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.

Mechanics of a two-fiber model with one nested fiber network, as applied to the collagen-fibrin system.

The mechanical behavior of collagen-fibrin (col-fib) co-gels is both scientifically interesting and clinically relevant. Collagen-fibrin networks are a staple of tissue engineering research, but the mechanical consequences of changes in co-gel composition have remained difficult to predict or even explain. We previously observed fundamental differences in failure behavior between collagen-rich and fibrin-rich co-gels, suggesting an essential change in how the two components interact as the co-gel's composition changes. In this work, we explored the hypothesis that the co-gel behavior is due to a lack of percolation by the dilute component. We generated a series of computational models based on interpenetrating fiber networks. In these models, the major network component percolated the model space but the minor component did not, instead occupying a small island embedded within the larger network. Each component was assigned properties based on a fit of single-component gel data. Island size was varied to match the relative concentrations of the two components. The model predicted that networks rich in collagen, the stiffer component, would roughly match pure-collagen gel behavior with little additional stress due to the fibrin, as seen experimentally. For fibrin-rich gels, however, the model predicted a smooth increase in the overall network strength with added collagen, as seen experimentally but not consistent with an additive parallel model. We thus conclude that incomplete percolation by the low-concentration component of a co-gel is a major determinant of its macroscopic properties, especially if the low-concentration component is the stiffer component. STATEMENT OF SIGNIFICANCE: Models for the behavior of fibrous networks have useful applications in many different fields, including polymer science, textiles, and tissue engineering. In addition to being important structural components in soft tissues and blood clots, these protein networks can serve as scaffolds for bioartificial tissues. Thus, their mechanical behavior, especially in co-gels, is both interesting from a materials science standpoint and significant with regard to tissue engineering.

Swelling of Collagen-Hyaluronic Acid Co-Gels: An In Vitro Residual Stress Model.

Tissue-equivalents (TEs), simple model tissues with tunable properties, have been used to explore many features of biological soft tissues. Absent in most formulations however, is the residual stress that arises due to interactions among components with different unloaded levels of stress, which has an important functional role in many biological tissues. To create a pre-stressed model system, co-gels were fabricated from a combination of hyaluronic acid (HA) and reconstituted Type-I collagen (Col). When placed in solutions of varying osmolarity, HA-Col co-gels swell as the HA imbibes water, which in turn stretches (and stresses) the collagen network. In this way, co-gels with residual stress (i.e., collagen fibers in tension and HA in compression) were fabricated. When the three gel types tested here were immersed in hypotonic solutions, pure HA gels swelled the most, followed by HA-Col co-gels; no swelling was observed in pure collagen gels. The greatest swelling rates and swelling ratios occurred in the lowest salt concentration solutions. Tension on the collagen component of HA-Col co-gels was calculated from a stress balance and increased nonlinearly as swelling increased. The swelling experiment results were in good agreement with the stress predicted by a fibril network + non-fibrillar interstitial matrix computational model.