Labral tears are often diagnosed in a clinical setting, suggesting that the labrum can be subjected to substantial loads in vivo (Blankenbaker et al., 2007; Burnett et al., 2006; Fitzgerald, 1995; Guevara et al., 2006; Leunig et al., 2004; Leunig et al., 1997; McCarthy and Lee, 2002; McCarthy et al., 2001; Neumann et al., 2007; Seldes et al., 2001; Wenger et al., 2004). There is an increased incidence of labral tears, labral hypertrophy, and labral calcification in hips that exhibit acetabular dysplasia (Dorrell and Catterall, 1986; Groh and Herrera, 2009; Guevara et al., 2006; Haene et al., 2007; Klaue et al., 1991; Leunig et al., 2004; Leunig et al., 1997), which suggests that the geometry of the dysplastic hip results in increased loads on the labrum in comparison to the normal hip.

Several studies have investigated the function of the labrum, but have not clearly determined the mechanical role of the labrum in the normal and dysplastic hip (Adeeb et al., 2004; Ferguson et al., 2000; Ferguson et al., 2000; Ferguson, 2001; Hlavacek, 2002; Konrath et al., 1998; Miozzari et al., 2004). In a cadaveric study of normal hips, removal of the labrum had no effect on contact stresses on the acetabular cartilage (Konrath et al., 1998). However, only the mid-stance of walking was simulated and the magnitude of the loads that were used in the study were about half of previously measured values for walking (Bergmann et al., 2001). Other studies reported that the labrum acts as a fluid seal on the joint during slow loading over longer periods of time (Adeeb et al., 2004; Ferguson et al., 2000; Ferguson et al., 2000; Ferguson et al., 2003; Hlavacek, 2002). It remains unclear whether the labrum contributes to joint stability and load transfer across the hip joint during activities of daily living.

A subject with representative acetabular geometry was selected from each population. The patient (female, 35 years old, 66 kg) had a 17° center-edge angle and 19° acetabular index, which approximately matched the median values for the patient population. The shallow acetabulum and lateral under-coverage seen in dysplastic patients are characterized by center-edge angles below 25° and acetabular indices above 10° (Clohisy et al., 2008). Similarly, a normal subject (male, 30 years old, 87 kg) was selected that approximately matched the median center-edge angle and acetabular index of the population of normal volunteers (32° center-edge angle, 9° acetabular index).

Volumetric image data were acquired using CT arthrography (Figure 1). Approximately 20 ml of a 2:1 mixture of 1% lidocaine hydrochloride to Iohexol (Omnipaque 350, GE Healthcare, Princeton, NJ) was injected into the joint space. CT images were acquired with a field of view encompassing the entire pelvis and both femurs (342 mm for the dysplastic patient, and 331 mm for the normal volunteer), 512×512 acquisition matrix, and 1 mm slice thickness. Subjects were imaged under traction to increase the joint space and thus improve contrast between the acetabular and femoral cartilage (Anderson et al., 2008).

Segmentation of volumetric CT data was performed with a combination of thresholding and manual techniques, using the Amira software (Visage Imaging, Inc., San Diego, CA). Because the resolution of the segmentation mask was tied to voxel size, images were resampled to a higher resolution prior to segmentation (1536×1536 matrix, 0.23×0.23×0.33 mm³ effective voxel size in the dysplastic patient and 0.22×0.22×0.33 mm³ effective voxel size in the normal subject). The boundary between the cartilage and labrum was not visible in CT image data, so the initial boundary was defined where the concave acetabulum transitioned into the convex acetabular rim (Figure 2). A previous investigation demonstrated that the extent of the labrum on the medial side of the acetabular rim is variable (Won et al., 2003). Therefore, a second boundary was placed approximately 2 mm medial to the baseline boundary to assess the effects of the labrum extending medial to the acetabular rim (Figure 2).

Element formulations and mesh densities for bones and cartilage were based on our previous study (Anderson et al., 2008) (Figure 3). Cortical bone was represented with shell elements (Hughes and Liu, 1981), with a position-dependent thickness (Anderson et al., 2005). Cartilage and labrum were represented with hexahedral elements (Puso, 2000; Simo and Taylor, 1991). Hexahedral meshes for the cartilage and labrum were generated from the segmented surfaces using TrueGrid (XYZ Scientific, Livermore, CA). All meshes were generated directly from the segmented surfaces, with no assumptions regarding the geometry of the articular surfaces. A mesh convergence study was performed for the labrum.

Constitutive models for bone and cartilage were identical to those in our previous study (Anderson et al., 2008). Cortical bone was represented as isotropic linear elastic (E = 17 GPa, ν = 0.29) (Dalstra and Huiskes, 1995). Cartilage was represented as neo-Hookean hyperelastic (G = 13.6 MPa, K = 1359 MPa) (Park et al., 2004). The labrum was represented as transversely isotropic hyperelastic (Quapp and Weiss, 1998). The matrix strain energy was chosen to yield the neo-Hookean constitutive model with shear modulus C₁. The equations describing the material behavior of the fibers included material coefficients that scaled the exponential stress (C₃), specified the rate of collagen uncrimping (C₄), specified the modulus of straightened collagen fibers (C₅), and specified the stretch at which the collagen was straightened (λ*).

Labrum material coefficients were determined by fitting the constitutive equation to an experimentally-derived expression for uniaxial stress-strain behavior along the fiber direction (C₁ = 1.4 MPa, C₃ = 0.05 MPa, C₄ = 36, C₅ = 66 MPa, λ* = 1.103) (Ferguson, 2001). Material incompressibility was assumed when determining material coefficients because labrum is less permeable than cartilage (Athanasiou et al., 1995; Ferguson, 2001; Mow et al., 1980) and cartilage has been demonstrated to behave as an incompressible elastic material over the loading frequencies in activities of daily living (Ateshian et al., 2007). To yield nearly incompressible material behavior, the bulk modulus was specified to be 3 orders of magnitude greater than C₁ The primary fiber direction was oriented circumferentially (Petersen et al., 2003).

Boundary conditions were chosen to simulate heel strike during walking (WHS, 233% body weight), mid-stance during walking (WMS, 203% body weight), heel strike while ascending stairs (AHS, 252% body weight) and heel strike while descending stairs (DHS, 261% body weight). Neutral pelvic and femoral orientation was established using anatomical landmarks (Bergmann et al., 2001). The orientation of the applied load and the femur relative to the pelvis were based on instrumented implant and gait data (Bergmann et al., 2001). The magnitude of applied load was scaled by subject body weight (Bergmann et al., 2001). The pubis and sacro-iliac joints were fixed rigidly in space (Anderson et al., 2008). Motion was applied superiorly to the distal femur. The femur was allowed to move in the medial-lateral and anterior-posterior directions to achieve equilibrium in the acetabulum. Four springs (k = 1 MPa) were used at the distal femur to remove rigid-body modes from the simulation. Tied and sliding contact algorithms based on the mortar method were used (Puso, 2004; Puso and Laursen, 2004). One sliding interface was defined between the femoral and acetabular cartilage, while a second interface was defined between the femoral cartilage and labrum. Models were analyzed with and without the labrum. Frictionless contact was assumed for all contact interfaces. The friction coefficient between articulating cartilage surfaces is very low, on the order of 0.01-0.02 in the presence of synovial fluid (Caligaris and Ateshian, 2008; Charnley, 1960; Schmidt and Sah, 2007). Therefore, it is reasonable to neglect frictional shear stresses between contacting articular surfaces. Models were preprocessed using PreView (http://mrl.sci.utah.edu/software.php), analyzed using the nonlinear implicit solver NIKE3D (Puso, 2007), and postprocessed using PostView (http://mrl.sci.utah.edu/software.php).

Parameter studies were completed to assess the effects of modeling assumptions. To assess the effect of material assumptions, a neo-Hookean constitutive model matched to that used for the simulated cartilage was substituted for the transversely isotropic constitutive model. Additionally, the labrum fiber stiffness was changed ±50% in the transversely isotropic constitutive model. To examine the effect of anatomical angles, the anatomical adduction angle was changed ±3° (approximately 1 standard deviation (Bergmann et al., 2001)) in all loading scenarios. Finally, the applied load was changed ±30% (approximately one standard deviation (Bergmann et al., 2001)) in WHS in the dysplastic model.

Changing the constitutive model from transversely isotropic to isotropic increased the load supported by the labrum 2-11% (Figure 7) and decreased the maximum deflection of the labrum 0-0.1 mm. The maximum deflection of the labrum occurred primarily in the radial direction and in approximately the same posterior-superior portion of the labrum for all loading scenarios (Figure 5C, asterisk). In the transversely isotropic labrum, the maximum deflection was 1.3 mm in WHS and WMS, and 1.5 mm in AHS and DHS. The maximum deflection of the labrum was 0.1 mm smaller in the isotropic labrum in WHS, WMS and AHS, but did not change in DHS.

Cartilage contact areas demonstrated small increases in most simulations without the labrum and correlated to the load supported by the cartilage (Figure 8), while average and peak cartilage contact stresses demonstrated minimal changes. Average cartilage contact stress in the normal model with the labrum was 1.1, 0.9, 1.3, and 1.0 MPa in WHS, WMS, AHS, and DHS, respectively. Average cartilage contact stress in the normal model without the labrum was 1.1, 0.9, 1.2, and 1.0 MPa in WHS, WMS, AHS, and DHS, respectively. Average cartilage contact stress in the dysplastic model with the labrum was 0.8, 0.8, 0.5, and 1.2 MPa in WHS, WMS, AHS, and DHS, respectively. Average cartilage contact stress in the dysplastic model without the labrum was 0.8, 0.8, and 1.1 MPa in WHS, WMS, and DHS, respectively. When the dysplastic model was used to simulate AHS without the labrum, the femoral head dislocated from the acetabulum, precluding calculation of average pressures. Peak cartilage contact stresses were between 6 MPa and 14 MPa for all simulations.

Cartilage contact stresses were only slightly altered when the labrum was removed, despite the increased force on the acetabular cartilage. Contact area on the articular cartilage correlated to the load supported by the cartilage, therefore there were minimal changes in stress with and without the labrum (Figure 8). This is consistent with the results of a previous experimental study, which reported that removal of the labrum had no significant effect on cartilage contact stresses in cadaveric hips (Konrath et al., 1998). Taken together, these results suggest that the labrum functions to stabilize the joint, rather than to decrease cartilage contact stresses, during activities of daily living.

Average contact stresses on the acetabular cartilage were slightly lower than those reported in previous studies (Anderson et al., 2008; Brown and Shaw, 1983; Konrath et al., 1998). However, average stresses must be compared with caution because a threshold is often used when reporting experimental measurements of contact stress, based on the minimum stress that can be detected (e.g., pressure-sensitive film ranges, 2.4 MPa and 1.7 MPa (Anderson et al., 2008; Konrath et al., 1998)). When results for average contact stress in this study were recalculated with thresholds matching experimental studies, the average stresses were in better agreement with the results of the studies referenced above. Peak contact stresses compared well to results from previous in vitro studies (Adams and Swanson, 1985; Afoke et al., 1987; Anderson et al., 2008; Brown and Shaw, 1983; von Eisenhart et al., 1999) and computational studies that used non-idealized geometry (Anderson et al., 2008; Brown and DiGioia, 1984).

The labrum supported more load when it was represented with an isotropic constitutive model than when it was represented with a transversely isotropic constitutive model. This result may seem counterintuitive at first glance, since the fiber stiffness (C₅) in the transversely isotropic constitutive model was larger than the shear modulus (C₁) in the isotropic constitutive model. Therefore, the transversely isotropic labrum could be expected to support greater loads and exhibit less deflection. However, the fibers were rarely loaded in tension during the simulations. Thus, the shear modulus (C₁) governed the material response of the labrum in simulations using both constitutive models. This also explains why changes to the fiber stiffness had a minimal effect. Many fiber-reinforced soft tissues are subjected to in situ stress (e.g., (Gardiner and Weiss, 2003)), which results in a stiffer material response for a given applied load. If in situ stresses were considered in these simulations, the fibers would support more load, thus yielding the expected result of increased load support with the addition of fiber reinforcement. However, given the current limitations in the literature, the constitutive model derived from bovine labrum data is expected to yield the most accurate model predictions.

Assumptions regarding the multiaxial material behavior of the labrum were necessary in this study because previous characterization of the material behavior of the labrum only performed material testing along the fiber direction. Two studies have reported material properties of human labrum. One tested pathologic tissue (Ishiko et al., 2005), and one reported only linear tensile and compressive moduli (Smith et al., 2009). The most complete characterization was performed using bovine labrum (Ferguson, 2001). From these data, the toe region along the fiber direction was assumed to represent the matrix response in all directions since multiaxial testing was not performed. In addition to uncertainty about the material behavior of the normal labrum, labra in dysplastic hips may have altered material properties due to effects such as hypertrophy and calcification (Klaue et al., 1991; Leunig et al., 2004; Leunig et al., 1997).

Parameter studies quantified the sensitivity of the simulations to assumed inputs. Large changes in load supported by the labrum with different boundaries between labrum and cartilage indicate that this boundary should be considered carefully in future modeling studies. This is particularly true when the models are generated from image data, in which the boundary is not visible. While these differences highlight the impact of this parameter on model results, the parameter study was not intended to address the possible clinical consequences of the boundary between cartilage and labrum. Changes in the magnitude of joint reaction force had no effect on the percent load supported by the labrum. Thus, the absolute load supported by the labrum scaled linearly with the joint reaction force, and the differences in kinematics between activities dictated any differences in percent load supported by the labrum. Since changes to adduction angle had minimal effect on percent load supported by the labrum, the direction of the applied load was more important than the anatomical orientation of the joint. This result is further demonstrated when comparing WHS and WMS. In WMS, the adduction angle of the load vector is larger than for WHS, and the labrum in the dysplastic model supported more load. This result is consistent with the findings of previous studies, which reported that the orientation of the abductor force affected predictions of stress in the acetabular cartilage, especially in simulations with small center-edge angles (Armand et al., 2005; Genda et al., 2001).

This study did not examine the possible effects of the sealing role of the labrum on predicted cartilage stresses and load support. Previous modeling and experimental studies suggest that the sealing role of the labrum may influence various aspects of hip biomechanics (Adeeb et al., 2004; Ferguson et al., 2000; Ferguson et al., 2000; Ferguson et al., 2003; Hlavacek, 2002). However, there is no direct evidence in the literature that the sealing role of the labrum influences loadsharing between the articular cartilage and labrum or contract pressure distributions during activities of daily living. The differences in loading conditions and frequency in the previous studies make it difficult to predict how the results could be interpreted in light of the present study. Activities of daily living such as walking primarily involve compressive forces across the joint, with a frequency of about 1 second (Bergmann et al., 2001). Based on the permeability of the labrum and articular cartilage, there should be minimal fluid exudation from these tissues during a cyclic loading over 1 second (Ateshian et al., 2007; Ferguson, 2001). While it may be possible to extend the present model to assess the influence of a labral seal, this was beyond the scope of the present study.