Development of a Hyperelastic Model for the Material Properties of Porcine Patellar Cartilage Richar

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Development of a Hyperelastic Model for the
Material Properties of Porcine Patellar
CartilageRichard Shoge, Dr. Peter MenteNorth
Carolina State University Department of
Biomedical Engineering
Abstract Understanding the mechanical causes of
the degradation of cartilage can lead to the
investigation of preventative measures to stop
debilitating diseases such as osteoarthritis. We
have developed a novel in vitro impact injury
model which incorporates shear and axial loading.
Stress-strain data from each zonal layer will be
fit to an Ogden hyperelastic equation using a
Levenberg-Marquandt nonlinear least squares
method. In previous literature, hyperelastic
modeling of the material properties have shown
success in accounting for the large strains
experienced by biological tissues. For stability
when implemented into a finite element program, a
constraint will be coded into the algorithm to
ensure that the function is monotonically
increasing.
Fitting the Data Using Hyperelastic Model
Ogden Hyperelastic Function

• Where s is the tissue stress, ? is the tissue
  stretch, and µi and ai are material
  constants. N6.
• This model provides more accurate fit for
  multiple experimental test data
• Ogden Equation will be fit to stress-strain data
  using Nonlinear least Squares Optimization
• - Marquard-Levenberg algorithm

Figure 2. Experimental set-up to measure zone
specific cartilage material properties in tension
(A) and compression (B).
Figure 1. A. Impact geometry showing the contact
radius. B. Zones where histology measurements
were made.

• - Tension and compression tests on cartilage
  taken from
• porcine patellas
• - Determined zone specific hyperelastic material
• properties for cartilage surface, mid, deep
  zones

Future Directions

• Incorporate Material Properties into a Finite
  Element Analysis of Axial and Shear Impactions

Study Objectives 1. Determine the material
properties of the three cartilage layers 2.
Develop finite element model of experimental
cartilage impactions 3. Correlate predicted
stress- strain distribution from our
finite element model with experimentally
observed matrix damage and chondrocyte
response
A. Example of a Finite Element Model of Cartilage
surface and Bone Layers. B. Close up of mesh
directly beneath the impactor with four tissue
layers cartilage (red),, calcified cartilage
(dark blue) subchondral bone (light blue), and
trabecular bone (green)
Acknowledgements Dr. Mente, NSF AGEP, Department
of Biomedical Engineering
Figure 3. Experimental stress-stretch curves for
porcine patellar cartilage from surface, mid and
deep zones.