Predicting Carpal Bone Kinematics Using an Expanded Digital Database of Wrist Carpal Bone Anatomy and Kinematics

Abstract

The wrist can be considered a 2 degrees-of-freedom joint with all movements reflecting the combination of flexion-extension and radial-ulnar deviation. Wrist motions are accomplished by the kinematic reduction of the 42 degrees-of-freedom of the individual carpal bones. While previous studies have demonstrated the minimal motion of the scaphoid and lunate as the wrist moves along the dart-thrower's path or small relative motion between hamate-capitate-trapezoid, an understanding of the kinematics of the complete carpus across all wrist motions remains lacking. To address this, we assembled an open-source database of in vivo carpal motions and developed mathematical models of the carpal kinematics as a function of wrist motion. Quadratic surfaces were trained for each of the 42-carpal bone degrees-of-freedom and the goodness of fits were evaluated. Using the models, paths of wrist motion that generated minimal carpal rotations or translations were determined. Model predictions were best for flexion-extension, radial-ulnar deviation, and volar-dorsal translations for all carpal bones with R ² > 0.8, while the estimates were least effective for supination-pronation with R ² < 0.6. The wrist path of motion's analysis indicated that the distal row of carpal bones moves rigidly together (<3° motion), along the anatomical axis of wrist motion, while the bones in the proximal row undergo minimal motion when the wrist moves in a path oblique to the main axes. The open-source dataset along with its graphical user interface and mathematical models should facilitate clinical visualization and enable new studies of carpal kinematics and function. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:2661-2670, 2019.

Keywords: carpal database; carpal kinematics; kinematics modeling; open-source database; wrist motion.

Figure 1.

Wrist motions within the carpal dataset for all 120 wrists. Wrist motion was defined as the motion of capitate in the radial coordinate system, and each point depicts the motion of the wrist in a single task.

Figure 2.

Radial coordinate system and the helical axis of motion parameters. n is a vector defining the orientation of the screw axis (n_x, n_y, n_z), and φ_tot is the rotation about the axis. This angle can be decomposed into rotational components (φ_tot.n_x, φ_tot.n_y, φ_tot.n_z).

Figure 3.

Training set (motions used to construct the model) from 86 wrists and test set (motions used to evaluate the model) from 30 wrists were randomly selected from the database. Each data point has 42 other dimensions for 7 carpal bones and 6 degrees-of-freedom.

Figure 4.

The flexion-extension of scaphoid (SCA_FE) as the function of wrist motion for the database (Left), quadratic model’s prediction (Middle), and the model error (Right). The model error (the differences between the training values and predicted values) qualitatively demonstrate a similar model performance in all regions. Each triangle’s face color is the average of the SCA_FE at each vertex.

Figure 5.

Mathematical model errors for scaphoid flexion-extension (SCA_FE), the histogram of errors based on the wrist movement for each octant of RU and FE. The middle figure shows the model error across kinematics space, and every histogram shows the errors in every subdivision. The octants are defined based on the relationship between radial (R)/ulnar (U) deviation and flexion (F)/extension (E) of the wrist. For example, UE defines the region that the ulnar deviation is larger than extension, and FR describes the region that flexion is larger than radial deviation.

Figure 6.

Wrist paths that generate minimal flexion-extension, radial-ulnar deviation, radial-ulnar translation, and volar-dorsal translation of carpal bones. Different patterns of wrist paths were seen for the carpal bones in the distal row (i.e., hamate, capitate, trapezoid, and trapezium) and proximal row (i.e., triquetrum, lunate, and scaphoid).