# Bridging local and global tortuosity of retinal vessels: Objective testing of index performance

## TL;DR

This paper introduces a new method to objectively measure the overall tortuosity of retinal vessels by combining local and global indices.

## Contribution

The novel framework evaluates global tortuosity using vessel compositionality and eliminates subjective assessments.

## Key findings

- The framework identifies optimal combinations of local indices and global weighting schemes.
- Factors like vessel partitioning and weighting schemes significantly influence global tortuosity.
- The method provides a mathematical and objective evaluation of tortuosity measures.

## Abstract

Retinal vessel tortuosity is a clinically significant parameter that aids in the diagnosis and risk stratification of various ocular and systemic diseases. While local tortuosity indices aim to quantify the winding nature of vessels in the intuitive way perceived by ophthalmologists, their integration into global measures for entire networks remains challenging. This study introduces a novel framework for objectively evaluating global tortuosity indices based on the concept of vessel compositionality. Within this framework, we compare the tortuosity of an unbranched vessel segment to the combined tortuosities of its constituent sub-segments. By analyzing the relationship between local and global tortuosity measures across a representative set of vessel segments, we can objectively assess (using the Spearman rank correlation coefficient) their performance and identify optimal combinations of local indices and global weighting schemes. This approach eliminates the need for subjective assessments of the global tortuosity by specialists, providing a purely mathematical and objective evaluation. Our findings demonstrate the influence of different factors on global tortuosity, including vessel partitioning, local index selection, and weighting schemes. This framework provides a valuable tool for understanding the behavior of tortuosity measures and optimizing their application in clinical settings.