The Biomechanics of the Glenohumeral Articulation and Implications for Prosthetic Design

Fig. 31.1

The force from deltoid contraction (gray) acts some distance from the center of glenohumeral rotation and therefore acts both to rotate the joint and to translate this superiorly

When a force is applied to the proximal humerus, the direction of this force determines whether the shoulder will remain stable or whether subluxation will occur. If we assume in the first instance that the effects of friction are negligible, then the glenohumeral joint force must be exactly perpendicular to the articular surfaces at their point of contact. That is, the position of the humeral head will move across the glenoid surface until the point of glenohumeral contact directly opposes the applied force. If no such point of contact exists then the joint will not be stable as indicated in Fig. 31.2. This is the fundamental geometrical contact requirement for joint stability. Indeed, many of the experimental observations on shoulder behavior are a direct consequence of this fundamental principle.

Fig. 31.2

Under conditions of zero friction stability of the glenohumeral joint depends on whether the humeral head can slide over the glenoid surface to find a contact that is perpendicular to the applied force. The condition on the left is stable; that on the right is not

Under the action of the deltoid muscle alone, the shoulder joint would tend to be unstable. The large range of motion requires that joint ligaments remain slack and only apply their passive constraints at extremes of motion. Active stabilization is needed and this is provided by the additional contraction of the rotator cuff muscles. To understand this combined effect of deltoid and rotator cuff contraction we must consider how their forces can be combined into a single “resultant” force. To combine the effects of two or more forces that act in different directions we can use the parallelogram of forces as shown in Fig. 31.3. Note that the muscles that give rise to these force do not have to be attached physically to the same point, the parallelogram represents only their directions and not their physical location.

Fig. 31.3

The length of the two connecting sides of the parallelogram F1 and F2 represents the magnitude of two forces. The resultant force R is represented in both magnitude and direction by the diagonal across the parallelogram of forces

Also, the parallelogram of forces can be used to uncouple a single force R into its horizontal and vertical components, R_x and R_y respectively, as shown in Fig. 31.4.

Fig. 31.4

A single force R can be separated into its horizontal and vertical components, R_x and R_y using the parallelogram of forces concept. The two forces R_x and R_y will thus produce exactly the same effect as R

When performing any of the activities of daily living, numerous forces act upon the humerus. These forces are derived from muscle actions, ligament constraints, and any supported weights. If at such a time the arm is held in a steady position, then the humerus itself is said to be in a state of mechanical “equilibrium” in which all applied moments (forces multiplied by the distance to the center of rotation) balance, so the net turning effect is zero. Also, all the applied forces similarly balance, so that all the horizontal and vertical components sum to zero, and consequently the net resultant force on the humerus is zero.

Armed with these three basic concepts of (i) the geometric contact requirements for joint stability, (ii) the parallelogram of forces, and (iii) the balance of turning moments and forces for mechanical equilibrium, we now have the tools necessary for a mechanical analysis of the glenohumeral joint.

Glenohumeral Force and Joint Stability

Before considering the forces that act across the shoulder, let us first examine the stability of the anatomical glenohumeral joint. Any glenohumeral joint force R can be uncoupled using the parallelogram of forces into a force R _xdirected centrally into the glenoid and a second shearing force R _ycomponent that is perpendicular to this as shown in Fig. 31.4. R _xtends to stabilize the joint whilst the component R _ytends to cause the joint to dislocate. The dominate effect depends on the curvature of the glenoid.

Iannotti et al. [9] have conducted a detailed study into the geometry of the glenohumeral joint and have found the geometry of the anatomical humeral and glenoid surfaces to be approximately spherical. The average radius of curvature of the normal glenoid surface is 27 mm with an average supero-inferior dimension of 39 mm. Therefore, in the scapular plane, this average glenoid surface will subtend an arc of ±46° about the center of the glenoid as shown in Fig. 31.5. In the absence of other factors, the requirement for joint stability is that the direction of the joint force R must be within this arc. That is:

${R}_y/{R}_x< \tan\ 46{}^{\circ}$

${R}_y/{R}_x<1.04$

Therefore, whilst this R _y/R _xratio value will normally vary as the shoulder moves, it must always be less than unity for the shoulder joint to remain stable in the supero-inferior direction. A consequence is that a high R _xforce component will increase glenohumeral stability. Subluxation forces will therefore be directly proportional to the applied joint load, as has been observed experimentally by both Fukuda et al. [7] and Severt et al. [8]. Lippit et al. [15] referred to this effect as “concavity compression”, noting that increased stability correlated with the depth of the glenoid concavity and indicated that scapular movement may also help centralize the glenohumeral articulation.

Fig. 31.5

This scale drawing shows the mean anatomical supero-inferior dimension of the glenoid and the maximum angle of the joint resultant force R for joint stability. To maintain R within this maximum limit the ratio of R_x:R_y must be less than 1:1.04. The angle 46° determines the “constraint,” the higher this angle is the more constrained is the joint

Other factors will also play a role in augmenting the stability of the glenohumeral joint. The periphery of the joint is surrounded by a fibrous tissue labrum that further resists joint subluxation by effectively extending the glenoid surface through a greater arc than is shown in Fig. 31.5. The labrum consequently increases resistance to subluxation by between 18 and 52 % around the glenoid [15]. However, on the other hand, the deformation of the humeral and glenoid articular cartilage will modify surface curvature under loading so that subluxation may begin inside the glenoid periphery. The above theoretical maximum R _y/R _xratio for the normal glenoid therefore probably overestimates the limit to glenoid stability.

The humeral head radius of curvature is found typically to be 2 mm smaller than the radius of the glenoid [9, 15]. Although the deformation of the articular cartilage that covers the opposing surfaces will accommodate some of this mismatch, the curvature difference will give the humeral head the capacity to slide across the face of the glenoid somewhat to find a position of mechanical equilibrium as shown in Fig. 31.2.

Constraint and Conformity of the Glenoid Surface

The angle subtended by the glenoid, as shown in Fig. 31.5, determines the constraint of the glenohumeral joint. The more the glenoid surface wraps around the humeral head, the greater is the joint stability, but this increased constraint reduces the available range of motion. Therefore, a compromise is needed. In the shoulder, the need for a great range of motion requires a significantly reduced constraint than, for example, in the hip where a greater stability and reduced motion is more suitable.

A second feature that defines the glenohumeral articulation is the conformity that is given by the mismatch between the radii of curvature of the opposing contact surfaces. As noted above, the glenoid radius of curvature may typically be 2 mm larger than that of the opposing humeral surface, enabling some degree of translation of the humeral head across the glenoid surface [11]. Therefore, one would expect any increase in conformity to reduce range of motion to some degree, as this sliding motion is more limited, although Harryman et al. [8] found this effect to be small. Reduced conformity does lead to reduced contact areas and thus increased contact stresses, so that again some form of compromise is required.

From the analysis given above, the maximum R _y/R _xratio defining the limit for the stable shoulder will increase as the constraint increases, varying with the tangent of the glenoid angle as shown in Fig. 31.6. Conformity would not be expected to affect the stability in the same way.

Fig. 31.6

Variation of the maximum R_y/R_x value with the geometric constraint of the glenoid. The mark (^*) shows the constraint of the average anatomical glenoid and (o) shows the comparable position of the Neer prosthetic glenoid

Forces in the Abducted Shoulder

Analysis of the kinematics of the shoulder is complex in three dimensions. The joint itself is a mechanically indeterminate system so that, for instance, the same amount of glenohumeral movement can be achieved though different muscle actions [24]. However, an insight into the basic mechanics and the stabilizing action of the rotator cuff can be gained from a simple two-dimensional mechanical analysis. The first such analysis was conducted by Poppen et al. [16] and the analysis presented here is a derivation of this approach.

Here we will consider the situation shown in Fig. 31.1, in which the deltoid muscle alone is acting to abduct the humerus in the scapular plane [1]. The major effect of the rotator cuff musculature in this two-dimensional analysis is to pull the humeral head into the face of the glenoid, though supraspinatus is also able to abduct the shoulder [1]. The role of the rotator cuff musculature in other planes, such as for humeral internal and external rotation, cannot be considered in this two-dimensional analysis.

A first example considers a horizontally outstretched arm of 10 % body weight (0.1 W) supporting a further 0.1 W weight in the hand. In this arrangement, the force exerted by the deltoid muscle in order to maintain equilibrium with a horizontal abduction is shown in Fig. 31.7. For equilibrium, the clockwise turning moment of the loaded arm must be matched by the anti-clockwise turning moment generated by the deltoid. That is:

$0.1\mathrm{W}\times \mathrm{L}+0.1\mathrm{W}\times 2\mathrm{L}=0.1\times \mathrm{L}\times {\mathrm{F}}_{\mathrm{deltoid}}$

${\mathrm{F}}_{\mathrm{deltoid}}=3\mathrm{W}$

So that despite a fairly low physical loading (0.2 W), a deltoid force of three times body weight is needed to maintain equilibrium. This is simply because the deltoid acts through a small moment arm of only 5 % of the limb length (2 L), and thus a much higher force is needed to create an equivalent turning moment.

Fig. 31.7

Loading example of the horizontal arm. The hand is carrying a weight of 10 % body weight (0.1 W) and the weight of the arm itself (0.1 W) acts through the center of the limb. The two loads provide a clockwise turning moment that must be balanced by the anticlockwise moment of the deltoid force for the arm to remain abducted in equilibrium

The parallelogram of forces can be used to combine the forces that are now acting on the humerus into a single resultant force R as shown in Fig. 31.8. To maintain equilibrium this joint force is counteracted by an equal opposing reaction force from the glenoid onto the humerus. The single joint force R can be uncoupled using the same technique to give its horizontal and vertical components that are R _xand R _y. In this way R _xis simply the combined horizontal effect of the two original forces and R _yis likewise their combined vertical effect. Therefore, for the mechanical equilibrium shown in Fig. 31.8:

${R}_x=3\mathrm{W} \cos 20{}^{\circ}=2.82\mathrm{W}$