Two human subjects were selected from a series of 6 patients with traditional acetabular dysplasia and 18 normal volunteers that were recruited as part of a separate study. All subjects gave informed consent and were included following IRB approval. Patients with symptomatic acetabular dysplasia were screened with anteroposterior (A-P) radiographs. Those with lateral center-edge angles less than 20° were identified as having traditional acetabular dysplasia. Normal volunteers had no history of hip pathology or pain.
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 (). 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
Coronal CT slice of the dysplasia patient. Structures of interest are highlighted.
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 (). 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 Boundaries between the cartilage and labrum that were used in the model of the normal hip. The solid black line indicates the baseline boundary, while the dotted black line indicates the medial boundary, as described in the text. A – superior (more ...)
Element formulations and mesh densities for bones and cartilage were based on our previous study (Anderson et al., 2008
) (). 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.
Discretized hemipelvis (white), acetabular cartilage (yellow), and labrum (red) in the normal model. A – oblique view of shell and hexahedral meshes. B – medial view of shell and hexahedral meshes.
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.
Percent load supported by the labrum, average contact stress on the articular cartilage, contact area on the articular cartilage, and deflection of the labrum were determined. Percent load was calculated from the ratio of contact interface force to applied load. Cartilage contact stress was sampled on the surface of the acetabular cartilage. Cartilage contact area was calculated by summing the surface area of each element in the acetabular cartilage that was in contact with the femoral cartilage. Total deflection of the labrum was sampled through the thickness and maximum values were obtained.