Biomechanics Principles and Applications - Donald R. Peterson & Joseph D. Bronzino

Note: A total of 143 N axial force applied across the wrist.

Source: Horii E., Garcia-Elias M., An K.N., Bishop A.T.,

Cooney W.P., Linscheid R.L., and Chao E.Y. 1990. J. Bone Joint

Surg. 15A: 393.

transmits 31% of the total applied force, the scapho–capitate joint transmits 19%, the luno-capitate joint transmits 29%, and the triquetral-hamate joints transmits 21% of the load.

A limited amount of studies have been done to determine the contact areas in the midcarpal joint. Viegas et al. [1990] have found four general areas of contact: the scapho-trapezial-trapezoid (STT), the scapho-capitate (SC), the capito-lunate (CL), and the triquetral-hamate (TH). The high pressure contact area accounted for only 8% of the available joint surface with a load of 32 lbs and increased to a maximum of only 15% with a load of 118 lbs. The total contact area, expressed as a percentage of the total available joint area for each fossa was: STT = 1.3%, SC = 1.8%, CL = 3.1%, and TH = 1.8%.

The correlation between the pressure loading in the wrist and the progress of degenerative osteoarthritis associated with pathological conditions of the forearm was studied in a cadaveric model [Sato, 1995]. Malunion after distal radius fracture, tear of triangular fibrocartilage, and scapholunate dissociation were all responsible for the alteration of the articulating pressure across the wrist joint. Residual articular incongruity of the distal radius following intra-articular fracture has been correlated with early osteoarthritis. In an in vitro model, step-offs of the distal radius articular incongruity were created. Mean contact stress was significantly greater than the anatomically reduced case at only 3 mm of step-off [Anderson et al., 1996].

3.6.3 Axes of Rotation

The complexity of joint motion at the wrist makes it difficult to calculate the instant center of motion. However, the trajectories of the hand during radioulnar deviation and flexion/extension, when they occur in a fixed plane, are circular, and the rotation in each plane takes place about a fixed axis. These axes are located within the head of the capitate and are not altered by the position of the hand in the plane of rotation [Youm et al., 1978]. During radioulnar deviation, the instant center of rotation lies at a point in the capitate situated distal to the proximal end of this bone by a distance equivalent to approximately one-quarter of its total length (Figure 3.28). During flexion/extension, the instant center is close to the proximal cortex of the capitate, which is somewhat more proximal than the location for the instant center of radioulnar deviation.

Normal carpal kinematics were studied in 22 cadaver specimens using a biplanar radiography method. The kinematics of the trapezium, capitate, hamate, scaphoid, lunate, and triquetrum were determined during wrist rotation in the sagittal and coronal plane [Kobagashi et al., 1997]. The results were expressed using the concept of the screw displacement axis and covered to describe the magnitude of rotation about and translation along three orthogonal axes. The orientation of these axes is expressed relative to the radius

3

1

FIGURE 3.28 The location of the center of rotation during ulnar deviation (left) and extension (right), determined graphically using two metal markers embedded in the capitate. Note that during radial–ulnar deviation the center lies at a point in the capitate situated distal to the proximal end of this bone by a distance equivalent to approximately one-quarter of its total longitudinal length. During flexion–extension, the center of rotation is close to the proximal cortex of the capitate. (From Youm Y., McMurty R.Y., Flatt A.E., and Gillespie T.E. 1978. J. Bone Joint Surg. 60A: 423. With permission.)

during sagittal plane motion of the wrist (Table 3.18). The scaphoid exhibited the greatest magnitude of rotation and the lunate displayed the least rotation. The proximal carpal bones exhibited some ulnar deviation in 60◦ of wrist flexion. During coronal plane motion (Table 3.19), the magnitude of radial–ulnar deviation of the distal carpal bones was mutually similar and generally of a greater magnitude than that of the proximal carpal bones. The proximal carpal bones experienced some flexion during radial deviation of the wrist and extension during ulnar deviation of the wrist.

TABLE 3.18 Individual Carpal Rotation Relative to the Radius (Deg) (Sagittal Plane Motion of the Wrist)

a N-E60: neutral to 60◦ of extension; N-E30: neutral to 30◦ of extension; N-F30: neutral to 30◦ of flexion; N-F60: neutral to 60◦ of flexion.

SD = standard deviation.

Source: Kobayashi M., Berger R.A., Nagy L. et al. 1997. J. Biomech. 30: 8, 787.

TABLE 3.19 Individual Carpal Rotation to the Radius (Deg) (Coronal Plane Motion of the Wrist)

a N-RD15: neutral to 15◦ of radial deviation; N-UD30: neutral to 30◦ of ulnar deviation; N-UD15: neutral to 15◦ of ulnar deviation.

SD = standard deviation.

Source: Kobayashi M., Berger R.A., Nagy L. et al. 1997. J. Biomech. 30: 8, 787.

3.7 Hand

The hand is an extremely mobile organ that is capable of conforming to a large variety of object shapes and coordinating an infinite variety of movements in relation to each of its components. The mobility of this structure is possible through the unique arrangement of the bones in relation to one another, the articular contours, and the actions of an intricate system of muscles. Theoretical and empirical evidence suggest that limb joint surface morphology is mechanically related to joint mobility, stability, and strength [Hamrick, 1996].

3.7.1 Geometry of the Articulating Surfaces

Three-dimensional geometric models of the articular surfaces of the hand have been constructed. The sagittal contours of the metacarpal head and proximal phalanx grossly resemble the arc of a circle [Tamai et al., 1988]. The radius of curvature of a circle fitted to the entire proximal phalanx surface ranges from 11 to 13 mm, almost twice as much as that of the metacarpal head, which ranges from 6 to 7 mm (Table 3.20). The local centers of curvature along the sagittal contour of the metacarpal heads are not fixed. The locus of the center of curvature for the subchondral bony contour approximates the locus of the center for the acute curve of an ellipse (Figure 3.29). However, the locus of center of curvature for the articular cartilage contour approximates the locus of the obtuse curve of an ellipse.

The surface geometry of the thumb carpometacarpal (CMC) joint has also been quantified [Athesian et al., 1992]. The surface area of the CMC joint is significantly greater for males than for females (Table 3.21). The minimum, maximum, and mean square curvature of these joints is reported in Table 3.21. The curvature of the surface is denoted by κ and the radius of curvature is ρ = 1/κ . The curvature is negative when the surface is concave and positive when the surface is convex.

TABLE 3.20 Radius of Curvature of the

Middle Sections of the Metacarpal Head and

Proximal Phalanx Base

Source: Tamai K., Ryu J., An K.N., Linscheid R.L., Cooney W.P., and Chao E.Y.S. 1988. J. Hand Surg. 13A: 521.

A

A

A

Local center of bony contour

Local center of cartilage contour

FIGURE 3.29 The loci of the local centers of curvature for subchondral bony contour of the metacarpal head approximates the loci of the center for the acute curve of an ellipse. The loci of the local center of curvature for articular cartilage contour of the metacarpal head approximates the loci of the bony center of the obtuse curve of an ellipse. (From Tamai K., Ryu J., An K.N., Linscheid R.L., Cooney W.P., and Chao E.Y.S. 1988. J. Hand Surg. 13A: 521. Reprinted with permission of Churchill Livingstone.)

TABLE 3.21 Curvature of Carpometacarpal Joint Articular Surfaces

Note: Radius of curvature: ρ = 1/κ .

Source: Athesian J.A., Rosenwasser M.P., and Mow V.C. 1992. J. Biomech. 25: 591.

3.7.2 Joint Contact

The size and location of joint contact areas of the metacarpophalangeal (MCP) joint changes as a function of the joint flexion angle (Figure 3.30). The radioulnar width of the contact area becomes narrow in the neutral position and expands in both the hyperextended and fully flexed positions [An and Cooney, 1991].

Passive hyperext

Active extension

Neutral

45° Flexion

90° Flexion

Volar

FIGURE 3.30 (a) Contact area of the MCP joint in five joint positions. (b) End on view of the contact area on each of the proximal phalanx bases. The radioulnar width of the contact area becomes narrow in the neutral position and expands in both the hyperextended and fully flexed positions. (From An K.N. and Cooney W.P. 1991. In B.F. Morrey (Ed.), Joint Replacement Arthroplasty, pp. 137–146, New York, Churchill Livingstone. By permission of Mayo Foundation.)

FIGURE 3.31 Summary of the contact areas for all specimens, in lateral pinch with a 25 N load. All results from the right hand are transposed onto the schema of a carpometacarpal joint from the left thumb. (From Ateshian G.A., Ark J.W., Rosenwasser M.P., et al. 1995. J. Orthop. Res. 13: 450.)

In the neutral position, the contact area occurs in the center of the phalangeal base, this area being slightly larger on the ulnar than on the radial side.

The contact areas of the thumb carpometacarpal joint under the functional position of lateral key pinch and in the extremes of range of motion were studied using a stereophotogrammetric technique [Ateshian et al., 1995]. The lateral pinch position produced contact predominately on the central, volar, and volar–ulnar regions of the trapezium and the metacarpals (Figure 3.31). Pelligrini et al. [1993] noted that the palmar compartment of the trapeziometacarpal joint was the primary contact area during flexion adduction of the thumb in lateral pinch. Detachment of the palmar beak ligament resulted in dorsal translation of the contact area producing a pattern similar to that of cartilage degeneration seen in the osteoarthritic joint.

3.7.3 Axes of Rotation

Rolling and sliding actions of articulating surfaces exist during finger joint motion. The geometric shapes of the articular surfaces of the metacarpal head and proximal phalanx, as well as the insertion location of the collateral ligaments, significantly govern the articulating kinematics, and the center of rotation is not fixed but rather moves as a function of the angle of flexion [Pagowski and Piekarski, 1977]. The instant centers of rotation are within 3 mm of the center of the metacarpal head [Walker and Erhman, 1975]. Recently the axis of rotation of the MCP joint has been evaluated in vivo by Fioretti [1994]. The instantaneous helical axis of the MCP joint tends to be more palmar and tends to be displaced distally as flexion increases (Figure 3.32).

The axes of rotation of the CMC joint have been described as being fixed [Hollister et al., 1992], but others believe that a polycentric center of rotation exists [Imaeda et al., 1994]. Hollister et al. [1992] found that axes of the CMC joint are fixed and are not perpendicular to each other, or to the bones, and do not intersect. The flexion/extension axis is located in the trapezium, and the abduction/adduction axis is on the first metacarpal. In contrast, Imaeda et al. [1994] found that there was no single center of rotation, but rather the instantaneous motion occurred reciprocally between centers of rotations within the trapezium and the metacarpal base of the normal thumb. In flexion/extension, the axis of rotation was located within the trapezium, but for abduction/adduction the center of rotation was located distally to the trapezium and within the base of the first metacarpal. The average instantaneous center of circumduction was at approximately the center of the trapezial joint surface (Table 3.22).