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Shoulder prosthesis subluxation: Theory and experiment
Shoulder prosthesis subluxation: Theory and experiment Carolyn Anglin, PhD, Urs P. Wyss, PhD, and David R. Pichora, MD, Winterthur, Switzerland, and Kingston, Ontario, Canada
The articular shapes of the humeral and glenoid components in total shoulder arthroplasty affect the loading, translation, and contact stresses in the joint, thereby affecting stability, glenoid loosening, and wear. Experiments were conducted to determine the subluxation load and corresponding translation for 6 types of glenoid components. The effects of shape, size, testing direction, compressive load, testing speed, testing medium, bone substitute properties, and repeated subluxations were investigated and compared with theoretical, rigid-body predictions. The subluxation load, varying from 45% to 98% of the axial load for the prostheses tested, is affected by glenoid constraint (ie, the maximum slope at the glenoid articular rim), the compressive load, the coefficient of friction, and the deformability of the articular edge. Rigid-body theory overestimated the experimental load, which was not surprising given the visible deformations, but provides a framework to highlight the relevant design parameters. The subluxation translation, ranging from 1 to 13 mm for the prostheses tested, is determined by the glenoid length and by the conformity between the humeral and glenoid radii. Experimental translations were greater than rigid-body predictions for the most conforming prostheses and roughly equal for less conforming prostheses. The goals of this study were to characterize the subluxation load and translation of a variety of types of prostheses, to develop the rigid-body basis for these results, to compare the rigidbody and experimental results, and to locate experimentally the glenoid articular rim for further testing. (J Shoulder Elbow Surg 2000;9:104-14.)
S
houlder prosthesis components have been designed with many variations in conformity and constraint. In particular, the 1970s saw the development of several constrained systems designed to address the problem From Sulzer Orthopedics Ltd, Winterthur, Switzerland, and Clinical Mechanics Group, Queen’s University, Kingston, Canada. Supported by Sulzer Orthopedics Ltd, Queen’s University, and the Ontario government. Reprint requests: Urs P. Wyss, PhD, Sulzer Orthopedics Ltd, PO Box 65, CH-8404 Winterthur, Switzerland. Copyright © 2000 by Journal of Shoulder and Elbow Surgery Board of Trustees. 1058-2746/2000/$12.00 + 0 32/1/105139 doi:10.1067/mse.2000.105139
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of glenohumeral instability. These fixed-fulcrum designs were largely abandoned because of high rates of loosening from the bone.6,26 More recently, discussion has focused on the optimal amount of conformity or mismatch between the humeral and glenoid components. Prostheses may have any combination of conformity and constraint, for example, high conformity and low constraint.23 The stability characteristics of both the natural joint and prosthetic replacements have been studied previously,10,15,17,19,20,23 but the only comparison to theoretical predictions was by Karduna et al,15 who compared measured and predicted radial mismatches. Constraint has been defined in different and often misleading ways. We define constraint as the maximum slope at the glenoid rim, which is determined by the angle enclosed by the glenoid, as demonstrated in Figure 1. Constraint is not defined by the “wall height”10,17 or by the “depth,”19,20 except when prostheses of the same length are being compared, since a given wall height for a large prosthesis would be less constraining than for a small prosthesis as a result of the change in the enclosed angle. Furthermore the constraint is unrelated to the humeral head size.23 The terms conformity and constraint are often used interchangeably; a theoretical understanding of subluxation helps to clarify these issues. A current controversy is the degree of conformity or mismatch that is desirable between the humeral and glenoid component radii. In the anatomic joint a flexible conformity exists in which the bony glenoid is flatter than the humeral head, but the glenoid bone together with the deformable cartilage and labrum form a spherical match with the humeral head.18,24 A prosthetic glenoid currently does not offer the same versatility, and one radius must be chosen. The choice of conformity affects the active translations, the joint contact stresses, and the translation to the articular rim. Karduna et al16 showed that a prosthesis radial mismatch of approximately 3 to 5 mm (ie, a radial conformity of 0.80 to 0.88) most closely reproduced the translations in the natural joint during normal active abduction (patients with rotator cuff disease and instability often show greater translations13,22). On the other hand, if the conformity is lower, the contact area is smaller and the contact stresses are larger. By this reasoning a conforming prosthesis should lead to less wear. However, as soon as there is eccentric translation, the humeral head in a
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Figure 1 Glenoid constraint is dependent on θ, which defines both the maximum slope (tan θ) at the glenoid rim and the angle enclosed by the glenoid from the deepest point on the glenoid. For symmetrical glenoids the total enclosed angle is 2θ.
conforming design must either deform into the polyethylene or move out toward the rim. This leads to increased stresses, increased rocking moments, and consequently an increased likelihood of wear and loosening.7,8 Friedman9 recorded such posterior rim loading in vivo during horizontal flexion and extension with patients who had received total shoulder replacements but showed no clinical instability. This correlates with clinical findings of posterior polyethylene wear in retrieved components.5,9,12,26 Less conforming designs offer the possibility of transferring more load to the soft tissues before reaching subluxation, thereby reducing the eccentric loads believed to lead to glenoid loosening. Given that central wear of the glenoid components is not currently a clinical concern, a less conforming design appears to offer advantages. Because joint translation, loading, and contact stresses are all influenced by the articular surface shapes of the humeral and glenoid components, these factors should be considered in prosthesis design and selection. The purposes of this study were to determine experimentally the load and translation required for subluxation for a variety of prosthesis types and to understand the results on a theoretical basis. Because loosening of the glenoid component is thought to be due to eccentric rim loading, the rim location is also useful for further testing.2 METHODS AND MATERIAL Test method A schematic of the test setup is shown in Figure 2. The bone substitute, consisting of a rigid polyurethane foam block (Last-a-Foam FR6720, General Plastics, Tacoma, WA), was prepared with the standard surgical instrumentation. The mechanical properties of the bone substitute (E = 193 MPa, σu = 7.6 MPa) were selected to rep-
Figure 2 Schematic of the biaxial testing apparatus. The humeral head is compressed horizontally into the glenoid and translated vertically. The subluxation load is the peak shear load for the given axial compressive load.
resent average properties of glenoid cancellous bone based on a cadaver study of 10 glenoids.3 The glenoid component was cemented into the bone substitute with the superoinferior axis oriented along the central axis of the block. The block was press-fit into a metal holder with either the superoinferior axis vertical or the anteroposterior axis vertical. With a dye the contact point for the humeral head was located to within ±0.5 mm of the central axis of the glenoid. The 2 most conforming glenoids left no mark but could be positioned easily to their deepest point. A pneumatic cylinder (SMC, Tokyo) compressed the humeral head horizontally into the glenoid at a constant given load (750 N, see following text), the load being electronically controlled to within 5 N of the given load. An Instron 8502 hydraulic testing machine (with a 1000-N load cell) translated the humeral head
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Figure 3 Subluxation load equilibrium. The subluxation load (Fv) depends on the slope of the glenoid rim (tanθ), the compressive load (Fh), and the coefficient of friction (see equation 3).
vertically. Both the glenoid and the humeral head traveled on linear bearings. Five triangular ramp displacement cycles large enough to reach a peak load top and bottom on each cycle were completed in the superoinferior direction. This was repeated in the anteroposterior direction. The purpose of the 5 cycles was to consider the effect of repeated subluxations in a patient with recurrent instability. The vertical and horizontal displacements and loads were recorded simultaneously on a computer. The horizontal displacement was measured by a linear-variable-differential-transformer; the horizontal load was measured by recording the electronically controlled pressure and converting it to a calibrated force; the vertical displacement and load were recorded by the hydraulic testing machine. The data were analyzed to find the peak load on each cycle and the corresponding subluxation translation relative to the deepest point on the glenoid; the deepest point was identified by the minimum horizontal displacement. Friction in the vertical bearing was measured in both directions by running the test without the head in contact with the glenoid; this friction load was subtracted from the subluxation load. The tests were conducted in air without a lubricant at room temperature except when a comparison was made with circulating water heated to 37°C. Air was the standard testing method, because the results were later used for a glenoid edge loading and displacement test that could not be immersed in water.2 The standard displacement speed was 50 mm/min to avoid excessive polyethylene creep or stress relaxation1; a speed of 15 mm/min was tested for comparison. The horizontal compressive load was 750 N. Together with the vertical shear load, this led to maximum resultant loads between 820 N and 1050 N, or approximately one to one-and-a-half times body weight. Although normal loading on the glenohumeral joint is lower, even activities of daily living can exert glenohumeral contact forces of several times body weight. The given loading was estimated
to represent the contact forces while carrying a 5- to 8-kg suitcase at the side or lifting a 2- to 4-kg box with both hands to shoulder height; it is also on the same order as (though even less than) getting in and out of a chair using the arms and walking with a cane.2 Rigid-body theory For subluxation or dislocation to occur, the resultant force must be directed outside of the glenoid surface. The subluxation load is therefore the equilibrium load when the humeral head is tangent to the rim of the glenoid. This is controlled by the maximum slope of the glenoid and by friction (Figure 3). The theoretical derivation assumes rigid bodies, that is, point contact and no deformations (which is only approximated at lower loads) and no tilting of the glenoid component. To allow a comparison of the subluxation load at different compressive loads and to provide a quick understanding of the relative magnitude of the subluxation load, the subluxation load is divided by the compressive load to give the force ratio. Summing the vertical and horizontal forces gives:
Subluxation load = Fv = Fn · sin θ + Ff · cos θ
(1)
Compressive load = Fh = Fn · cos θ – Ff · sin θ (2) Assuming the frictional force to be proportional to the normal force, then Ff = µ·Fn, where µ is the coefficient of friction. Dividing equation (1) by equation (2) gives:
Fv sin θ + µ · cos θ Force ratio = = = Fh cos θ – µ · sin θ tan θ + µ (3) 1 – µ · tan θ
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where, as shown in Figure 3: L tan θ = = Slope of glenoid edge R–d
(4)
For the theoretical calculations, a coefficient of friction of 0.07 was assumed. This was based on tests using the same test protocol but with the prosthesis articular surface sawed off and ground flat. The subluxation translation is the displacement to bring the humeral head from the deepest position on the glenoid to just into contact with the glenoid rim. Beyond this point the slope decreases; thus in the absence of restraining soft tissues the load continues to decrease. Referring to Figure 4, the translation distance, l, from the glenoid axis to the humeral head axis, is derived by similar triangles as:
l R–r = L R
(5)
Thus the subluxation translation is:
r Translation (l) = L · 1 – = L · (1 – conformity) = R mismatch L · (6) R
Because the effect of mismatch on translation depends on the glenoid radius, prostheses should be compared by their conformity rather than their mismatch. These equations were presented by Karduna et al14,15 and Walker et al25 but were not expressed in terms of the slope of the glenoid edge, the enclosed glenoid angle, the conformity, and the mismatch. The use of these terms helps to conceptualize the important factors in prosthesis design. The concept of the force ratio was introduced by Fukuda et al,10 who called it the stability ratio. Prostheses Six commercially manufactured, all-polyethylene, cemented prostheses were investigated. The glenoids possessed a wide range of characteristics (Table I) including sizes from extra-small to extra-large, enclosed angles from 14° to 45°, and conformities from 0.46 to 1.00 (ie, mismatches from 0 to 30 mm). The standard protocol (air, 50 mm/min, 750 N) was used for 2 samples of each prosthesis type in all 4 directions. Two additional prostheses of type C-XL were tested in 37°C water instead of air; 1 additional A-XL was tested at 15 mm/min instead of 50 mm/min, and 1 additional A-XL was cemented into a bone substitute with an elastic modulus of 66 MPa instead of the standard bone substitute with an elastic modulus of 193 MPa. Statistical evaluations of the effect of the testing parameters were made with the Student t test with α = .05.
RESULTS The experimental force ratios, ranging from 0.22 to 0.98, were lower than those predicted by treating the glenoid and humeral head as rigid bodies, as expected (Figure 5); the polyethylene deformation was visi-
Figure 4 Subluxation translation (l). Translation depends on the conformity between the humeral radius (r) and glenoid radius (R) and the glenoid length (L) (see equation 6).
ble. The discrepancy was greater for prostheses with greater constraint, that is, for those with a higher predicted force ratio. The experimental translations, ranging from 1.2 mm to 13.5 mm, were larger than the rigid-body predictions when the predicted translations were <3 mm, matching more closely at higher translations (Figure 6). By back-calculating with the experimental translation, the effective glenoid radius was 2 to 5 mm greater than the nominal glenoid radius. Only the results from the first cycle are presented here, because this represents the initial resistance to subluxation. Both theoretically and experimentally, large differences in subluxation load and translation were seen among the prostheses, particularly among the first 3 types, A-C (Figure 7, A, B). Prostheses C to F offered similar force ratios but different translations. In fact, their experimental force ratios were similar despite rigid-body-predicted differences. Consistent with Figure 6, the experimental translations matched the rigid-body predictions more closely for higher translations. The repeatability of the force ratio was excellent, having an average range between the 2 values of 0.02 (ie, 15 N); translation was less repeatable for the first 2 types of prosthesis, but for the remaining 4 types the average range between the 2 values was 0.09 mm, as shown in Figure 7, B. The primary reason for the translation variability for prosthesis A was the difficulty of defining the center position because of its flatness; the variability for prosthesis B was because 1 of the 2 prostheses was incorrectly cemented at an angle such that one side was higher than the other. For types B and C, both the force ratio and translation increased with size; for type A the force ratio changed little with size, whereas translation increased dramatically (Figure 8, A, B). Thus the trends with size
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Figure 5 Rigid-body theory versus experimental force ratio (subluxation load divided by compressive load). The experimental results were lower than predicted by rigid-body theory, especially at higher force ratios. The compressive load was 750 N. The coefficient of friction assumed in the following rigid-body calculations was 0.07.
Table I Prosthesis details (see Figure 3 for definitions) Characteristic Sizes tested Glenoid superior and inferior angles (°), θ Glenoid anterior and posterior angles (°), θ
A*
D
E
XL XS
L
L
45 38
33 22
40
43
40
17 14
31 26
23 14
27
28
29
56 40
26.5 20.5
35.6 31.8
29.5
29.5
25
26 20
26 20
26 20
26
26
25
XL S S:25, I:18 S:31, I:14
B
C
XL XS
F 1-size (M)
Glenoid radius (mm), R Humeral radius† (mm), r Conformity = r / R 0.46 0.50
0.98 0.98
0.73 0.63
0.88
0.88
1.00
Mismatch = R - r (mm) 30 20
0.5 0.5
9.4 11.8
3.5
3.5
0.0
S:5.4, I:2.6 S:5.7, I:1.1
7.8 4.3
5.7 2.9
6.7
7.8
5.8
3.9 2.1
2.8 1.5
3.3
3.4
3.2
18.75 12.5
19.25 13.0
18.75
20.0
16.0
13.75 9.0
13.75 9.5
13.5
13.75
12.25
Superior and inferior articular depths (mm), d Anterior and posterior articular depths (mm), d 2.3 1.3 Superior and inferior half-chords (mm), L S:24, I:17 S:20.5,I:9.5 Anterior and posterior half-chords (mm), L 16.0 10.0 S, Superior; I, inferior. *Prosthesis A is asymmetrical. †A variety of head sizes are available clinically for prostheses A to E.
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were design-dependent. A large head was used with the large components and a small head with the small components (Table I). The superoinferior direction consistently provided a higher subluxation force (more stability) than the anteroposterior direction (Figure 9, A). Translations were smaller in the anterior-posterior direction (Figure 9, B) but not by as great a difference as predicted from rigid-body theory. In all cases the force ratio decreased asymptotically from the first to the fifth cycle (by 0.04 ± 0.03 N/N), stabilizing by the fifth cycle. Translations increased asymptotically over the 5 cycles (by 0.71 mm ± 0.36 mm), also stabilizing by the fifth cycle. The medium (air at room temperature or water at 37°C) had a small but statistically significant effect on the force ratio: the force ratio in 37°C water was approximately 5% lower. There was no consistent trend for translation. Neither testing speed (50 mm/min compared with 15 mm/min) nor bone substitute properties (E = 193 MPa versus 66 MPa) showed a noticeable effect on the subluxation results.
DISCUSSION The difference between the experimental force ratios and the rigid-body predictions was likely primarily due to polyethylene deformation. This deformation could be seen visually, flattening the glenoid slope. The conclusion, not surprisingly, is that a polyethylene prosthesis does not act as a rigid body, especially given the high loads applied. On the other hand, the rigid-body analysis does provide a framework to conceptualize the important factors relevant to subluxation. The amount of deformation depended on the prosthesis design. Thinner, more peaked rims (eg, A and D to F) tended to deform more than rounded rims (B and C); prosthesis E was slightly more constrained than prosthesis D in their undeformed states, but this presented no difference experimentally because of the more peaked rim on prosthesis E. Prostheses with higher constraint tended to deform more than those with less constraint because of the higher loads. As made clear from the rigid-body analysis and confirmed experimentally by Karduna et al,17 the subluxation load is not affected by conformity. A material with a higher elastic modulus and yield strength would act more like a rigid body and would thus be expected to experience a closer match between the rigid-body prediction and the experimental results. On an absolute basis the subluxation load increases with compressive load (comparable to pressing rather than resting a golf ball on its tee); on a relative basis, however, the force ratio decreases with compressive load, implying increasing deformation.10,15,16,20 Thus force ratios can only be compared at the same compressive load. Experimental translations were typically higher than
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Figure 6 Rigid-body theory versus experimental subluxation translation. The experimental translations were higher than those predicted by rigid-body theory at low translations.
predicted theoretically, especially when the translations were small. This was presumably mostly the result of polyethylene deformation. The increase in effective radius was consistent with the findings of Karduna et al,15 who furthermore reported increasing translations with increasing compressive loads. Because of the sometimes large differences between the theoretical and experimental results, it is necessary to conduct this subluxation test if the glenoid edge location is required for further testing. The anteroposterior force ratios and translations were lower than those in the superoinferior direction. This result is consistent with the theory; because they both have the same radius, but the superoinferior axis is longer, the constraint is greater.20 The small lack of symmetry between superior and inferior or between anterior and posterior may have been due to several reasons: an uneven cemented position, reduced polyethylene deformation inferiorly caused by the often greater width, manufacturing variations, or greater friction in the vertical bearing when traveling downward (ie, inferiorly or posteriorly) in the loaded condition (this was seen on the flattened prosthesis). Translations were referenced to the deepest point, but this was less exact in flatter designs, and the translations would not have been centered if the prosthesis were not cemented evenly. The prostheses tested offered greater stability (ie, a higher force ratio) than the natural glenoid. In the natural glenoid Lippitt et al20 reported force ratios in the superior direction of 0.59 with a 50-N compressive load and 0.51 with a 100-N compressive load; the force ratio for the natural glenoid for a 750-N compressive load would be much lower. The prosthesis
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A
B
Figure 7 A, Rigid-body-predicted and experimental force ratios by prosthesis type (largest size, superior direction, n = 2); maximum/mean/minimum shown for experimental results. B, Subluxation translation by prosthesis type (largest size, superior direction, n = 2); maximum/mean/minimum shown for experimental results. Prosthesis A is asymmetrical; the translation from the center as opposed to the deepest point was 11.1 mm. The rigid-body-predicted translation for prosthesis F is zero.
results ranged from 0.45 to 0.98 for a 750-N compressive load. The difference in force ratio appeared to have less to do with differences in the unloaded shape (comparing Table I with Friedman9) and more to do with greater deformation in the natural joint.15 Except at the extremes of motion, the position of the anatomic humeral head on the natural glenoid is pri-
marily controlled by the shape of the articular surfaces, by the rotator cuff muscles, which actively center the head, and by the tilt (ie, version) of the glenoid.4,16,21 The test method used in this study was designed to evaluate the intrinsic stability of the prosthesis system. The resistance or contribution to subluxation of the ligaments, capsule, and passive muscle bulk was only rep-
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A
B
Figure 8 A, Effect of size on experimental force ratio (superior direction, n = 2); maximum/mean/minimum shown. The effect of size was design-dependent and cannot be generalized. B, Effect of size on experimental subluxation translation (superior direction, n = 2); maximum/mean/minimum shown. If the same head size had been used, the larger component would have shown much larger translations.
resented by means of the net load applied. That is, if the intrinsic subluxation load is 500 N, this may represent an external shear load of 600 N and a resistive load of 100 N. The external shear load required for subluxation would thus increase in vivo if the soft tissues were involved at the given translation. Conversely, for a given external load, the translation would decrease.
The soft tissues can also act to destabilize the joint if they are asymmetrically tight.11 Whereas testing was only conducted with the 0° glenoid version, other angles could be easily tested or calculated. An interesting addition to this study would be to compare the subluxation load for the components alone with that for components implanted into cadavers with
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A
B
Figure 9 A, Effect of testing direction on experimental force ratio (largest size, n = 2); maximum/mean/minimum shown. Possible reasons for the discrepancies between superior and inferior and anterior and posterior are described in the Discussion section. Prosthesis A is asymmetrical superoinferiorly. B, Effect of testing direction on experimental subluxation translation (largest size, n = 2); maximum/mean/minimum shown.
the soft tissues intact. For the more conforming prostheses, there is likely to be little effect, because the translations were very small; for the less conforming prostheses, there would likely be a variable effect between individuals. Estimating from the work of Blasier et al,4 the contribution of the capsule at 10-mm anterior displacement could be up to 200 N (ie, a change in force ratio
of 0.27 at 750 N); the contribution at normal anatomic translations would be expected to be much less. Regardless of the soft tissue contribution, the subluxation translation represents the distance to the glenoid rim, and the subluxation load represents the load that would be applied to the prosthesis under rim loading. After the substrate tests, which showed no signifi-
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cant differences for the 2 bone substitutes, it was decided that it was unnecessary to compare the performance in cadaver bone; the polyurethane foam was preferred due to its consistent properties and size and its ease of handling. The primary limitation of this work is that no attempt was made to refine the theory to improve the match between theory and experiment. Nevertheless, the relative effects of glenoid length, width, radius, articular depth, and conformity could be established from the rigid-body theory. From a design perspective the subluxation load is controlled by the maximum slope at the glenoid rim (ie, the constraint), and translation is controlled by the conformity and glenoid length. The confusion in the literature between conformity and constraint and their effects probably arose because more constrained prostheses tend to be more conforming. Geometrically, for the same length of prosthesis, if the glenoid radius is made larger (less conforming), the slope at the rim (constraint) must inevitably decrease. Confusion also stems from the use of the word “stability”: if it means the maximum shear load, then the relevant parameter is constraint, not conformity; if it means minimum translation, then conformity is relevant, not constraint; if stability means fixation quality in the bone (ie, likelihood of loosening), then highly constrained prostheses have shown poor “stability.”
CONCLUSIONS Six types of glenoid prosthesis were characterized by their subluxation load and translation, issues that are relevant to glenohumeral stability, glenoid loosening, and wear.2 Even though all of the prostheses tested would be classified as nonconstrained, they presented a large variation in the force ratio. A single value for each prosthesis is not sufficient, because it changes with prosthesis size, testing direction, and compressive load. Table II describes the effects of different variables on the subluxation force ratio and subluxation translation, indicating whether this effect is based on the rigid-body theory or experimental deformations. Experimental force ratios and translations should not be predicted from the rigid-body theory because of polyethylene deformation. On the other hand, the theory can be used to aid design and clarify the analysis. Additional consideration should be given to the rim design to inhibit deformation.
Table II Summary of effects on force ratio and translation
Variable Constraint (theory) Conformity (theory) Glenoid length (theory) Friction (theory) Compressive load (exp’t) Rim deformation (exp’t) Water @37°C vs. @RTAir (exp’t) Repeated Sublux’s (exp’t)
2. 3. 4.
5. 6. 7. 8. 9. 10. 11.
12.
13. 14. 15.
We thank René Flachsmann, previously of Sulzer Orthopedics Ltd, for designing the test apparatus, and Gerry Saunders of the Clinical Mechanics Group at Queen’s University for building the apparatus.
16.
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1. American Society for Testing and Materials (ASTM). Standard specification for ultra-high-molecular-weight polyethylene pow-
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Effect on force ratio
Effect on subluxation translation
↑ — — ↑ ↓ ↓ ↓ ↓
— ↓ ↑ — — ↑ — ↑
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23. Severt R, Thomas BJ, Tsenter MJ, Amstutz HC, Kabo JM. The influence of conformity and constraint on translational forces and frictional torque in total shoulder arthroplasty. Clin Orthop 1993;292:151-8. 24. Soslowsky LJ, Flatow EL, Bigliani LU, Mow VC. Articular geometry of the glenohumeral joint. Clin Orthop 1992;285:18190. 25. Walker PS, Ambarek MS, Morris JR, Olanlokun K, Cobb A. Anterior-posterior stability in partially conforming condylar knee replacement. Clin Orthop 1995;310:87-97. 26. Wirth MA, Rockwood CAJ. Current concepts review: complications of total shoulder-replacement arthroplasty. J Bone Joint Surg Am 1996;78A:603-16.
The articular shapes of the humeral and glenoid components in total shoulder arthroplasty affect the loading, translation, and contact stresses in the joint, thereby affecting stability, glenoid loosening, and wear. Experiments were conducted to determine the subluxation load and corresponding translation for 6 types of glenoid components. The effects of shape, size, testing direction, compressive load, testing speed, testing medium, bone substitute properties, and repeated subluxations were investigated and compared with theoretical, rigid-body predictions. The subluxation load, varying from 45% to 98% of the axial load for the prostheses tested, is affected by glenoid constraint (ie, the maximum slope at the glenoid articular rim), the compressive load, the coefficient of friction, and the deformability of the articular edge. Rigid-body theory overestimated the experimental load, which was not surprising given the visible deformations, but provides a framework to highlight the relevant design parameters. The subluxation translation, ranging from 1 to 13 mm for the prostheses tested, is determined by the glenoid length and by the conformity between the humeral and glenoid radii. Experimental translations were greater than rigid-body predictions for the most conforming prostheses and roughly equal for less conforming prostheses. The goals of this study were to characterize the subluxation load and translation of a variety of types of prostheses, to develop the rigid-body basis for these results, to compare the rigidbody and experimental results, and to locate experimentally the glenoid articular rim for further testing. (J Shoulder Elbow Surg 2000;9:104-14.)
S
houlder prosthesis components have been designed with many variations in conformity and constraint. In particular, the 1970s saw the development of several constrained systems designed to address the problem From Sulzer Orthopedics Ltd, Winterthur, Switzerland, and Clinical Mechanics Group, Queen’s University, Kingston, Canada. Supported by Sulzer Orthopedics Ltd, Queen’s University, and the Ontario government. Reprint requests: Urs P. Wyss, PhD, Sulzer Orthopedics Ltd, PO Box 65, CH-8404 Winterthur, Switzerland. Copyright © 2000 by Journal of Shoulder and Elbow Surgery Board of Trustees. 1058-2746/2000/$12.00 + 0 32/1/105139 doi:10.1067/mse.2000.105139
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of glenohumeral instability. These fixed-fulcrum designs were largely abandoned because of high rates of loosening from the bone.6,26 More recently, discussion has focused on the optimal amount of conformity or mismatch between the humeral and glenoid components. Prostheses may have any combination of conformity and constraint, for example, high conformity and low constraint.23 The stability characteristics of both the natural joint and prosthetic replacements have been studied previously,10,15,17,19,20,23 but the only comparison to theoretical predictions was by Karduna et al,15 who compared measured and predicted radial mismatches. Constraint has been defined in different and often misleading ways. We define constraint as the maximum slope at the glenoid rim, which is determined by the angle enclosed by the glenoid, as demonstrated in Figure 1. Constraint is not defined by the “wall height”10,17 or by the “depth,”19,20 except when prostheses of the same length are being compared, since a given wall height for a large prosthesis would be less constraining than for a small prosthesis as a result of the change in the enclosed angle. Furthermore the constraint is unrelated to the humeral head size.23 The terms conformity and constraint are often used interchangeably; a theoretical understanding of subluxation helps to clarify these issues. A current controversy is the degree of conformity or mismatch that is desirable between the humeral and glenoid component radii. In the anatomic joint a flexible conformity exists in which the bony glenoid is flatter than the humeral head, but the glenoid bone together with the deformable cartilage and labrum form a spherical match with the humeral head.18,24 A prosthetic glenoid currently does not offer the same versatility, and one radius must be chosen. The choice of conformity affects the active translations, the joint contact stresses, and the translation to the articular rim. Karduna et al16 showed that a prosthesis radial mismatch of approximately 3 to 5 mm (ie, a radial conformity of 0.80 to 0.88) most closely reproduced the translations in the natural joint during normal active abduction (patients with rotator cuff disease and instability often show greater translations13,22). On the other hand, if the conformity is lower, the contact area is smaller and the contact stresses are larger. By this reasoning a conforming prosthesis should lead to less wear. However, as soon as there is eccentric translation, the humeral head in a
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Figure 1 Glenoid constraint is dependent on θ, which defines both the maximum slope (tan θ) at the glenoid rim and the angle enclosed by the glenoid from the deepest point on the glenoid. For symmetrical glenoids the total enclosed angle is 2θ.
conforming design must either deform into the polyethylene or move out toward the rim. This leads to increased stresses, increased rocking moments, and consequently an increased likelihood of wear and loosening.7,8 Friedman9 recorded such posterior rim loading in vivo during horizontal flexion and extension with patients who had received total shoulder replacements but showed no clinical instability. This correlates with clinical findings of posterior polyethylene wear in retrieved components.5,9,12,26 Less conforming designs offer the possibility of transferring more load to the soft tissues before reaching subluxation, thereby reducing the eccentric loads believed to lead to glenoid loosening. Given that central wear of the glenoid components is not currently a clinical concern, a less conforming design appears to offer advantages. Because joint translation, loading, and contact stresses are all influenced by the articular surface shapes of the humeral and glenoid components, these factors should be considered in prosthesis design and selection. The purposes of this study were to determine experimentally the load and translation required for subluxation for a variety of prosthesis types and to understand the results on a theoretical basis. Because loosening of the glenoid component is thought to be due to eccentric rim loading, the rim location is also useful for further testing.2 METHODS AND MATERIAL Test method A schematic of the test setup is shown in Figure 2. The bone substitute, consisting of a rigid polyurethane foam block (Last-a-Foam FR6720, General Plastics, Tacoma, WA), was prepared with the standard surgical instrumentation. The mechanical properties of the bone substitute (E = 193 MPa, σu = 7.6 MPa) were selected to rep-
Figure 2 Schematic of the biaxial testing apparatus. The humeral head is compressed horizontally into the glenoid and translated vertically. The subluxation load is the peak shear load for the given axial compressive load.
resent average properties of glenoid cancellous bone based on a cadaver study of 10 glenoids.3 The glenoid component was cemented into the bone substitute with the superoinferior axis oriented along the central axis of the block. The block was press-fit into a metal holder with either the superoinferior axis vertical or the anteroposterior axis vertical. With a dye the contact point for the humeral head was located to within ±0.5 mm of the central axis of the glenoid. The 2 most conforming glenoids left no mark but could be positioned easily to their deepest point. A pneumatic cylinder (SMC, Tokyo) compressed the humeral head horizontally into the glenoid at a constant given load (750 N, see following text), the load being electronically controlled to within 5 N of the given load. An Instron 8502 hydraulic testing machine (with a 1000-N load cell) translated the humeral head
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Figure 3 Subluxation load equilibrium. The subluxation load (Fv) depends on the slope of the glenoid rim (tanθ), the compressive load (Fh), and the coefficient of friction (see equation 3).
vertically. Both the glenoid and the humeral head traveled on linear bearings. Five triangular ramp displacement cycles large enough to reach a peak load top and bottom on each cycle were completed in the superoinferior direction. This was repeated in the anteroposterior direction. The purpose of the 5 cycles was to consider the effect of repeated subluxations in a patient with recurrent instability. The vertical and horizontal displacements and loads were recorded simultaneously on a computer. The horizontal displacement was measured by a linear-variable-differential-transformer; the horizontal load was measured by recording the electronically controlled pressure and converting it to a calibrated force; the vertical displacement and load were recorded by the hydraulic testing machine. The data were analyzed to find the peak load on each cycle and the corresponding subluxation translation relative to the deepest point on the glenoid; the deepest point was identified by the minimum horizontal displacement. Friction in the vertical bearing was measured in both directions by running the test without the head in contact with the glenoid; this friction load was subtracted from the subluxation load. The tests were conducted in air without a lubricant at room temperature except when a comparison was made with circulating water heated to 37°C. Air was the standard testing method, because the results were later used for a glenoid edge loading and displacement test that could not be immersed in water.2 The standard displacement speed was 50 mm/min to avoid excessive polyethylene creep or stress relaxation1; a speed of 15 mm/min was tested for comparison. The horizontal compressive load was 750 N. Together with the vertical shear load, this led to maximum resultant loads between 820 N and 1050 N, or approximately one to one-and-a-half times body weight. Although normal loading on the glenohumeral joint is lower, even activities of daily living can exert glenohumeral contact forces of several times body weight. The given loading was estimated
to represent the contact forces while carrying a 5- to 8-kg suitcase at the side or lifting a 2- to 4-kg box with both hands to shoulder height; it is also on the same order as (though even less than) getting in and out of a chair using the arms and walking with a cane.2 Rigid-body theory For subluxation or dislocation to occur, the resultant force must be directed outside of the glenoid surface. The subluxation load is therefore the equilibrium load when the humeral head is tangent to the rim of the glenoid. This is controlled by the maximum slope of the glenoid and by friction (Figure 3). The theoretical derivation assumes rigid bodies, that is, point contact and no deformations (which is only approximated at lower loads) and no tilting of the glenoid component. To allow a comparison of the subluxation load at different compressive loads and to provide a quick understanding of the relative magnitude of the subluxation load, the subluxation load is divided by the compressive load to give the force ratio. Summing the vertical and horizontal forces gives:
Subluxation load = Fv = Fn · sin θ + Ff · cos θ
(1)
Compressive load = Fh = Fn · cos θ – Ff · sin θ (2) Assuming the frictional force to be proportional to the normal force, then Ff = µ·Fn, where µ is the coefficient of friction. Dividing equation (1) by equation (2) gives:
Fv sin θ + µ · cos θ Force ratio = = = Fh cos θ – µ · sin θ tan θ + µ (3) 1 – µ · tan θ
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where, as shown in Figure 3: L tan θ = = Slope of glenoid edge R–d
(4)
For the theoretical calculations, a coefficient of friction of 0.07 was assumed. This was based on tests using the same test protocol but with the prosthesis articular surface sawed off and ground flat. The subluxation translation is the displacement to bring the humeral head from the deepest position on the glenoid to just into contact with the glenoid rim. Beyond this point the slope decreases; thus in the absence of restraining soft tissues the load continues to decrease. Referring to Figure 4, the translation distance, l, from the glenoid axis to the humeral head axis, is derived by similar triangles as:
l R–r = L R
(5)
Thus the subluxation translation is:
r Translation (l) = L · 1 – = L · (1 – conformity) = R mismatch L · (6) R
Because the effect of mismatch on translation depends on the glenoid radius, prostheses should be compared by their conformity rather than their mismatch. These equations were presented by Karduna et al14,15 and Walker et al25 but were not expressed in terms of the slope of the glenoid edge, the enclosed glenoid angle, the conformity, and the mismatch. The use of these terms helps to conceptualize the important factors in prosthesis design. The concept of the force ratio was introduced by Fukuda et al,10 who called it the stability ratio. Prostheses Six commercially manufactured, all-polyethylene, cemented prostheses were investigated. The glenoids possessed a wide range of characteristics (Table I) including sizes from extra-small to extra-large, enclosed angles from 14° to 45°, and conformities from 0.46 to 1.00 (ie, mismatches from 0 to 30 mm). The standard protocol (air, 50 mm/min, 750 N) was used for 2 samples of each prosthesis type in all 4 directions. Two additional prostheses of type C-XL were tested in 37°C water instead of air; 1 additional A-XL was tested at 15 mm/min instead of 50 mm/min, and 1 additional A-XL was cemented into a bone substitute with an elastic modulus of 66 MPa instead of the standard bone substitute with an elastic modulus of 193 MPa. Statistical evaluations of the effect of the testing parameters were made with the Student t test with α = .05.
RESULTS The experimental force ratios, ranging from 0.22 to 0.98, were lower than those predicted by treating the glenoid and humeral head as rigid bodies, as expected (Figure 5); the polyethylene deformation was visi-
Figure 4 Subluxation translation (l). Translation depends on the conformity between the humeral radius (r) and glenoid radius (R) and the glenoid length (L) (see equation 6).
ble. The discrepancy was greater for prostheses with greater constraint, that is, for those with a higher predicted force ratio. The experimental translations, ranging from 1.2 mm to 13.5 mm, were larger than the rigid-body predictions when the predicted translations were <3 mm, matching more closely at higher translations (Figure 6). By back-calculating with the experimental translation, the effective glenoid radius was 2 to 5 mm greater than the nominal glenoid radius. Only the results from the first cycle are presented here, because this represents the initial resistance to subluxation. Both theoretically and experimentally, large differences in subluxation load and translation were seen among the prostheses, particularly among the first 3 types, A-C (Figure 7, A, B). Prostheses C to F offered similar force ratios but different translations. In fact, their experimental force ratios were similar despite rigid-body-predicted differences. Consistent with Figure 6, the experimental translations matched the rigid-body predictions more closely for higher translations. The repeatability of the force ratio was excellent, having an average range between the 2 values of 0.02 (ie, 15 N); translation was less repeatable for the first 2 types of prosthesis, but for the remaining 4 types the average range between the 2 values was 0.09 mm, as shown in Figure 7, B. The primary reason for the translation variability for prosthesis A was the difficulty of defining the center position because of its flatness; the variability for prosthesis B was because 1 of the 2 prostheses was incorrectly cemented at an angle such that one side was higher than the other. For types B and C, both the force ratio and translation increased with size; for type A the force ratio changed little with size, whereas translation increased dramatically (Figure 8, A, B). Thus the trends with size
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Figure 5 Rigid-body theory versus experimental force ratio (subluxation load divided by compressive load). The experimental results were lower than predicted by rigid-body theory, especially at higher force ratios. The compressive load was 750 N. The coefficient of friction assumed in the following rigid-body calculations was 0.07.
Table I Prosthesis details (see Figure 3 for definitions) Characteristic Sizes tested Glenoid superior and inferior angles (°), θ Glenoid anterior and posterior angles (°), θ
A*
D
E
XL XS
L
L
45 38
33 22
40
43
40
17 14
31 26
23 14
27
28
29
56 40
26.5 20.5
35.6 31.8
29.5
29.5
25
26 20
26 20
26 20
26
26
25
XL S S:25, I:18 S:31, I:14
B
C
XL XS
F 1-size (M)
Glenoid radius (mm), R Humeral radius† (mm), r Conformity = r / R 0.46 0.50
0.98 0.98
0.73 0.63
0.88
0.88
1.00
Mismatch = R - r (mm) 30 20
0.5 0.5
9.4 11.8
3.5
3.5
0.0
S:5.4, I:2.6 S:5.7, I:1.1
7.8 4.3
5.7 2.9
6.7
7.8
5.8
3.9 2.1
2.8 1.5
3.3
3.4
3.2
18.75 12.5
19.25 13.0
18.75
20.0
16.0
13.75 9.0
13.75 9.5
13.5
13.75
12.25
Superior and inferior articular depths (mm), d Anterior and posterior articular depths (mm), d 2.3 1.3 Superior and inferior half-chords (mm), L S:24, I:17 S:20.5,I:9.5 Anterior and posterior half-chords (mm), L 16.0 10.0 S, Superior; I, inferior. *Prosthesis A is asymmetrical. †A variety of head sizes are available clinically for prostheses A to E.
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were design-dependent. A large head was used with the large components and a small head with the small components (Table I). The superoinferior direction consistently provided a higher subluxation force (more stability) than the anteroposterior direction (Figure 9, A). Translations were smaller in the anterior-posterior direction (Figure 9, B) but not by as great a difference as predicted from rigid-body theory. In all cases the force ratio decreased asymptotically from the first to the fifth cycle (by 0.04 ± 0.03 N/N), stabilizing by the fifth cycle. Translations increased asymptotically over the 5 cycles (by 0.71 mm ± 0.36 mm), also stabilizing by the fifth cycle. The medium (air at room temperature or water at 37°C) had a small but statistically significant effect on the force ratio: the force ratio in 37°C water was approximately 5% lower. There was no consistent trend for translation. Neither testing speed (50 mm/min compared with 15 mm/min) nor bone substitute properties (E = 193 MPa versus 66 MPa) showed a noticeable effect on the subluxation results.
DISCUSSION The difference between the experimental force ratios and the rigid-body predictions was likely primarily due to polyethylene deformation. This deformation could be seen visually, flattening the glenoid slope. The conclusion, not surprisingly, is that a polyethylene prosthesis does not act as a rigid body, especially given the high loads applied. On the other hand, the rigid-body analysis does provide a framework to conceptualize the important factors relevant to subluxation. The amount of deformation depended on the prosthesis design. Thinner, more peaked rims (eg, A and D to F) tended to deform more than rounded rims (B and C); prosthesis E was slightly more constrained than prosthesis D in their undeformed states, but this presented no difference experimentally because of the more peaked rim on prosthesis E. Prostheses with higher constraint tended to deform more than those with less constraint because of the higher loads. As made clear from the rigid-body analysis and confirmed experimentally by Karduna et al,17 the subluxation load is not affected by conformity. A material with a higher elastic modulus and yield strength would act more like a rigid body and would thus be expected to experience a closer match between the rigid-body prediction and the experimental results. On an absolute basis the subluxation load increases with compressive load (comparable to pressing rather than resting a golf ball on its tee); on a relative basis, however, the force ratio decreases with compressive load, implying increasing deformation.10,15,16,20 Thus force ratios can only be compared at the same compressive load. Experimental translations were typically higher than
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Figure 6 Rigid-body theory versus experimental subluxation translation. The experimental translations were higher than those predicted by rigid-body theory at low translations.
predicted theoretically, especially when the translations were small. This was presumably mostly the result of polyethylene deformation. The increase in effective radius was consistent with the findings of Karduna et al,15 who furthermore reported increasing translations with increasing compressive loads. Because of the sometimes large differences between the theoretical and experimental results, it is necessary to conduct this subluxation test if the glenoid edge location is required for further testing. The anteroposterior force ratios and translations were lower than those in the superoinferior direction. This result is consistent with the theory; because they both have the same radius, but the superoinferior axis is longer, the constraint is greater.20 The small lack of symmetry between superior and inferior or between anterior and posterior may have been due to several reasons: an uneven cemented position, reduced polyethylene deformation inferiorly caused by the often greater width, manufacturing variations, or greater friction in the vertical bearing when traveling downward (ie, inferiorly or posteriorly) in the loaded condition (this was seen on the flattened prosthesis). Translations were referenced to the deepest point, but this was less exact in flatter designs, and the translations would not have been centered if the prosthesis were not cemented evenly. The prostheses tested offered greater stability (ie, a higher force ratio) than the natural glenoid. In the natural glenoid Lippitt et al20 reported force ratios in the superior direction of 0.59 with a 50-N compressive load and 0.51 with a 100-N compressive load; the force ratio for the natural glenoid for a 750-N compressive load would be much lower. The prosthesis
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A
B
Figure 7 A, Rigid-body-predicted and experimental force ratios by prosthesis type (largest size, superior direction, n = 2); maximum/mean/minimum shown for experimental results. B, Subluxation translation by prosthesis type (largest size, superior direction, n = 2); maximum/mean/minimum shown for experimental results. Prosthesis A is asymmetrical; the translation from the center as opposed to the deepest point was 11.1 mm. The rigid-body-predicted translation for prosthesis F is zero.
results ranged from 0.45 to 0.98 for a 750-N compressive load. The difference in force ratio appeared to have less to do with differences in the unloaded shape (comparing Table I with Friedman9) and more to do with greater deformation in the natural joint.15 Except at the extremes of motion, the position of the anatomic humeral head on the natural glenoid is pri-
marily controlled by the shape of the articular surfaces, by the rotator cuff muscles, which actively center the head, and by the tilt (ie, version) of the glenoid.4,16,21 The test method used in this study was designed to evaluate the intrinsic stability of the prosthesis system. The resistance or contribution to subluxation of the ligaments, capsule, and passive muscle bulk was only rep-
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A
B
Figure 8 A, Effect of size on experimental force ratio (superior direction, n = 2); maximum/mean/minimum shown. The effect of size was design-dependent and cannot be generalized. B, Effect of size on experimental subluxation translation (superior direction, n = 2); maximum/mean/minimum shown. If the same head size had been used, the larger component would have shown much larger translations.
resented by means of the net load applied. That is, if the intrinsic subluxation load is 500 N, this may represent an external shear load of 600 N and a resistive load of 100 N. The external shear load required for subluxation would thus increase in vivo if the soft tissues were involved at the given translation. Conversely, for a given external load, the translation would decrease.
The soft tissues can also act to destabilize the joint if they are asymmetrically tight.11 Whereas testing was only conducted with the 0° glenoid version, other angles could be easily tested or calculated. An interesting addition to this study would be to compare the subluxation load for the components alone with that for components implanted into cadavers with
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A
B
Figure 9 A, Effect of testing direction on experimental force ratio (largest size, n = 2); maximum/mean/minimum shown. Possible reasons for the discrepancies between superior and inferior and anterior and posterior are described in the Discussion section. Prosthesis A is asymmetrical superoinferiorly. B, Effect of testing direction on experimental subluxation translation (largest size, n = 2); maximum/mean/minimum shown.
the soft tissues intact. For the more conforming prostheses, there is likely to be little effect, because the translations were very small; for the less conforming prostheses, there would likely be a variable effect between individuals. Estimating from the work of Blasier et al,4 the contribution of the capsule at 10-mm anterior displacement could be up to 200 N (ie, a change in force ratio
of 0.27 at 750 N); the contribution at normal anatomic translations would be expected to be much less. Regardless of the soft tissue contribution, the subluxation translation represents the distance to the glenoid rim, and the subluxation load represents the load that would be applied to the prosthesis under rim loading. After the substrate tests, which showed no signifi-
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cant differences for the 2 bone substitutes, it was decided that it was unnecessary to compare the performance in cadaver bone; the polyurethane foam was preferred due to its consistent properties and size and its ease of handling. The primary limitation of this work is that no attempt was made to refine the theory to improve the match between theory and experiment. Nevertheless, the relative effects of glenoid length, width, radius, articular depth, and conformity could be established from the rigid-body theory. From a design perspective the subluxation load is controlled by the maximum slope at the glenoid rim (ie, the constraint), and translation is controlled by the conformity and glenoid length. The confusion in the literature between conformity and constraint and their effects probably arose because more constrained prostheses tend to be more conforming. Geometrically, for the same length of prosthesis, if the glenoid radius is made larger (less conforming), the slope at the rim (constraint) must inevitably decrease. Confusion also stems from the use of the word “stability”: if it means the maximum shear load, then the relevant parameter is constraint, not conformity; if it means minimum translation, then conformity is relevant, not constraint; if stability means fixation quality in the bone (ie, likelihood of loosening), then highly constrained prostheses have shown poor “stability.”
CONCLUSIONS Six types of glenoid prosthesis were characterized by their subluxation load and translation, issues that are relevant to glenohumeral stability, glenoid loosening, and wear.2 Even though all of the prostheses tested would be classified as nonconstrained, they presented a large variation in the force ratio. A single value for each prosthesis is not sufficient, because it changes with prosthesis size, testing direction, and compressive load. Table II describes the effects of different variables on the subluxation force ratio and subluxation translation, indicating whether this effect is based on the rigid-body theory or experimental deformations. Experimental force ratios and translations should not be predicted from the rigid-body theory because of polyethylene deformation. On the other hand, the theory can be used to aid design and clarify the analysis. Additional consideration should be given to the rim design to inhibit deformation.
Table II Summary of effects on force ratio and translation
Variable Constraint (theory) Conformity (theory) Glenoid length (theory) Friction (theory) Compressive load (exp’t) Rim deformation (exp’t) Water @37°C vs. @RTAir (exp’t) Repeated Sublux’s (exp’t)
2. 3. 4.
5. 6. 7. 8. 9. 10. 11.
12.
13. 14. 15.
We thank René Flachsmann, previously of Sulzer Orthopedics Ltd, for designing the test apparatus, and Gerry Saunders of the Clinical Mechanics Group at Queen’s University for building the apparatus.
16.
REFERENCES
17.
1. American Society for Testing and Materials (ASTM). Standard specification for ultra-high-molecular-weight polyethylene pow-
18.
Effect on force ratio
Effect on subluxation translation
↑ — — ↑ ↓ ↓ ↓ ↓
— ↓ ↑ — — ↑ — ↑
der and fabricated form for surgical implants. Designation F648-96. Anglin C. Shoulder prosthesis testing. PhD dissertation. Kingston: Queen’s University; 1999. Anglin C, Tolhurst P, Wyss UP, Pichora DR. Glenoid cancellous bone modulus and strength. J Biomech 1999;32:1091-7. Blasier RB, Guldberg RE, Rothman ED. Anterior shoulder stability: contributions of rotator cuff forces and the capsular ligaments in a cadaver model. J Shoulder Elbow Surg 1992;1: 140-50. Cofield RH. Uncemented total shoulder arthroplasty: a review. Clin Orthop 1994;307:86-93. Cofield RH, Edgerton BC. Total shoulder arthroplasty: complications and revision surgery. Instr Course Lect 1990;39:44962. Flatow EL. Prosthetic design considerations in total shoulder arthroplasty. Semin Arthroplas 1995;6:233-44. Friedman RJ. Biomechanics of total shoulder arthroplasty: a preoperative and postoperative analysis. Semin Arthroplast 1995; 6:222-32. Friedman RJ. Glenohumeral translation after total shoulder arthroplasty. J Shoulder Elbow Surg 1992;1:312-6. Fukuda K, Chen C-M, Cofield RH, Chao EYS. Biomechanical analysis of stability and fixation strength of total shoulder prostheses. Orthopedics 1988;11:141-9. Harryman DT, Sidles JA, Clark JM, McQuade KJ, Gibb TD, Matsen FA III. Translation of the humeral head on the glenoid with passive glenohumeral motion. J Bone Joint Surg Am 1990;72A:1334-43. Harryman DT, Sidles JA, Harris SL, Lippitt SB, Matsen FA III. The effect of articular conformity and size of the humeral head component on laxity and motion after glenohumeral arthroplasty. J Bone Joint Surg Am 1995;77A:555-63. Howell SM, Galinat BJ, Renzi AJ, Marone PJ. Normal and abnormal mechanics of the glenohumeral joint in the horizontal plane. J Bone Joint Surg Am 1988;70A:227-32. Karduna AR. The causes and effects of translation at the natural and prosthetically reconstructed glenohumeral joint. PhD dissertation. University of Pennsylvania; 1995. Karduna AR, Williams GR, Iannotti JP, Williams JL. Total shoulder arthroplasty: a study of the forces and strains at the glenoid component. Trans ASME 1998;120:92-9. Karduna AR, Williams GR, Williams JL, Iannotti JP. Glenohumeral joint translations before and after total shoulder arthroplasty. J Bone Joint Surg Am 1997;79A:1166-74. Karduna AR, Williams GR, Williams JL, Iannotti JP. Joint stability after total shoulder arthroplasty in a cadaver model. J Shoulder Elbow Surg 1997;6:506-11. Kelkar RK, Flatow EL, Bigliani LU, Mow VC. The effects of articular congruence and humeral head rotation on glenohumeral
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kinematics, BED-Vol 28, Advances in Bioengineering, ASME. 1994. Lazarus MD, Sidles JA, Harryman DT II, Matsen FA III. Effect of a chondral-labral defect on glenoid concavity and glenohumeral stability: a cadaveric model. J Bone Joint Surg Am 1996;78A:94-102. Lippitt SB, Vanderhooft JE, Harris SL, Sidles JA, Harryman DT II, Matsen FA. Glenohumeral stability from concavity-compression: a quantitative analysis. J Shoulder Elbow Surg 1993;2:27-35. Pagnani MJ, Warren RF. Stabilizers of the glenohumeral joint. J Shoulder Elbow Surg 1994;3:173-90. Poppen NK, Walker PS. Normal and abnormal motion of the shoulder. J Bone Joint Surg Am 1976;58A:195-201.
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23. Severt R, Thomas BJ, Tsenter MJ, Amstutz HC, Kabo JM. The influence of conformity and constraint on translational forces and frictional torque in total shoulder arthroplasty. Clin Orthop 1993;292:151-8. 24. Soslowsky LJ, Flatow EL, Bigliani LU, Mow VC. Articular geometry of the glenohumeral joint. Clin Orthop 1992;285:18190. 25. Walker PS, Ambarek MS, Morris JR, Olanlokun K, Cobb A. Anterior-posterior stability in partially conforming condylar knee replacement. Clin Orthop 1995;310:87-97. 26. Wirth MA, Rockwood CAJ. Current concepts review: complications of total shoulder-replacement arthroplasty. J Bone Joint Surg Am 1996;78A:603-16.