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

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.

Keywords: computed tomography; distal radius; joint inclination; rotational alignment; three-dimensional analysis.

Figure 1

Representative images for each reference point and normal vector. (1) Radial styloid process, (2) Volar edge of the sigmoid notch, (3) Dorsal edge of the sigmoid notch.

Figure 2

Angles of vectors in the xy, yz, and xz planes. (a) Angle of vector in the yz-plane. (b) Angle of vector in the xy-plane. (c) Angle of vector in the xz-plane.

Figure 3

Coordinates of three reference points in the axial plane (yz-plane). (a) Results of coordinates for males. (b) Results of coordinates for females. Orange dots indicate the radial styloid process: reference point (1). Gray dots indicate the sigmoid notch volar edge: reference point (2). Yellow dots indicate the sigmoid notch dorsal edge: reference point (3). Blue dots indicate the barycenter.

Figure 4

Coordinates of three reference points in the sagittal plane (xy-plane). (a) Results of coordinates for males. (b) Results of coordinates for females. Orange dots indicate the radial styloid process: reference point (1). Gray dots indicate the sigmoid notch volar edge: reference point (2). Yellow dots indicate the sigmoid notch dorsal edge: reference point (3). Blue dots indicate the barycenter.

Figure 5

The area of the plane enclosed by the three reference points. The area was significantly larger in males than in females (*: p < 0.01).

Figure 6

Correlation between the vector angles of the xy, yz, and xz planes. (a) Correlation between the vector angles of the xy-plane and yz-plane. (b) Correlation between the vector angles of the yz-plane and xz-plane. (c) Correlation between the vector angles of the xy-plane and xz-plane.

Figure 7

Correlations between the vector angles of the xy and yz planes and 3D-PT and 3D-RI. (a) Correlation between the vector angle of the xy-plane and 3D-PT. (b) Correlation between the vector angle of yz-plane and 3D-RI.