# A Novel Method to Represent the Three-Dimensional Inclination of the Distal Radius Joint Surface

## TL;DR

This study introduces a 3D method to measure the distal radius joint surface, revealing gender differences and offering a new approach for treating wrist fractures.

## Contribution

A novel 3D method to quantify the inclination of the distal radius joint surface, including rotational alignment.

## Key findings

- Significant gender differences were found in the 3D vector components and angles of the distal radius joint surface.
- The new 3D method showed strong correlations with traditional 2D parameters like palmar tilt and radial inclination.
- The method enables assessment of rotational alignment, which is not possible with conventional 2D techniques.

## Abstract

Objectives: This study aims to define three-dimensional (3D) parameters for the inclination of the distal radius joint surface. The goal is to develop standardized parameters for fracture reduction through comprehensive 3D evaluations of the joint surfaces. Methods: We analyzed 112 CT scans of unaffected wrists (56 males and 56 females) to construct 3D models of the distal radius. Using 3D coordinates, the normal vectors and angles were calculated based on three reference points on the distal radius joint surface. These normal vector components were then converted into unit vector components A, B, and C for the x, y, and z axes, respectively. Additionally, the angles of these unit vectors were assessed in the xy, yz, and xz planes. The 3D measurements were compared between males and females and against traditional two-dimensional (2D) parameters such as palmar tilt and radial inclination. Results: For males, the unit vector components were as follows: A: −0.14 ± 0.09, B: −0.92 ± 0.02, and C: −0.36 ± 0.07; for females, A: −0.21 ± 0.08, B: −0.90 ± 0.03, and C: −0.36 ± 0.05. Significant differences were found between males and females for the A and B vector components (representing the palmar–dorsal and proximal–distal axes, p < 0.01). The angles of the unit vectors in the xy, yz, and xz planes were 8.9 ± 5.4°/12.9 ± 5.0°, 21.3 ± 4.1°/22.1 ± 3.2°, and 22.2 ± 14.8°/28.8 ± 10.1° for males and females, respectively. There were significant differences between males and females in the angles of the xy and xz planes (sagittal and axial planes, p < 0.01). Strong correlations were observed between the xy-plane vectors and palmar tilt (r = 0.96), as well as between the yz-plane vectors and radial inclination (r = 0.88). Conclusions: This study evaluated the 3D inclination of the distal radius joint surface, revealing significant gender differences. This method, which also allows for the assessment of rotational alignment—difficult with conventional techniques—is expected to be a key 3D parameter in treating distal radius fractures.