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, µ0, 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, µ0, 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 µ0 and α for future cartilage tissue engineering studies. The Ogden model was demonstrated to fit the full strain range with high accuracy (R2 = 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.

Regenerative Engineering of a Biphasic Patient-Fitted Temporomandibular Joint Condylar Prosthesis.

Regenerative medicine approaches to restore the mandibular condyle of the temporomandibular joint (TMJ) may fill an unmet patient need. In this study, a method to implant an acellular regenerative TMJ prosthesis was developed for orthotopic implantation in a pilot goat study. The scaffold incorporated a porous, polycaprolactone-hydroxyapatite (PCL-HAp, 20wt% HAp) 3D printed condyle with a cartilage-matrix-containing hydrogel. A series of material characterizations was used to determine the structure, fluid transport, and mechanical properties of 3D printed PCL-HAp. To promote marrow uptake for cell seeding, a scaffold pore size of 152 ± 68 µm resulted in a whole blood transport initial velocity of 3.7 ± 1.2 mm·s-1 transported to the full 1 cm height. The Young's modulus of PCL was increased by 67% with the addition of HAp, resulting in a stiffness of 269 ± 20 MPa for etched PCL-HAp. In addition, the bending modulus increased by 2.06-fold with the addition of HAp to 470 MPa for PCL-HAp. The prosthesis design with an integrated hydrogel was compared with unoperated contralateral control and no-hydrogel group in a goat model for 6 months. A guide was used to make the condylectomy cut, and the TMJ disc was preserved. MicroCT assessment of bone suggested variable tissue responses with some regions of bone growth and loss, although more loss may have been exhibited by the hydrogel group than the no-hydrogel group. A benchtop load transmission test suggested that the prosthesis was not shielding load to the underlying bone. Although variable, signs of neocartilage formation were exhibited by Alcian blue and collagen II staining on the anterior, functional surface of the condyle. Overall, this study demonstrated signs of functional TMJ restoration with an acellular prosthesis. There were apparent limitations to continuous, reproducible bone formation, and stratified zonal cartilage regeneration. Future work may refine the prosthesis design for a regenerative TMJ prosthesis amenable to clinical translation.

Residual stress and osmotic swelling of the periodontal ligament.

Osmotic swelling and residual stress are increasingly recognized as important factors in soft tissue biomechanics. Little attention has been given to residual stress in periodontal ligament (PDL) biomechanics despite its rapid growth and remodeling potential. Those tissues that bear compressive loads, e.g., articular cartilage, intervertebral disk, have received much attention related to their capacities for osmotic swelling. To understand residual stress and osmotic swelling in the PDL, it must be asked (1) to what extent, if any, does the PDL exhibit residual stress and osmotic swelling, and (2) if so, whether residual stress and osmotic swelling are mechanically significant to the PDL's stress/strain behavior under external loading. Here, we incrementally built a series of computer models that were fit to uniaxial loading, osmotic swelling and residual stretch data. The models were validated with in vitro shear tests and in vivo tooth-tipping data. Residual stress and osmotic swelling models were used to analyze tension and compression stress (principal stress) effects in PDL specimens under external loads. Shear-to-failure experiments under osmotic conditions were performed and modeled to determine differences in mechanics and failure of swollen periodontal ligament. Significantly higher failure shear stresses in swollen PDL suggested that osmotic swelling reduced tension and thus had a strengthening effect. The in vivo model's first and third principal stresses were both higher with residual stress and osmotic swelling, but smooth stress gradients prevailed throughout the three-dimensional PDL anatomy. The addition of PDL stresses from residual stress and osmotic swelling represents a unique concept in dental biomechanics.