- Email: [email protected]
Stress analyses of glenoid components in total shoulder arthroplasty
Stress analyses arthroplasty
of glenoid
Kenneth D. Stone, MD, John J. Grabowski, Kai N. An, PhD, Rochester, Minn
MS,
components
Robert H. Cofield,
Finite element analysis wus used to characterize the local stresses at the bone-impfanf interface of 2 different types of glenoid components presently used in unconstrained total shoulder arthroplasty. A series of Z-dimensional finite element meshes was developed to model the glenoid in 2 mutually perpendicular planes with and without implanted components. One of the implants modeled was a cemented all-polyethylene component, and the second was an uncemented metal-backed component. A variety of parameters were sfudied ;ncluding the resultant loading direction (concentric versus eccentric), keel geometry, subchondral bone infegrify and cement mantle size. Resulfs of the analyses show that the cemented all-polyethylene design demonstrated an overall stress pattern that was closer to that of the intact glenoid. When the effects of concentric and eccentric loading conditions were compared, the overall stress magnitudes in the subchondral bone were found to be much lower with the uncemented metal-backed component than with its cemented a/l-polyethylene counterpart. This finding suggests that some degree of stress shielding may be associated with fhe metal-backed componenf. In addition, under both the concentric and eccentric loading conditions, extremely high stress regions were found within the polyethylene near the polyethylene-metal interface of the uncemented metal-backed component. {J Shoulder Elbow Surg 7 999;8:
157 -8.)
U
nconstrained total shoulder arthroplasty has proven to be a successful treatment modality for select patients with glenohumeral arthrosis. Although the high success rate quoted in several published clinical series is between 85% and 95%, glenoid component loosening rates have been quoted to be in the range of 2% to
From
the
Mayo Supported Research Reprint
Blomechanrcs
Laboratory,
Cllnlc/Mayo
by a restdent and Education
requests:
Ku/-Nan
research Foundation An,
chanics Laboratory, Mayo Street, SW, Rochester, MN Copyright Board
0 1999 of Trustees.
1058.2746/99/$8.00
Department
of Orthopedics,
grant from (OREF).
the
Foundation
by Journal + 0
PhD,
Director,
Clnic/Mayo 55905 of Shoulder
32/l/90178
Orthopedic
Orthopedic Foundation, and
Elbow
Blame200
Flrst
Surgery
in total shoulder
MD,
Bernard
F. Morrey,
MD,
and
10% by clinical criteria ographic appearance
and 30% to 60% by the radiof lucent lines at 5 years.4,6,7,10,12,14,22 A n increased rate of glenoid component loosening and the presence of radiolucent lines has been associated with rotator cuff deficiency.8 On clinical evaluation rotator cuff deficiency is often characterized by a superior subluxation of the humeral head relative to the glenoid.15 This phenomenon produces a resultant load vector on the glenoid surface that is directed in a posterior and superior direction. It has been suggested that this type of eccentric loading of the glenoid component may predispose the component to an accelerated rate of failure.* It is hypothesized that the stress fields associated with an eccentrically loaded component are significantly different from those of a concentrically loaded component. It is not known how the glenoid surface loading condition interacts with the keel geometry and method of fixation to influence the stress field adjacent to the glenoid surface. The resulting mechanical environment may or may not be desirable for the maintenance of long-term bony fixation. Published studies investigating the mechanical environment at the interface of glenoid components are scant. In 1983, Rohlmann et al19 published the first theoretical study analyzing the interior stresses of a scapula with an implanted glenoid replacement prosthesis. Finite element analysis was used to study a reverse-articulation type device, the Kolbel/Friedebold prosthesis. A relatively coarse 3-dimensional mesh consisting of 1233 three-dimensional hexahedral elements was developed for the study. The entire scapula was modeled, and an ingenious approach for the application of boundary conditions was investigated. In 1 case boundary conditions were defined by the use of spring elements to simulate the nonrigid medial scapular border constraints imposed by the shoulder girdle musculature. The results from this analysis were then compared with the results of a case in which the medial scapular border was rigidly fixed. On the basis of this comparison, the investigators concluded that the boundary conditions at the medial scapular border did not have a significant effect on the stresses in the glenoid region. In 1988 Orr et aI16 performed a single-plane 2dimensional finite element study of a number of glenoid implants. A maximum of 1200 elements were used to represent the geometry in each model. To the authors’ knowledge this publication represents the first in the
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English literature to attempt theoretical modeling of the scapula with an implanted glenoid prosthesis. One of the geometries selected for study was based on a glenoid component that is currently in use (Neer II system, Kirschner Medical, Fairtown, NJ). Their results led to the conclusion that the addition of metal backing to the glenoid component decreased the subchondral stresses. It was also noted that a semiconstrained design that restricted superior motion of the implant produced higher trabecular stresses. A more recently published finite element study was performed by Friedman et al.9 Single-plane 2-dimensional modeling was performed to examine the stresses associated with glenoid component fixation. A number of component geometries were investigated with a bony geometry that was identical to that used by Orr et al.16 A maximum of 855 elements were used in the construction of each model. The study included the analysis of a component that incorporated screw fixation; however, the screws did not engage the scapular cortex. It is also interesting to note that in modeling a fibrous tissue interface between the implant and the underlying cancellous bone, the authors selected a Poisson’s ratio very close to that of an incompressible fluid. The conclusions drawn from this study were the stresses in a cemented all-polyethylene component were closer to those of the intact glenoid, the introduction of a soft tissue interposition layer produced higher local stresses, and the use of diverging screws offered no advantage over parallel screws. In an attempt to understand further the underlying mechanisms and stresses involved in the problem of glenoid component loosening, a series of 2-dimensional finite element models was developed to analyze load transmission to the glenoid in 2 mutually perpendicular planes, One of the planes can be described as parallel to the plane of the scapula or, more precisely, as a 30” anterior oblique plane. The second plane lies perpendicular to the first, such that it transects the scapula and lies nearly parallel to the transverse or axial plane of the human body. Analysis was performed with 2 different glenoid component geometries, each using a different fixation method. A cemented all-polyethylene component and an uncemented metal-backed component from the Cofield Total Shoulder System (Smith & Nephew Richards Inc., Memphis, Tenn) were selected for the study. The mating articular surfaces of the components in this system are designed to be completely congruent. The parameters investigated were the direction of the resultant joint surface loading vector, the effects of the keel geometry, the size of the cement mantle, and the subchondral bone integrity. METHODS
The bone geometry was based on a pair of cadaveric scapulae. The scapulae were selected on the basis of size
J Shoulder Elbow Surg March/April 1999
and condition including the absence of bony degenerative changes at the glenoid surface. The pair chosen was from a 62-year-old man who was approximately 6 feet, 2 inches in stature. The scapulae were stripped of all soft tissue and immersed in a sodium hypochlorite bath. Model construction. The preserved intact scapulae were then placed into a computed tomography scanner to obtain 1.5 mm axial sections through the area of the glenoid; data were stored for later applications. Full-scale replicas of the rosthetic components were molded from epoxy resin. Ny Pon screws of the same diameter were used in place of the titanium alloy screws of the uncemented metal-backed rosthesis. These 2 screws were of equal and sufficient Pength to engage the anterior cortex of the scapula by both screws. With the manufacturer’s equipment and suggested technique, the cartilage was reamed away from the surface of each glenoid and the bone prepared. The replica components were then im lanted into the cadaveric scapulae by an experienced s1:oulder surgeon (RHC). Computed tomography scanning of the scapulae was repeated after the components were in place. A 3-dimensional reconstruction of the computed tomography data was performed for the intact and implanted scapulae (ANALYZE, Biomedical Imaging Resource, Mayo Foundation, Rochester, Minn). With ANALYZE, il-dimensional images at the specific planes of interest were identified and-stared. The images were then manually digitized to obtain the geometry and material distribution information necessary for finite element modeling. Modeling was performed with ANSYS 5.OA (Swanson Analysis Systems, Inc., Houston, Pa) operating on an SGI 4D/420 computer system (Silicon Graphics, Inc., Mountainview, Calif). Geometric and material boundaries were defined and matched to produce an identical mesh for all models in a given plane. Automated meshing was used for element generation (Figure I). Eight-noded quadrilateral or 6-noded triangular elements were used to create the mesh for the bone and implant materials. Such higher order elements provided better contouring to fit the irregular geometry and more accurately describe the displacements of the structure. The largest of the models consisted of more than 5500 elements. Analysis of convergence was erformed to confirm adeP quate mesh refinement with a pane stress approach with a model thickness of 1 mm. Material property values were taken from current literature and were assumed to be linearly elastic and isotropic [Table I). All material interfaces were assumed to be perfectly bonded. To compensate for the loss of structural integrity inherent in a 2-dimensional representation of a 3-dimensional cylindric cortical shell, a side plate construct similar to that used b Weinans et al21 was incorporated. The plate consisted o Y 4-node quadrilateral and 3-node triangular elements. The plate had uniform thickness (1 mm) and was attached at the outer edges of the model. The elastic modulus was empirically derived based on the results of a series of iterative solutions. The optimum elastic modulus minimized the effect of artificial stress risers while it simultaneously maintained a principal stress field that was similar to that seen in the intact model without a side plate construct. Boundary conditions were established well away from the glenoid surface. In the frontal plane models this was accomplished by extending 2 columns of cortical bone in
Volume
Table
Stone
Elbow Surg
J Shoulder
8, Number
I Material
properties
8.0 0.4
Cortical bone Cancellous bone UHMWPE Ti-6A14V Alloy Cement Cartilage Sideplate material were
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Materials
Values
et al
2
0.5 1 12.0
2.0 0.003 8.0 from
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in the literature.s,4,‘5
the medial direction, similar to the actual structure of the scapula. Material distribution plots for the scapular plane are shown in Figure 2, A, D, and G. The medial end of each cortical column was rigidly fixed. In the transverse lane the anterior and posterior scapular cortical shell was Pinearly extrapolated in the medial direction. Material distribution plots for the transverse plane are shown in Figure 3, A, D, and G. It should be emphasized that because the region of interest is located within the neck and body of the glenoid, the stresses associated with the fixed boundaries were well beyond the region of interest. Loading conditions. Two types of joint surface loads were used in anal sis, concentric and eccentric. The concentric load case i: ad a resultant load vector directed at the center of the articular surface. The eccentric load case was constructed with the intention of representing rotator inatus deficiency. Thus the resultant surface cuff or supras load vector s R ould be directed superiorly in the frontal plane and posteriorly in the transverse plane. The precise direction of the load vector associated with unknown. For the purposes of a cuff deficiency is current1 this study, the vector was c 1: osen to be 20” superiorly and 10” posteriorly in the frontal and transverse planes, respectively. This load direction provided insight into the effects of eccentric loading behavior while maintaining a stable loading configuration for the congruent joint geometry of the Cofield system. The ‘oint surface resultant vector was arbitrarily assigne cl a magnitude of 10 N for both the concentric and h a 10 N load may not have eccentric load cases. Althou direct clinical relevance, the B oad was sufficient to produce stress pattern variations among the unit thickness modeling groups. The ultimate goal of the study was to examine the relative changes in the stress distribution patterns produced by the prosthetic components compared with the patterns associated with the intact glenoid. Unlike previous studies,9<‘6 articular surface loading conditions were not assigned as localized nodal loads in an arbitrary distribution but were based on a more realistic surface distribution. The surface distribution was based on a theoretical description developed by Pauwelsl* and further expounded by An et al.1 The distribution assumed a perfect1 concentric and spheric joint geometry with the resultant Yoad vector passing through the center of the radius of curvature; material deformation was assumed to be zero at the contact surfaces. Pauwels’ equations were used to calculate the location and magnitude of the maximum normal load vector on the glenoid surface. The
Figure 1 A, Finite element mesh in oblique frontal plane. Note boundary conditions at right-hand side Finite element mesh in axial or transverse plane.
or scapular of mesh. B,
remaining load distribution was proportional to the cosine of the angle from the maximum load vector. The surface load distributions in the frontal plane are shown in Figure 2, 8, E, and Hand C, F, and 1. For the finite element model the load distributions were a plied with normal surface pressures at the appropriate e Pement faces. Keel geometry. The degree of stress shielding associated with the keel design of the glenoid components was also examined. By reassignment of the material properties to the appropriate elements, it was possible to vary the keel eometry without altering the model mesh. The stress trans f er that occurred as a result of the keel’s proximity to the cortical bone in the anterior portion of the scapula was particularly interesting. This transfer was evaluated b conducting an analysis of the uncemented metal-backe J component in which a small defect was created in the anterior cortex to prevent direct stress transfer to the cortical wall. Cement mantle size. Effects associated with the size of the cement mantle used in conjunction with the all-polyeth-
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ylene component were also investigated. The geometry obtained from a computed tomography scan of the specimen was used as a reference to enlarge the area containing cement manually. On computational analysis this procedure was accomplished by reassigning the material properties of the ap ropriate elements. The cement mantle area was increase cp by 50% in both frontal and transverse models. The results of the anal ses performed for both the “normal” and “enlarge CT” cement mantles were then compared. Subchondral bone integrity. The mechanical significance of the subchondral bone was investigated by varying its thickness. In the model the subchondral bone was represented by a thin layer of cortical bone directly beneath the glenoid surface. To represent a typical glenoid surface reamed for implantation, a cortical thickness of approximately one third of that seen in the intact glenoid was used. For the purposes of this evaluation, the analysis was then repeated with this cortical layer completely omitted. RESULTS
The following discussion is based on examination of the model stresses obtained by application of the von Mises’ stress criterion. This expression incorporates both the shear and normal stress components into a single term, thus simplifying comparison of the overall stress state for a variety of model parameters (Figures 2 and 3, A through I). Any further use of the word “stress” in this text implies the von Mises’ stress unless otherwise stated. It should also be noted that the stress differences that are stated in the following text represent relative differences in the stress magnitudes among the various models in this study. Extrapolation of the modeled stress data to estimate component failure is not valid because of the current modeling assumptions and limitations. Loading conditions. For the purposes of this section, evaluation of the results has been limited to common areas within each model that demonstrate notable stress differences. Analysis of these regions provides an equivalent basis for comparison among the different models and load cases. Frontal plane: For the concentrically loaded intact glenoid, the principal stress patterns were strongly correlated with the trabecular orientation pattern seen in cross sections of cadaveric glenoids. This has been noted in the literature’6 and directly confirmed in several sections produced for the purposes of this study. The principal stress field observed in the intact glenoid was closer in appearance to the cemented all-polyethylene component than to the uncemented metal-backed component. The trabecular bone stress in the regions immediately adjacent to the screws of the uncemented metalbacked component (Figure 2, /-I) were found to be as much as 80% lower than those in the intact glenoid (Figure 2, B). For the cemented all-polyethylene component (Figure 2, E), the trabecular bone stress in the
J Shoulder Elbow Sorg March/April 7999
region adjacent to the cement mantle were found to be approximately 25% higher than the corresponding area in the intact model. For the eccentric load case (Figure 2, C, F, and I), examination of the subchondral bone layer showed that the 20” superiorly directed load produced dramatic increases in the maximum stress compared with the concentric load cases (Figure 2, 13, E, H). Maximum stress increases of 60% and 50% were noted for the cemented all-polyethylene (Figure 2, F) and uncemented metal-backed components (Figure 2, /), respectively. In the case of the uncemented metal-backed component, the superior-most screw was subjected to significantly greater stresses during eccentric loading, a 130% increase compared with concentric loading. It was also noted that bending stresses in the central peg of the keel were significantly greater for the eccentric versus the concentric loading case. Transverse plane: As was the case in the frontal plane, analysis in the transverse plane demonstrated that the uncemented metal-backed component had lower stresses localized to the subchondral region (Figure 3, H and i). The stresses were decreased by as much as 25% relative to those seen in the cemented all-polyethylene component (Figure 3, E and F). From examination in this plane, it was also evident that eccentric loading produced lower cortical and trabecular stresses compared with the concentrically loaded models. Keel geometry. Stress shielding caused by stress transfer through the keel was significant in the uncemented component (Figure 3, H and /) and also, to a lesser degree, in the cemented component (Figure 3, E and F). The distance between the tip of the central peg or keel and the adjacent anterior cortex of the scapula was crucial to this effect. This was further elucidated by conducting an analysis of the uncemented metalbacked component with a small defect in the anterior cortex, thus preventing direct stress transfer to the anterior cortical wall. Cement mantle size. A 50% enlargement of the cement mantle size led to an increase in the trabecular bone stress adjacent to the cement mantle from 10% to as much as 50%, particularly in areas where the mantle was close to the cortical shell. The orientation of the principal stress pattern was not significantly altered by the larger mantle with the exception of a few small localized regions in which the mantle was near the cortical tables of the scapula. Subchondral bone integrity. To determine its mechanical role, the thickness of subchondral bone immediately adjacent to the glenoid surface was altered. Removal of this bone layer resulted in an increase in the underlying trabecular bone stresses with a concomitant decrease in the load shared by the peripheral cortical shell in all load cases. This effect was more pronounced in the cemented all-polyethylene component. The subchondral bone stresses resulting from an
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Figure 2 A, Material distribution used for analysis of intact glenoid model in frontal plane. Articular-cartilage geometry is not anatomically accurate but is based on similar geometry seen with glenoid prosthesis in place. This allows model to behave analytically as if it were in full concentric contact with average-sized adult humeral head 44 mm in diameter. B, von Mises’ stress plot of concentrically loaded intact glenoid in frontal plane showing stress distribution in unit thickness model. C, von Mises’ stress plot of eccentrically loaded intact glenoid in frontal plane showing stress distribution in unit thickness model. D, Material distribution used for analysis of cemented all-polyethylene component in frontal plane. E, von Mises’ stress plot of concentrically loaded cemented all-polyethylene component in frontal plane showing stress distribution in unit thickness model. F, von Mises’ stress plot of eccentrically loaded cemented all-polyethylene component in frontal plane showing stress distribution in unit thickness model. G, Material distribution used for analysis of uncemented metalbacked component in frontal plane. H, von Mises’ stress plot of concentrically loaded uncemented metal-back component in frontal plane showing stress distribution in unit thickness model. I, von Mises’ stress plot of eccentrically loaded uncemented metal-back component in frontal plane showing stress distribution in unit thickness model.
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et al
.
E
Figure 3 A, Material distribution used for anolysis of intact glenoid model in transverse plane. Articular cartilage geometry is not anatomically accurate but is based on similar geometry seen with glenoid prosthesis in place. This allows model to behave analyticolly as if it were in full concentric contact with average-sized adult humeral head 44 mm in diameter. B, von Mises’ stress plot of concentrically loaded intact glenoid in transverse plane showing stress distribution in unit thickness model. C, von Mises’ stress plot of eccentrically loaded intact glenoid in transverse plane showing stress distribution in unit thickness model. D, Material distribution used for the analysis of cemented oll-polyethylene component in transverse plane. E, von Mises’ stress plot of concentrically loaded cemented oll-polyethylene component in transverse plane showing stress distribution in unit thickness model. F, von Mises’ stress plot of eccentrically loaded cemented all-polyethylene component in transverse plane showing stress distribution in unit thickness model. G, Material distribution used for analysis of uncemented metal-backed component in transverse plane. H, von Mises’ stress plot of concentrically loaded uncemented metal-back component in transverse plane showing stress distribution in unit thickness model. I, von Mises’ stress plot of eccentrically loaded uncemented metal-back component in transverse plane showing stress distribution in unit thickness model.
J Shoulder Elbow Surg Volume 8, Number 2
eccentrically applied load were lower in the uncemented metal-backed component. Another interesting finding to note was the extremely high stress concentration present in the polyethylene insert used with the uncemented metal-backed component. The peak stress region was limited to within a few millimeters of the interface between the polyethylene insert and the metal base. The magnitude of the normal compressive stresses in this region reached levels that were more than double the stress applied to the articular surface of the polyethylene insert. This finding was present in both the concentric and eccentric load cases.
DISCUSSION This study used finite element analysis to model an intact glenoid and 2 implanted glenoid components. In the approximation of such a complex biologic system, certain assumptions must be made to achieve acceptable solutions in an efficient manner. A brief discussion of the assumptions made in the development of this study is provided. Perfectly bonded interfaces were assumed for all models in this study. The use of “interface” or “contact” elements to model the material interfaces and articulating surface may well have produced a closer approximation of the mechanical behavior in the glenoid prosthesis construct. However, defining the material interfaces in such a manner presents a challenge in mathematic modeling that requires the application of computationally intensive nonlinear, iterative solution techniques. The application of contact elements in this field is relatively new and currently evolving. This analysis was limited to the investigation of congruent glenoid geometries and components that were subjected to distributed static loads. In both load cases the load was distributed across the entire surface of the glenoid. The use of noncongruent systems would result in a smaller area of load application producing higher localized stresses in the region of contact. In addition, the contact or loading region may actually shift as the applied load increases. This is particularly true with the eccentric load case, in which a cuff deficiency would result in translation of the humeral head within the glenoid fossa during loading. However, because of these modeling limitations, such issues were beyond the scope of this investigation. In this study a 2-dimensional modeling approach was used to model a complex 3-dimensional glenoid structure. Such a simplification can result in a loss of the structure’s mechanical integrity. This loss is due to the inability of the 2-dimensional model to adequately compensate for the out-of-plane forces present in a 3-dimensional structure. In the particular case of the glenoid, the loss of the mechanical integrity of the circumferential cortical structure will have an impact on the results. Ideally, 3-dimensional modeling would eliminate this problem, but such analyses performed at this level of
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mesh refinement are currently expensive in terms of computer resources. The application of the side plate represents an attempt to compensate for the limitations of 2-dimensional analysis in an efficient manner. However, it should be noted that its presence makes it difficult to draw conclusions regarding the absolute stress magnitude that would be present in a full-thickness or 3-dimensional construct. As in any biomechanical application of the finite element method, model validation should be discussed. Ideally, experimental validation is desirable for any such study. Many investigators would argue that it is mandatory. Attempts at experimental validation are often impractical or misleading. In the case of this study, the region of greatest interest lies within the interior architecture of the glenoid. Measuring the stress in this region by the use of experimental techniques such as strain gauges or transducers would require violation of the very structure being studied. In addition, the use of such approaches can produce misleading results because of the creation of artificial stress risers that are not present in the intact structure. It could be argued that the glenoid surface or implant interface could be instrumented without structural damage. However, this type of approach will not directly provide stress data regarding the trabecular bone and the interior of the glenoid. In summary, a series of biplanar 2-dimensional finite element models were developed to study 2 fundamentally different component fixation designs used in a total shoulder arthroplasty system. Analysis of the cemented all-polyethylene design revealed an overall trabecular stress pattern similar to that of the intact glenoid. Enlargement of the cement mantle had little effect on the trabecular stress. When compared with the cemented all-polyethylene component, the uncemented metal-backed component displayed lower subchondral stresses for both load cases; this effect was more pronounced during eccentric loading. This result suggests that an uncemented metal-backed component may be better suited for a rotator cuff deficient shoulder. In addition, significant trabecular stress shielding was noted under both concentric and eccentric loading conditions, particularly with the uncemented metal-backed component. The results of this study suggest that the cemented all-polyethylene design may offer good fixation when the trabecular bone beneath the glenoid surface is of sufficient quantity and quality to support the polyethylene-cement composite. The uncemented metalbacked component may provide better fixation when a slightly eccentric load is anticipated. One potential problem became evident during the analysis of the uncemented design. High polyethylene stress regions were present at the polyethylene-metal interface in relation to the all-polyethylene component. This result suggests that this interface will be the site of initial polyethylene yielding and, ultimately, component
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failure at loads that are lower than those necessary to cause failure of the all-polyethylene component. However, because of the limitations of this model, the exact load required to cause yield cannot be adequately determined. The information produced by this study represents a small but significant step toward understanding many of the mechanical aspects associated with the bony fixation of implanted glenoid components. Future investigation into the phenomena surrounding glenoid component loosening is necessary and has much potential. As computing resources and capabilities expand to become more cost-efficient, new approaches to be considered might include the incorporation of 3-dimensional modeling, anisotropic material properties, gap or interface elements, and computational bone remodeling techniques. REFERENCES An KN, Himeno S, Tsumura H, Kawar T, Chao EYS. Pressure distributron on artrcular surfaces. applicatron to joint stab+ evaluation J Bromech 1990,23,1013-20 Bassett RW, Browne AO, Morrey BF, An KN Glenohumeral muscle force and moment mechamcs in a posrtron of shoulder rnstabilrty. J Biomech 1990,23.405-l 5 Black J. Orthopaedrc bromaterrals in research and practrce Church111 Livrngstone; New York 1988. P 180-98 Boyd AD, Aliabadi P, ThornhIll TS Postoperative proxrmal migration rn total shoulder arthroplasty, incrdence and signrficance J Arthroplasty 199 1;6 3 l-7 Callahan TD, Johnson ME, Chao EYS Shoulder strength analySIS using the Cybex II tsokrnetrc dynamometer Clan Orthop 1991,271.249-57. Cofield RH. Total shoulder arthroplasty with the Neer prosthesis. J Bone Joint Surg Am 1984,66A 899-906 Frggie HE, lnglis AE, Goldberg VM, Ranawat CS, Figgre MP, WrleJM. An analysrs of factors affecting the long-term results of total shoulder arthroplasty In inflammatory arthrrtrs J Arthroplasty 1988;3 123-30
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Surg
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Franklin JL, Barrett WP, Jackins SE, Matsen FA. Glenoid loosening In total shoulder arthroplasty Association with rotator cuff deficiency J Arthroplasty 1988;3:39-46 9. Friedman RJ, LaBerge M, Dooley RL, O’Hara AL. Finite element modeling of the glenoid component. effect of design parameters on stress drstribution. J Shoulder Elbow Surg 1992; 1 .26 l-70. 10. Hawkins RJ, Bell RH, Jallay B. Total shoulder arthroplasty C/in Orthop 1989;242.188-94 11 Howell SM, Galinat BJ, Renzr AJ, Marone PJ. Normal and abnormal mechanrcs of the glenohumeral joint in the horizontal plane. J Bone Joint Surg Am 1988;70-A,227-32. 12 McElwain JP, Englrsh E. The early postoperatrve results of porous-coated total shoulder arthroplasty Clan Orthop 1987, 218.217-24 13 Morrey BF, An KN Biomechanrcs of the shoulder In. Rockwood CA. Matsen FA. editors. The shoulder. Philadelohia, WB Saunders,’ 1990. P 2’08-45. 14 Neer CS. Glenohumeral arthroplasty. In. Neer CS, editor Shoulder reconstruction Philadelphra~ WB Saunders, 1990. P. 146-60. 15 Neer CS, Craig EV, Fukuda H. Cuff-tear arthropathy. J Bone Jotnt Surg am 1983;65A. 1232-44. 16 Orr TE, Carter DR, Schurman DJ. Stress analyses of glenold component designs. Clan Orthop 1988,232.2 17-24 New York, Plenum Press, 1979. P 1 1 1 17 Park JB. Biomaterials. 18 Pauwels F The distribution of pressure In the elbow taint together with fundamental remarks on taint pressure. In. BiomechanICS of the locomotor apparatus. New York: Springer-Verlag; 1980 P. 41 l-4 19 Rohlmann A, Mobner U, Eberlein R, Bergmann G Spannungsanalyse am schulterblatt nach schulteraelenkersatz (Stress analyses at the scapula after shoulder jolt replacement) Biomed Tech 1983.28:224-34 20 Shah JS, Ju SH, Rowlands RE, An KN, Chao EYS Analysrs of friction In human tornt contact BED-Vol 26, 1993 Advances m Broengineering American Society of Mechanical Engineering 1993 p 51-54. 21 Wernans H, Hurskes R, Grootenboer HJ The behavior of adaptive bone-remodeling srmulatron models J Biomech 1992,25, 1425-4 1. 22 Weiss AP, Adams MA, Moore JR, Wetland Al. Unconstramed shoulder arthroplasty A five-year average follow-up study Clan Orthop 1990;257:86-93
of glenoid
Kenneth D. Stone, MD, John J. Grabowski, Kai N. An, PhD, Rochester, Minn
MS,
components
Robert H. Cofield,
Finite element analysis wus used to characterize the local stresses at the bone-impfanf interface of 2 different types of glenoid components presently used in unconstrained total shoulder arthroplasty. A series of Z-dimensional finite element meshes was developed to model the glenoid in 2 mutually perpendicular planes with and without implanted components. One of the implants modeled was a cemented all-polyethylene component, and the second was an uncemented metal-backed component. A variety of parameters were sfudied ;ncluding the resultant loading direction (concentric versus eccentric), keel geometry, subchondral bone infegrify and cement mantle size. Resulfs of the analyses show that the cemented all-polyethylene design demonstrated an overall stress pattern that was closer to that of the intact glenoid. When the effects of concentric and eccentric loading conditions were compared, the overall stress magnitudes in the subchondral bone were found to be much lower with the uncemented metal-backed component than with its cemented a/l-polyethylene counterpart. This finding suggests that some degree of stress shielding may be associated with fhe metal-backed componenf. In addition, under both the concentric and eccentric loading conditions, extremely high stress regions were found within the polyethylene near the polyethylene-metal interface of the uncemented metal-backed component. {J Shoulder Elbow Surg 7 999;8:
157 -8.)
U
nconstrained total shoulder arthroplasty has proven to be a successful treatment modality for select patients with glenohumeral arthrosis. Although the high success rate quoted in several published clinical series is between 85% and 95%, glenoid component loosening rates have been quoted to be in the range of 2% to
From
the
Mayo Supported Research Reprint
Blomechanrcs
Laboratory,
Cllnlc/Mayo
by a restdent and Education
requests:
Ku/-Nan
research Foundation An,
chanics Laboratory, Mayo Street, SW, Rochester, MN Copyright Board
0 1999 of Trustees.
1058.2746/99/$8.00
Department
of Orthopedics,
grant from (OREF).
the
Foundation
by Journal + 0
PhD,
Director,
Clnic/Mayo 55905 of Shoulder
32/l/90178
Orthopedic
Orthopedic Foundation, and
Elbow
Blame200
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Surgery
in total shoulder
MD,
Bernard
F. Morrey,
MD,
and
10% by clinical criteria ographic appearance
and 30% to 60% by the radiof lucent lines at 5 years.4,6,7,10,12,14,22 A n increased rate of glenoid component loosening and the presence of radiolucent lines has been associated with rotator cuff deficiency.8 On clinical evaluation rotator cuff deficiency is often characterized by a superior subluxation of the humeral head relative to the glenoid.15 This phenomenon produces a resultant load vector on the glenoid surface that is directed in a posterior and superior direction. It has been suggested that this type of eccentric loading of the glenoid component may predispose the component to an accelerated rate of failure.* It is hypothesized that the stress fields associated with an eccentrically loaded component are significantly different from those of a concentrically loaded component. It is not known how the glenoid surface loading condition interacts with the keel geometry and method of fixation to influence the stress field adjacent to the glenoid surface. The resulting mechanical environment may or may not be desirable for the maintenance of long-term bony fixation. Published studies investigating the mechanical environment at the interface of glenoid components are scant. In 1983, Rohlmann et al19 published the first theoretical study analyzing the interior stresses of a scapula with an implanted glenoid replacement prosthesis. Finite element analysis was used to study a reverse-articulation type device, the Kolbel/Friedebold prosthesis. A relatively coarse 3-dimensional mesh consisting of 1233 three-dimensional hexahedral elements was developed for the study. The entire scapula was modeled, and an ingenious approach for the application of boundary conditions was investigated. In 1 case boundary conditions were defined by the use of spring elements to simulate the nonrigid medial scapular border constraints imposed by the shoulder girdle musculature. The results from this analysis were then compared with the results of a case in which the medial scapular border was rigidly fixed. On the basis of this comparison, the investigators concluded that the boundary conditions at the medial scapular border did not have a significant effect on the stresses in the glenoid region. In 1988 Orr et aI16 performed a single-plane 2dimensional finite element study of a number of glenoid implants. A maximum of 1200 elements were used to represent the geometry in each model. To the authors’ knowledge this publication represents the first in the
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English literature to attempt theoretical modeling of the scapula with an implanted glenoid prosthesis. One of the geometries selected for study was based on a glenoid component that is currently in use (Neer II system, Kirschner Medical, Fairtown, NJ). Their results led to the conclusion that the addition of metal backing to the glenoid component decreased the subchondral stresses. It was also noted that a semiconstrained design that restricted superior motion of the implant produced higher trabecular stresses. A more recently published finite element study was performed by Friedman et al.9 Single-plane 2-dimensional modeling was performed to examine the stresses associated with glenoid component fixation. A number of component geometries were investigated with a bony geometry that was identical to that used by Orr et al.16 A maximum of 855 elements were used in the construction of each model. The study included the analysis of a component that incorporated screw fixation; however, the screws did not engage the scapular cortex. It is also interesting to note that in modeling a fibrous tissue interface between the implant and the underlying cancellous bone, the authors selected a Poisson’s ratio very close to that of an incompressible fluid. The conclusions drawn from this study were the stresses in a cemented all-polyethylene component were closer to those of the intact glenoid, the introduction of a soft tissue interposition layer produced higher local stresses, and the use of diverging screws offered no advantage over parallel screws. In an attempt to understand further the underlying mechanisms and stresses involved in the problem of glenoid component loosening, a series of 2-dimensional finite element models was developed to analyze load transmission to the glenoid in 2 mutually perpendicular planes, One of the planes can be described as parallel to the plane of the scapula or, more precisely, as a 30” anterior oblique plane. The second plane lies perpendicular to the first, such that it transects the scapula and lies nearly parallel to the transverse or axial plane of the human body. Analysis was performed with 2 different glenoid component geometries, each using a different fixation method. A cemented all-polyethylene component and an uncemented metal-backed component from the Cofield Total Shoulder System (Smith & Nephew Richards Inc., Memphis, Tenn) were selected for the study. The mating articular surfaces of the components in this system are designed to be completely congruent. The parameters investigated were the direction of the resultant joint surface loading vector, the effects of the keel geometry, the size of the cement mantle, and the subchondral bone integrity. METHODS
The bone geometry was based on a pair of cadaveric scapulae. The scapulae were selected on the basis of size
J Shoulder Elbow Surg March/April 1999
and condition including the absence of bony degenerative changes at the glenoid surface. The pair chosen was from a 62-year-old man who was approximately 6 feet, 2 inches in stature. The scapulae were stripped of all soft tissue and immersed in a sodium hypochlorite bath. Model construction. The preserved intact scapulae were then placed into a computed tomography scanner to obtain 1.5 mm axial sections through the area of the glenoid; data were stored for later applications. Full-scale replicas of the rosthetic components were molded from epoxy resin. Ny Pon screws of the same diameter were used in place of the titanium alloy screws of the uncemented metal-backed rosthesis. These 2 screws were of equal and sufficient Pength to engage the anterior cortex of the scapula by both screws. With the manufacturer’s equipment and suggested technique, the cartilage was reamed away from the surface of each glenoid and the bone prepared. The replica components were then im lanted into the cadaveric scapulae by an experienced s1:oulder surgeon (RHC). Computed tomography scanning of the scapulae was repeated after the components were in place. A 3-dimensional reconstruction of the computed tomography data was performed for the intact and implanted scapulae (ANALYZE, Biomedical Imaging Resource, Mayo Foundation, Rochester, Minn). With ANALYZE, il-dimensional images at the specific planes of interest were identified and-stared. The images were then manually digitized to obtain the geometry and material distribution information necessary for finite element modeling. Modeling was performed with ANSYS 5.OA (Swanson Analysis Systems, Inc., Houston, Pa) operating on an SGI 4D/420 computer system (Silicon Graphics, Inc., Mountainview, Calif). Geometric and material boundaries were defined and matched to produce an identical mesh for all models in a given plane. Automated meshing was used for element generation (Figure I). Eight-noded quadrilateral or 6-noded triangular elements were used to create the mesh for the bone and implant materials. Such higher order elements provided better contouring to fit the irregular geometry and more accurately describe the displacements of the structure. The largest of the models consisted of more than 5500 elements. Analysis of convergence was erformed to confirm adeP quate mesh refinement with a pane stress approach with a model thickness of 1 mm. Material property values were taken from current literature and were assumed to be linearly elastic and isotropic [Table I). All material interfaces were assumed to be perfectly bonded. To compensate for the loss of structural integrity inherent in a 2-dimensional representation of a 3-dimensional cylindric cortical shell, a side plate construct similar to that used b Weinans et al21 was incorporated. The plate consisted o Y 4-node quadrilateral and 3-node triangular elements. The plate had uniform thickness (1 mm) and was attached at the outer edges of the model. The elastic modulus was empirically derived based on the results of a series of iterative solutions. The optimum elastic modulus minimized the effect of artificial stress risers while it simultaneously maintained a principal stress field that was similar to that seen in the intact model without a side plate construct. Boundary conditions were established well away from the glenoid surface. In the frontal plane models this was accomplished by extending 2 columns of cortical bone in
Volume
Table
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8, Number
I Material
properties
8.0 0.4
Cortical bone Cancellous bone UHMWPE Ti-6A14V Alloy Cement Cartilage Sideplate material were
taken
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table Elastic modulus (GPa)
Materials
Values
et al
2
0.5 1 12.0
2.0 0.003 8.0 from
several
sources
Poisson’s ratio
0.35 0.21 0.40 0.33 0.23 0.45 0.35
in the literature.s,4,‘5
the medial direction, similar to the actual structure of the scapula. Material distribution plots for the scapular plane are shown in Figure 2, A, D, and G. The medial end of each cortical column was rigidly fixed. In the transverse lane the anterior and posterior scapular cortical shell was Pinearly extrapolated in the medial direction. Material distribution plots for the transverse plane are shown in Figure 3, A, D, and G. It should be emphasized that because the region of interest is located within the neck and body of the glenoid, the stresses associated with the fixed boundaries were well beyond the region of interest. Loading conditions. Two types of joint surface loads were used in anal sis, concentric and eccentric. The concentric load case i: ad a resultant load vector directed at the center of the articular surface. The eccentric load case was constructed with the intention of representing rotator inatus deficiency. Thus the resultant surface cuff or supras load vector s R ould be directed superiorly in the frontal plane and posteriorly in the transverse plane. The precise direction of the load vector associated with unknown. For the purposes of a cuff deficiency is current1 this study, the vector was c 1: osen to be 20” superiorly and 10” posteriorly in the frontal and transverse planes, respectively. This load direction provided insight into the effects of eccentric loading behavior while maintaining a stable loading configuration for the congruent joint geometry of the Cofield system. The ‘oint surface resultant vector was arbitrarily assigne cl a magnitude of 10 N for both the concentric and h a 10 N load may not have eccentric load cases. Althou direct clinical relevance, the B oad was sufficient to produce stress pattern variations among the unit thickness modeling groups. The ultimate goal of the study was to examine the relative changes in the stress distribution patterns produced by the prosthetic components compared with the patterns associated with the intact glenoid. Unlike previous studies,9<‘6 articular surface loading conditions were not assigned as localized nodal loads in an arbitrary distribution but were based on a more realistic surface distribution. The surface distribution was based on a theoretical description developed by Pauwelsl* and further expounded by An et al.1 The distribution assumed a perfect1 concentric and spheric joint geometry with the resultant Yoad vector passing through the center of the radius of curvature; material deformation was assumed to be zero at the contact surfaces. Pauwels’ equations were used to calculate the location and magnitude of the maximum normal load vector on the glenoid surface. The
Figure 1 A, Finite element mesh in oblique frontal plane. Note boundary conditions at right-hand side Finite element mesh in axial or transverse plane.
or scapular of mesh. B,
remaining load distribution was proportional to the cosine of the angle from the maximum load vector. The surface load distributions in the frontal plane are shown in Figure 2, 8, E, and Hand C, F, and 1. For the finite element model the load distributions were a plied with normal surface pressures at the appropriate e Pement faces. Keel geometry. The degree of stress shielding associated with the keel design of the glenoid components was also examined. By reassignment of the material properties to the appropriate elements, it was possible to vary the keel eometry without altering the model mesh. The stress trans f er that occurred as a result of the keel’s proximity to the cortical bone in the anterior portion of the scapula was particularly interesting. This transfer was evaluated b conducting an analysis of the uncemented metal-backe J component in which a small defect was created in the anterior cortex to prevent direct stress transfer to the cortical wall. Cement mantle size. Effects associated with the size of the cement mantle used in conjunction with the all-polyeth-
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ylene component were also investigated. The geometry obtained from a computed tomography scan of the specimen was used as a reference to enlarge the area containing cement manually. On computational analysis this procedure was accomplished by reassigning the material properties of the ap ropriate elements. The cement mantle area was increase cp by 50% in both frontal and transverse models. The results of the anal ses performed for both the “normal” and “enlarge CT” cement mantles were then compared. Subchondral bone integrity. The mechanical significance of the subchondral bone was investigated by varying its thickness. In the model the subchondral bone was represented by a thin layer of cortical bone directly beneath the glenoid surface. To represent a typical glenoid surface reamed for implantation, a cortical thickness of approximately one third of that seen in the intact glenoid was used. For the purposes of this evaluation, the analysis was then repeated with this cortical layer completely omitted. RESULTS
The following discussion is based on examination of the model stresses obtained by application of the von Mises’ stress criterion. This expression incorporates both the shear and normal stress components into a single term, thus simplifying comparison of the overall stress state for a variety of model parameters (Figures 2 and 3, A through I). Any further use of the word “stress” in this text implies the von Mises’ stress unless otherwise stated. It should also be noted that the stress differences that are stated in the following text represent relative differences in the stress magnitudes among the various models in this study. Extrapolation of the modeled stress data to estimate component failure is not valid because of the current modeling assumptions and limitations. Loading conditions. For the purposes of this section, evaluation of the results has been limited to common areas within each model that demonstrate notable stress differences. Analysis of these regions provides an equivalent basis for comparison among the different models and load cases. Frontal plane: For the concentrically loaded intact glenoid, the principal stress patterns were strongly correlated with the trabecular orientation pattern seen in cross sections of cadaveric glenoids. This has been noted in the literature’6 and directly confirmed in several sections produced for the purposes of this study. The principal stress field observed in the intact glenoid was closer in appearance to the cemented all-polyethylene component than to the uncemented metal-backed component. The trabecular bone stress in the regions immediately adjacent to the screws of the uncemented metalbacked component (Figure 2, /-I) were found to be as much as 80% lower than those in the intact glenoid (Figure 2, B). For the cemented all-polyethylene component (Figure 2, E), the trabecular bone stress in the
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region adjacent to the cement mantle were found to be approximately 25% higher than the corresponding area in the intact model. For the eccentric load case (Figure 2, C, F, and I), examination of the subchondral bone layer showed that the 20” superiorly directed load produced dramatic increases in the maximum stress compared with the concentric load cases (Figure 2, 13, E, H). Maximum stress increases of 60% and 50% were noted for the cemented all-polyethylene (Figure 2, F) and uncemented metal-backed components (Figure 2, /), respectively. In the case of the uncemented metal-backed component, the superior-most screw was subjected to significantly greater stresses during eccentric loading, a 130% increase compared with concentric loading. It was also noted that bending stresses in the central peg of the keel were significantly greater for the eccentric versus the concentric loading case. Transverse plane: As was the case in the frontal plane, analysis in the transverse plane demonstrated that the uncemented metal-backed component had lower stresses localized to the subchondral region (Figure 3, H and i). The stresses were decreased by as much as 25% relative to those seen in the cemented all-polyethylene component (Figure 3, E and F). From examination in this plane, it was also evident that eccentric loading produced lower cortical and trabecular stresses compared with the concentrically loaded models. Keel geometry. Stress shielding caused by stress transfer through the keel was significant in the uncemented component (Figure 3, H and /) and also, to a lesser degree, in the cemented component (Figure 3, E and F). The distance between the tip of the central peg or keel and the adjacent anterior cortex of the scapula was crucial to this effect. This was further elucidated by conducting an analysis of the uncemented metalbacked component with a small defect in the anterior cortex, thus preventing direct stress transfer to the anterior cortical wall. Cement mantle size. A 50% enlargement of the cement mantle size led to an increase in the trabecular bone stress adjacent to the cement mantle from 10% to as much as 50%, particularly in areas where the mantle was close to the cortical shell. The orientation of the principal stress pattern was not significantly altered by the larger mantle with the exception of a few small localized regions in which the mantle was near the cortical tables of the scapula. Subchondral bone integrity. To determine its mechanical role, the thickness of subchondral bone immediately adjacent to the glenoid surface was altered. Removal of this bone layer resulted in an increase in the underlying trabecular bone stresses with a concomitant decrease in the load shared by the peripheral cortical shell in all load cases. This effect was more pronounced in the cemented all-polyethylene component. The subchondral bone stresses resulting from an
/ Shoulder Elbow Surg Volume 8, Number 2
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Figure 2 A, Material distribution used for analysis of intact glenoid model in frontal plane. Articular-cartilage geometry is not anatomically accurate but is based on similar geometry seen with glenoid prosthesis in place. This allows model to behave analytically as if it were in full concentric contact with average-sized adult humeral head 44 mm in diameter. B, von Mises’ stress plot of concentrically loaded intact glenoid in frontal plane showing stress distribution in unit thickness model. C, von Mises’ stress plot of eccentrically loaded intact glenoid in frontal plane showing stress distribution in unit thickness model. D, Material distribution used for analysis of cemented all-polyethylene component in frontal plane. E, von Mises’ stress plot of concentrically loaded cemented all-polyethylene component in frontal plane showing stress distribution in unit thickness model. F, von Mises’ stress plot of eccentrically loaded cemented all-polyethylene component in frontal plane showing stress distribution in unit thickness model. G, Material distribution used for analysis of uncemented metalbacked component in frontal plane. H, von Mises’ stress plot of concentrically loaded uncemented metal-back component in frontal plane showing stress distribution in unit thickness model. I, von Mises’ stress plot of eccentrically loaded uncemented metal-back component in frontal plane showing stress distribution in unit thickness model.
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et al
.
E
Figure 3 A, Material distribution used for anolysis of intact glenoid model in transverse plane. Articular cartilage geometry is not anatomically accurate but is based on similar geometry seen with glenoid prosthesis in place. This allows model to behave analyticolly as if it were in full concentric contact with average-sized adult humeral head 44 mm in diameter. B, von Mises’ stress plot of concentrically loaded intact glenoid in transverse plane showing stress distribution in unit thickness model. C, von Mises’ stress plot of eccentrically loaded intact glenoid in transverse plane showing stress distribution in unit thickness model. D, Material distribution used for the analysis of cemented oll-polyethylene component in transverse plane. E, von Mises’ stress plot of concentrically loaded cemented oll-polyethylene component in transverse plane showing stress distribution in unit thickness model. F, von Mises’ stress plot of eccentrically loaded cemented all-polyethylene component in transverse plane showing stress distribution in unit thickness model. G, Material distribution used for analysis of uncemented metal-backed component in transverse plane. H, von Mises’ stress plot of concentrically loaded uncemented metal-back component in transverse plane showing stress distribution in unit thickness model. I, von Mises’ stress plot of eccentrically loaded uncemented metal-back component in transverse plane showing stress distribution in unit thickness model.
J Shoulder Elbow Surg Volume 8, Number 2
eccentrically applied load were lower in the uncemented metal-backed component. Another interesting finding to note was the extremely high stress concentration present in the polyethylene insert used with the uncemented metal-backed component. The peak stress region was limited to within a few millimeters of the interface between the polyethylene insert and the metal base. The magnitude of the normal compressive stresses in this region reached levels that were more than double the stress applied to the articular surface of the polyethylene insert. This finding was present in both the concentric and eccentric load cases.
DISCUSSION This study used finite element analysis to model an intact glenoid and 2 implanted glenoid components. In the approximation of such a complex biologic system, certain assumptions must be made to achieve acceptable solutions in an efficient manner. A brief discussion of the assumptions made in the development of this study is provided. Perfectly bonded interfaces were assumed for all models in this study. The use of “interface” or “contact” elements to model the material interfaces and articulating surface may well have produced a closer approximation of the mechanical behavior in the glenoid prosthesis construct. However, defining the material interfaces in such a manner presents a challenge in mathematic modeling that requires the application of computationally intensive nonlinear, iterative solution techniques. The application of contact elements in this field is relatively new and currently evolving. This analysis was limited to the investigation of congruent glenoid geometries and components that were subjected to distributed static loads. In both load cases the load was distributed across the entire surface of the glenoid. The use of noncongruent systems would result in a smaller area of load application producing higher localized stresses in the region of contact. In addition, the contact or loading region may actually shift as the applied load increases. This is particularly true with the eccentric load case, in which a cuff deficiency would result in translation of the humeral head within the glenoid fossa during loading. However, because of these modeling limitations, such issues were beyond the scope of this investigation. In this study a 2-dimensional modeling approach was used to model a complex 3-dimensional glenoid structure. Such a simplification can result in a loss of the structure’s mechanical integrity. This loss is due to the inability of the 2-dimensional model to adequately compensate for the out-of-plane forces present in a 3-dimensional structure. In the particular case of the glenoid, the loss of the mechanical integrity of the circumferential cortical structure will have an impact on the results. Ideally, 3-dimensional modeling would eliminate this problem, but such analyses performed at this level of
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mesh refinement are currently expensive in terms of computer resources. The application of the side plate represents an attempt to compensate for the limitations of 2-dimensional analysis in an efficient manner. However, it should be noted that its presence makes it difficult to draw conclusions regarding the absolute stress magnitude that would be present in a full-thickness or 3-dimensional construct. As in any biomechanical application of the finite element method, model validation should be discussed. Ideally, experimental validation is desirable for any such study. Many investigators would argue that it is mandatory. Attempts at experimental validation are often impractical or misleading. In the case of this study, the region of greatest interest lies within the interior architecture of the glenoid. Measuring the stress in this region by the use of experimental techniques such as strain gauges or transducers would require violation of the very structure being studied. In addition, the use of such approaches can produce misleading results because of the creation of artificial stress risers that are not present in the intact structure. It could be argued that the glenoid surface or implant interface could be instrumented without structural damage. However, this type of approach will not directly provide stress data regarding the trabecular bone and the interior of the glenoid. In summary, a series of biplanar 2-dimensional finite element models were developed to study 2 fundamentally different component fixation designs used in a total shoulder arthroplasty system. Analysis of the cemented all-polyethylene design revealed an overall trabecular stress pattern similar to that of the intact glenoid. Enlargement of the cement mantle had little effect on the trabecular stress. When compared with the cemented all-polyethylene component, the uncemented metal-backed component displayed lower subchondral stresses for both load cases; this effect was more pronounced during eccentric loading. This result suggests that an uncemented metal-backed component may be better suited for a rotator cuff deficient shoulder. In addition, significant trabecular stress shielding was noted under both concentric and eccentric loading conditions, particularly with the uncemented metal-backed component. The results of this study suggest that the cemented all-polyethylene design may offer good fixation when the trabecular bone beneath the glenoid surface is of sufficient quantity and quality to support the polyethylene-cement composite. The uncemented metalbacked component may provide better fixation when a slightly eccentric load is anticipated. One potential problem became evident during the analysis of the uncemented design. High polyethylene stress regions were present at the polyethylene-metal interface in relation to the all-polyethylene component. This result suggests that this interface will be the site of initial polyethylene yielding and, ultimately, component
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failure at loads that are lower than those necessary to cause failure of the all-polyethylene component. However, because of the limitations of this model, the exact load required to cause yield cannot be adequately determined. The information produced by this study represents a small but significant step toward understanding many of the mechanical aspects associated with the bony fixation of implanted glenoid components. Future investigation into the phenomena surrounding glenoid component loosening is necessary and has much potential. As computing resources and capabilities expand to become more cost-efficient, new approaches to be considered might include the incorporation of 3-dimensional modeling, anisotropic material properties, gap or interface elements, and computational bone remodeling techniques. REFERENCES An KN, Himeno S, Tsumura H, Kawar T, Chao EYS. Pressure distributron on artrcular surfaces. applicatron to joint stab+ evaluation J Bromech 1990,23,1013-20 Bassett RW, Browne AO, Morrey BF, An KN Glenohumeral muscle force and moment mechamcs in a posrtron of shoulder rnstabilrty. J Biomech 1990,23.405-l 5 Black J. Orthopaedrc bromaterrals in research and practrce Church111 Livrngstone; New York 1988. P 180-98 Boyd AD, Aliabadi P, ThornhIll TS Postoperative proxrmal migration rn total shoulder arthroplasty, incrdence and signrficance J Arthroplasty 199 1;6 3 l-7 Callahan TD, Johnson ME, Chao EYS Shoulder strength analySIS using the Cybex II tsokrnetrc dynamometer Clan Orthop 1991,271.249-57. Cofield RH. Total shoulder arthroplasty with the Neer prosthesis. J Bone Joint Surg Am 1984,66A 899-906 Frggie HE, lnglis AE, Goldberg VM, Ranawat CS, Figgre MP, WrleJM. An analysrs of factors affecting the long-term results of total shoulder arthroplasty In inflammatory arthrrtrs J Arthroplasty 1988;3 123-30
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Franklin JL, Barrett WP, Jackins SE, Matsen FA. Glenoid loosening In total shoulder arthroplasty Association with rotator cuff deficiency J Arthroplasty 1988;3:39-46 9. Friedman RJ, LaBerge M, Dooley RL, O’Hara AL. Finite element modeling of the glenoid component. effect of design parameters on stress drstribution. J Shoulder Elbow Surg 1992; 1 .26 l-70. 10. Hawkins RJ, Bell RH, Jallay B. Total shoulder arthroplasty C/in Orthop 1989;242.188-94 11 Howell SM, Galinat BJ, Renzr AJ, Marone PJ. Normal and abnormal mechanrcs of the glenohumeral joint in the horizontal plane. J Bone Joint Surg Am 1988;70-A,227-32. 12 McElwain JP, Englrsh E. The early postoperatrve results of porous-coated total shoulder arthroplasty Clan Orthop 1987, 218.217-24 13 Morrey BF, An KN Biomechanrcs of the shoulder In. Rockwood CA. Matsen FA. editors. The shoulder. Philadelohia, WB Saunders,’ 1990. P 2’08-45. 14 Neer CS. Glenohumeral arthroplasty. In. Neer CS, editor Shoulder reconstruction Philadelphra~ WB Saunders, 1990. P. 146-60. 15 Neer CS, Craig EV, Fukuda H. Cuff-tear arthropathy. J Bone Jotnt Surg am 1983;65A. 1232-44. 16 Orr TE, Carter DR, Schurman DJ. Stress analyses of glenold component designs. Clan Orthop 1988,232.2 17-24 New York, Plenum Press, 1979. P 1 1 1 17 Park JB. Biomaterials. 18 Pauwels F The distribution of pressure In the elbow taint together with fundamental remarks on taint pressure. In. BiomechanICS of the locomotor apparatus. New York: Springer-Verlag; 1980 P. 41 l-4 19 Rohlmann A, Mobner U, Eberlein R, Bergmann G Spannungsanalyse am schulterblatt nach schulteraelenkersatz (Stress analyses at the scapula after shoulder jolt replacement) Biomed Tech 1983.28:224-34 20 Shah JS, Ju SH, Rowlands RE, An KN, Chao EYS Analysrs of friction In human tornt contact BED-Vol 26, 1993 Advances m Broengineering American Society of Mechanical Engineering 1993 p 51-54. 21 Wernans H, Hurskes R, Grootenboer HJ The behavior of adaptive bone-remodeling srmulatron models J Biomech 1992,25, 1425-4 1. 22 Weiss AP, Adams MA, Moore JR, Wetland Al. Unconstramed shoulder arthroplasty A five-year average follow-up study Clan Orthop 1990;257:86-93