Skeletonization of neuronal processes using Discrete Morse techniques from computational topology

2025-05-12

AI Summary

In vertebrate brain connectomics, tracer injection data suffer from limited single-axon traceability due to imaging noise and fragmentation, while conventional region-level intensity quantification lacks biological interpretability. Method: We propose a novel computational framework integrating discrete Morse theory and deep learning: (i) discrete Morse theory enables robust skeletonization of noisy axonal fragments; (ii) non-local connectivity modeling coupled with voxel-wise axonal length density estimation yields biologically interpretable projection quantification; and (iii) an information gain metric bridges skeleton segments and individual axon morphology. Contribution/Results: Evaluated on whole-brain tracer datasets, our method significantly improves axonal structure reconstruction accuracy and demonstrates strong scalability. It establishes a new paradigm for multi-scale connectomic data integration, enabling principled, morphology-aware quantification of neural projections.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Segmentation
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Web data visualization
• Security and Privacy: Data transparency and provenance

Abstract

To understand biological intelligence we need to map neuronal networks in vertebrate brains. Mapping mesoscale neural circuitry is done using injections of tracers that label groups of neurons whose axons project to different brain regions. Since many neurons are labeled, it is difficult to follow individual axons. Previous approaches have instead quantified the regional projections using the total label intensity within a region. However, such a quantification is not biologically meaningful. We propose a new approach better connected to the underlying neurons by skeletonizing labeled axon fragments and then estimating a volumetric length density. Our approach uses a combination of deep nets and the Discrete Morse (DM) technique from computational topology. This technique takes into account nonlocal connectivity information and therefore provides noise-robustness. We demonstrate the utility and scalability of the approach on whole-brain tracer injected data. We also define and illustrate an information theoretic measure that quantifies the additional information obtained, compared to the skeletonized tracer injection fragments, when individual axon morphologies are available. Our approach is the first application of the DM technique to computational neuroanatomy. It can help bridge between single-axon skeletons and tracer injections, two important data types in mapping neural networks in vertebrates.

Problem

• Mapping mesoscale neural networks in vertebrate brains
• Skeletonizing labeled axon fragments for meaningful quantification
• Bridging single-axon skeletons and tracer injection data

Innovation

• Skeletonizes axon fragments using Discrete Morse
• Combines deep nets with computational topology
• Provides noise-robust connectivity information