Quasi-linear Viscoelastic Model Research Articles

Viscoelastic Properties of Human Tracheal Tissues.

The physiological performance of trachea is highly dependent on its mechanical behavior, and therefore, the mechanical properties of its components. Mechanical characterization of trachea is key to succeed in new treatments such as tissue engineering, which requires the utilization of scaffolds which are mechanically compatible with the native human trachea. In this study, after isolating human trachea samples from brain-dead cases and proper storage, we assessed the viscoelastic properties of tracheal cartilage, smooth muscle, and connective tissue based on stress relaxation tests (at 5% and 10% strains for cartilage and 20%, 30%, and 40% for smooth muscle and connective tissue). After investigation of viscoelastic linearity, constitutive models including Prony series for linear viscoelasticity and quasi-linear viscoelastic, modified superposition, and Schapery models for nonlinear viscoelasticity were fitted to the experimental data to find the best model for each tissue. We also investigated the effect of age on the viscoelastic behavior of tracheal tissues. Based on the results, all three tissues exhibited a (nonsignificant) decrease in relaxation rate with increasing the strain, indicating viscoelastic nonlinearity which was most evident for cartilage and with the least effect for connective tissue. The three-term Prony model was selected for describing the linear viscoelasticity. Among different models, the modified superposition model was best able to capture the relaxation behavior of the three tracheal components. We observed a general (but not significant) stiffening of tracheal cartilage and connective tissue with aging. No change in the stress relaxation percentage with aging was observed. The results of this study may be useful in the design and fabrication of tracheal tissue engineering scaffolds.

A viscoelastic analysis of the P56 mouse brain under large-deformation dynamic indentation.

We present the first mechanical characterization of the viscoelastic response for different regions of mouse brain. Force-relaxation tests are performed under large strain dynamic micro-indentation, and viscoelastic models are used subsequently, providing time-dependent mechanical properties of brain tissue under loading conditions comparable to what is experienced in TBI. The unique mechanical properties of different brain regions are highlighted, with substantial variations in the viscoelastic properties and damping ratio of each region. Cortex and pons were the stiffest regions, while the thalamus and medulla were most compliant. The cerebellum and thalamus had highest damping ratio values and those of the medulla were lowest. The reported material parameters can be implemented into finite element computer models of the mouse to investigate the effects of trauma on individual brain regions.

Viscoelasticity of brain corpus callosum in biaxial tension

Computational models of the brain rely on accurate constitutive relationships to model the viscoelastic behavior of brain tissue. Current viscoelastic models have been derived from experiments conducted in a single direction at a time and therefore lack information on the effects of multiaxial loading. It is also unclear if the time-dependent behavior of brain tissue is dependent on either strain magnitude or the direction of loading when subjected to tensile stresses. Therefore, biaxial stress relaxation and cyclic experiments were conducted on corpus callosum tissue isolated from fresh ovine brains. Results demonstrated the relaxation behavior to be independent of strain magnitude, and a quasi-linear viscoelastic (QLV) model was able to accurately fit the experimental data. Also, an isotropic reduced relaxation tensor was sufficient to model the stress-relaxation in both the axonal and transverse directions. The QLV model was fitted to the averaged stress relaxation tests at five strain magnitudes while using the measured strain history from the experiments. The resulting model was able to accurately predict the stresses from cyclic tests at two strain magnitudes. In addition to deriving a constitutive model from the averaged experimental data, each specimen was fitted separately and the resulting distributions of the model parameters were reported and used in a probabilistic analysis to determine the probability distribution of model predictions and the sensitivity of the model to the variance of the parameters. These results can be used to improve the viscoelastic constitutive models used in computational studies of the brain.

Virtual Breast Quasi-static Elastography (VBQE).

Viscoelasticity Imaging (VEI) has been proposed to measure relaxation time constants for characterization of in vivo breast lesions. In this technique, an external compression force on the tissue being imaged is maintained for a fixed period of time to induce strain creep. A sequence of ultrasound echo signals is then utilized to generate time-resolved strain measurements. Relaxation time constants can be obtained by fitting local time-resolved strain measurements to a viscoelastic tissue model (e.g., a modified Kevin-Voigt model). In this study, our primary objective is to quantitatively evaluate the contrast transfer efficiency (CTE) of VEI, which contains useful information regarding image interpretations. Using an open-source simulator for virtual breast quasi-static elastography (VBQE), we conducted a case study of contrast transfer efficiency of VEI. In multiple three-dimensional (3D) numerical breast phantoms containing various degrees of heterogeneity, finite element (FE) simulations in conjunction with quasi-linear viscoelastic constitutive tissue models were performed to mimic data acquisition of VEI under freehand scanning. Our results suggested that there were losses in CTE, and the losses could be as high as -18 dB. FE results also qualitatively corroborated clinical observations, for example, artifacts around tissue interfaces.

The Transverse Isotropy of Spinal Cord White Matter Under Dynamic Load.

The rostral-caudally aligned fiber-reinforced structure of spinal cord white matter (WM) gives rise to transverse isotropy in the material. Stress and strain patterns generated in the spinal cord parenchyma following spinal cord injury (SCI) are multidirectional and dependent on the mechanism of the injury. Our objective was to develop a WM constitutive model that captures the material transverse isotropy under dynamic loading. The WM mechanical behavior was extracted from the published tensile and compressive experiments. Combinations of isotropic and fiber-reinforcing models were examined in a conditional quasi-linear viscoelastic (QLV) formulation to capture the WM mechanical behavior. The effect of WM transverse isotropy on SCI model outcomes was evaluated by simulating a nonhuman primate (NHP) contusion injury experiment. A second-order reduced polynomial hyperelastic energy potential conditionally combined with a quadratic reinforcing function in a four-term Prony series QLV model best captured the WM mechanical behavior (0.89 < R2 < 0.99). WM isotropic and transversely isotropic material models combined with discrete modeling of the pia mater resulted in peak impact forces that matched the experimental outcomes. The transversely isotropic WM with discrete pia mater resulted in maximum principal strain (MPS) distributions which effectively captured the combination of ipsilateral peripheral WM sparing, ipsilateral injury and contralateral sparing, and the rostral/caudal spread of damage observed in in vivo injuries. The results suggest that the WM transverse isotropy could have an important role in correlating tissue damage with mechanical measures and explaining the directional sensitivity of the spinal cord to injury.

A non-linear viscoelastic model to describe the mechanical behavior's evolution of biodegradable polymers during hydrolytic degradation

The biodegradable triblock copolymer PLA-b-PEG-b-PLA presents, in its initial state, a non-linear viscoelastic behavior. Its mechanical properties evolves during the in vitro degradation process. Tensile and relaxation tests are performed at 2%, 4% and 6% of load strain for different degradation steps. In order to describe the behavior of the polymer during degradation, an adaptive quasi-linear viscoelastic model is considered. In a first step, the model calibrated on the non-degraded state, perfectly fits the load and relaxation curves for every strain. Then, based on considerations about the preservation of the normalized relaxation curves over degradation time, the adaptive quasi-linear viscoelastic model is adapted to degradation. A degradation parameter that drives the mechanical degradation kinetics is deduced for every tested degradation states. A physically motivated model is finally used to describe the degradation parameter at every degradation step. The whole constitutive model is very accurate to fit the mechanical curves at every strain during degradation.

THE EFFECT OF DISPLACEMENT RATE ON VISCOELASTIC PROPERTIES OF RAT CERVIX

Determining the viscoelastic response of cervix at different displacement rates can provide sufficient information for the normal mechanical behavior of the tissue in assessment of cervical insufficiency. The objective of this study was to investigate the effect of displacement rate on viscoelastic properties of rat cervix. Different displacement rates were employed to measure the tensile and load-relaxation properties of cervices from virgin and 16 days post-conception pregnant rats. After preconditioning, the displacement of 2[Formula: see text]mm was applied to the distal halves of five pregnant rat’s cervices and 1 millimeter to the five virgin samples circumferentially. Uniaxial tension tests were employed at the displacement rates of 0.01, 0.1 and 1 mm/s randomly and were held for 10 min while the tissues were relaxed. Tensile and load-relaxation curves were well described by a quasi-linear viscoelastic model. Statistical analysis revealed significant correlation between the change in displacement rate and the elastic response, as well as the viscous response of the virgin samples. For pregnant samples, though, the correlation was found significant between the displacement rate and the elastic response of the tissue. Virgin tissue is strongly viscoelastic. Quantitative measurements of cervical mechanical properties will lead to a more accurate assessment of cervical insufficiency and prediction of preterm birth.

Passive mechanical properties of ovine rumen tissue

ABSTRACTMechanical and structural properties of ovine rumen tissue have been determined using uniaxial tensile testing of tissue from four animals at five rumen locations and two orientations. Animal and orientation did not have a significant effect on the stress-strain response, but there was a significant difference between rumen locations. Histological studies showed two orthogonal muscle layers in all regions except the reticulum, which has a more isotropic structure. A quasi-linear viscoelastic model was fitted to the relaxation stage for each region. Model predictions of the ramp stage had RMS errors of 13–24% and were within the range of the experimental data.

A physically-based, quasilinear viscoelasticity model for the dynamic response of polyurea

Polyurea, a promising material for damage mitigation in impact scenarios, has been investigated through plane-wave, pressure-shear plate impact (PSPI) experiments to obtain its mechanical response at high pressures and high strain rates. Based on these experimental results, a physically-based, quasi-linear, viscoelasticity model is introduced to capture the observed nonlinear pressure-volume behavior, the strong dependence of shearing resistance on pressure, and the strong relaxation of deviatoric stresses. This model has been implemented in finite element software ABAQUS to simulate the response of polyurea P1000 under the impact conditions of a variety of PSPI experiments. Simulation results agree reasonably well with those of the experiments.

Quasi-Linear Viscoelastic Model of the Articular Disc of the Temporomandibular Joint

A precise characterization of the articular disc of the temporomandibular joint (TMJ) is essential to study the masticatory biomechanics. The disc is responsible for the load distribution over the articular surface and for absorbing impacts during mastication. The main objective of this work is to characterize the mechanical behaviour of the articular disc under compression, the usual stress state during mastication. A quasi-linear viscoelastic (QLV) model, with a hyperelastic response for the elastic function, is proposed to describe the mechanical behaviour of the articular disc. The validity of that simplified model relies on the independence of their constants with the strain level and strain rate. The independence of the strain level was proved in a previous work. In this paper, different loading rates were tested to fully confirm the validity of the model in the physiological range of loads. Moreover, the strong non-linearity of the stress-strain relation made the exponential strain energy function the most suitable of the different models tried to represent the elastic response of the QLV model.

Numerical simulation of blood flow through a capillary using a non-linear viscoelastic model.

In this article, a periodic developing blood flow in a capillary is simulated using a non-linear viscoelastic model for the first time. Here, the Giesekus model is used as the constitutive equation, and based on the experimental data, the best value for the mobility factor and zero shear rate viscosity are derived. The numerical solution of the problem is obtained using the finite volume method. The algorithm of the solution is pressure implicit with splitting of operators (PISO). The simulation carried out using the Giesekus, Oldroyd-B and Newtonian models and the results indicate that the Giesekus model presents a more accurate solution for the stress and velocity fields than the Newtonian and Oldroyd-B models. The previous studies on this problem were restricted to the linear and quasi-linear viscoelastic models. It is shown that only non-linear viscoelastic models can accurately describe the experimental data of unsteady blood flow in capillaries.

A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials.

The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress-relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's 'box'-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress-relaxation data in an unbiased way. Our 'discrete QLV' (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress-relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.

Microstructural properties and mechanics vary between bundles of the human anterior cruciate ligament during stress-relaxation

Previous studies have shown different elastic properties between the anteromedial (AM) and posterolateral (PL) bundles of the human anterior cruciate ligament (ACL). However, it is unknown if the two bundles of the ACL exhibit distinct time-dependent properties and microstructural organization, which have important implications for fully understanding the structure-function relationships of this oft-injured ligament. The goal of this study was to quantify the viscoelastic material properties and collagen fiber alignment of the AM and PL bundles in 16 human ACLs during stress-relaxation mechanical tests using the quasi-linear viscoelastic (QLV) model and a quantitative polarization imaging technique. We hypothesized that the AM and PL bundles would exhibit differences in the instantaneous mechanical and organizational properties (i.e., immediately following a step increase in strain), but similar time-dependent changes during stress-relaxation. Results showed that AM samples exhibited larger peak/equilibrium stresses and less stress-relaxation during a 300-s hold compared to PL samples. The AM bundle demonstrated stronger and more uniform collagen fiber alignment (i.e., higher degree of linear polarization (DoLP) values and less distributed angle of polarization (AoP) values) compared to the PL bundle, and larger changes in alignment strength during the hold. Results suggest that the AM bundle is the more “dominant” bundle, with significantly different mechanical and material properties in stress-relaxation. While more research is needed to better understand how these findings relate to the pathophysiology of ACL tears and can best guide treatment, the findings provide additional insight into the microstructural properties and biomechanics of the human ACL.

Impact problem for the quasi-linear viscoelastic standard solid model

The one-dimensional impact problem in the case of Fung’s quasi-linear viscoelastic model is studied for the relaxation function of the standard solid model (or Zener model). Additionally, quasi-linear viscoelastic Maxwell and Kelvin–Voigt models are recovered as limit cases. The results of numerical simulations for some illustrative values of the dimensionless problem parameters are presented. The obtained results can be of interest for biomedical testing.

Overview of the DAEDALOS project

The “Dynamics in Aircraft Engineering Design and Analysis for Light Optimized Structures” (DAEDALOS) project aimed to develop methods and procedures to determine dynamic loads by considering the effects of dynamic buckling, material damping and mechanical hysteresis during aircraft service. Advanced analysis and design principles were assessed with the scope of partly removing the uncertainty and the conservatism of today's design and certification procedures. To reach these objectives a DAEDALOS aircraft model representing a mid-size business jet was developed. Analysis and in-depth investigation of the dynamic response were carried out on full finite element models and on hybrid models. Material damping was experimentally evaluated, and different methods for damping evaluation were developed, implemented in finite element codes and experimentally validated. They include a strain energy method, a quasi-linear viscoelastic material model, and a generalized Maxwell viscous material damping. Panels and shells representative of typical components of the DAEDALOS aircraft model were experimentally tested subjected to static as well as dynamic loads. Composite and metallic components of the aircraft model were investigated to evaluate the benefit in terms of weight saving.

The impact of rotator cuff deficiency on structure, mechanical properties, and gene expression profiles of the long head of the biceps tendon (LHBT): Implications for management of the LHBT during primary shoulder arthroplasty.

The long head of the biceps tendon (LHBT) occupies a unique proximal intra-articular and distal extra-articular position within the human shoulder. In the presence of a rotator cuff (RC) tear, the LHBT is recruited into an accelerated role undergoing potential mechanical and biochemical degeneration. Intra-articular sections of the LHBT were harvested during primary shoulder arthroplasty from patients with an intact or deficient RC. LHBTs were stained (H&E, Alcian Blue) and subjected to histologic analysis using the semiquantitative Bonar scale and measurement of collagen orientation. LHBTs (n = 12 per group) were also subjected to gene-expression analyses via an RT(2) -PCR Profiler Array quantifying 84 genes associated with cell-cell and cell-matrix interactions. LHBTs (n = 18 per group) were biomechanically tested with both stress-relaxation and load-to-failure protocols and subsequently modeled with the Quasilinear Viscoelastic (QLV) and Structural-Based Elastic (SBE) models. While no histologic differences were observed, significant differences in mechanical testing, and viscoelastic modeling parameters were found. PCR arrays identified five genes that were differentially expressed between RC-intact and RC-deficient LHBT groups. LHBTs display signs of pathology regardless of RC status in the arthroplasty population, which may be secondary to both glenohumeral joint arthritis and the additional mechanical role of the LHBT in this population.

On application of Fung's quasi-linear viscoelastic model to modeling of impact experiment for articular cartilage

A one-dimensional impact problem for articular cartilage is considered. Behavior of the coefficient of restitution, peak strain, maximum stress in the drop-weight impact experiment is studied in detail. The non-linear viscoelastic Hunt–Crossley model previously used to fit experimental data is compared with a new quasi-linear viscoelastic Kelvin–Voigt model enriched in Fung's non-linear assumptions. It has been shown that the new model, having clear physical sense, better describes the experimental data.

Measurement of the viscoelastic mechanical properties of the skin tissue under uniaxial loading

Skin as an external membrane has a key asset in the human body, i.e. heat balance and protection from the peripheral mechanical loads. The mechanical properties of the skin tissue are almost intricate under various loading conditions that may also differ according to the anatomical locations of a body. Although the mechanical properties of the skin tissue have been largely studied using different testing methods as well as different material models, the time-dependent viscoelastic mechanical behavior of the skin in different anatomical regions has not been quantified via the Quasi-linear viscoelastic model. In this study, the quasi-linear viscoelastic mechanical properties of the rat back and abdomen skins were computed under uniaxial loading. The relaxation test was carried out on the back and abdomen of eight rats and afterward the quasi-linear viscoelastic coefficients were calculated by fitting the quasi-linear viscoelastic model to the experimental stress–relaxation data. The results revealed that the peak stress in the abdomen skin samples is slightly higher than that of the back ones. Besides, the stress reached to a balance in 100 s for both the back and abdomen skin tissues in tension. The findings of this study may have implications not only for understanding the viscoelastic time-dependent mechanical behavior of the back and abdomen skin tissues but also to give a biomechanical awareness in a variety of areas such as tissue engineering, dermatology, and cosmetics industry.

Characterisation and modelling of brain tissue for surgical simulation

Interactive surgical simulators capable of providing a realistic visual and haptic feedback to users are a promising technology for medical training and surgery planification. However, modelling the physical behaviour of human organs and tissues for surgery simulation remains a challenge. On the one hand, this is due to the difficulty to characterise the physical properties of biological soft tissues. On the other hand, the challenge still remains in the computation time requirements of real-time simulation required in interactive systems. Real-time surgical simulation and medical training must employ a sufficiently accurate and simple model of soft tissues in order to provide a realistic haptic and visual response.This study attempts to characterise the brain tissue at similar conditions to those that take place on surgical procedures. With this aim, porcine brain tissue is characterised, as a surrogate of human brain, on a rotational rheometer at low strain rates and large strains. In order to model the brain tissue with an adequate level of accuracy and simplicity, linear elastic, hyperelastic and quasi-linear viscoelastic models are defined. These models are simulated using the ABAQUS finite element platform and compared with the obtained experimental data.

A nonlinear integral model for describing responses of viscoelastic solids

In this paper we develop a model as well as carry out experiments to test the efficacy of the model, for a class of non-aging isotropic viscoelastic solids. We fashion a nonlinear integral model, which belongs to the class of quasi-linear viscoelastic models, for solid-like materials, which upon linearization reduces to a linear viscoelastic model. The model is defined by separating the normalized time function and nonlinear stress measure that describes the elastic response of the materials. In the case of isotropic materials we consider two independent normalized time functions and two nonlinear stress measures, which are expressed in terms of the stress invariants I1 and I2. We discuss the methodology of the material parameter characterization based on the experimental data available for polyoxymethylene (POM) under quasi-static ramp with constant rate and creep loadings. The response predicted by the nonlinear integral model calibrated by the material parameters obtained through data reduction is then tested against other experimental data under various loading histories. The nonlinear viscoelastic model is capable of capturing the three-dimensional response of POM polymers under various histories of inputs both under stress and strain controlled loadings. Finally we present solutions to boundary value problems (BVPs) of a concentric cylinder made of POM under internal pressure in order to demonstrate one of the applications in which POM is used. The design of structural elements made of POM can be undertaken by using models of the class developed in this work.