# A Linkage Representation of the Human Hand Skeletal System Using CT Hand Scan Images
###### Abstract  
The present study proposed a method for establishing a linkage representation of the human hand skeletal system. Hand skeletons of 15 male subjects were reconstructed from computed tomography (CT) scans in 10 different postures selected from a natural hand-closing motion. The wrist joint center was estimated as the intersection of the centerline of the metacarpal of the middle finger and the distal wrist create. The remaining joint centers were kinematically estimated based on the relative motion between the distal bone segment and the proximal bone segment of a given joint. A hand linkage representation was then formed by connecting the derived joint centers. Regression models for predicting internal hand link lengths using hand length as the independent variable were established. In addition, regression models for predicting the joint center coordinates of the thumb carpometacarpal (CMC) and finger metacarpophalangeal (MCP) joints using hand length or hand breadth were established. Our models showed higher \(R^{2}\) values and lower maximum standard errors than the existing models. The findings of the present study can be applied to hand models for ergonomic design and biomechanical modeling. Keywords:linkage representation; hand skeletal system; joint center of rotation; CT scan +
Footnote †: journal: Medical  
Buchholz et al. [8] measured link lengths and bone lengths with six fresh cadaver hands using radiographic techniques. They anatomically estimated joint centers as the center of curvature of the head of the bone proximal to the corresponding joint. They also estimated joint centers of proximal interphalangeal (PIP) and distal interphalangeal (DIP) joints using [PERSON]'s method [9] and found small differences (<1.4 mm) from those of the anatomical estimation. Regression formulas for predicting joint centers from bone lengths and those for predicting link lengths from hand lengths were established in their study. [PERSON] et al. 's study has several limitations as follows. First, joint centers were estimated anatomically rather than kinematically. Though they compared their anatomically estimated joint centers of PIP and DIP joints to those estimated by [PERSON]'s method and found small differences between the two results, they did not compare the estimation methods for the corpometacarpal (CMC) and metacarpophalangeal (MCP) joints. Furthermore, [PERSON]'s method is considered crude and error prone [1]. Second, they used cadaver hands to estimate joint centers that might not be the same as those estimated in vivo [1]. Third, two-dimensional (2D) radiographic images taken from the sagittal view were used to estimate the joint centers that can be different from those estimated using a three-dimensional (3D) hand skeleton. [PERSON] et al. [10] reconstructed a 3D hand skeleton from magnetic resonance imaging (MRI) scans and estimated the location of a finger joint CoR as the center of curvature of the portion of the head of the proximal bone segment in contact with the base of the distal bone segment of the finger joint in the sagittal plane. However, their method is still based on anatomy rather than kinematics. Joint centers or CoRs can be estimated using surface-marker-defined finger motions recorded from a motion capture system. Algorithms for estimating CoRs from surface-marker motion data have been developed [11; 12; 13; 14]. For example, [PERSON] et al. [14] estimated finger joint CoRs from surface-marker flexion-extension motions by minimizing the time-variance of the internal link lengths based on an empirically quantifiable relationship between the local movement of a surface marker around a joint and the corresponding joint flexion-extension angle. However, the estimated CoRs could be affected by the deformation and movement of the dorsal finger skin where the marker is attached during finger movement.