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, USA2Northeastern University, Boston, MA, USA

email: kaiyuho @ usc.edu , web: http://pt.usc.edu/labs/mbrl

INTRODUCTION Finite element (FE) analysis is a non-invasive method to estimate subject-specific bone stress. Given the inhomogeneity nature 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 studying patellofemoral joint (PFJ) cartilage contact problems. To address this issue, a FE model was developed to acquire subject-specific heterogeneous material property of the patella using water-fat IDEAL magnetic resonance imaging (MRI). As such, the purpose of this pilot study was to compare peak von Mises stress of the patella bone at the cartilage-bone interface among 3 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 was in 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 geometry was obtained 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 was estimated from IDEAL IP MRI with the assistance of a calcium hydroxyapatite phantom.4 The 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 was then registered to the position of each structure on the weight-bearing MRI (Fig.1C).3 Quadriceps 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 on isotropic 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 14.8 GPa throughout the entire volume of patella. For each model, the femur and tibia were 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/vastus intermedius, vastus medialis, and vastus lateralis) made up of 6 equivalent uniaxial connector elements. The patellar tendon was modeled as six uniaxial, tension-only elements with stiffness of 4334 N/mm.3 The 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. von Mises distribution of patella at the cartilage-bone interface in 3 conditions.

CONCLUSIONS In the present study, a method to generate a subject-specific, heterogeneous patella FE model starting from IDEAL MRI was developed. Such an approach was deemed valid as there was excellent agreement in PFJ contact area based on MRI measurements. When comparing the heterogeneous, 2-material, and homogeneous models, meaningful differences 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 asses PFJ cartilage contact problems.

REFERENCES1. Taddei F, et al. J Biomech 39, 2457-2467,

2006.2. Keyak JH, et al. J Biomed Eng 15, 505-509,

19933. Farrokhi S, et al Osteoarthritis Cartilage In

Press.4. Ho KY, et al. Proceedings of ISMRM'115. Chen YJ, et al. J Appl Biomech 26, 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.

ACKNOWLEDGEMENTS This study is supported by the International Society of Biomechanics Student Dissertation Award.

Peak von Mises stress (MPa)

Contact Area (mm2)

Heterogeneous

2.62 255.96

2-material 2.83 255.97Homogeneous 2.32 255.99