Viscoelastic properties and residual strain in a tensile creep test on bovine temporomandibular articular discs

Comparison of the Trueness of Fits of the Biphasic Transverse Isotropic and Kelvin Models to the Tensile Behavior of Temporomandibular Joint Disc

This technical brief explores the validity and trueness of fit for using the transverse isotropic biphasic and Kelvin models (first and second order generalized) for characterization of the viscoelastic tensile properties of the temporomandibular joint (TMJ) discs from pigs and goats at a strain rate of 10 mm/min. We performed incremental stress-relaxation tests from 0 to 12% strain, in 4% strain steps on pig TMJ disc samples. In addition, to compare the outcomes of these models between species, we also performed a single-step stress-relaxation test of 10% strain. The transverse isotropic biphasic model yielded reliable fits in reference to the least root mean squared error method only at low strain, while the Kelvin models yielded good fits at both low and high strain, with the second order generalized Kelvin model yielding the best fit. When comparing pig to goat TMJ disc in 10% strain stress-relaxation test, unlike the other two Kelvin models, the transverse isotropic model did not fit well for this larger step. In conclusion, the second order Kelvin model showed the best fits to the experimental data of both species. The transverse isotropic biphasic model did not fit well with the experimental data, although better at low strain, suggesting that the assumption of water flow only applies while uncrimping the collagen fibers. Thus, it is likely that the permeability from the biphasic model is not truly representative, and other biphasic models, such as the poroviscoelastic model, would likely yield more meaningful outputs and should be explored in future works.

Identification of Biomechanical Properties of Temporomandibular Discs

Material

Experimental and model tests were conducted on ten fresh porcine temporomandibular joint discs. The average thickness of disc tissue was, accordingly, 2.77 mm for the anterior zone, 3.98 mm for the posterior, and 1.54 mm for the intermediate. The selection of research material in the form of porcine discs was due to the similarity to human discs.

Methods

Discs were loaded in cycles, a temporary course with the amplitude 3 N and frequency 0.07 Hz, and growth in the load was 1 N/s. The selection of load frequency was due to real conditions of temporomandibular joint functioning during mastication. The necessary experimental research was conducted on a testing machine with a measurement range of 2.5 kN.

Results

The obtained numeric calculation results indicate that the number of load cycles has a decisive impact on the limitation of energy dispersion capacity through disc tissue. This phenomenon was observed in all the studies on the disc areas. Along with the growth in load cycles, discs are stiffened, and the most significant stiffness was observed in the intermediate area.

Conclusions

Based on the conducted research, it should be concluded that excessive load affecting temporomandibular joints caused by the act of mastication and occlusal forces generated during parafunction and in people with defined long-term bruxism has crucial importance on biomechanical disc properties and hence the course of temporomandibular joint conditions.

Effect of Pre-Stress on the Dynamic Tensile Behavior of the TMJ Disc

Previous dynamic analyses of the temporomandibular joint (TMJ) disc have not included a true preload, i.e., a step stress or strain beyond the initial tare load. However, due to the highly nonlinear stress-strain response of the TMJ disc, we hypothesized that the dynamic mechanical properties would greatly depend on the preload, which could then, in part, account for the large variation in the tensile stiffnesses reported for the TMJ disc in the literature. This study is the first to report the dynamic mechanical properties as a function of prestress. As hypothesized, the storage modulus (E′) of the disc varied by a factor of 25 in the mediolateral direction and a factor of 200 in the anteroposterior direction, depending on the prestress. Multiple constant strain rate sweeps were extracted and superimposed via strain-rate frequency superposition (SRFS), which demonstrated that the strain rate amplitude and strain rate were both important factors in determining the TMJ disc material properties, which is an effect not typically seen with synthetic materials. The presented analysis demonstrated, for the first time, the applicability of viscoelastic models, previously applied to synthetic polymer materials, to a complex hierarchical biomaterial such as the TMJ disc, providing a uniquely comprehensive way to capture the viscoelastic response of biological materials. Finally, we emphasize that the use of a preload, preferably which falls within the linear region of the stress-strain curve, is critical to provide reproducible results for tensile analysis of musculoskeletal tissues. Therefore, we recommend that future dynamic mechanical analyses of the TMJ disc be performed at a controlled prestress corresponding to a strain range of 5–10%.

Viscoelastic material model for the temporomandibular joint disc derived from dynamic shear tests or strain-relaxation tests

Viscoelastic material models for the temporomandibular joint disc, based upon strain relaxation, were considered to underestimate energy absorption for loads with time constants beyond the relaxation time. Therefore, the applicability of a material model that takes the viscous behavior at a wide range of frequencies into account was assessed. To that purpose a non-linear multi-mode Maxwell model was tested in cyclic large-strain compression tests. Its material constants were approximated from dynamic small-strain shear deformation tests. The storage and loss moduli as obtained from a disc sample could be approximated with a four-mode Maxwell model. In simulated large-strain compression tests it behaved similarly as observed from the experimental tests. The underestimation of energy dissipation, as obtained from a single-mode Maxwell model was considerably reduced, especially for deformations with a higher strain rate. Furthermore, in contrast to the latter it was able to predict the increase of the stress amplitude with the compression frequency much better. In conclusion, the applied four-mode Maxwell model, based upon dynamic shear tests, was considered more suitable to predict higher frequency viscoelastic response, for instance during shock absorption, than a model based upon strain-relaxation.

Fracture toughness estimation for the TMJ disc

J contour integral fracture toughness of the temporomandibular (TMJ) disc was estimated from a computational model based on fracture load data derived from experimental tests. The computational model involved a stress analysis of TMJ disc specimens with cracks oriented parallel and perpendicular to the primary collagen fiber axis within the intermediate zone of the disc. The results demonstrated differences occurred between crack orientations when an orthotropic model was used. Fracture toughness was much lower for a crack oriented parallel to the collagen fiber direction than that for a crack oriented perpendicularly. Thickness, crack size, and anisotropy ratio were observed as additional variables affecting the fracture toughness of the TMJ disc. Future model enhancements may be achieved by considering the poroviscoelastic nature of the TMJ disc.

Biomechanical behavior of the temporomandibular joint disc

The temporomandibular joint (TMJ) disc consists mainly of collagen fibers and proteoglycans constrained in the interstices of the collagen fiber mesh. This construction results in a viscoelastic response of the disc to loading and enables the disc to play an important role as a stress absorber during function. The viscoelastic properties depend on the direction (tension, compression, and shear) and the type of the applied loading (static and dynamic). The compressive elastic modulus of the disc is smaller than its tensile one because the elasticity of the disc is more dependent on the collagen fibers than on the proteoglycans. When dynamic loading occurs, the disc is likely to behave less stiffly than under static loading because of the difference of fluid flow through and out of the disc during loading. In addition, the mechanical properties change as a result of various intrinsic and extrinsic factors in life such as aging, trauma, and pathology. Information about the viscoelastic behavior of the disc is required for its function to be understood and, for instance, for a suitable TMJ replacement device to be constructed. In this review, the biomechanical behavior of the disc in response to different loading conditions is discussed.

Strain-rate effect on the biomechanical response of bovine temporomandibular joint disk under compression

This study evaluates the effect of strain rate on the biomechanical responses of bovine temporomandibular joint (TMJ) disk under compression. Ten specimens derived from the central region of bovine TMJ disks were used for compression tests. Each specimen was loaded upto 20% of strain with seven different strain rates: 1, 10, 20, 30, 40, 50, and 60%/s. Although the stress-strain curves presented similar patterns for all the specimens, the strain-rate effect was obvious. The linear modulus by regression fit for the linear part of the curve was significantly larger at 60%/s of strain rate than at the lower strain rates. The "supplemental stress" ratio (SSR) obviously increased with the augmentation of the strain rate. At strain rates of 30-60%/s, the SSR was significantly larger than those at strain rates below 20%/s. These findings indicate that although water easily can move through the TMJ disk at the lower strain rates, the higher strain rates make such movement difficult. It is concluded that the secondary changes of the TMJ disk may be dependent on the pattern and velocity of masticatory mandibular movements directly associated with the dynamic strain rate in the TMJ disk.

Dynamic properties of bovine temporomandibular joint disks change with age

The temporomandibular joint disk exhibits morphological and biochemical age-related changes. However, the possible age-related changes of the dynamic viscoelasticity in the disk are unclear. We tested the hypothesis that the dynamic viscoelastic properties of the disk change with age. Thirty-six disks from young-adult, adult, and mature-adult cattle were used for dynamic tensile tests. In all disks, the magnitudes of the complex modulus, the storage modulus, and the loss modulus increased as the frequency increased. The mature-adult disks had higher values of these moduli than did the younger disks. The loss tangent ranged from 0.1 to 0.3, which means that the disk has relatively large elasticity and relatively small viscosity. It was concluded that both the elasticity and viscosity of the disk increase with age. This may reflect age-related changes in biochemical composition.

The regional difference of viscoelastic property of bovine temporomandibular joint disc in compressive stress-relaxation

An in vitro experimental technique was performed to measure the viscoelastic properties of the bovine disc. Thirteen TMJ discs from young cattle (3-year-old) were used. Each disc was divided into five specimens of anterior, central, posterior, lateral and medial regions, and they were used for compression tests. A series of stress-relaxation tests was conducted for each specimen from 5% strain up to 20% strain with 5% intervals. The stress-relaxation was monitored over a period of 5 min. Each region exhibited a different biomechanical behavior, which is presumably related to the organization and distribution of proteoglycans that indirectly modulate the stiffness of the collagen network. It is suggested that an improved understanding of the viscoelastic properties of the disc under function may guide consideration for design and selection of biomaterials for TMJ reconstruction.