Axons, the long cable-like projections that carry signals between neurons, are fundamental to the structural integrity and function of the nervous system. Measuring their density and organization is central to understanding diseases such as multiple sclerosis, in which axonal loss drives progressive disability, as well as Alzheimer’s disease and traumatic brain injury. The Bielschowsky silver stain, first introduced in 1902, remains a workhorse of clinical neuropathology because it renders thin axons and neurofibrils dark against a paler background. But converting these images into reliable numbers has long been a bottleneck. Manual counting and stereological sampling are slow and scale poorly, while shortcuts such as optical density measurements are confounded by stain quality and by silver deposits in non-axonal tissue. Line-intersection counting, another common surrogate, depends on arbitrary line placement and local fiber orientation.

Classical image-processing approaches fare no better. Color-deconvolution techniques, which work reasonably well on brightly colored immunohistochemical stains, perform poorly on the monochromatic, heterogeneous contrast of silver impregnations. Existing deep learning pipelines for axon segmentation, such as AxonDeepSeg and DeepACSON, were built for electron microscopy, immunofluorescence, or myelin-specific stains, and none had been optimized for brightfield silver-stained histology. BasNet was designed specifically to fill that gap, trained entirely on manually annotated Bielschowsky-stained tissue.

The architecture is an attention U-Net, an encoder-decoder convolutional network in which so-called attention gates selectively emphasize task-relevant features while suppressing background noise. The encoder compresses the image through four hierarchical levels, expanding from 32 to 256 channels with each downsampling step, while the decoder reconstructs a full-resolution segmentation map. At every skip connection, an attention gate computes spatial attention coefficients that weight encoder features according to their relevance, a mechanism that proved particularly valuable in silver-stained tissue, where non-specific background silver deposition can trigger false positives in a standard U-Net. The complete network contains approximately 7.85 million trainable parameters and processes 256 by 256 pixel RGB patches, outputting a binary mask in which axon pixels are distinguished from background.

Training presented two classic challenges: extreme class imbalance, with axons occupying only about 30 percent of the pixels, and the need to recover very thin, elongated structures. The team addressed both with Focal Tversky Loss, a function that penalizes false negatives more heavily than false positives and applies a quadratic focusing factor that concentrates learning on difficult boundary regions. This asymmetry was deliberate. For axon density quantification, a missed axon directly reduces the density estimate, whereas slight over-segmentation is less harmful. The design shows in the results: mean recall of 0.754 consistently exceeded mean precision of 0.717 on the test set. An ablation study confirmed that the attention gates improved mean test Dice from 0.699 to 0.715, a small but consistent gain achieved at a cost of only about one percent additional parameters.

The training data were laborious to produce. Two medical doctors annotated 33 image tiles covering more than 25 million pixels, drawn from 26 whole-slide images spanning gray matter, white matter, demyelinated lesions, and background regions from the brains of four multiple sclerosis patients obtained through the German MS Brain Bank. Slides were prepared by different technicians at different times, deliberately capturing the real-world staining variability that plagues clinical material. The tiles were subdivided into more than 86,000 augmented training patches, and a leave-one-WSI-out cross-validation across twelve folds confirmed that no single training slide was disproportionately critical to performance, with Dice scores ranging narrowly between 0.687 and 0.725.

The most telling evaluation was a direct comparison with human variability. When two independent raters segmented the same two tiles, their mutual agreement, measured by the F1 or Dice coefficient, was 0.637 and 0.671. The model’s agreement with each individual rater ranged from 0.681 to 0.736, meeting or exceeding the human-to-human ceiling on both tiles. Comparable benchmarks in the literature, such as inter-rater Dice scores of around 0.78 for optic nerve axons and an average Jaccard index of 0.653 for nuclei segmentation, place BasNet squarely within the range of inter-observer disagreement. The authors conclude that the principal remaining source of error is annotation ambiguity rather than model limitation. On the held-out test set the model achieved a mean Dice of 0.717 and an intersection over union of 0.584, though performance varied widely across tiles, from perfect scores on a background tile to a low of 0.392 on a poorly stained slide, mirroring the difficulties that poor staining quality also poses to human annotators.

Beyond tile-level scores, the team demonstrated a pipeline that scales to whole slides. Aggregated segmentation masks produce spatially resolved maps of axon density at 70 micrometer resolution, revealing the expected anatomy: uniformly bright white matter tracts, a dimmer and more variable cortical ribbon, and visibly reduced density in multiple sclerosis lesions. A structural tensor analysis, built on image gradients and eigen decomposition, additionally yields maps of dominant fiber orientation and local coherency, a fractional anisotropy-like measure of directional alignment. Highly organized fiber bundles appear bright and smoothly colored, while crossing-fiber zones, cortex, and lesion borders show low coherency, consistent with known disruption of the tissue’s myeloarchitecture. These outputs provide quantitative readouts suitable for downstream statistical analysis and cohort comparison, in place of arbitrary sampling decisions.

As a benchmark comparison, the team trained nnU-Net v2, a widely used self-configuring segmentation framework, on the identical data. Their compact attention U-Net achieved a higher mean Dice on both the full eight-tile test set, 0.717 versus 0.555, and the seven axon-bearing tiles, 0.677 versus 0.634, while using roughly six times fewer parameters than nnU-Net’s self-configured network. The advantage was clearest on a white matter tile where axons run perpendicular to the cutting plane and appear as small cross-sectional profiles. The authors caution that with only eight test tiles, this comparison should be read as an honest benchmark rather than a definitive ranking.

The study has clear limitations. All tissue came from a single disease context, multiple sclerosis, and followed a single staining protocol, and all training data were digitized at one resolution of 0.273 micrometers per pixel. Preliminary tests at coarser resolutions looked visually convincing but were not quantitatively evaluated, and generalization to other silver impregnation methods or other laboratories remains unverified. The annotation set of 33 tiles is small, and the inter-rater ceiling was estimated from just two tiles. Nevertheless, the team has released the full pipeline as open-source software, with the trained model hosted on Hugging Face and the source code archived on Zenodo, making it immediately deployable on tiled images and whole-slide scans. The researchers envision future integration with multimodal registration frameworks that would align these histological orientation maps with ex vivo and in vivo MRI data, establishing a quantitative histological ground truth for microstructure imaging and opening a new bridge between the microscopic world of silver-stained axons and the macroscopic images used in clinical neurology.

Subject of Research: Automated deep learning segmentation of axons in Bielschowsky silver-stained histological brain sections

Article Title: BasNet: Attention U-Net-Based Automated Axon Segmentation in Bielschowsky Silver-Stained Histology

Article References: Schönenberger, L., Egli, L., Gkotsoulias, D., Stadelmann, C., & Granziera, C. (2026). BasNet: Attention U-Net-Based Automated Axon Segmentation in Bielschowsky Silver-Stained Histology. Neuroinformatics, 24(3), Article 59. https://doi.org/10.1007/s12021-026-09815-z

Image Credits: AI Generated

DOI: 10.1007/s12021-026-09815-z

Keywords: Bielschowsky silver stain, axon segmentation, attention U-Net, deep learning, computational pathology, multiple sclerosis, neuropathology, image segmentation, axon density, whole-slide imaging, Focal Tversky Loss, Neuroinformatics