Postprint version. Published in Biomechanics and Modeling in Mechanobiology, December 1, 2012.
The definitive version is available at https://doi.org/10.1007/s10237-012-0463-y.
A continuum mixture model with distinct collagen (COL) and glycosaminoglycan elastic constituents was developed for the solid matrix of immature bovine articular cartilage. A continuous COL fiber volume fraction distribution function and a true COL fiber elastic modulus ( Ef) were used. Quantitative polarized light microscopy (qPLM) methods were developed to account for the relatively high cell density of immature articular cartilage and used with a novel algorithm that constructs a 3D distribution function from 2D qPLM data. For specimens untreated and cultured in vitro, most model parameters were specified from qPLM analysis and biochemical assay results; consequently, Ef was predicted using an optimization to measured mechanical properties in uniaxial tension and unconfined compression. Analysis of qPLM data revealed a highly anisotropic fiber distribution, with principal fiber orientation parallel to the surface layer. For untreated samples, predicted Ef values were 175 and 422 MPa for superficial (S) and middle (M) zone layers, respectively. TGF- \upbeta 1 treatment was predicted to increase and decrease Ef values for the S and M layers to 281 and 309 MPa, respectively. IGF-1 treatment was predicted to decrease Ef values for the S and M layers to 22 and 26 MPa, respectively. A novel finding was that distinct native depth-dependent fiber modulus properties were modulated to nearly homogeneous values by TGF- \upbeta 1 and IGF-1 treatments, with modulated values strongly dependent on treatment.