# Skeletonization of neuronal processes using Discrete Morse techniques from computational topology

## TL;DR

This paper introduces a new method using computational topology to better understand the structure of neurons in the brain.

## Contribution

The novel contribution is applying Discrete Morse techniques to skeletonize axon fragments in tracer data for neuroanatomy.

## Key findings

- The Discrete Morse technique combined with deep nets improves noise-robust skeletonization of labeled axons.
- An information theoretic measure is introduced to quantify additional insights from individual axon morphologies.
- The approach is scalable and demonstrated on whole-brain tracer data.

## 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.