The Ogden model for hydrogels in tissue engineering: Modulus determination with compression to failure.

Hydrogel mechanical properties for tissue engineering are often reported in terms of a compressive elastic modulus derived from a linear regression of a typically non-linear stress-strain plot. There is a need for an alternative model to fit the full strain range of tissue engineering hydrogels. Fortunately, the Ogden model provides a shear modulus, μ, and a nonlinear parameter, α, for routine analysis of compression to failure. Three example hydrogels were tested: (1) pentenoate-modified hyaluronic acid (PHA), (2) dual-crosslinked PHA and polyethylene glycol diacrylate (PHA-PEGDA), and (3) composite PHA-PEGDA hydrogel with cryoground devitalized cartilage (DVC) at 5, 10, and 15%w/v concentration (DVC5, DVC10, and DVC15, respectively). Gene expression analyses suggested that the DVC hydrogels supported chondrogenesis of human bone marrow mesenchymal stem cells to some degree. Both linear regression (5 to 15% strain) and Ogden fits (to failure) were performed. The compressive elastic modulus, E, was over 4-fold higher in the DVC15 group relative to the PHA group (129 kPa). Similarly, the shear modulus, μ, was over 3-fold higher in the DVC15 group relative to the PHA group (37 kPa). The PHA group exhibited a much higher degree of nonlinearity (α = 10) compared to the DVC15 group (α = 1.4). DVC hydrogels may provide baseline targets of μ and α for future cartilage tissue engineering studies. The Ogden model was demonstrated to fit the full strain range with high accuracy (R = 0.998 ± 0.001) and to quantify nonlinearity. The current study provides an Ogden model as an attractive alternative to the elastic modulus for tissue engineering constructs.