# Automatic measurements of volar tilt and radial inclination of the distal radius on 3D models: validation against manual methods

## TL;DR

This paper introduces a new 3D algorithm to measure wrist bone alignment, which is more accurate and reliable than traditional 2D methods.

## Contribution

The novel contribution is an open-source algorithm for automatic 3D measurements of distal radius alignment with strong agreement to manual methods.

## Key findings

- Automatic 3D measurements showed small mean differences compared to manual 2D measurements (e.g., 2.0° for volar tilt in malunited radii).
- Strong agreement was found between automatic and manual 3D measurements.
- Landmark deviations averaged 2.5° for longitudinal axis differences.

## Abstract

Assessing distal radius malunions traditionally relies on measuring volar tilt and radial inclination in 2D radiographs. Reliability of these parameters is limited by projection errors and landmark ambiguity. Using 3D models allows more precise quantification of these parameters. This study validated an algorithm for measuring volar tilt and radial inclination on 3D virtual models of malunited and healthy radii. The algorithm establishes a 3D coordinate system and anatomical landmarks replicating conventional 2D definitions to maintain clinical compatibility. Automatic 3D measurements on models from 16 participants were compared with manual measurements on 2D radiographs (by three surgeons in consensus) and on 3D models (by two independent raters). Agreement was assessed using Bland–Altman analysis, and landmark discrepancies were quantified. Mean differences between automatic 3D and manual 2D measurements were small: for volar tilt, 2.0° in malunited and 3.5° in healthy radii; for radial inclination, 1.5° and 2.3°, respectively. Strong agreement was also found between automatic and manual 3D measurements. Landmark deviations ranged from 0.5 to 2.8 mm, with an average longitudinal axis difference of 2.5°. This open-source algorithm provides a reproducible 3D assessment of distal radius alignment. By closely matching 2D standards, the algorithm has a high potential for clinical integration.

The online version contains supplementary material available at 10.1038/s41598-025-33737-6.