AMERICAN SOCIETY OF BIOMECHANICS Presented at the Twenty-First Annual Meeting of the American Society of Biomechanics Clemson University, South Carolina September 24-27, 1997

INTRODUCTION

An algorithm for quantifying and visualizing the three dimensional (3D) kinematics of the carpal bones of the wrist in vivo was developed.

REVIEW AND THEORY

It is well appreciated that the carpal bones exhibit complex 3D kinematics during normal wrist motion. However, quantification of carpal kinematics has been limited in the past to cadaveric studies because of the small size of the carpal bones and the need for invasive markers. Cadaveric studies are limited in their ability to simulate physiological loading patterns, healing effects, and rehabilitation. Several studies have examined the relative 3D posture and orientation of the carpal bones [1,2,4], but a quantitative analysis of 3D carpal kinematics in vivo has not yet been accomplished. It is also well appreciated that the motions of the carpal bones are coupled in 3D. Coupled motions are motions that are not separable and distinct from the main motion. Such motions are extremely difficult to fully appreciate from graphs. The purpose of this work was to describe an algorithm and to demonstrate its application for in vivo 3D kinematic analysis.

PROCEDURES

The algorithm consists of image acquisition, segmentation of bone surfaces, kinematics, and visualization. Image Acquisition. Multiple positions of the wrist were imaged using CT (HiSpeed Advantage, GE Medical Systems, Milwaukee, WI). The subject's (n = 1) wrists were positioned within the gantry in a custom positioning jig. Volume images were collected in axial format with typical voxel dimensions of 0.2x0.2x1 mm3. All image processing was performed on a Silicon Graphics workstation (Indigo2 XZ, SGI, Mountain View, CA) using the 3D biomedical imaging software system Analyze (Biomedical Imaging Resource, Rochester, MN).

Segmentation of Bone Surfaces. CT volumes were thresholded to emphasize the outer cortical shell. Contours were extracted after each bone cross-section was closed and filled. Automated matching of the contours to each bone is not presently attainable because of the number of bones, the complexity of the contours, and the potential for branching and holes. Interactive software (Open Inventor, C++, SGI; MATLAB, Mathworks, Natick, MA) was developed that allows visualization and manipulation of these contours in 3D to allow the user to define the correct contour-bone associations.

Kinematics. Each bone was assumed to move independently as a rigid body. Kinematic values were calculated using an existing method that minimizes the mean squared distance between two bone surfaces [3]. Bone kinematics were described using the helical axes of motion (HAM) parameters of rotation and translation about the helical axis. Additionally, kinematic error was studied using a cadaveric wrist specimen at four calibrated positions, allowing six kinematic comparisons (n = 6).

Visualization. Visualizing bone position and orientation is helpful to ensure algorithm success and can also provide diagnostic assistance [1]. Specifically written code in C++ and Open Inventor was utilized for visualization and animation.

RESULTS

Kinematic error was influenced by the particular carpal bone and the varied with the direction of motion (Table 1).

Table 1. Average 3D kinematic error.

	Trans. (mm)	Rot. (deg)
Scaphoid	1.7 ± 1.4	1.0 ± 0.9
Lunate	2.7 ± 2.0	1.7 ± 1.7

The 3D in vivo motions were complex and coupled as the capitate moved with wrist position and the scaphoid moved in an almost orthogonal direction (Table 2 and Figure 1).

Table 2. HAM rotations and translations (n = 1). The orientations and positions of helical axes are rendered in Figure 1.

	Radial Deviation	Ulnar Deviation
Capitate	34°, 0.7 mm	26°, 2.6 mm
Scaphoid	18°, 0.6 mm	25°, 2.6 mm

Figure 1. Palmer view of the left wrist of a healthy subject in neutral 1A and white), radial deviation (light gray), and ulnar deviation (dark gray). The motions of capitate (C) and scaphoid (S) are rendered (1B and 1C) with their respective helical axes for each wrist position. The radius (R) and ulna (U) are also rendered.

DISCUSSION

These data demonstrate the ability to accurately and noninvasively measure 3D joint kinematics in vivo. While we have shown that it is possible to precisely measure 3D carpal motion from CT volume images, the level of accuracy necessary to detect pathologic aberrations in kinematics is unknown.

The accuracy and visualization capabilities of the algorithm described herein will enable intricate analysis and deeper understanding of normal and abnormal carpal kinematics, carpal nonunions, malunited distal radius fractures, and metacarpophalangeal implants.

REFERENCES

[1] Belsole RJ et al. (1991) J Hand Surg., 16A(1): 82 - 90.

[2] Patterson RM et al. (1995) J Hand Surg, 20A(6):923-929.

[3] Pelizzari CA et al. (1989) J Comput Assist Tomogr. 13:20-26.

[4] Viegas SF et al., (1993) J Hand Surg., 18A(2): 341- 349.

ACKNOWLEDGMENTS

Supported in part by NIH AR44005.