# Quantification of relative neurite tortuosity using Fourier transforms

## TL;DR

This paper introduces a new method using Fourier transforms to measure the tortuosity of nerve fibers in images without needing full segmentation.

## Contribution

The novel contribution is a Fourier transform-based method for quantifying neurite tortuosity without requiring complete segmentation or manual scoring.

## Key findings

- The method accurately distinguishes scale variant and scale invariant tortuosity in simulated datasets.
- It successfully identifies differences in neurite tortuosity between the peripheral and central cornea in murine images.
- The approach enables rapid and accurate measurement without manual training or curation.

## Abstract

The tortuosity of nerve fibers has been shown to be important for identifying and monitoring clinically relevant manifestations resulting from of a variety of ocular and systemic disease pathologies and disorders. However, quantifying tortuosity in dense neurite networks can prove challenging, as existing methods require manual scoring and/or complete segmentation of the neurite network.

We measured neurite tortuosity by quantifying the degree of directional coherence in the Fourier transform of segmented neurite masks. This allowed for the analysis of neurite tortuosity without requiring complete segmentation of the neurite network. We were also able to adapt this method to measure tortuosity at different length and size scales.

With this novel method, neurite tortuosity was accurately quantified in simulated data sets at multiple length scales and scale variant and scale invariant tortuosity was accurately distinguished. Use of this method on images of murine corneal neurites correctly distinguished known differences between neurite tortuosity in the peripheral and central cornea.

Other methods require complete segmentation of neurites, which can be prohibitive in dense and/or sparsely labeled neurite networks such as in the cornea. Additionally, other methods require manual curation, manual scoring, or generation of a curated training set, while our novel method directly measures tortuosity as an intrinsic property of the image.

We report the use of Fourier transforms for quantification of neurite tortuosity at multiple length scales, and with an image input that contains incompletely segmented neurites. This new method does not require manual training or curation, allowing a direct and rapid measurement of neurite tortuosity, thereby enhancing the accuracy and utility of neurite tortuosity measurements for evaluation of ocular and systemic disease pathology.