ESTIMATION OF PATELLA BONE STRESS:A COMPARISON OF HOMOGENEOUS AND HETEROGENEOUS FINITE ELEMENT MODELS
1Kai-Yu Ho, 2Nazanin Mokarram, 1Nicholas H. Yang,2Ashkan Vaziri,1Christopher M. Powers
1University of Southern California, Los Angeles, CA, USA
2Northeastern University, Boston, MA, USA
email: , web:
INTRODUCTION
Finite element (FE) analysis is a non-invasive method to estimate subject-specific bone stress.Given the inhomogeneitynature of bone, density-based heterogeneous bone modeling has been considered as the most accurate approach for computing bone stress.1 Traditionally, voxel-based bone densities can be measured with quantitative computed tomography (QCT), and the average density of several voxels can be assigned to a corresponding element.1,2 However, as articular cartilage exhibits little signal on QCT, such an approach becomes challenging when studyingpatellofemoral joint (PFJ) cartilage contact problems. To address this issue,a FE model was developedto acquire subject-specific heterogeneousmaterial propertyof the patella usingwater-fat IDEAL magnetic resonance imaging (MRI). As such, the purpose of this pilot study was to compare peak von Mises stress of the patellabone at the cartilage-bone interface among3 FE patella models (heterogeneous, 2-material consisting of uniform cortical and trabecular bone, and homogeneous). The validity of each model was evaluated by comparing the predicted PFJ contact area to that acquired from MRI.3
METHODS
Subject-specific PFJ geometry of a single female subject with patellofemoral pain wasin this study. Input parameters for the FE model included: 1) PFJ geometry, 2) elastic modulus of patella, 3) weight-bearing PFJ kinematics, and 4) quadriceps muscle forces (Fig. 1). PFJ geometrywasobtained from sagittal plane MR IDEAL in-phase images acquired with a 3.0 T MR scanner(General Electric Healthcare) and manually segmented (Fig. 1A). The FE mesh of cartilage, femur and tibia was created using FE pre-processor (Hypermesh, Altair Engineering Inc.).Voxel-wise bone density of patella wasestimatedfrom IDEAL IPMRIwith the assistance of a calcium hydroxyapatite phantom.4The elastic moduli were then calculated based on the density measures.The patella mesh was created with heterogeneous elastic modulus assigned to each element using Mimics software (Materialise) (Fig.1B). The FE mesh of cartilage and bone wasthen registered to the position of each structure on the weight-bearing MRI (Fig.1C).3Quadriceps muscle forces were estimated using a previously described EMG driven model (Fig.1D).5
Fig. 1.Finite Element Modeling Pipeline.
Quasi-static loading simulations were performed using a nonlinear FE solver (Abaqus, SIMULIA)at 45° of knee flexion. Three assignments of elastic modulus were performed onisotropic tetrahedral continuum elements of patella (i.e., heterogeneous, 2-material, and homogeneous models)with Poisson ratio of 0.3. The heterogeneous patella model was generated as described above with the elastic modulus ranging from 3.9 to 14.8 GPa. The 2-material patella consisted of cortical bone with an elastic modulus 14.8 GPa and trabecular bone with elastic modulus 3.9 GPa. The homogeneous patella was generated with elastic modulus 14.8GPa throughout the entire volume of patella. For each model, the femur and tibiawere modeled as rigid and the cartilage of the patella and femur was modeled as homogeneous isotropic tetrahedral continuum elements (elastic modulus of 4 MPa3 and Poisson ratio of 0.473). Quadriceps muscles were divided into 3 functional groups(rectus femoris/vastusintermedius, vastusmedialis, and vastuslateralis) made up of 6 equivalent uniaxialconnector elements.The patellar tendon was modeled as six uniaxial, tension-only elements with stiffness of 4334 N/mm.3The model outputs included peak von Mises stress and PFJ contact area.
RESULTS AND DISCUSSION
All three models demonstrated similar von Mises stress distribution with the peak stress being located on the lateral facet of patella (Fig.2). Compared to the heterogeneous model, the difference in peak von Mises stress was 0.21 MPa (8.0%) for the 2-material model and 0.30 MPa (11.5%) for the homogeneous model (Table 1). The predicted contact area of 3 FE models matched well with the contact area measured from MRI (255.16 mm2; Table 1).
Fig. 2.vonMises distribution of patella at the cartilage-bone interface in 3 conditions.
CONCLUSIONS
In the present study, a method to generate a subject-specific, heterogeneouspatella FE model starting from IDEAL MRI was developed. Such an approach was deemed valid as there was excellent agreement in PFJ contact area basedon MRI measurements. Whencomparing the heterogeneous, 2-material, and homogeneous models, meaningfuldifferences in peak von Mises stress were found(8.0 to 11.5%). Therefore, it may be important to consider the heterogeneity of bone when developing bone FE models to assesPFJcartilage contact problems.
REFERENCES
1.Taddei F, et al. J Biomech39, 2457-2467, 2006.
2.Keyak JH, et al. J Biomed Eng15, 505-509, 1993
3.Farrokhi S, et alOsteoarthritis CartilageIn Press.
4.Ho KY, et al. Proceedings of ISMRM'11
5.Chen YJ, et al. J Appl Biomech26, 415-423, 2010.
Table 1:Peak von Mises stress of patella at the cartilage-bone interface and cartilage contact area at 45° of knee flexion with 3 assignments of elastic modulus.
Peak von Misesstress (MPa)
/ Contact Area (mm2)Heterogeneous / 2.62 / 255.96
2-material / 2.83 / 255.97
Homogeneous / 2.32 / 255.99
ACKNOWLEDGEMENTS
This study is supported by the International Society of Biomechanics Student Dissertation Award.