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Finite element analysis of the mechanical behavior of a scapula implanted with a glenoid prosthesis
Clinical Biomechanics 16 (2001) 566±575
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Finite element analysis of the mechanical behavior of a scapula implanted with a glenoid prosthesis Estivalezes a, R. Darmana a, M. Mansat b, J. Egan c B. Couteau a,*, P. Mansat b, E. a
INSERM, Laboratoire de Biom ecanique, H^ opital Purpan, CHU Purpan, BP 3103, 31026 Toulouse cedex 3, France b Service d'Orthop edie et Traumatologie, H^ opital Purpan, Toulouse, France c E-Tech Ltd., Sheeld, UK Received 1 March 2000; accepted 27 March 2001
Abstract Objective. The objective of the present study was to analyze the mechanical eect of some of the surgical variables encountered during shoulder arthroplasty using the ®nite element method. The eect of one eccentric load case, cement thickness and conformity has been investigated. Design. A 3D ®nite element model of a healthy cadaveric scapula implanted with an anatomically shaped glenoid has been developed from computed tomography (CT) images. Background. Glenoid component ®xation can present the most dicult problem in total shoulder arthroplasty, loosening of this component remains one of the main complications. Methods. The 3D ®nite element model was ®rst validated by comparison with experimental measurements and by ®tting of the mechanical properties of the cortical bone. Then the articular pressure location, the surface contact geometry and the cement thickness have been analyzed to observe their eect on stresses and displacements at the interfaces and within the scapular bone. Results. The antero-posterior bending of the scapula was a notable feature and this was accentuated when an eccentric load was applied. The gleno-humeral contact area had a major role on the stress level in the supporting structures though but not on the global displacements. Varying the cement mantle modi®ed stresses according to the load case and it essentially changed the lateromedial displacement of the cement relatively to the bone. Conclusions. This analysis provided an insight into the mechanical eects of an implanted scapula according to dierent parameters related to implantation technique. Relevance Results emphasized the role of some of the parameters a clinician may face. They demonstrated the importance of the humeral head centering in the horizontal plane. Conformity decreasing may involve drastic increase of stresses within structures and a thick cement mantle is not necessarily advantageous relatively to the stresses at the cement/bone interface. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Shoulder; Prosthesis; Glenoid; Finite element analysis; Computed tomography
1. Introduction Loosening of the glenoid component is one of the major causes of failure in total shoulder arthroplasty. Clinical and radiographic observations show that loosening generally occurs at the bone±cement interface. The incidence of radiolucent areas surrounding a glenoid
*
Corresponding author. E-mail address: [email protected] (B. Couteau).
prosthesis has been reported to be between 22% and 95% [1]. Fundamentally, loosening which is characterized by bone resorption and interfacial micromotion, depends on the state of the underlying bone quality, the implant design, the implantation technique as well as the condition of the rotator cu muscular system. The gleno-humeral joint reactive force has been found to range from 370 to 2070 N [2±4] or from 0.4 to 2.4 body weight [5±7] depending on the daily activities. Proximal migration in total shoulder arthroplasty seems to be frequently observed [8]. Moreover, the shoulder can be
0268-0033/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 8 - 0 0 3 3 ( 0 1 ) 0 0 0 2 9 - 8
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anteriorly or posteriorly unstable [9,10]. This eccentric loading can thus contribute a `rocking-horse' eect that may initiate glenoid component loosening after total shoulder arthroplasty. Consequently, the durability of glenoid prosthesis ®xation is one important step in total shoulder arthroplasty. Previous experimental studies have compared glenoid prosthesis stability and the pull-out strength of these glenoid components [11,12]. However, these studies were performed with arti®cial glenoid cavities. Mathematical models have also been developed in order to calculate the stresses within the scapular bone with or without an implant. Initially, these scapular models were developed in two dimensions [13±15]; then 3D models appeared [16±19] to account for the asymmetry of the scapular bone. Among these studies, two [16,19] have shown reasonable agreement between their numerical and experimental results in spite of the complexity of the structure. The purpose of this study was to develop and to validate a 3D ®nite element model of the scapula implanted with an anatomically shaped glenoid prosthesis in order to analyze parameters that re¯ect the surgical variables a clinician may face during total shoulder arthroplasty. Generally, surgical variables include the quality and quantity of bone stock, the eect of disease such as rheumatoid arthritis or osteoarthritis on the surrounding soft tissue resulting in eccentric joint loads, balancing of these soft tissues by the surgeon, whether or not cement is used, the amount, thickness and areas of placement, the type of prosthesis, the state of conformity and so on. In the present study, we analyzed the sensitivity of the mechanical behavior relatively to different articular load locations (defect of balancing of soft tissues) and relatively to dierent contact areas (eect of the conformity). Then, in order to quantify the role of the cement volume on the transfer of the loads through to the scapular bone, dierent cement thickness have been simulated. The originality of this model lied in the realism of the cement mantle and in the possibility of simulating dierent thickness.
2.1. Experimental testing The experimental set-up has been described in detail by Barea et al. [18] who tested a glenoid with and without an implant in order to validate corresponding ®nite element models and to compare strain level before and after implantation. The home-made compressive testing machine was made of radiolucent polyamide and allowed a 90° abduction (Fig. 1) of shoulder with a calibrated load of 700 N [5] whilst enabling a simultaneous CT scan to be acquired. Articular contact surfaces were measured by using pressure sensitive ®lm (Fuji ®lms prescale super low pressure type, Fuji Films, Tokyo) and cortical bone deformations were recorded by means of four surface-mounted uniaxial strain gages (KYOMA strain gages, type KFG 10-120C111L1M2R). Two gages were attached onto the anterior face of the scapula and the two others were attached onto the posterior face near the glenoid neck and near the upper extremity of the lateral column (Fig. 2). Uniaxial strain gages have been used because of their small overall dimensions. Indeed, strain gages have to be
Fig. 1. Mounting ®xture principle allowing a 90° abduction to be simulated.
2. Methods Experimental measurements have been performed on a fresh cadaver shoulder into which was implanted an appropriately sized S&N anatomic keeled glenoid prosthesis (Smith & Nephew, Memphis, USA). The cadaveric scapula with the implant was then scanned using computed tomography (CT) to allow a 3D reconstruction and mechanical modeling. CT scan slices were performed in the transverse plane then FE model's axes were de®ned according to the normal of the articular surface.
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Fig. 2. Location of the uniaxial strain gages.
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stuck to ¯at areas. Only small areas of the glenoid surface can be assumed to be perfectly ¯at. 2.2. Finite element modeling The CT scan exam of the implanted scapula mounted onto the polyamide loading ®xture (Siemens, Somatom DRH2) was performed using the following protocol: two millimeters thick CT images were taken at 2 mm intervals with a resolution close to 0.25 mm/pixel. The CT images were processed on a Silicon Graphics workstation using a custom software (SIP305, ÓINSERM) that allows the bone contours to be extracted and converted into mathematics entities. The three-dimensional reconstruction of the glenoid was obtained by reading these bone contours into the pre- and post-processing software PATRAN V7.5 (ÓMSC Software). This geometry was then meshed with eight noded hexahedral elements that were attributed with appropriate material properties (polyethylene, cement, cancellous bone, cortical bone). The ®nite element model including the standard anatomically shaped glenoid component comprised 25 319 elements and 29 156 nodes (Fig. 3). The mechanical properties of the arti®cial components (glenoid prosthesis and cement) have been provided by their manufacturers. Mechanical parameters of the cancellous bone tissue were inferred from a previous work [20] speci®c to the glenoid and those from the cortical bone were de®ned in order to allow the theoretical model to match the experiment strain measure-
ments (Table 1). That is, the value of Young's modulus for the cortical bone was chosen to minimize the difference between the experimental strain measurements and numerical strain levels from the ®nite element analysis. As part of the validation step, an articular contact pressure equivalent to a 700 N force was applied through the experimental ®xture with a 90° abduction. This load corresponded to the most referenced data [5] which stated that force for 90° abduction was approximately 0.9 times body weight. The 700 N could thus represent the force exerted in a shoulder of a 80 kg person. In the model, the equilibrium of the structure was maintained by constraining the most medial nodes of the scapular bone to not translate. The eect of joint contact position was analyzed by simulating dierent locations for the gleno-humeral contact pressure. According to clinical observations [21± 25], pathological glenoid erosion has been reported to occur posteriorly, centrally or superiorly. Persistent humeral head subluxation following total shoulder arthroplasty may result in premature loosening of the glenoid component. In order to understand the eect of eccentric loads on the glenoid implant ®xation, two articular contact locations, centrally, and postero-superior, have been compared. The magnitude of these contact pressures was set to create an equivalent force of 1000 N, corresponding to a typical gleno-humeral contact force recorded on healthy subjects during activities of daily living [7].
Fig. 3. Finite element mesh of the scapula (a) with the anatomically shaped glenoid (b).
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Table 1 Mechanical properties of the dierent materials Materials
Mechanical properties
Data source
UHWPE PMMA cement Spongious bone
E 964 MPa, m 0:34 E 2000 MPa, m 0:23 E11 342:10 MPa, E22 212:77 MPa, E33 194:44 MPa, m12 m13 m23 0:26, G12 G13 G23 100 MPa E 16 000 MPa, m 0:3
Manufacturer Manufacturer Previous study [20]
Cortical bone
Dierence minimizing
Spongious bone was orthotropic with direction 1 normal to the center of the articular surface, direction 2 parallel to the supero-inferior axis and direction 3 parallel to the postero-anterior axis.
A reduction in articular conformity was analyzed by simulating smaller areas of gleno-humeral contact. An equivalent force (1000 N) of the pressure was retained and the ®rst contact area was given by the area three times measured (150 mm2 ) with a pressure sensitive ®lms (Fig. 4). As the shape of this area did not appear particularly circular, as might be expected for a sphere± sphere contact, the pressure in the FEA model was uniformly applied over the area of contact. The second contact area analyzed was chosen to be three times smaller (50 mm2 ) than the ®rst. This corresponded to the contact surface given by the Hertz contact theory with a 4 mm radial mismatch as recommended by Ianotti ey al. [21]. These contact areas are thus typical of what might occur clinically. In order to assess the role of the cement thickness, mechanical simulations of centered and eccentric loads were performed with a normal cement mantle and with a particularly thick cement mantle. The normal cement mantle was obtained after performing an in vitro shoulder arthroplasty by one of us with the required surgical experience. Cement thickness was not constant, and varied from 2 to 4 mm around the glenoid prosthesis and no cement was placed under the circumference of the ¯ange. The cement mantle was then
reconstructed by CT-scanning the cadaveric scapula with the glenoid prosthesis implanted. The thicker cement mantle corresponded to one approximately a double thickness (4±8 mm) in which most of the supporting subchondral cancellous bone beneath the glenoid had been removed. The computer FEA model could then simulate the stresses and displacements at the prosthesis±cement interface, the cement±bone interface and throughout the scapular bone.
Fig. 4. Articular contact surface measured by using pressure sensitive ®lm.
Fig. 5. Comparison of experimentally measured strains with that obtained numerically from the ®nite element model.
3. Results 3.1. Validation of the FEA model The experimental validation of the model was conducted by comparing the experimentally measured strains with those from the numerical model in which the values of the mechanical properties of the cortical bone were adjusted (Fig. 5). The standard deviation of the experimental data was provided through three times repeat measurements. The variation of the numerical data was given by the values at the ®nite element nodes that de®ned the gage location. The dierence between
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the ®nite element model and the experimental results has been found to vary from 5% to 20%, except for the anterior±superior gage (606%) for which the experimental strain level was very low. Indeed, the strain in this location has been found to be only 1 10 6 and 5 10 6 , respectively, for the experimental and numerical measurements, which may account for the elevated error in this region. In conclusion, the comparison of experimental data with numerical data demonstrated a reasonable correlation. 3.2. Articular contact location With the centered load the maximum tensile stresses appeared at the prosthetic keel/cement interface near the articular surface (1.34 MPa). Principal tensile stresses at the prosthesis ¯ange/cement interface were lower than 1.06 MPa and tensile stresses at the bone/cement interface were lower at a maximum of 0.91 MPa (Fig. 6(a)). Concerning the principal compressive stresses, the maximum value was at the cement interface below the articulating surface (5.58 MPa). The compressive stresses at the bone/cement interface were lower ()3 MPa) than those occurring at the interface between the articular surface of the prosthesis and the cement (Fig. 6(b)). With the non-centered load, the maximum tensile stresses (2.4 MPa) appeared at the prosthesis cement interface below the articulating surface (Fig. 7(a)). At the cement/bone interface, a maximum tensile stresses (2.08 MPa) appeared in the region adjacent to the articular contact and a second stress peak (1.38 MPa) was located at the opposite side of the glenoid. A high compressive principal stress peak ()11.8 MPa) occurred supero-posteriorly at the prosthesis/cement interface adjacent to the articular contact location (Fig. 7(b)). Concerning the displacements of the entire cement mantle, the centered load induced anterior displace-
ments while the non-centered load induced posterior displacements. Magnitudes of these displacements were twice as large for the eccentric load than for the centered load (Fig. 8). With the centered load, the latero-medial displacement (x component) was positive throughout. Whereas with the eccentric load, the x displacement of the posterior region was positive, i.e., in the same direction as the load, and the x displacement of the anterior part was negative, indicative of the bending motion of the cement mantle and scapular structures. With the centered load, displacements occurred principally in the medial (0.12 mm) and anterior (0.17 mm) directions and secondarily in the superior ()0.05 mm) direction. With the eccentric load, displacements occurred principally in the posterior (0.48 mm) direction and secondarily in the medio-lateral (0.17 mm) and superior (0.16 mm) directions. The tendency of the loaded scapula to bend about a superior±inferior axis was a dominant feature that was accentuated by the superoposterior loading. 3.3. Articular conformity The reduction of the contact area had a major in¯uence on the stresses level. Actually, when the contact area of the centered load was reduced, tensile and compressive stress peaks at the prosthesis±cement interface varied, respectively, from 1.34 to 2.56 MPa and from )5.58 to )11.3 MPa (Fig. 9). When the contact area decreased with the eccentric load, the maximal principal tensile stresses increased from 2.40 to 2.93 MPa and the corresponding compressive stresses increased from )11.8 to )15.4 MPa (Fig. 10). Stresses at the cement/bone interface were particularly raised in the regions located directly below the articular pressure. The reduction of contact area has a negligible eect on the displacement of the loaded cement mantle within the scapular bone. When the load was applied centrally,
Fig. 6. Maximal (a) and minimal (b) principal stresses in the cement mantle with the centered load (150 mm2 ) ± postero-lateral view.
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Fig. 7. Maximal (a) and minimal (b) principal stresses in the cement mantle with the non-centered load (150 mm2 ) ± postero-lateral view.
Fig. 8. Deformed (shaded shape) and undeformed cement mantle (gray wireframe) with the centered and non-centered load ± lateral view.
the displacements remained unchanged for both the small and large areas of contact. With the eccentric load, the main eect was an increase of the superior translation with the smaller contact area. Nevertheless, the superior translation remained lower (0.2 mm) than the posterior translation (0.5 mm).
3.4. Cement thickness With the centered load, stresses in the thicker cement mantle were very similar to stresses in the normal cement mantle (Fig. 11). Between the normal and thick cement mantle, maximal principal tensile stresses varied
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Fig. 9. Maximal (a) and minimal (b) principal stresses in the cement mantle with the centered load (50 mm2 ) ± postero-lateral view.
Fig. 10. Maximal (a) and minimal (b) principal stresses in the cement mantle with the non-centered load (50 mm2 ) ± postero-lateral view.
from 1.34 to 1.42 MPa and minimal principal compressive stresses varied from )5.58 to )5.33 MPa. Conversely, with the eccentric load, principal stresses in the thick cement mantle were around 30% higher than stresses in the normal cement mantle. This stress level change occurred particularly adjacent to the region of the articular contact (Fig. 12). The cement mantle thickness had a major role on the latero-medial displacement of the cement mantle relative to the scapular bone under the centered load. In fact, between the normal and thicker cement mantles, the displacement of the mantle itself decreased by 10% whilst the displacement of the surrounding bone was negligible. In the others directions or with the eccentric loads, displacement changes were less than 3%.
4. Discussion In this study, a 3D ®nite element model of a scapula implanted with a prosthetic glenoid has been developed. Comparison with experimental measurements enabled an assessment of the validity of the model. Following this validation, a set of parameters that relate to the surgical variables encountered at total shoulder arthroplasty have been analyzed. Assumptions about bone mechanical properties and prosthesis interface behavior implicit in the ®nite element model did not aect the comparison with the experimental strain gauge measurements. Indeed, the mechanical properties of bone tissues were assumed to be linearly elastic and the cement/bone interface was considered to be perfectly bonded. Assumptions about bone materials or
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Fig. 11. Maximal and minimal principal stresses in the thick cement mantle with the centered load (150 mm2 ).
Fig. 12. Maximal and minimal principal stresses in the thick cement mantle with the non-centered load (150 mm2 ).
interface behavior can be sources of error. Bone is dicult to characterize due to its inhomogeneity and anisotropy. By considering mechanical properties measured from 11 healthy pairs of glenoids [14], a reasonable accuracy for the numerical model has been found using a homogeneous cancellous bone. This approach compares well with a similar validation procedure [13] that used 18 strain gauges to validate a three-dimensional ®nite element model of a healthy scapula. Despite the small dierences in quantitative values, this study [13] also showed a reasonable agreement between strains from a FE model and those from experimental measurements. Thus, 3D ®nite element modeling of the scapula can provide a good approximation of strain and stress ®elds at the cortical surface. The assumed perfectly bonded interfaces were probably not fully representative of in vivo conditions, since
it would seem that majority of glenoid implants reveal the presence of a membranous tissue surrounding the cement mantle. The present study does not claim to represent this physiology since the precise location and thickness of this tissue is generally not well de®ned. Actually, the location determination of this surrounding tissue may vary according to the orientation of the radiography. The aim of this ®rst approach was the assessment of the role of dierent clinical parameters using a 3D model that assumed perfectly bonded interfaces. The next step will be to take into account the characteristics of dierent pathologies [15] as well as actual implant position, by using CT scan slices from patients. For instance, in osteoarthritis, the reinforcement of the glenoid bone at the posterior region may restrict the ¯exural sensitivity of the scapula.
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The displacement analysis showed the eect of repositioning the articular pressure location from a central to a superior±posterior location. The posterior±anterior (z) component of the displacements of the cement mantle presented the greatest magnitude compared with the latero-medial (x) and superior±inferior (y) displacements. This demonstrated the tendency of the scapula to undergo a bending motion about the vertical central axis of the glenoid. With the o-center load, the displacements in z direction was approximately twice as great as displacements in the two orthogonal x and y directions. This can be explained by the anatomy of the scapula in the transverse plane which is cone-shaped, and which leads to an emphasized bending motion with the ocenter load. Indeed, this bending phenomenon about the scapular notch is a most striking feature. It may be speculated that this serves a physiological role as a shock absorber by eectively increasing the compliance of the bony structures of the shoulder. However, when implanted with prosthesis this scapular bending, particularly if this is exaggerated by an o-center loading, may be detrimental if it weakens the implant or cement ®xation. The cement interfaces stresses are shown to be increased with the o-center loading, which is indicative of a greater demand on the cement/bone ®xation. In glenoids with primary osteoarthritis, often the humeral head is displaced posteriorly. According to our results, such an abnormal posterior articular contact may result in excessive posterior bending. The great bone density [15] that we observed at the posterior margin of glenoids with primary osteoarthritis is probably the consequence of this excessive bending eect. The tendency of the scapula to bend about the vertical axis of the glenoid indicates that 2D models [6,8] are not appropriate to fully analyze prosthesis design performance. It has been demonstrated in this study that eccentric loads can produce drastic tensile stress peaks at the cement/bone interface. With the centered load the tensile (1.34 MPa) and maximum shear (3.18 Mpa) stresses were already critical relatively to the apparent strength of the cement bone interface [26], respectively, equal to 1.35 and 2.25 MPa. Eccentric load induced approximately twice higher tensile and maximum shear stresses. It can be thus speculated that this may promote in a very short time local debonding of the surfaces and then progressive loosening of the implant or cement. One of the main complications of total shoulder arthroplasty is shoulder instability [27] classi®ed according to the gleno-humeral translation (anterior, posterior superior or inferior). Since shoulder instability is liable to involve eccentric or translated articular loads, the consequences of such load cases require investigation. The conformity of the glenoid contact did not seem to have a major role on the global displacements of the implanted glenoid. Unlike the displacements, the inter-
nal stresses were appreciably modi®ed by a reduction of the articular contact area. Dierences appeared locally, in the regions close to the contact location. This result was in agreement with that found using a 2D model [9] in which high conformity presented lower cement stresses compared with a low conformity contact. This has also been experimentally veri®ed [28] by means of strain gauges at the glenoid keel: nonconforming components increased maximum compressive strains by almost 50%. Thus, while the gleno-humeral radial mismatch may be good because it has a signi®cant in¯uence on the joint kinematics [29], the downside is the increased levels of stress transmitted to the dierent structures (glenoid and cement). For example, the cement compressive stress peak varied from )11.8 to )15.4 MPa when the superior±posterior articular contact area was decreased. The eects of cement mantle size are dependent on the position of the gleno-humeral contact. With the centered load, the change of stresses within the cement between the normal and thick mantle was negligible. On the other hand, when the load case was o-centered, stresses within a thicker cement mantle were greater than stresses within normal cement thickness. On that account, tensile and maximum shear stresses reached, respectively, 3.16 and 7.7 MPa which is much higher than the measured apparent strength of the cement/bone interface [26]. With the thick cement mantle, there was probably a direct transfer of the articular load to the cement through the articular surface of the prosthesis. With the normal, i.e., `standard' cement thickness, a large portion of this eccentric load was transmitted to the subchondral bone surrounding the cement mantle. Von Mises stresses in the surrounding bone decreased by on average 10% (from 25.5 to 22.9 MPa) between the thick and normal cement mantle. This indicates that the thicker cement acts to divert more of the applied loads away from the surrounding glenoid bone. The stier cement structure is thus stress shielding the peri-prosthetic bone in the case of the o-center loading. Here, there is a discrepancy between the results of the present study and those obtained from a 2D model [30]. However, the role of the cement thickness described in the present study appears to be consistent with the principle of stress shielding. Finally, on one hand a thin cement mantle can promote high cement displacements relatively to the bone when the load is centered and on the other hand a thick cement mantle may promote the resorption of the surrounding bone by stress shielding when the load is o center. From experience, surgeons have a tendency to minimize the cement thickness. The ideal cement mantle is probably the one that ensures a good stability with limited motion (<150 lm) and the one which allows the surrounding bone to be correctly loaded. This suggests that the characteristics of the glenoid cement mantle have an important role in determining the clinical outcome of total shoulder arthroplasty.
B. Couteau et al. / Clinical Biomechanics 16 (2001) 566±575
5. Conclusions A 3D scapular model with an implant has been used to assess the in¯uence of dierent parameters that can vary with respect to the surgical technique. This provided an insight into the mechanical behavior of an implanted scapula. This model showed the high sensitivity of the scapula to bend in the antero-posterior direction. Now, it would be interesting to investigate the role of this bending in the glenoid loosening process or in the development of glenoid prosthesis radiolucencies. The contact area analysis emphasized the compromise between internal stress levels and articular degree of motion. The eects of cement mantle size are dependent on the position of the gleno-humeral contact. Indeed, these mechanical eects of the dierent clinical parameters are not particularly intuitive and this suggests that the 3D modeling can add valuable information to help interpret glenoid implant performance. As the reconstruction technique was based on CT images, such an analysis might be used with CT images from patients. This `in vivo' analysis would be particularly relevant since it has been demonstrated that pathological glenoids [15] presented geometrical and also dierences in bone material property distributions. Acknowledgements This study was supported by 3M Sante. The authors are also grateful to Christophe Barea and to Marie± Christine Hobatho for the development of the experimental set-up. References [1] Brems J. The glenoid component in total shoulder arthroplasty. J Shoulder Elbow Surg 1993;2:47±54. [2] Van Der Helm FCT, Veeger HEJ. Quasi-static analysis of muscle forces in the shoulder mechanism during wheel chair propulsion. J Biomech 1996;29:39±52. [3] Karlsson D, Peterson B. Towards a model for force predictions in the human shoulder. J Biomech 1992;25:189±99. [4] Beuchel FF, Pappas MJ, DePalma AF. Floating socket total shoulder replacement: anatomical biomechanical and surgical rationale. J Biomed Mater Res 1978;12:89±114. [5] Poppen NK, Walker PS. Forces at the glenohumeral joint in abduction. Clin Orthop 1978;135:165±70. [6] Inman VT, Saunders JB, Abbot LC. Observations on the function of the shoulder joint. J Bone J Surg 1944;26:1. [7] Anglin C, Wyss UP, Pichora DR. Glenohumeral contact forces during ®ve activities of daily living. In: Proceedings of the First Conference of the International Shoulder Group, 1996, p. 13±8. [8] Boyd AD, Aliabadi P, Thornill TS. Postoperative proximal migration in total shoulder arthroplasty ± incidence and significance. J Arthroplasty 1991;6:31±7. [9] Moeckel BH, Altchek DW, Warren RF, Wickiewicz TL, Dines DM. Instability of the shoulder after arthroplasty. J Bone J Surg A 1993;75:492±7.
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[10] Co®eld RH, Edgerton BC. Total shoulder arthroplasty: complications and revision surgery. Instructional Course Lectures 1990;39:449±62. [11] Anglin C, Nyeler RW, Wyss UP. Pegged versus keeled glenoids: omparisons of laboratory ®xation performance. In: XXVIIth ISB Congress Proceedings, 1999, p. 611. [12] Fukuda K, Chen CM, Co®eld RH, Chao EYS. Biomechanical analysis of stability and ®xation strength of total shoulder prostheses. Orthopedics 1988;11:141±9. [13] Orr TE, Carter DR, Schurman DJ. Stress analyses of glenoid component designs. Clin Orthop 1988;232:217±24. [14] Friedman RJ, Laberge M, Dooley RL, O'Hara AL. Finite element modeling of the glenoid component: eect of design parameters on stress distribution. J Shoulder Elbow Surg 1992;1:261±70. [15] Lacroix D, Prendergast PJ. Stress analysis of glenoid component designs for shoulder arthroplasty. Proc Inst Mech Eng 1997;211(H):467±74. [16] Lacroix D, Prendergast PJ. 3D ®nite element analysis of glenoid prosthesis for total shoulder arthroplasty. J Biomech 1998;31(Suppl 1):52. [17] Tomaszeswski PR, Ondrla JM. Incongruency and its relation to stress in prosthetic shoulder components. Orthop Res Soc 1992;425. [18] Barea C, Hobatho MC, Darmana R, Mansat M. 3D ®nite element study of glenoid implants in total shoulder arthroplasty. Comput Meth Biomech Biomed Eng 1998;2:471±8. [19] Gupta S, Van Der Helm F, Kaptein BL, Van Keulen F. Spoor CW, Sterk J. Experimental validation of three-dimensional ®nite element modelling of scapula. In: XVIIth ISB Proceedings, 1999, p. 574. [20] Mansat P, Barea C, Hobatho MC. Anatomic variation of the mechanical properties of the glenoid. J Shoulder Elbow Surg 1998;7:109±15. [21] Ianotti JP, Gabriel JP, Schneck SL, Evans BG, Misra S. The normal glenohumeral relationships. J Bone J Surg A 1992;74:491± 500. [22] Couteau B, Mansat P, Mansat M, Darmana R, Egan J. In vivo characterization of glenoid using computed tomography. J Shoulder Elbow Surg 2001;Mar±Apr 10(2):116±22. [23] Badet R, Boulahia A, Walch G. Measure tomodensitometrique de la subluxation humerale antero-posterieure. Proposition d'une methode. Application a l'Omarthrose centree. Rev Chir Orthop 1998;84:508±14. [24] Neer CS. Reconstructive surgery and rehabilitation of the shoulder. In: Kelly WN, Harris ED, Ruddy S, Sledge CB, editors. Textbook of rheumatology. Philadelphia: WB Saunders; 1985. p. 1944±59. [25] Co®eld RH. Total shoulder arthroplasty with the neer prosthesis. J Bone Joint Surg Am B 1984;62:116. [26] Mann KA, Werner FW, Ayers DC. Mechanical strength of the cement bone interface is greater in shear than in tension. J Biomech 1999;32:1251±4. [27] Wirth MA, Rockwood CA. Complications of shoulder arthroplasty. Clin Orthop Rel Res 1994;307:47±69. [28] Karduna AR, Williams GR, Iannotti JP, Williams JL. Total shoulder arthroplasty biomechanics: a study of the forces and strains at the glenoid component. J Biomech Eng 1998;120:92±9. [29] Karduna AR, Williams GR, Williams JL, Iannotti JP. Kinematics of the gleno-humeral joint: eects of muscle forces, ligamentous constraints and articular geometry. J Orthop Res 1996;14:986±93. [30] Stone KD, Grabowski JJ, Co®el RH, Morrey BF, An KA. Stress analysis of glenoid components in total shoulder arthroplasty. J Shoulder Elbow Surg 1999;8:151±8.
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Finite element analysis of the mechanical behavior of a scapula implanted with a glenoid prosthesis Estivalezes a, R. Darmana a, M. Mansat b, J. Egan c B. Couteau a,*, P. Mansat b, E. a
INSERM, Laboratoire de Biom ecanique, H^ opital Purpan, CHU Purpan, BP 3103, 31026 Toulouse cedex 3, France b Service d'Orthop edie et Traumatologie, H^ opital Purpan, Toulouse, France c E-Tech Ltd., Sheeld, UK Received 1 March 2000; accepted 27 March 2001
Abstract Objective. The objective of the present study was to analyze the mechanical eect of some of the surgical variables encountered during shoulder arthroplasty using the ®nite element method. The eect of one eccentric load case, cement thickness and conformity has been investigated. Design. A 3D ®nite element model of a healthy cadaveric scapula implanted with an anatomically shaped glenoid has been developed from computed tomography (CT) images. Background. Glenoid component ®xation can present the most dicult problem in total shoulder arthroplasty, loosening of this component remains one of the main complications. Methods. The 3D ®nite element model was ®rst validated by comparison with experimental measurements and by ®tting of the mechanical properties of the cortical bone. Then the articular pressure location, the surface contact geometry and the cement thickness have been analyzed to observe their eect on stresses and displacements at the interfaces and within the scapular bone. Results. The antero-posterior bending of the scapula was a notable feature and this was accentuated when an eccentric load was applied. The gleno-humeral contact area had a major role on the stress level in the supporting structures though but not on the global displacements. Varying the cement mantle modi®ed stresses according to the load case and it essentially changed the lateromedial displacement of the cement relatively to the bone. Conclusions. This analysis provided an insight into the mechanical eects of an implanted scapula according to dierent parameters related to implantation technique. Relevance Results emphasized the role of some of the parameters a clinician may face. They demonstrated the importance of the humeral head centering in the horizontal plane. Conformity decreasing may involve drastic increase of stresses within structures and a thick cement mantle is not necessarily advantageous relatively to the stresses at the cement/bone interface. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Shoulder; Prosthesis; Glenoid; Finite element analysis; Computed tomography
1. Introduction Loosening of the glenoid component is one of the major causes of failure in total shoulder arthroplasty. Clinical and radiographic observations show that loosening generally occurs at the bone±cement interface. The incidence of radiolucent areas surrounding a glenoid
*
Corresponding author. E-mail address: [email protected] (B. Couteau).
prosthesis has been reported to be between 22% and 95% [1]. Fundamentally, loosening which is characterized by bone resorption and interfacial micromotion, depends on the state of the underlying bone quality, the implant design, the implantation technique as well as the condition of the rotator cu muscular system. The gleno-humeral joint reactive force has been found to range from 370 to 2070 N [2±4] or from 0.4 to 2.4 body weight [5±7] depending on the daily activities. Proximal migration in total shoulder arthroplasty seems to be frequently observed [8]. Moreover, the shoulder can be
0268-0033/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 8 - 0 0 3 3 ( 0 1 ) 0 0 0 2 9 - 8
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anteriorly or posteriorly unstable [9,10]. This eccentric loading can thus contribute a `rocking-horse' eect that may initiate glenoid component loosening after total shoulder arthroplasty. Consequently, the durability of glenoid prosthesis ®xation is one important step in total shoulder arthroplasty. Previous experimental studies have compared glenoid prosthesis stability and the pull-out strength of these glenoid components [11,12]. However, these studies were performed with arti®cial glenoid cavities. Mathematical models have also been developed in order to calculate the stresses within the scapular bone with or without an implant. Initially, these scapular models were developed in two dimensions [13±15]; then 3D models appeared [16±19] to account for the asymmetry of the scapular bone. Among these studies, two [16,19] have shown reasonable agreement between their numerical and experimental results in spite of the complexity of the structure. The purpose of this study was to develop and to validate a 3D ®nite element model of the scapula implanted with an anatomically shaped glenoid prosthesis in order to analyze parameters that re¯ect the surgical variables a clinician may face during total shoulder arthroplasty. Generally, surgical variables include the quality and quantity of bone stock, the eect of disease such as rheumatoid arthritis or osteoarthritis on the surrounding soft tissue resulting in eccentric joint loads, balancing of these soft tissues by the surgeon, whether or not cement is used, the amount, thickness and areas of placement, the type of prosthesis, the state of conformity and so on. In the present study, we analyzed the sensitivity of the mechanical behavior relatively to different articular load locations (defect of balancing of soft tissues) and relatively to dierent contact areas (eect of the conformity). Then, in order to quantify the role of the cement volume on the transfer of the loads through to the scapular bone, dierent cement thickness have been simulated. The originality of this model lied in the realism of the cement mantle and in the possibility of simulating dierent thickness.
2.1. Experimental testing The experimental set-up has been described in detail by Barea et al. [18] who tested a glenoid with and without an implant in order to validate corresponding ®nite element models and to compare strain level before and after implantation. The home-made compressive testing machine was made of radiolucent polyamide and allowed a 90° abduction (Fig. 1) of shoulder with a calibrated load of 700 N [5] whilst enabling a simultaneous CT scan to be acquired. Articular contact surfaces were measured by using pressure sensitive ®lm (Fuji ®lms prescale super low pressure type, Fuji Films, Tokyo) and cortical bone deformations were recorded by means of four surface-mounted uniaxial strain gages (KYOMA strain gages, type KFG 10-120C111L1M2R). Two gages were attached onto the anterior face of the scapula and the two others were attached onto the posterior face near the glenoid neck and near the upper extremity of the lateral column (Fig. 2). Uniaxial strain gages have been used because of their small overall dimensions. Indeed, strain gages have to be
Fig. 1. Mounting ®xture principle allowing a 90° abduction to be simulated.
2. Methods Experimental measurements have been performed on a fresh cadaver shoulder into which was implanted an appropriately sized S&N anatomic keeled glenoid prosthesis (Smith & Nephew, Memphis, USA). The cadaveric scapula with the implant was then scanned using computed tomography (CT) to allow a 3D reconstruction and mechanical modeling. CT scan slices were performed in the transverse plane then FE model's axes were de®ned according to the normal of the articular surface.
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Fig. 2. Location of the uniaxial strain gages.
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stuck to ¯at areas. Only small areas of the glenoid surface can be assumed to be perfectly ¯at. 2.2. Finite element modeling The CT scan exam of the implanted scapula mounted onto the polyamide loading ®xture (Siemens, Somatom DRH2) was performed using the following protocol: two millimeters thick CT images were taken at 2 mm intervals with a resolution close to 0.25 mm/pixel. The CT images were processed on a Silicon Graphics workstation using a custom software (SIP305, ÓINSERM) that allows the bone contours to be extracted and converted into mathematics entities. The three-dimensional reconstruction of the glenoid was obtained by reading these bone contours into the pre- and post-processing software PATRAN V7.5 (ÓMSC Software). This geometry was then meshed with eight noded hexahedral elements that were attributed with appropriate material properties (polyethylene, cement, cancellous bone, cortical bone). The ®nite element model including the standard anatomically shaped glenoid component comprised 25 319 elements and 29 156 nodes (Fig. 3). The mechanical properties of the arti®cial components (glenoid prosthesis and cement) have been provided by their manufacturers. Mechanical parameters of the cancellous bone tissue were inferred from a previous work [20] speci®c to the glenoid and those from the cortical bone were de®ned in order to allow the theoretical model to match the experiment strain measure-
ments (Table 1). That is, the value of Young's modulus for the cortical bone was chosen to minimize the difference between the experimental strain measurements and numerical strain levels from the ®nite element analysis. As part of the validation step, an articular contact pressure equivalent to a 700 N force was applied through the experimental ®xture with a 90° abduction. This load corresponded to the most referenced data [5] which stated that force for 90° abduction was approximately 0.9 times body weight. The 700 N could thus represent the force exerted in a shoulder of a 80 kg person. In the model, the equilibrium of the structure was maintained by constraining the most medial nodes of the scapular bone to not translate. The eect of joint contact position was analyzed by simulating dierent locations for the gleno-humeral contact pressure. According to clinical observations [21± 25], pathological glenoid erosion has been reported to occur posteriorly, centrally or superiorly. Persistent humeral head subluxation following total shoulder arthroplasty may result in premature loosening of the glenoid component. In order to understand the eect of eccentric loads on the glenoid implant ®xation, two articular contact locations, centrally, and postero-superior, have been compared. The magnitude of these contact pressures was set to create an equivalent force of 1000 N, corresponding to a typical gleno-humeral contact force recorded on healthy subjects during activities of daily living [7].
Fig. 3. Finite element mesh of the scapula (a) with the anatomically shaped glenoid (b).
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Table 1 Mechanical properties of the dierent materials Materials
Mechanical properties
Data source
UHWPE PMMA cement Spongious bone
E 964 MPa, m 0:34 E 2000 MPa, m 0:23 E11 342:10 MPa, E22 212:77 MPa, E33 194:44 MPa, m12 m13 m23 0:26, G12 G13 G23 100 MPa E 16 000 MPa, m 0:3
Manufacturer Manufacturer Previous study [20]
Cortical bone
Dierence minimizing
Spongious bone was orthotropic with direction 1 normal to the center of the articular surface, direction 2 parallel to the supero-inferior axis and direction 3 parallel to the postero-anterior axis.
A reduction in articular conformity was analyzed by simulating smaller areas of gleno-humeral contact. An equivalent force (1000 N) of the pressure was retained and the ®rst contact area was given by the area three times measured (150 mm2 ) with a pressure sensitive ®lms (Fig. 4). As the shape of this area did not appear particularly circular, as might be expected for a sphere± sphere contact, the pressure in the FEA model was uniformly applied over the area of contact. The second contact area analyzed was chosen to be three times smaller (50 mm2 ) than the ®rst. This corresponded to the contact surface given by the Hertz contact theory with a 4 mm radial mismatch as recommended by Ianotti ey al. [21]. These contact areas are thus typical of what might occur clinically. In order to assess the role of the cement thickness, mechanical simulations of centered and eccentric loads were performed with a normal cement mantle and with a particularly thick cement mantle. The normal cement mantle was obtained after performing an in vitro shoulder arthroplasty by one of us with the required surgical experience. Cement thickness was not constant, and varied from 2 to 4 mm around the glenoid prosthesis and no cement was placed under the circumference of the ¯ange. The cement mantle was then
reconstructed by CT-scanning the cadaveric scapula with the glenoid prosthesis implanted. The thicker cement mantle corresponded to one approximately a double thickness (4±8 mm) in which most of the supporting subchondral cancellous bone beneath the glenoid had been removed. The computer FEA model could then simulate the stresses and displacements at the prosthesis±cement interface, the cement±bone interface and throughout the scapular bone.
Fig. 4. Articular contact surface measured by using pressure sensitive ®lm.
Fig. 5. Comparison of experimentally measured strains with that obtained numerically from the ®nite element model.
3. Results 3.1. Validation of the FEA model The experimental validation of the model was conducted by comparing the experimentally measured strains with those from the numerical model in which the values of the mechanical properties of the cortical bone were adjusted (Fig. 5). The standard deviation of the experimental data was provided through three times repeat measurements. The variation of the numerical data was given by the values at the ®nite element nodes that de®ned the gage location. The dierence between
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the ®nite element model and the experimental results has been found to vary from 5% to 20%, except for the anterior±superior gage (606%) for which the experimental strain level was very low. Indeed, the strain in this location has been found to be only 1 10 6 and 5 10 6 , respectively, for the experimental and numerical measurements, which may account for the elevated error in this region. In conclusion, the comparison of experimental data with numerical data demonstrated a reasonable correlation. 3.2. Articular contact location With the centered load the maximum tensile stresses appeared at the prosthetic keel/cement interface near the articular surface (1.34 MPa). Principal tensile stresses at the prosthesis ¯ange/cement interface were lower than 1.06 MPa and tensile stresses at the bone/cement interface were lower at a maximum of 0.91 MPa (Fig. 6(a)). Concerning the principal compressive stresses, the maximum value was at the cement interface below the articulating surface (5.58 MPa). The compressive stresses at the bone/cement interface were lower ()3 MPa) than those occurring at the interface between the articular surface of the prosthesis and the cement (Fig. 6(b)). With the non-centered load, the maximum tensile stresses (2.4 MPa) appeared at the prosthesis cement interface below the articulating surface (Fig. 7(a)). At the cement/bone interface, a maximum tensile stresses (2.08 MPa) appeared in the region adjacent to the articular contact and a second stress peak (1.38 MPa) was located at the opposite side of the glenoid. A high compressive principal stress peak ()11.8 MPa) occurred supero-posteriorly at the prosthesis/cement interface adjacent to the articular contact location (Fig. 7(b)). Concerning the displacements of the entire cement mantle, the centered load induced anterior displace-
ments while the non-centered load induced posterior displacements. Magnitudes of these displacements were twice as large for the eccentric load than for the centered load (Fig. 8). With the centered load, the latero-medial displacement (x component) was positive throughout. Whereas with the eccentric load, the x displacement of the posterior region was positive, i.e., in the same direction as the load, and the x displacement of the anterior part was negative, indicative of the bending motion of the cement mantle and scapular structures. With the centered load, displacements occurred principally in the medial (0.12 mm) and anterior (0.17 mm) directions and secondarily in the superior ()0.05 mm) direction. With the eccentric load, displacements occurred principally in the posterior (0.48 mm) direction and secondarily in the medio-lateral (0.17 mm) and superior (0.16 mm) directions. The tendency of the loaded scapula to bend about a superior±inferior axis was a dominant feature that was accentuated by the superoposterior loading. 3.3. Articular conformity The reduction of the contact area had a major in¯uence on the stresses level. Actually, when the contact area of the centered load was reduced, tensile and compressive stress peaks at the prosthesis±cement interface varied, respectively, from 1.34 to 2.56 MPa and from )5.58 to )11.3 MPa (Fig. 9). When the contact area decreased with the eccentric load, the maximal principal tensile stresses increased from 2.40 to 2.93 MPa and the corresponding compressive stresses increased from )11.8 to )15.4 MPa (Fig. 10). Stresses at the cement/bone interface were particularly raised in the regions located directly below the articular pressure. The reduction of contact area has a negligible eect on the displacement of the loaded cement mantle within the scapular bone. When the load was applied centrally,
Fig. 6. Maximal (a) and minimal (b) principal stresses in the cement mantle with the centered load (150 mm2 ) ± postero-lateral view.
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Fig. 7. Maximal (a) and minimal (b) principal stresses in the cement mantle with the non-centered load (150 mm2 ) ± postero-lateral view.
Fig. 8. Deformed (shaded shape) and undeformed cement mantle (gray wireframe) with the centered and non-centered load ± lateral view.
the displacements remained unchanged for both the small and large areas of contact. With the eccentric load, the main eect was an increase of the superior translation with the smaller contact area. Nevertheless, the superior translation remained lower (0.2 mm) than the posterior translation (0.5 mm).
3.4. Cement thickness With the centered load, stresses in the thicker cement mantle were very similar to stresses in the normal cement mantle (Fig. 11). Between the normal and thick cement mantle, maximal principal tensile stresses varied
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Fig. 9. Maximal (a) and minimal (b) principal stresses in the cement mantle with the centered load (50 mm2 ) ± postero-lateral view.
Fig. 10. Maximal (a) and minimal (b) principal stresses in the cement mantle with the non-centered load (50 mm2 ) ± postero-lateral view.
from 1.34 to 1.42 MPa and minimal principal compressive stresses varied from )5.58 to )5.33 MPa. Conversely, with the eccentric load, principal stresses in the thick cement mantle were around 30% higher than stresses in the normal cement mantle. This stress level change occurred particularly adjacent to the region of the articular contact (Fig. 12). The cement mantle thickness had a major role on the latero-medial displacement of the cement mantle relative to the scapular bone under the centered load. In fact, between the normal and thicker cement mantles, the displacement of the mantle itself decreased by 10% whilst the displacement of the surrounding bone was negligible. In the others directions or with the eccentric loads, displacement changes were less than 3%.
4. Discussion In this study, a 3D ®nite element model of a scapula implanted with a prosthetic glenoid has been developed. Comparison with experimental measurements enabled an assessment of the validity of the model. Following this validation, a set of parameters that relate to the surgical variables encountered at total shoulder arthroplasty have been analyzed. Assumptions about bone mechanical properties and prosthesis interface behavior implicit in the ®nite element model did not aect the comparison with the experimental strain gauge measurements. Indeed, the mechanical properties of bone tissues were assumed to be linearly elastic and the cement/bone interface was considered to be perfectly bonded. Assumptions about bone materials or
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Fig. 11. Maximal and minimal principal stresses in the thick cement mantle with the centered load (150 mm2 ).
Fig. 12. Maximal and minimal principal stresses in the thick cement mantle with the non-centered load (150 mm2 ).
interface behavior can be sources of error. Bone is dicult to characterize due to its inhomogeneity and anisotropy. By considering mechanical properties measured from 11 healthy pairs of glenoids [14], a reasonable accuracy for the numerical model has been found using a homogeneous cancellous bone. This approach compares well with a similar validation procedure [13] that used 18 strain gauges to validate a three-dimensional ®nite element model of a healthy scapula. Despite the small dierences in quantitative values, this study [13] also showed a reasonable agreement between strains from a FE model and those from experimental measurements. Thus, 3D ®nite element modeling of the scapula can provide a good approximation of strain and stress ®elds at the cortical surface. The assumed perfectly bonded interfaces were probably not fully representative of in vivo conditions, since
it would seem that majority of glenoid implants reveal the presence of a membranous tissue surrounding the cement mantle. The present study does not claim to represent this physiology since the precise location and thickness of this tissue is generally not well de®ned. Actually, the location determination of this surrounding tissue may vary according to the orientation of the radiography. The aim of this ®rst approach was the assessment of the role of dierent clinical parameters using a 3D model that assumed perfectly bonded interfaces. The next step will be to take into account the characteristics of dierent pathologies [15] as well as actual implant position, by using CT scan slices from patients. For instance, in osteoarthritis, the reinforcement of the glenoid bone at the posterior region may restrict the ¯exural sensitivity of the scapula.
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The displacement analysis showed the eect of repositioning the articular pressure location from a central to a superior±posterior location. The posterior±anterior (z) component of the displacements of the cement mantle presented the greatest magnitude compared with the latero-medial (x) and superior±inferior (y) displacements. This demonstrated the tendency of the scapula to undergo a bending motion about the vertical central axis of the glenoid. With the o-center load, the displacements in z direction was approximately twice as great as displacements in the two orthogonal x and y directions. This can be explained by the anatomy of the scapula in the transverse plane which is cone-shaped, and which leads to an emphasized bending motion with the ocenter load. Indeed, this bending phenomenon about the scapular notch is a most striking feature. It may be speculated that this serves a physiological role as a shock absorber by eectively increasing the compliance of the bony structures of the shoulder. However, when implanted with prosthesis this scapular bending, particularly if this is exaggerated by an o-center loading, may be detrimental if it weakens the implant or cement ®xation. The cement interfaces stresses are shown to be increased with the o-center loading, which is indicative of a greater demand on the cement/bone ®xation. In glenoids with primary osteoarthritis, often the humeral head is displaced posteriorly. According to our results, such an abnormal posterior articular contact may result in excessive posterior bending. The great bone density [15] that we observed at the posterior margin of glenoids with primary osteoarthritis is probably the consequence of this excessive bending eect. The tendency of the scapula to bend about the vertical axis of the glenoid indicates that 2D models [6,8] are not appropriate to fully analyze prosthesis design performance. It has been demonstrated in this study that eccentric loads can produce drastic tensile stress peaks at the cement/bone interface. With the centered load the tensile (1.34 MPa) and maximum shear (3.18 Mpa) stresses were already critical relatively to the apparent strength of the cement bone interface [26], respectively, equal to 1.35 and 2.25 MPa. Eccentric load induced approximately twice higher tensile and maximum shear stresses. It can be thus speculated that this may promote in a very short time local debonding of the surfaces and then progressive loosening of the implant or cement. One of the main complications of total shoulder arthroplasty is shoulder instability [27] classi®ed according to the gleno-humeral translation (anterior, posterior superior or inferior). Since shoulder instability is liable to involve eccentric or translated articular loads, the consequences of such load cases require investigation. The conformity of the glenoid contact did not seem to have a major role on the global displacements of the implanted glenoid. Unlike the displacements, the inter-
nal stresses were appreciably modi®ed by a reduction of the articular contact area. Dierences appeared locally, in the regions close to the contact location. This result was in agreement with that found using a 2D model [9] in which high conformity presented lower cement stresses compared with a low conformity contact. This has also been experimentally veri®ed [28] by means of strain gauges at the glenoid keel: nonconforming components increased maximum compressive strains by almost 50%. Thus, while the gleno-humeral radial mismatch may be good because it has a signi®cant in¯uence on the joint kinematics [29], the downside is the increased levels of stress transmitted to the dierent structures (glenoid and cement). For example, the cement compressive stress peak varied from )11.8 to )15.4 MPa when the superior±posterior articular contact area was decreased. The eects of cement mantle size are dependent on the position of the gleno-humeral contact. With the centered load, the change of stresses within the cement between the normal and thick mantle was negligible. On the other hand, when the load case was o-centered, stresses within a thicker cement mantle were greater than stresses within normal cement thickness. On that account, tensile and maximum shear stresses reached, respectively, 3.16 and 7.7 MPa which is much higher than the measured apparent strength of the cement/bone interface [26]. With the thick cement mantle, there was probably a direct transfer of the articular load to the cement through the articular surface of the prosthesis. With the normal, i.e., `standard' cement thickness, a large portion of this eccentric load was transmitted to the subchondral bone surrounding the cement mantle. Von Mises stresses in the surrounding bone decreased by on average 10% (from 25.5 to 22.9 MPa) between the thick and normal cement mantle. This indicates that the thicker cement acts to divert more of the applied loads away from the surrounding glenoid bone. The stier cement structure is thus stress shielding the peri-prosthetic bone in the case of the o-center loading. Here, there is a discrepancy between the results of the present study and those obtained from a 2D model [30]. However, the role of the cement thickness described in the present study appears to be consistent with the principle of stress shielding. Finally, on one hand a thin cement mantle can promote high cement displacements relatively to the bone when the load is centered and on the other hand a thick cement mantle may promote the resorption of the surrounding bone by stress shielding when the load is o center. From experience, surgeons have a tendency to minimize the cement thickness. The ideal cement mantle is probably the one that ensures a good stability with limited motion (<150 lm) and the one which allows the surrounding bone to be correctly loaded. This suggests that the characteristics of the glenoid cement mantle have an important role in determining the clinical outcome of total shoulder arthroplasty.
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5. Conclusions A 3D scapular model with an implant has been used to assess the in¯uence of dierent parameters that can vary with respect to the surgical technique. This provided an insight into the mechanical behavior of an implanted scapula. This model showed the high sensitivity of the scapula to bend in the antero-posterior direction. Now, it would be interesting to investigate the role of this bending in the glenoid loosening process or in the development of glenoid prosthesis radiolucencies. The contact area analysis emphasized the compromise between internal stress levels and articular degree of motion. The eects of cement mantle size are dependent on the position of the gleno-humeral contact. Indeed, these mechanical eects of the dierent clinical parameters are not particularly intuitive and this suggests that the 3D modeling can add valuable information to help interpret glenoid implant performance. As the reconstruction technique was based on CT images, such an analysis might be used with CT images from patients. This `in vivo' analysis would be particularly relevant since it has been demonstrated that pathological glenoids [15] presented geometrical and also dierences in bone material property distributions. Acknowledgements This study was supported by 3M Sante. The authors are also grateful to Christophe Barea and to Marie± Christine Hobatho for the development of the experimental set-up. References [1] Brems J. The glenoid component in total shoulder arthroplasty. J Shoulder Elbow Surg 1993;2:47±54. [2] Van Der Helm FCT, Veeger HEJ. Quasi-static analysis of muscle forces in the shoulder mechanism during wheel chair propulsion. J Biomech 1996;29:39±52. [3] Karlsson D, Peterson B. Towards a model for force predictions in the human shoulder. J Biomech 1992;25:189±99. [4] Beuchel FF, Pappas MJ, DePalma AF. Floating socket total shoulder replacement: anatomical biomechanical and surgical rationale. J Biomed Mater Res 1978;12:89±114. [5] Poppen NK, Walker PS. Forces at the glenohumeral joint in abduction. Clin Orthop 1978;135:165±70. [6] Inman VT, Saunders JB, Abbot LC. Observations on the function of the shoulder joint. J Bone J Surg 1944;26:1. [7] Anglin C, Wyss UP, Pichora DR. Glenohumeral contact forces during ®ve activities of daily living. In: Proceedings of the First Conference of the International Shoulder Group, 1996, p. 13±8. [8] Boyd AD, Aliabadi P, Thornill TS. Postoperative proximal migration in total shoulder arthroplasty ± incidence and significance. J Arthroplasty 1991;6:31±7. [9] Moeckel BH, Altchek DW, Warren RF, Wickiewicz TL, Dines DM. Instability of the shoulder after arthroplasty. J Bone J Surg A 1993;75:492±7.
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