations in (m-n) use all histological ROIs and assume a single subject/donor scanned with dMRI. The 95 % confidence intervals (shaded areas in (m)) were computed across 1000 noise realizations. The dashed lines illustrate theoretical perfect agreement. The legends provide metrics computed over all ROIs, including Pearson's correlation coefficient (R) and the corresponding p-value, the normalized root-mean-square error (NRMSE), and the fitting success rate (S) (see Section 4.7 for metric definitions).](https://www.researchgate.net/publication/389550229/figure/fig2/AS:11431281313723445@1741105997705/Comparison-of-r-eff-across-modalities-a-b-Histological-spatial-patterns-of-r-eff_Q320.jpg)
![Fig. 5 Regions of interest in different spaces and their registration. (a-d) Regions of interest (ROIs) shown in different spaces: (a) histology, (b) ex-vivo dMRI, (c) MNI space (overlaid on T1-weighted template), (d) in-vivo dMRI (overlaid on T1-weighted image). Polygons and circles indicate ROI boundaries and centroids, with colors representing tissue sample CC-01 (magenta) or CC-02 (green). (e) Registration between histology and ex-vivo dMRI. We bisected the brain along the mid-sagittal plane, indicated by the red line, yielding hemispheric sections for histology (left) and ex-vivo dMRI (right). We first defined histological ROIs near the mid-sagittal plane; then, we manually defined corresponding ROIs in ex-vivo dMRI. Magnified views illustrate an example of matching ROIs in histology and ex-vivo dMRI (extracted tissue area in histology and magenta area in ex-vivo dMRI). Note that we scanned only part of the genu with ex-vivo dMRI. (f ) Registration between histology and MNI space. We manually created two-dimensional tissue masks (left image) for the images in (a) and registered these masks with the mid-sagittal slice of a fractional anisotropy (FA) atlas (the FSL HCP-1065 FA atlas [46], thresholded at FA ≥ 0.3) in MNI space (see red area in right image). (g) Registration between MNI space and in-vivo dMRI. We simultaneously registered T 1 -weighted image and FA map in native space to their corresponding templates in MNI space (the FSL HCP-1065 FA atlas and the FSL MNI152 T 1 -weighted template [46]).](https://www.researchgate.net/publication/389550229/figure/fig4/AS:11431281313624220@1741105998107/Regions-of-interest-in-different-spaces-and-their-registration-a-d-Regions-of-interest_Q320.jpg)
February 2025
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The MRI-visible axon radius is a potential clinical biomarker for, e.g., neurological disorders. However, its clinical potential remains untapped, as in-vivo MRI-based estimation lacks validation in humans and currently requires specialized research scanners. Here, we assess state-of-the-art MRI methods for axon radius estimation against a new, open-access histological gold standard of two densely sampled human corpora callosa, enabling validation via quantitative spatial correlations. Our findings show a significant correlation between estimates from histology and in-vivo dMRI acquired with a research scanner. Critically, our simulations suggest that these findings can be translated from research to clinical scanners, enabling clinical adoption. We propose specific clinical scanner protocols and illustrate their potential in a hypothetical application distinguishing individuals with autism spectrum disorder from healthy controls. Overall, our study provides promising evidence for the validity of the MRI-visible axon radius and outlines a pathway to its clinical application, while critically discussing remaining challenges.
![Figure 5: Schematic of the generation of axon ensembles with erroneous, medium-sized axon radii. The input axon ensemble (a) was manipulated (b) based on an error model (c) to generate axon radii ensembles with erroneous medium-sized axon radii (d). To model the error as a function of the axon radius, distinct parameters of the error model were determined per axon radii bin j ∈ [1, J = 5] (see details on the binning below). To obtain an erroneous axon radii ensemble (d), we employed the error model (c.4) for each bin j as follows: First, randomly drawn, missed (false negative; FN) axon radii were removed (b.1, purple) according to the false negative rate (FNR j ; c.4.i, see Eq. (6)). Then, axon radii were perturbed (b.2) according to the residuals of partially or fully detected (true positive; TP) axons (∆r j ; c.4.ii, see Eq. (7)). Finally, randomly drawn, falsely detected (false positive; FP) axon radii were added (b.3, orange) according to the false discovery rate (FDR j ; c.4.iii, see Eq. (8)) and the distribution of FP axon radii (r FP,j ; c.4.iii). To determine the parameters of the error model, we pooled over five pairs of corresponding predictions (c.2, yellow) and references (c.2, red) randomly drawn from 30 pairs (c.1). The J bins were chosen to contain the same number of reference axon radii per bin. For each bin j, axons of corresponding predictions (c.3.i) and references (c.3.iii) were compared (c.3.ii) to classify non-overlapping axons as FP (entirely yellow in c.3.ii) or FN (entirely red in c.3.ii) and partially or fully overlapping axons as TP (partially or fully green in c.3.ii and c.4.ii). Then (c.4), we determined the parameters of the error model.](https://www.researchgate.net/publication/352123749/figure/fig1/AS:1031006786166786@1622822581044/Schematic-of-the-generation-of-axon-ensembles-with-erroneous-medium-sized-axon-radii_Q320.jpg)
