Finite element implementation of a model for finite deformable, biphasic biological tissues with transversely isotropic statistically distributed fibers.
Wu-JZ; Herzog-W; Federico-S
Proceedings of the 7th World Congress of Biomechanics, July 6-11, 2014, Boston, Massachusetts. Eugene, OR: American Society of Biomechanics, 2014 Jul; :801-802
INTRODUCTION: The mechanical behavior of articular cartilage is complex: it is time-dependent, non-linear anisotropic, structurally heterogeneous, asymmetric in tension-compression. Many of these aspects are attributed to the distributed collagen fibers, which form a three-dimensional network that is adapted to the mechanical loading of the joint. The distribution of collagen fibers across articular cartilage layers is statistical in nature. Therefore, cartilage models including probability distributions of the collagen fibers are promising for tackling practical problems. In order for engineers and researchers to solve real problems, such cartilage models should be implemented into commercial finite element (FE) software tools. METHODS: A collagen probability distribution model was implemented into the commercial FE software COMSOL. The collagen fibers were represented by five sets with different colatitude orientations (theta) varying in a range of 0-90 deg with cartilage depth and distributed across the cartilage thickness. Each of the five fiber sets was considered to be evenly distributed in a range of 0-90 deg in the longitudinal direction. The assumed depth-dependent fiber orientation and volumetric concentration were based on published experimental data. Both collagen fibers and solid cartilage matrix were considered to be nonlinearly elastic. The hydraulic permeability was assumed to be isotropic, but depth- and deformation-dependent. The COMSOL Standard and Structural modules were applied to construct the model. Darcy's equation was solved by an analog to the diffusion process. Biphasic modeling was simulated by coupling diffusion with dynamic solid mechanics. Numerical tests were performed using confined compressions of an axi-symmetric specimen. RESULTS AND DISCUSSION: The simulations showed that that cartilage strain is approximately evenly distributed through about 80% of the cartilage thickness, increases by approximately 90% in the superficial zone within about 20% of the cartilage thickness, and reaches its maximum at the contact surface. These predictions on the depth-dependent strain distributions across the cartilage layer are consistent with published experimental observations. Our results indicate that the effects of the distributed fiber orientation cannot be simulated by simply using a depth-dependent permeability and elastic modulus in an otherwise isotropic model.
Collagen-fibrils; Models; Fiber-deposition; Mathematical-models; Simulation-methods; Tissue-culture; Tissue-distribution; Biological-function; Biological-factors
Proceedings of the 7th World Congress of Biomechanics, July 6-11, 2014, Boston, Massachusetts