To our knowledge this is the first study to validate FE predictions of cartilage contact pressure with experimental measurements using a cadaveric human hip joint. The purpose of developing and validating a subject-specific model was to ensure that the chosen computational protocol could produce a model capable of predicting in vitro cartilage contact pressures. The FE model provided very reasonable predictions of both the spatial distribution and magnitude of cartilage contact pressure under the simulated loading conditions. Excellent predictions were obtained for simulated stair-climbing. The posterior aspect of the bi-centric experimental contact pattern was not predicted by the FE model for walking and descending stairs. Nevertheless, the magnitude of pressure in these locations was low in comparison to the anterior region where the FE models provided more reasonable correspondence.
Small manual rotations of the pressure film were necessary to minimize RMS errors for simulated walking and stair-climbing. In contrast, the descending stairs case required a substantial amount of manual rotation (). It is likely that the majority of misalignment error was due to the method of digitizing the film fiducials during the experiment. It was necessary to move the linear actuator up by ~20 mm to access the film markers. It was assumed that this displacement resulted in a perfect vertical translation for purposes of defining the marker coordinates, but when the coordinates were plotted relative to the translated model they did not reside on the surface of the cartilage. This offset was minor during walking and stair-climbing but was greater during descending stairs. The femur was in extension for this loading activity and when the translation was applied, the femoral neck would have contacted the edge of the acetabulum, resulting in an offset of the film marker coordinates. Contact in this location would not have occurred with the hip in moderate and deep flexion during walking and stair-climbing.
The finding that RMS magnitude errors decreased when the bounds of pressure were increased suggests that the models were best suited for predicting localized “hot spots”. Therefore, the modeling strategies developed herein may be well suited for predicting the primary region of contact, which may be sufficient for many patient-specific modeling applications.
FE predictions of average pressure and contact area were not overly sensitive to changes in the cartilage shear modulus, bulk modulus or thickness (±10%). However, greater changes in peak pressure were noted (up to ~25%). This finding demonstrates that peak pressure prediction requires more accurate model inputs for cartilage geometry and material properties than for average pressure prediction.
Computational models of the hip have often represented bones as rigid structures [12
], which is an attractive simplification because solution times are greatly reduced. The present study demonstrated that the assumption of rigid bones can alter predictions of cartilage contact stresses in the hip. The effect is modulated by the specific boundary and loading conditions in the model. Because the consequence of the rigid bone assumption cannot be assessed without a direct comparison to the case of deformable bones, investigators should use caution when representing the bones as rigid for modeling cartilage contact mechanics in the human hip.
Although the contralateral pelvis was left intact in the experimental study, the FE models assumed that the pubis joint was rigid. The results of the sensitivity study that removed the pubis constraint demonstrated only minor differences in FE predicted cartilage contact mechanics, thereby giving credence to this model assumption. While this simplification was warranted for the current study, it may not be appropriate for models where load is directed more medially (e.g. simulations of side-impact loading [45
Since the reported elastic modulus of trabecular bone is orders of magnitude less than cortical bone, we investigated whether or not trabecular bone needed to be represented in the models. The results of the sensitivity study suggest that it plays little mechanical role with regard to cartilage contact stresses. Therefore, for patient-specific modeling applications it may be appropriate to exclude trabecular bone, assuming that similar boundary and loading conditions are assigned.
Experimental studies have used pressure sensitive film to measure hip joint contact pressures under similar loading conditions [8
]. Peak pressures measured by von Eisenhart-Rothe et al. [13
] ranged from 7 MPa at 50% body weight to 9 MPa at 300% body weight, in fair agreement with the results of the current study. Bi-centric, horseshoe shaped patterns extended from the anterior to posterior aspect of the femur were noted [13
]. Afoke et al. [8
] measured peak pressures on the order of 10 MPa at 350% body weight and the anterorsuperior surface of the cartilage was identified as an area of high pressure [8
]. All of these studies reported irregular, non-symmetric pressure distributions [8
Large differences in material properties, geometry and boundary conditions make it impossible to directly compare the FE predictions from this study with prior modeling studies, but some general trends can be identified. Nearly all FE hip joint modeling studies to date have used two-dimensional, plane strain models [9
] with either rigid [12
] or deformable bones [9
]. To our knowledge, the earliest FE contact model was reported by Brown and DiGioia [9
]. In this study, FE predicted pressures were irregularly distributed over the surface of the femoral head. Values of peak pressure were on the order of 4 MPa at loads representative of those applied in the current study. Rapperport et al. [21
] developed a similar model that predicted peak pressures on the order of 5 MPa at 1000 N of load. Using rigid bone models resulted in predictions only slightly different than the deformable bone model.
Macirowski et al. [12
] used a combined experimental/analytical approach to model fluid flow and matrix stresses in a biphasic contact model of a cadaveric acetabulum. To our knowledge, this is the only previous FE study to explicitly model the acetabular cartilage thickness. The acetabulum was step loaded to 900 N using an instrumented femoral prosthesis, yielding peak contact pressures on the order of 5 MPa. When the experimentally measured total surface stress was applied to the FE model, average predicted pressures (solid stress + fluid pressures) were approximately 1.75 MPa. The lower range of pressure used to determine average pressures was not specified, making it impossible to directly compare average results. However, scaling the applied load of our model to 900 N and assuming a lower bound of 0.3 MPa to calculate average pressure (lowest pressure isobar indicated by Macirowski et al.) yields average pressures of 2.47±0.29 MPa over the three loading scenarios analyzed, which is in good agreement with Macirowski et al’s predictions.
Yoshida et al. [20
] developed a dynamic DEA model to investigate the distribution of hip joint contact pressures using the Bergmann gait data. The model assumed spherical geometry and concentric articulation. Qualitatively, our predictions of primary contact during simulated walking, descending stairs, and stair-climbing are in good agreement with the results of this study, but the spatial distributions of contact were markedly different. Peak pressures during walking, descending stairs, and stair-climbing in the study by Yoshida et al. (3.26, 3.77, 5.71 MPa, respectively) were substantially less than those predicted in the current study.
With the exception of the study by Macirowski et al., the FE models developed herein predicted higher contact pressures than previous FE and DEA, studies. This discrepancy is most likely due to the assumptions of spherical geometry and concentric articulation in the prior computational studies. Although the literature suggests that normal hips may be modeled as spherical structures with concentric articulation [19
], the hip joint is not spherical and cartilage thickness is not uniform [12
The aforementioned computational models assumed a cartilage modulus ranging from 10-15 MPa [9
] yet cartilage was given a baseline modulus of ~40 MPa (G=6.8 MPa) in the current study. While one might expect that a higher modulus would result in equivalently higher contact pressures, the results of our sensitivity studies demonstrate that this is not the case, as changes in the cartilage shear modulus of ±50% resulted in only a ±25% and ±10% change in peak and average contact pressures, respectively. Even with a 25% reduction, peak pressures predicted in this study were still nearly double those reported previously [9
Several limitations of the current study must be mentioned. First, only one model was developed, based on a singe CT image dataset. However, extensive sensitivity studies were conducted on this single model to understand the importance of model inputs and material properties. In the future, we plan to develop several more subject-specific models to ensure that the protocol utilized herein produces accurate models. Secondly, experimental loads were based on average in vivo data from older patients who had already undergone treatment for advanced hip OA. Given the large inter-patient variation in joint kinematics observed by Bergmann et al. [15
], the use of average loading data likely did not accurately represent the actual kinematics for the specimen in this study. Our approach is justified since the objective of the experimental protocol was to apply realistic loading and boundary conditions that could be reproduced in the FE simulations for model validation.
Pressure film was chosen to measure cartilage contact pressures in this study since: 1) it is reasonably accurate (10- 15% error [49
]), 2) it can be cut into rosette patterns to conform to highly spherical surfaces (thereby preventing crinkle artifact) and, 3) it is inexpensive and has been used extensively in prior studies of hip joint contact stresses [8
]. A limitation of film pressure measurement is that the technique records a “high watermark” rather than measurements of dynamic pressures or the time-loading history [51
]. However, film measurements have been shown to be equivalent to the contact stresses resulting from an incompressible elastic analysis [53
], making the use of pressure film appropriate in the current study. Pressure film would not be appropriate for dynamic loading studies (e.g. simulations over entire gait cycle) since it is inaccurate in shear. However, prediction of dynamic pressures was not a goal of this study. Rather, the objective was to predict cartilage pressures at peak joint reaction force in the gait cycle during static, unidirectional loading. Results from the pressure measurements indicate that contact occurred beyond the perimeter of the film during simulated walking and descending stairs. While it would be desirable to capture the entire region of contact, it was not feasible to do so using larger rosettes as they caused excessive overlap and crinkle artifact during pilot testing. Finally, it was found that all of the films were saturated making it impossible to determine the true values of experimental peak pressures. However, our pilot study demonstrated that the low range pressure film was the best choice for the experiment. In addition, less than 5% of the film pixels had saturated pressures, suggesting that peak pressures were very close to the saturation limit of the film (10 MPa).
Removal of the labrum is noted as a potential limitation to this study since this structure was healthy in the specimen tested. The labrum was removed because: 1) labral geometry could not be distinguished from the CT data as a separate entity since it had the same image intensity as the adjacent cartilage, and 2) labral tissue properties and a corresponding constitutive equation have not been extensively reported in the literature.
The literature regarding the contribution of the labrum to hip cartilage mechanics is unclear [44
]. Using pressure film, Konrath et al. [55
] found no significant changes in contact area, mean pressure, or maximum pressure in the anterior or superior acetabulum and only noted a significant decrease in the maximum pressure in the posterior acetabulum when the labrum was removed. In contrast, an in vitro study Ferguson et al. [54
] demonstrated that hip joints with the labrum removed consolidated more and had substantially decreased intra-articular pressures under both constant and cyclical loads. As a precursor to including the labrum in future FE modeling studies, it is clear that more extensive material testing is necessary to characterize the labrum’s constitutive behavior along with effective methods to distinguish this structure from adjacent cartilage in the image data.
Although actions of individual muscles were not considered, the equivalent joint reaction force was based on in vivo data [15
]. The primary focus of the present research was to quantify cartilage contact pressures in the peri-acetabular region rather than bone stresses in areas where muscles were attached. Therefore, we could justifiably model the action of all muscles as a single equivalent force vector acting through the hip joint.
Although cartilage exhibits biphasic material behavior [56
], it was represented as incompressible hyperelastic in this study. In vitro studies suggest that fluid flow is minimal during fast loading [12
], making our assumption of incompressibility warranted given the loading rates used in the experiments. We recently demonstrated the equivalence between biphasic and incompressible hyperelastic FE predictions during instantaneous loading [57
]. Cartilage also exhibits depth dependent material properties [58
], variation in stiffness over its surface [43
] and tension-compression nonlinearity [60
]. Incorporating these aspects might have resulted in different, perhaps better, predictions of contact stress magnitude and distribution. Future modeling efforts should investigate the importance of these effects via sensitivity studies.
As discussed above, simplified analytical models or population based approaches to patient hip joint modeling have not yielded predictions that are consistent with in vitro data. Although it is possible that these discrepancies are due to model assumptions, it is difficult to pinpoint sources of error unless some reference standard (i.e. experimental data) is available for comparison. Therefore, we believe subject-specific modeling is a necessary precursor to either population or patient-specific modeling. The benefit of using a subject-specific approach first is that computational predictions can be directly compared to data obtained experimentally. The ability to directly quantify model accuracy is lost in population or patient based studies as direct validation is impossible. With a validated protocol in place it becomes much more feasible to develop patient-specific models that provide clinically meaningful data in terms of improving the diagnosis and treatment of hip OA, and for the study of pathologies such as hip dysplasia.
In conclusion, our approach for subject-specific FE modeling of the hip joint produced very reasonable predictions of cartilage contact pressures and areas when compared directly to pressure film measurements. Predictions were in good agreement with other experimental studies that used pressure film, piezoelectric sensors and instrumented prostheses [8
]. The sensitivity studies established the modeling inputs and assumptions that are important for predicting contact pressures. The validated FE modeling procedures developed in this study provide the basis for the future analysis of patient-specific FE models of hip cartilage mechanics.