F. Werner

WERNERF@VAX.CS.HSCSYR.EDU

B. Buchholz

BUCHHOLZB@WOODS.ULOWELL.EDU

March 1, 1994

SCOPE: This document defines a joint coordinate system for three dimensional rotational and translational motions in the hand and wrist. It is only one component of an overall standard being developed by the ISB on how to report kinematic data.

SIGNIFICANCE: In the study of joint kinematics, it is important to have common terminology that can be used by different investigators. Measurements by one research group, perhaps using a new methodology, can thus be compared to those by other groups.

RATIONALE: This document is based upon the ISB Standardization and Terminology Committee's recommendations for standardization in the reporting of kinematic data (draft version 4.1, 4/3/92). This document addresses only parts 2 and 5 of the ISB proposed standard. Part two requires a definition of the segmental local center of mass reference frames, and part five requires a definition of a method for expressing the relative attitudes of the body segments with respect to each other. The other parts of the proposed standard cover a definition of the global reference frame (part 1), global displacements (part 3), global attitudes (part 4), and joint moments (part 6).

Separate coordinate systems have been developed for each bone that is distal to the elbow, so that relative motion between any two adjacent segments may be described. These systems are then also applicable to global wrist motion as well as to motion of the individual components that cause the global motion. Global wrist motion is typically considered as the motion of the second and/or third metacarpal with respect to the radius and is achieved by movement of the carpal bones with respect to the radius as well as the numerous articulations of the eight carpal bones with respect to each other. Some researchers who only examine global wrist motion and have no need to examine carpal motion, can still use the definitions given for the radius and the metacarpal bones to describe wrist motion.

The ISB committee proposal recommends that orthogonal triads be fixed at the segmental center of mass. In the hand and wrist, the center of mass is simply not known for most of the segments or bones. Data from cadaver studies do exist that describe the center of mass location for the forearm and hand as a proportion of the entire length of each of these segments. These center of mass definitions may be fine for global wrist motions, but can not be used to describe the kinematics of the component parts. The phalanges can not be ignored and many researchers are examining individual movement of the carpal bones or movement of the radius with respect to the ulna. Therefore for this joint coordinate system application, the location of the orthogonal triad on each bone is primarily based on bony landmarks and is usually located at the axial center for long bones or the volumetric centroid for the carpal bones. (CT scans might be used to define the volumetric centroid, however this method may not be available or necessary for all applications.) If the center of mass location is necessary and defined, the origin may be translated from the bone center to the center of mass.

**DEFINITION OF SEGMENTAL LOCAL CENTER OF MASS REFERENCE**
**FRAME**

For each bone, a coordinate system is given, assuming that the forearm is initially in the standard anatomical position, with the palm forward (anterior), and the thumb lateral. The dorsum of the hand and forearm face posteriorly. In general, the positive Yi axis is directed proximally, and the positive Zi axis is directed to the right.

ULNA: The origin of the coordinate system is located midway between the distal ulna, at the level of the dome of the ulnar head; and the proximal ulna, at the level of the coronoid process. In the transverse plane it is at the approximate center of the tubular bone (at its moment of inertia). Since the Yi axis is directed proximally, the negative Yi axis is directed along the long shaft of the ulna from the specified origin to intersect with the center of the dome of the ulnar head. The positive Xi axis is directed anteriorly, oriented in the direction of the tuberosity of the ulna. The positive Zi axis is mutually perpendicular to the other two as defined by the right hand rule.

RADIUS: The origin of the coordinate system is located midway between the distal radius, at the level of the ridge between the radioscaphoid fossa and the radiolunate fossa; and the proximal radius, at the level of the depression in the proximal radial head. In the transverse plane it will be at the approximate center of the tubular bone (at its moment of inertia). Since the Yi axis is directed proximally, the negative Yi axis is directed along the long shaft of the radius from the specified origin to intersect with the ridge of bone between the radioscaphoid fossa and the radiolunate fossa (midway dorsally and palmarly along the ridge). The positive Zi axis is directed perpendicular to the Yi axis, to the right, in a plane defined by the tip of the radial styloid, the base of the concavity of the sigmoid notch and the specified origin. The positive Xi axis is mutually perpendicular to the other two as defined by the right hand rule.

CARPAL BONES: The eight carpal bones, scaphoid, lunate, triquetrum, pisiform, trapezium, trapezoid, capitate, and hamate, will be considered simultaneously. Most researchers only report angular changes in carpal bone motion and use the neutral wrist position as a neutral reference position. The neutral wrist position is when the wrist is in neutral flexion/extension and neutral radial/ulnar deviation such that the third metacarpal long axis is parallel with the Yi axis in the radius. These researchers define the motion relative to the radius and typically not the ulna. Therefore the orientation of the coordinate systems for each carpal bone should be parallel with the radius coordinate system when the wrist in the neutral position, using the previously defined convention for Xi, Yi, and Zi. At present, most researchers who need to define a coordinate system origin in a carpal bone use the volumetric centroid of the bone. Therefore it is proposed that, when necessary, the origin of a coordinate system in a carpal bone be located at the volumetric centroid of the bone.

METACARPALS: The five coordinate systems for the five metacarpals are described in the same manner. The major differences in the metacarpals are in the shape of their bases where "contact" with the carpals is made and their relative movement capabilities. In this regard, the first metacarpal has a very large range of motion. The third metacarpal has special significance because of its use in the definition of global wrist motion. Most researchers consider either the second or third metacarpal as representative of hand motion.

The origin for each of these coordinate systems is located midway between the base and head of each metacarpal. In the transverse plane, it will be at the approximate center of the tubular bone (at its moment of inertia). The positive Yi axis will be directed proximally, parallel to a line from the center of the distal head of the metacarpal to the midpoint of the base of the metacarpal. The positive Xi axis will be directed palmarly. The Xi and Yi axes will form a sagittal plane that splits the metacarpal into mirror images. The positive Zi axis will be directed laterally, perpendicular to both the Xi and Yi axes.

PHALANGES: The fourteen coordinate systems for the phalanges of the five digits can be described in a manner that is analogous to the description used for the metacarpal systems. The proximal and middle phalanges for the five digits are similar in shape as are the five distal phalanges.

Proximal Phalanges: The origin for each of these coordinate systems is located midway between the base and head of each phalanx. In the transverse plane, it will be at the approximate center of the tubular bone (at its moment of inertia). The positive Yi axis will be directed proximally, parallel to a line from the center of the distal head of the proximal phalanx to the center of the distal head of the metacarpal. The positive Xi axis will be directed palmarly. The Xi and Yi axes will form a sagittal plane that splits the phalanx into mirror images. The positive Zi axis will be directed laterally, perpendicular to both the Xi and Yi axes.

Middle Phalanges: The origin for each of these coordinate systems is located midway between the base and head of each phalanx. In the transverse plane, it will be at the approximate center of the tubular bone (at its moment of inertia). The positive Yi axis will be directed proximally, parallel to a line from the center of the distal head of the middle phalanx to the center of the distal head of the proximal phalanx. The positive Xi axis will be directed palmarly. The Xi and Yi axes will form a sagittal plane that splits the phalanx into mirror images. The positive Zi axis will be directed laterally, perpendicular to both the Xi and Yi axes.

Distal Phalanges: The origin for each of these coordinate systems is located midway between the base and head of each phalanx. In the transverse plane, it will be at the approximate center of the tubular bone (at its moment of inertia). The positive Yi axis will be directed proximally, parallel to a line from the center of the unguis of the distal phalanx to the center of the distal head of the middle phalanx. The positive Xi axis will be directed palmarly. The Xi and Yi axes will form a sagittal plane that splits the phalanx into mirror images. The positive Zi axis will be directed laterally, perpendicular to both the Xi and Yi axes.

**DEFINITION OF METHOD FOR EXPRESSING RELATIVE ATTITUDES**
**OF TWO SEGMENTAL COORDINATE SYSTEMS**

The methods of Grood and Suntay (1983) will be used to express the relative attitudes of two coordinate systems whenever possible. Applying these methods to the global wrist, interphalangeal, metacarpophalangeal, intercarpal, and radiocarpal joints is straight forward. A neutral posture can be defined as the position where the orientations of the proximal and distal segmental systems are identical. Flexion-extension will occur about the Zi-axis (proximal), rotation (pronation-supination) will occur about the Yj-axis (distal) and abduction-adduction (radio-ulnar deviation) will occur about the floating axis. This method allows for a relative attitude description that corresponds to clinical terminology.

Different methods will be needed for the five carpometacarpal joints and the radioulnar joint. The problem that arises with these joints is that the clinically neutral posture does not correspond to a position where the orientations of the proximal and distal segmental systems are identical for some of these joints. This problem can be overcome by stating the neutral posture using Grood and Suntay's method via an intermediate coordinate system, e.g. Cooney et al. (1981) described the neutral position of the trapeziometacarpal joint as being flexed 48 degrees, abducted 38 degrees and pronated 80 degrees with respect to the third metacarpal. In the case of the radioulnar joint, the Yi axes of the radius and ulna are not parallel. However, they only diverge by a few degrees depending upon the subject. Also, neither the radius or ulna can be considered proximal to the other. Therefore we are defining the motion between the radius and ulna as motion of the radius with respect to the ulna. The neutral position for the radius and ulna is clinically called neutral forearm rotation. With the elbow flexed to 90 degrees, this position can be visualized as when the thumb is pointing to the shoulder. In the standard anatomical position, the radius is supinated about the ulna. For the radioulnar joint, we propose an intermediate coordinate system whose origin is identical with the radial coordinate system origin. The orientation of this intermediate coordinate system will be identical to the ulnar coordinate system when the forearm is in neutral forearm rotation. The motion of the radius with respect to the ulna will then be described using the flexion/extension, radioulnar deviation, and pronation/supination definitions given above but using the intermediate coordinate system of the radius and the ulnar coordinate system. The user of this standard should define the orientation of the intermediate coordinate system relative to the anatomically based radial coordinate system.

**REFERENCES**

Cooney, Lucca, Chao and Lindscheid (1981) The kinesiology of the trapeziometacarpal joint, J Bone and Joint Surg 63A(9), 1371-1381.

Grood and Suntay (1983) A joint coordinate system for the clinical description of three-dimensional motions: Application to the knee, J Biomech Eng 105A, 136-144.