Laurin Mordhorst

Axon caliber determines signal conduction velocity and varies within and across the bundles that form the brain’s wiring. Our knowledge of this organization derives largely from 2D histology, assuming cylindrical axons whose calibers are described by their radius. However, recent 3D histology reveals substantial along-axon variability in radius, calling into question 2D-derived insights into axon radius and conduction velocity. We show in 450,000 3D axon reconstructions from male rats that—despite this individual variation—axon bundles possess stable radius distributions at the ensemble level. These distributions are faithfully captured by 2D cross-sections and yield robust conduction velocity predictions, as along-axon variability has only a modest effect. Conduction in large axons is particularly stable, supporting time-critical signaling. With 2D sampling validated, we leverage 46 million human corpus callosum axons from 2D histology to determine sample size requirements across neuroscience applications. Our findings show how axonal organization gives rise to stable ensemble statistics and conduction, explaining and reinforcing decades of 2D histology-based research.

Axons are the brain’s wiring, organized into bundles that connect nearby and distant regions. Axon caliber determines signal conduction velocity and varies both within and across bundles, reflecting the brain’s diverse functional demands. Much of what we know about this organization derives from 2D histology, assuming cylindrical axons whose calibers are described by their radius. Yet, recent 3D histology reveals that the radius varies along an individual axon—with implications for both characterizing axon caliber and potentially conduction velocity predictions. We show in 450,000 3D rat axon reconstructions that—despite this individual variation—axon bundles possess stable radius distributions at the ensemble level, which 2D cross-sections faithfully represent. This representativeness extends to conduction velocity predictions, as along-axon variation has only modest impact. In particular, large axons exhibit especially stable conduction, emphasizing their key role in time-critical signaling. With 2D sampling validated, we leverage 46 million human corpus callosum axons from 2D histology to determine sample size requirements across neuroscience applications. Our findings reinforce decades of 2D histology-based research on axon organization and its functional implications, while guiding future study design.

Post mortem MRI studies of formalin-fixed brain tissue are essential for linking in vivo MRI contrast to underlying microstructure measured with ex vivo histology, yet formalin not only preserves tissue but also systematically alters MRI-relevant physical properties. To systematically quantify and model these effects, we longitudinally characterized multi-parametric mapping (MPM) measures — longitudinal (R ₁ ) and effective transverse (R ₂ *) relaxation rates, proton density proxy (N _A ), and magnetization transfer saturation ratio (MT _sat ) — across the different post mortem processes, i.e. autolysis, fixation, and hydration. Five whole-human brains were scanned longitudinally during fixation (and in situ -after rehydration, when available), and compared with an independent in vivo cohort of 25 younger healthy participants. Each MPM parameter followed a distinct trajectory across different post mortem processes. The largest changes were found for R ₁ during fixation relative to in situ values (more than 250%), followed by R ₂ * with an almost 60% increase, and MT _sat with a 26% reduction from in vivo to in situ . N _A showed no detectable change during fixation. We developed models describing fixation-induced changes and tissue shrinkage. The R ₁ changes and tissue shrinkage were closely aligned, reflecting a likely common mechanism. MT _sat largely preserved tissue contrast during fixation and rehydration, supporting its use for spatial alignment between in vivo MRI, fixed-tissue MRI, and histology. With our quantitative assessment of post mortem process-dependent changes we provide a unique resource for future studies to better link in vivo to fixed post mortem MRI data and thereby bridge the gap to ex vivo histology.

The axon radius holds promise as a clinical MRI biomarker for neurological disorders. However, in-vivo MRI estimation appears infeasible on clinical scanners and lacks experimental validation. Crucially, existing histology is only sparsely sampled, enabling primarily qualitative assessment. Here, we use large-scale human brain histology, sampling 46 million axons across 35 corpus callosum regions with MRI-like sizes. By demonstrating a significant spatial correlation with histology on an advanced research scanner, we provide quantitative proof that MRI radius estimates reflect underlying microstructure—a critical milestone. The next milestone—translation to clinical scanners—appears feasible with now-available high-gradient systems according to simulations, but would require substantial SNR gains. Yet, we also identify a sensitivity bottleneck in current modeling that may offer a complementary path to improved sensitivity through future modeling advances. Overall, we provide promising evidence for the validity of MRI-based axon radius estimation and identify challenges that must be solved for clinical adoption.

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.

Diffusion MRI (dMRI) has become a crucial imaging technique in the field of neuroscience, with a growing number of clinical applications. Although most studies still focus on the brain, there is a growing interest in utilizing dMRI to investigate the healthy or injured spinal cord. The past decade has also seen the development of biophysical models that link MR-based diffusion measures to underlying microscopic tissue characteristics, which necessitates validation through ex vivo dMRI measurements. Building upon 13 years of research and development, we present an open-source, MATLAB-based academic software toolkit dubbed ACID: A Comprehensive Toolbox for Image Processing and Modeling of Brain, Spinal Cord, and Ex Vivo Diffusion MRI Data. ACID is an extension to the Statistical Parametric Mapping (SPM) software, designed to process and model dMRI data of the brain, spinal cord, and ex vivo specimens by incorporating state-of-the-art artifact correction tools, diffusion and kurtosis tensor imaging, and biophysical models that enable the estimation of microstructural properties in white matter. Additionally, the software includes an array of linear and non-linear fitting algorithms for accurate diffusion parameter estimation. By adhering to the Brain Imaging Data Structure (BIDS) data organization principles, ACID facilitates standardized analysis, ensures compatibility with other BIDS-compliant software, and aligns with the growing availability of large databases utilizing the BIDS format. Furthermore, being integrated into the popular SPM framework, ACID benefits from a wide range of segmentation, spatial processing, and statistical analysis tools as well as a large and growing number of SPM extensions. As such, this comprehensive toolbox covers the entire processing chain from raw DICOM data to group-level statistics, all within a single software package.

The effective transverse relaxation rate (R ₂ *) is sensitive to the microstructure of the human brain, e.g. the g-ratio characterising the relative myelination of axons. However, R ₂ * depends on the orientation of the fibres relative to the main magnetic field degrading its reproducibility and that of any microstructural derivative measure. To decipher its orientation-independent part (R _2,iso *), a second-order polynomial in time (M2) can be applied to single multi-echo gradient-recalled-echo (meGRE) measurements at arbitrary orientation. The linear-time dependent parameter, β ₁ , of M2 can be biophysically related to R _2,iso * when neglecting the signal from the myelin water (MW) in the hollow cylinder fibre model (HCFM). Here, we examined the effectiveness of M2 using experimental and simulated data with variable g-ratio and fibre dispersion. We showed that the fitted β ₁ effectively estimates R _2,iso *when using meGRE with long maximum echo time (TE _max ≈ 54 ms) but its microscopic dependence on the g-ratio was not accurately captured. This error was reduced to less than 12% when accounting for the MW contribution in a newly introduced biophysical expression for β ₁ . We further used this new expression to estimate the MW fraction (0.14) and g-ratio (0.79) in a human optic chiasm. However, the proposed method failed to estimate R _2,iso * for a typical in-vivo meGRE protocol (TE _max ≈ 18 ms). At this TE _max and around the magic angle, the HCFM-based simulations failed to explain the R ₂ *-orientation-dependence. In conclusion, estimation of R _2,iso * with M2 in vivo requires meGRE protocols with very long TE _max ≈ 54 ms.

Non-invasive assessment of axon radii via MRI bears great potential for clinical and neuroscience research as it is a main determinant of the neuronal conduction velocity. However, there is a lack of representative histological reference data on the scale of the cross-section of MRI voxels for validating the MRI-visible, effective radius ( r _eff ). Because the current gold standard stems from neuroanatomical studies designed to estimate the frequency-weighted arithmetic mean radius ( r _arith ) on small ensembles of axons, it is unsuited to estimate the tail-weighted r _eff . We propose CNN-based segmentation on high-resolution, large-scale light microscopy (lsLM) data to generate a representative reference for r _eff . In a human corpus callosum, we assessed estimation accuracy and bias of r _arith and r _eff . Furthermore, we investigated whether mapping anatomy-related variation of r _arith and r _eff is confounded by low-frequency variation of the image intensity, e.g., due to staining heterogeneity. Finally, we analyzed the potential error due to outstandingly large axons in r _eff . Compared to r _arith , r _eff was estimated with higher accuracy (normalized-root-mean-square-error of r _eff : 7.2 %; r _arith : 21.5 %) and lower bias (normalized-mean-bias-error of r _eff : − 1.7 %; r _arith : 16 %). While r _arith was confounded by variation of the image intensity, variation of r _eff seemed anatomy-related. The largest axons contributed between 0.9 % and 3 % to r _eff . In conclusion, the proposed method accurately estimates r _eff at MRI voxel resolution across a human corpus callosum sample. Further investigations are required to assess generalization to brain areas with different axon radii ensembles.