ESTIMATION OF PATELLA BONE STRESS: A COMPARISON OF HOMOGENEOUS AND
HETEROGENEOUS FINITE ELEMENT MODELS
1
Kai-Yu Ho, 2Nazanin Mokarram, 1Nicholas H. Yang, 2Ashkan Vaziri,1Christopher M. Powers
1
University of Southern California, Los Angeles, CA, USA
2
Northeastern 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, densitybased 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
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
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
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 2material 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.
REFERENCES
1. Taddei F, et al. J Biomech 39, 2457-2467, 2006.
2. Keyak JH, et al. J Biomed Eng 15, 505-509,
1993
3. Farrokhi S, et al Osteoarthritis Cartilage In
Press.
4. Ho KY, et al. Proceedings of ISMRM'11
5. 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.
Peak von Mises
Contact
stress (MPa)
Area (mm2)
2.62
255.96
Heterogeneous
2.83
255.97
2-material
2.32
255.99
Homogeneous
ACKNOWLEDGEMENTS
This study is supported by the International
Society of Biomechanics Student Dissertation
Award.