Incremental Stress-relaxation Tests Research Articles

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.

The posterior eye with age-related macular degeneration has isotropic and nonlinear viscoelastic properties

Here we characterize and compare the anisotropic and nonlinear viscoelastic properties of the posterior eye of advanced dry age-related macular degeneration (AMD) patients and age-matched normal subjects. Ten normal horizontal, ten normal vertical, ten AMD horizontal, and ten AMD vertical strips of the macular retina and the underlying choroid and sclera were preloaded, preconditioned, and subjected to incremental stress-relaxation tests in body-temperature saline. The stress-relaxation response was characterized by a fully nonlinear viscoelastic formulation in which the relaxation modulus was approximated by a Prony series and a second-order polynomial using the comprehensive viscoelastic characterization method. Normal retina, choroid, and sclera were found to be anisotropic, whereas AMD tissues were isotropic. AMD retina and choroid showed greater stress-relaxation response than normal tissues (p < 0.05), whereas AMD sclera had smaller stress-relaxation response than normal tissue (p < 0.05). The nonlinear viscoelastic stress-strain relationship of the posterior eye is hence describable for the first time.

Multiscale strain analysis of tendon subjected to shear and compression demonstrates strain attenuation, fiber sliding, and reorganization.

The manner in which strains are passed down the hierarchical length scales of tendons dictates how cells within the collagen network regulate the tissue response to loading. How tendons deform in different hierarchical levels under shear and compression is unknown. The aims of this study were: (i) to evaluate whether specific regions of bovine deep digital flexor tendons exhibited different strain attenuation from macro to micro length scales, and (ii) to elucidate mechanisms responsible for tendon deformation under shear and compression. Samples from distal and proximal regions of flexor tendons were subjected to three-step incremental stress-relaxation tests. Images of tissue markers, photobleached lines on collagen fibers, and nuclei locations were collected before and after loading. Results showed that strain transfer was attenuated from tissue to local matrix under both shear and compression. Nuclear aspect ratios exhibited smaller changes for distal samples, suggesting that cells are more shielded from deformation in the distal region. Collagen fiber sliding was observed to contribute significantly in response to shear, while uncrimping and fiber reorganization were the predominant mechanisms under compression. This study provides insight into microscale mechanisms responsible for multiscale strain attenuation of tendons under non-tensile macroscale loading.

Different regions of bovine deep digital flexor tendon exhibit distinct elastic, but not viscous, mechanical properties under both compression and shear loading

Tendons in different locations function in unique, and at times complex, invivo loading environments. Specifically, some tendons are subjected to compression, shear and/or torsion in addition to tensile loading, which play an important role in regulating tendon properties. To date, there have been few studies evaluating tendon mechanics when loaded in compression and shear, which are particularly relevant for understanding tendon regions that experience such non-tensile loading during normal physiologic function. The objective of this study was to evaluate mechanical responses of different regions of bovine deep digital flexor tendons (DDFT) under compressive and shear loading, and correlate structural characteristics to functional mechanical properties. Distal and proximal regions of DDFT were evaluated in a custom-made loading system via three-step incremental stress-relaxation tests. A two-relaxation-time solid linear model was used to describe the viscoelastic response. Results showed large differences in the elastic behavior between regions: distal region stresses were 4–5 times larger than proximal region stresses during compression and 2–3 times larger during shear. Surprisingly, the viscous (i.e., relaxation) behavior was not different between regions for either compression or shear. Histological analysis showed that collagen and proteoglycan in the distal region distributed differently from the proximal region. Results demonstrate mechanical differences between two regions of DDFT under compression and shear loading, which are attributed to variations of composition and microstructural organization. These findings deepen our understanding of structure–function relationships of tendon, particularly for tissues adapted to supporting combinations of tension, compression, and shear in physiological loading environments.

Viscoelasticity and compaction behaviour of the foam-like pomelo (Citrus maxima) peel

The pomelo (Citrus maxima) is the largest and heaviest fruit of the genus Citrus and can acquire considerable potential energy as it ripens hanging up to 15 m height. Its thick foam-like structured peel presumably acts inter alia as a shock absorbing layer, protecting the fruit as it impacts on the ground upon being shed. Thereby the peel dissipates kinetic energy by being compacted. In order to elucidate the compaction mechanism of the highly heterogeneous pomelo peel, we conducted incremental stress relaxation tests. Two different models describing the stress relaxation curves, namely, the well-known Maxwell model and the Peleg model were compared and found to be suitable to describe the stress relaxation. As the Peleg model involves only two constants describing the relaxation curves it was the method of choice for interpreting the compaction of the peel samples. The inverse of k 1 reflects the initial decay rate of the relaxation process and k 2 is a measure of the samples’ solidity. The behaviour of these constants with increasing strain indicates the strong influence of the peel samples’ geometry and composition which is attributed to the fruit shape, a gradual changing density of the peel, which can be considered as a stacked array of foam layers differing in density, and the turgescence of the biological cells.

Elastic and viscoelastic properties of a type I collagen fiber

A new mathematical model is presented to describe the elastic and viscoelastic properties of a single collagen fiber. The model is formulated by accounting for the mechanical contribution of the collagen fiber's main constituents: the microfibrils, the interfibrillar matrix and crosslinks. The collagen fiber is modeled as a linear elastic spring, which represents the mechanical contribution of the microfibrils, and an arrangement in parallel of elastic springs and viscous dashpots, which represent the mechanical contributions of the crosslinks and interfibrillar matrix, respectively. The linear elastic spring and the arrangement in parallel of elastic springs and viscous dashpots are then connected in series. The crosslinks are assumed to gradually break under strain and, consequently, the interfibrillar is assumed to change its viscous properties. Incremental stress relaxation tests are conducted on dry collagen fibers reconstituted from rat tail tendons to determine their elastic and viscoelastic properties. The elastic and total stress–strain curves and the stress relaxation at different levels of strain collected by performing these tests are then used to estimate the parameters of the model and evaluate its predictive capabilities.

A Nonlinear Model of Passive Muscle Viscosity

The material properties of passive skeletal muscle are critical to proper function and are frequently a target for therapeutic and interventional strategies. Investigations into the passive viscoelasticity of muscle have primarily focused on characterizing the elastic behavior, largely neglecting the viscous component. However, viscosity is a sizeable contributor to muscle stress and extensibility during passive stretch and thus there is a need for characterization of the viscous as well as the elastic components of muscle viscoelasticity. Single mouse muscle fibers were subjected to incremental stress relaxation tests to characterize the dependence of passive muscle stress on time, strain and strain rate. A model was then developed to describe fiber viscoelasticity incorporating the observed nonlinearities. The results of this model were compared with two commonly used linear viscoelastic models in their ability to represent fiber stress relaxation and strain rate sensitivity. The viscous component of mouse muscle fiber stress was not linear as is typically assumed, but rather a more complex function of time, strain and strain rate. The model developed here, which incorporates these nonlinearities, was better able to represent the stress relaxation behavior of fibers under the conditions tested than commonly used models with linear viscosity. It presents a new tool to investigate the changes in muscle viscous stresses with age, injury and disuse.

Intermediate Filament and Ecm Mechanics Deduced from Desmin Knockout Muscles

Desmin is the skeletal muscle intermediate filament protein that forms a mesh-like network around Z-disks and helps transmit force to the extracellular matrix (ECM). It generally functions as a mechanical integrator of the cell, maintaining lattice connectivity and enabling efficient force transmission. Desmin related myopathies have debilitating effects that range from muscle weakness and atrophy to cardiac and respiratory failure. Studies performed on desmin knockout muscles have begun to elucidate the physiological and biological roles of desmin, but the mechanical properties of the desmin network are still unknown.We performed incremental stress-relaxation tests on fibers and fiber bundles from desmin knockout and wildtype mouse EDL muscles to investigate how the absence of desmin affects the fiber and fiber bundle viscoelastic properties. Using these data, we developed a structural model with explicit elastic and viscous elements representing the desmin, the rest of the fiber and the ECM. Single fibers from desmin knockout muscles were significantly more compliant (linear modulus = 122±61 kPa) compared to wildtype fibers (176±49 kPa, p<0.05). These data demonstrate that the desmin matrix bears 30-40% of the passive load in muscle cells, a much greater fraction than previously believed. In contrast to fibers, bundles of fibers were nonlinear and demonstrated the opposite trend_bundles from desmin knockout muscles were over twice as stiff (440±237 kPa) compared to wildtype bundles (214±97 kPa) at 60% strain (p<0.0001). Time constants for stress-relaxation were larger for fibers than bundles and were significantly larger for knockout bundles compared to wildtype bundles. These data suggest a biological and biomechanical interaction between muscle cells and the ECM and may indicate that the ECM becomes stiffer in desmin knockout muscles in response to the more compliant fibers.

Viscoelastic characterization of the porcine temporomandibular joint disc under unconfined compression

Pathophysiology of the temporomandibular joint (TMJ) disc is central to many orofacial disorders; however, mechanical characterization of this tissue is incomplete. In this study, we identified surface–regional mechanical variations in the porcine TMJ disc under unconfined compression. The intermediate zone, posterior, anterior, lateral, and medial regions of eight TMJ discs were sectioned into inferior and superior surface samples. Surface–regional sections were then subjected to incremental stress relaxation tests. Single strain step (SSS) and final deformation (FD) viscoelastic models were fit to experimental data. Both models represented the experimental data with a high degree of accuracy ( R ¯ 2 = 0.93 ) . The instantaneous modulus and relaxation modulus for the TMJ disc sections were approximately 500 kPa and 80 kPa, respectively; the coefficient of viscosity was approximately 3.5 MPa-s. Strain dependent material properties were observed across the disc's surface–regions. Regional variations in stiffness were observed in both models. The relaxation modulus was largest in the inferior–medial parts of the disc. The instantaneous modulus was largest in the posterior and anterior regions of the disc. Surface-to-surface variations were observed in the relaxation modulus for only the FD model; the inferior surface was found to be more resistant to compression than the superior surface. The results of this study imply the stiffness of the TMJ disc may change as strain is applied. Furthermore, the lateral region exhibited a lower viscosity and stiffness compared to other disc regions. Both findings may have important implications on the TMJ disc's role in jaw motion and function.