Efficient and optimized identification of generalized Maxwell viscoelastic relaxation spectra

Viscoelastic relaxation spectra are essential for predicting and interpreting the mechanical responses of materials and structures. For biological tissues, these spectra must usually be estimated from viscoelastic relaxation tests. Interpreting viscoelastic relaxation tests is challenging because the inverse problem is expensive computationally. We present here an efficient algorithm that enables rapid identification of viscoelastic relaxation spectra. The algorithm was tested against trial data to characterize its robustness and identify its limitations and strengths. The algorithm was then applied to identify the viscoelastic response of reconstituted collagen, revealing an extensive distribution of viscoelastic time constants.

Sub-cellular force microscopy in single normal and cancer cells

This work investigates the biomechanical properties of sub-cellular structures of breast cells using atomic force microscopy (AFM). The cells are modeled as a triple-layered structure where the Generalized Maxwell model is applied to experimental data from AFM stress-relaxation tests to extract the elastic modulus, the apparent viscosity, and the relaxation time of sub-cellular structures. The triple-layered modeling results allow for determination and comparison of the biomechanical properties of the three major sub-cellular structures between normal and cancerous cells: the up plasma membrane/actin cortex, the mid cytoplasm/nucleus, and the low nuclear/integrin sub-domains. The results reveal that the sub-domains become stiffer and significantly more viscous with depth, regardless of cell type. In addition, there is a decreasing trend in the average elastic modulus and apparent viscosity of the all corresponding sub-cellular structures from normal to cancerous cells, which becomes most remarkable in the deeper sub-domain. The presented modeling in this work constitutes a unique AFM-based experimental framework to study the biomechanics of sub-cellular structures.

Pulsatile flow of non-Newtonian blood fluid inside stenosed arteries: Investigating the effects of viscoelastic and elastic walls, arteriosclerosis, and polycythemia diseases

BACKGROUND AND OBJECTIVE

In this study, the interaction of pulsatile blood flow with the viscoelastic walls of the axisymmetric artery is numerically investigated for different severities of stenosis. The geometry of artery is modeled by an axisymmetric cylindrical tube with a symmetric stenosis in a two-dimensional case. The effects of stenosis severity on the axial velocity profile, pressure distribution, streamlines, wall shear stress, and wall radial displacement for the viscoelastic artery are also compared to the elastics artery. Furthermore, the effects of atherosclerosis and polycythemia diseases on the hemodynamics and the mechanical behavior of arterial walls are investigated.

METHODS

The pulsatile flow of non-Newtonian blood is simulated inside the viscoelastic artery using the COMSOL Multiphysics software (version 5) and by employing the fluid-structure interaction (FSI) method and the arbitrary Lagrangian-Eulerian (ALE) method. Moreover, finite element method (FEM) is used to solve the governing equations on the unstructured grids. For modeling the non-Newtonian blood fluid and the viscoelastic arterial wall, the modified Casson model, and generalized Maxwell model are used, respectively.

RESULTS

According to the results, with stenosis severity increasing from 25% to 75% at the time of maximum volumetric flow rate, the maximum value of axial velocity and its gradient increase 7.9 and 19.6 times, and the maximum wall shear stress of viscoelastic wall increases 24.2 times in the constriction zone. With the progression of the atherosclerosis disease (fivefold growth of arterial elastic modulus), the wall radial displacement of viscoelastic arterial walls decreases nearly 40%.

CONCLUSIONS

In this study, axial velocity profile, pressure distribution, streamlines, wall radial displacement, and wall shear stress were examined for different percentages of stenosis (25%, 50%, and 75%). The atherosclerosis disease was investigated by the fivefold growth of viscoelastic arterial elastic modulus and polycythemia disease was examined by the 21-fold increase in the yield stress of the blood fluid. Furthermore, the comparison of results between the elastic and viscoelastic arterial walls shows that the wall radial displacement for viscoelastic artery is lower than that for the elastic artery as much as 21.7% for the severe stenosis of 75%.

Slow viscoelastic response of resilin

The high importance of resilin in invertebrate biomechanics is widely known. It is generally assumed to be an almost perfect elastomer in different tissues. Whereas mechanical properties of resilin were previously determined mainly in tension, here we aimed at studying its mechanical properties in compression. Microindentation of resilin from the wing hinge of Locusta migratoria revealed the clear viscoelastic response of resilin: about a quarter of the mechanical response was assigned to a viscous component in our experiments. Mechanical properties were characterized using a generalized Maxwell model with two characteristic time constants, poroelasticity theory, and alternatively using a 1D model with just one characteristic time constant. Slow viscous responses with 1.7 and 16 s characteristic times were observed during indentation. These results demonstrate that the locust flight system is adapted to both fast and slow mechanical processes. The fast highly elastic process is related to the flight function and the slow viscoelastic process may be related to the wing folding.

Tuning Viscoelasticity with Minor Changes in Speed of Sound in an Ultrasound Phantom Material

The acoustic properties of ultrasound phantom materials have always been important, but with new applications interrogating tissue mechanical properties, viscoelasticity has also become an interesting feature to consider. Along with Young's modulus, the viscous component of tissue is affected by certain diseases and can therefore be used as a biomarker. Furthermore, viscoelasticity varies between tissue types and individuals, and therefore it would be useful with a phantom material that reflects this physiological range. Here we describe a gel for ultrasound imaging with a range of mechanical properties given by mixing different ratios of two oil-based gels, clear ballistic and styrene-ethylene/butylene-styrene (SEBS). The gels were mixed in five different proportions, ranging from 0-100% of either gel. For each of the gel compositions, we measured time of flight to determine speed of sound, narrowband ultrasound transmission for attenuation, stress-relaxation for viscoelasticity, mass and volume. Analysis of the stress-relaxation data using the generalized Maxwell model suggests that the material can be described by five parameters, E₀, E₁, E₂, η₁ and η₂, and that each of these parameters decreases as more SEBS is incorporated into the mixed material. Instantaneous Young's modulus (the sum of E₀, E₁ and E₂ in our model) ranges between 49 and 117 kPa for the different ratios, similar to values reported for cancerous tissue. Despite the large span of obtainable mechanical properties, speed of sound is relatively constant regardless of composition, with mean value estimates (± 95 % CI) between 1438 ± 9 and 1455 ± 3 m/s for pure and mixed gels. This was attributed to a variation in density and Poisson's ratio, following from the relation linking them to speed of sound and elasticity. Furthermore, both speed of sound and attenuation were within a suitable range for ultrasound phantoms. Combining this ballistic gel with SEBS copolymer in oil allows for control of mechanical properties, both elastic and viscous as evaluated by the material model. Furthermore, it does so without compromising ease of use, longevity and safety of the pre-made gel.

On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

Atomic force microscopy (AFM) is a widely use technique to acquire topographical, mechanical, or electromagnetic properties of surfaces, as well as to induce surface modifications at the micrometer and nanometer scale. Viscoelastic materials, examples of which include many polymers and biological materials, are an important class of systems, the mechanical response of which depends on the rate of application of the stresses imparted by the AFM tip. The mechanical response of these materials thus depends strongly on the frequency at which the characterization is performed, so much so that important aspects of behavior may be missed if one chooses an arbitrary characterization frequency regardless of the materials properties. In this paper we present a linear viscoelastic analysis of intermittent-contact, nearly resonant dynamic AFM characterization of such materials, considering the possibility of multiple characteristic times. We describe some of the intricacies observed in their mechanical response and alert the reader about situations where mischaracterization may occur as a result of probing the material at frequency ranges or with probes that preclude observation of its viscoelastic behavior. While we do not offer a solution to the formidable problem of inverting the frequency-dependent viscoelastic behavior of a material from dynamic AFM observables, we suggest that a partial solution is offered by recently developed quasi-static force-distance characterization techniques, which incorporate viscoelastic models with multiple characteristic times and can help inform dynamic AFM characterization.

Theoretical stress mechanism and structural integrity of viscoelastic propellant grains with variable Poisson's ratio

For the propellant grain of solid rocket motors (SRMs) with circular inner surfaces, the generalized Maxwell model (GMM) and the generalized Kelvin-Voigt model (GKV) are used to characterize the relaxation properties of the grain's elastic modulus and the creep properties of Poisson's ratio, respectively. Based on the elastic-viscoelastic correspondence principle, an analytical expression for viscoelastic stress that simultaneously considers the time-dependent nature of elastic modulus and Poisson's ratio is derived. Based on this, a parametric analysis of the stress distribution in the grain under internal pressure is conducted. The results indicate that the hoop stress on the inner surface of the grain is most critical at the beginning of loading. As the thickness of the propellant grain increases, this initial tensile stress decreases moderately, but the duration of tensile stress increases. Increasing the thickness or stiffness of the combustion chamber casing moderately reduces the hoop stress during the initial loading and shortens the duration of tensile stress. Accurate measurement of the creep properties of Poisson's ratio has a significant impact on improving calculation accuracy. The stress calculation results under gradual pressurization are lower than those under instantaneous pressurization. The conclusions provide a reference for analyzing the structural integrity of propellant grains.

Effect of Micellar Shape on Viscoelastic Behavior and Gel Network Structure of Hydrogel Formed by Surfactant-mediated Gelation Using Glutamic-acid-based Organogelator

Surfactant-mediated gelation (SMG) is a technique used to form hydrogels by solubilizing water-insoluble low-molecular-weight organogelators in surfactant micelles. In this study, we investigated the viscoelastic behavior of SMG hydrogels and the effect of micellar shape on their gel network structure using a glutamic acid-based organogelator. Stress-strain curves obtained from static viscoelasticity measurements showed that a wormlike micelle-mediated gel (W-SMG) exhibited a higher stress than a spherical micelle-mediated gel (S-SMG). From the viscosity-shear rate curve (flow curve), we inferred that the SMG gel exhibited a shear thickening behavior, particularly W-SMG. Microscopic observations revealed that W-SMG formed a denser and more uniform gel network than S-SMG when subjected to strong shearing. W-SMG showed remarkable adhesiveness and a significantly higher tensile normal stress than S-SMG. The storage modulus and loss modulus of W-SMG and the wormlike micellar solution obtained from frequency sweep measurements of the dynamic viscoelasticity were analyzed by Maxwell fitting. The wormlike micellar solution produced a good fit with the single Maxwell model, whereas W-SMG produced the best fit with the generalized Maxwell model comprising two Maxwell elements. From the relaxation time characteristics obtained from the Maxwell model, W-SMG was found to be a viscoelastic material coexisting with a structure having a short relaxation time derived from the gel network and a long relaxation time derived from the wormlike micelle. Under the oscillation strain measured by a rheometer, W-SMG showed a greater normal stress than the wormlike micellar solution, indicating a significant Weissenberg effect.