Barcodes distinguish morphology of neuronal tauopathy

TL;DR

This paper introduces a topological method using barcodes to analyze neuronal morphology, revealing significant differences between healthy neurons and those affected by tauopathy, especially in branch length and number.

Contribution

It demonstrates the equivalence of persistent homology and the topological morphology descriptor when using path length, and introduces topological morphology functions for neuron analysis.

Findings

Healthy and tauopathy-affected neurons show significant morphological differences.

Persistence images reveal shorter and fewer branches in diseased neurons.

Topological methods provide interpretable summaries of neuronal structure.

Abstract

The geometry of neurons is known to be important for their functions. Hence, neurons are often classified by their morphology. Two recent methods, persistent homology and the topological morphology descriptor, assign a morphology descriptor called a barcode to a neuron equipped with a given function, such as the Euclidean distance from the root of the neuron. These barcodes can be converted into matrices called persistence images, which can then be averaged across groups. We show that when the defining function is the path length from the root, both the topological morphology descriptor and persistent homology are equivalent. We further show that persistence images arising from the path length procedure provide an interpretable summary of neuronal morphology. We introduce {topological morphology functions}, a class of functions similar to Sholl functions, that can be recovered from the associated topological morphology descriptor. To demonstrate this topological approach, we compare healthy cortical and hippocampal mouse neurons to those affected by progressive tauopathy. We find a significant difference in the morphology of healthy neurons and those with a tauopathy at a postsymptomatic age. We use persistence images to conclude that the diseased group tends to have neurons with shorter branches as well as fewer branches far from the soma.