Local Viscoelastic Properties Research Articles

Dynamics of Hybrid Poly(acrylamide-co-N,N-dimethylacrylamide) Hydrogels Containing Silica Nanoparticles Studied by Dynamic Light Scattering

Nanohybrid gels based on poly(acrylamide-co-N,N-dimethylacrylamide), P(AAm-co-DMA), and colloidal silica nanoparticles were synthesized by radical polymerization, and the influence of hydrogen bonding between DMA and silica nanoparticles on the dynamics of the network and the nanoparticles were studied by dynamic light scattering. As previously reported, in the case of polyacrylamide homopolymer, PAAm, which have no hydrogen bonding with silica, we observed two decay modes in the hybrid gels, a gel mode and a Brownian diffusion mode of silica nanoparticles. When we increased the DMA weight fraction (or physical cross-link density), we observed (1) a higher scattered light intensity than the silica suspension and the gel without silica, (2) an increased plateau value of the autocorrelation function, (3) a slowing down of the silica diffusion mode, and (4) no influence on the gel mode. These results, compared with those of the mixtures of the linear PDMA and silica nanoparticles in solution (showing an increase in the scattered light intensity and in the hydrodynamic radius), indicate that the P(AAm-co-DMA) hybrid gels have a more heterogeneous structure due to the adsorption of the polymer on the silica nanoparticles, and that the silica nanoparticles, trapped in the network due to the adsorption of the polymer, show a cage dynamics in the network. The local viscoelastic properties probed by the bound nanoparticles are discussed.

Localization of Viscous Behavior and Shear Energy Dissipation in Articular Cartilage Under Dynamic Shear Loading

Though remarkably robust, articular cartilage becomes susceptible to damage at high loading rates, particularly under shear. While several studies have measured the local static and steady-state shear properties of cartilage, it is the local viscoelastic properties that determine the tissue's ability to withstand physiological loading regimens. However, measuring local viscoelastic properties requires overcoming technical challenges that include resolving strain fields in both space and time and accurately calculating their phase offsets. This study combined recently developed high-speed confocal imaging techniques with three approaches for analyzing time- and location-dependent mechanical data to measure the depth-dependent dynamic modulus and phase angles of articular cartilage. For sinusoidal shear at frequencies f = 0.01 to 1 Hz with no strain offset, the dynamic shear modulus |G*| and phase angle δ reached their minimum and maximum values (respectively) approximately 100 μm below the articular surface, resulting in a profound focusing of energy dissipation in this narrow band of tissue that increased with frequency. This region, known as the transitional zone, was previously thought to simply connect surface and deeper tissue regions. Within 250 μm of the articular surface, |G*| increased from 0.32 ± 0.08 to 0.42 ± 0.08 MPa across the five frequencies tested, while δ decreased from 12 deg ± 1 deg to 9.1 deg ± 0.5 deg. Deeper into the tissue, |G*| increased from 1.5 ± 0.4 MPa to 2.1 ± 0.6 MPa and δ decreased from 13 deg ± 1 deg to 5.5 deg ± 0.2 deg. Viscoelastic properties were also strain-dependent, with localized energy dissipation suppressed at higher shear strain offsets. These results suggest a critical role for the transitional zone in dissipating energy, representing a possible shift in our understanding of cartilage mechanical function. Further, they give insight into how focal degeneration and mechanical trauma could lead to sustained damage in this tissue.

Studying Single Red Blood Cells Under a Tunable External Force by Combining Passive Microrheology with Raman Spectroscopy

The dynamic micromechanical and structural properties of single human red blood cells are studied using a combination of dual trap optical tweezers and confocal Raman spectroscopy. Such a combination permits us to show a direct relationship between the rheological properties and chemical structure conformation. The frequency dependence of the complex stiffness of the cells was measured using both one and two probe response functions under identical experimental conditions. Both the microrheology and Raman measurements were performed at different stretching forces applied to the cell. A detailed analysis of the auto- and cross-correlated probe motions allows exploring the local and overall viscoelastic properties of the cells over a controlled range of the deformations. The observed growth of the cell viscoelasticity with stretching was associated with structural changes in the cell membrane monitored via the Raman spectroscopy.

Force measurements on cargoes in living cells reveal collective dynamics of microtubule motors

Many cellular cargoes move bidirectionally along microtubules, driven by teams of plus- and minus-end-directed motor proteins. To probe the forces exerted on cargoes during intracellular transport, we examined latex beads phagocytosed into living mammalian macrophages. These latex bead compartments (LBCs) are encased in membrane and transported along the cytoskeleton by a complement of endogenous kinesin-1, kinesin-2, and dynein motors. The size and refractive index of LBCs makes them well-suited for manipulation with an optical trap. We developed methods that provide in situ calibration of the optical trap in the complex cellular environment, taking into account any variations among cargoes and local viscoelastic properties of the cytoplasm. We found that centrally and peripherally directed forces exerted on LBCs are of similar magnitude, with maximum forces of ~20 pN. During force events greater than 10 pN, we often observe 8-nm steps in both directions, indicating that the stepping of multiple motors is correlated. These observations suggest bidirectional transport of LBCs is driven by opposing teams of stably bound motors that operate near force balance.

Estimating the local viscoelastic properties from dispersive shear waves using time–frequency ridge analysis

Modulated low-frequency shear waves can be non-invasively generated locally within a medium, by the oscillatory acoustic radiation force resulting from the interference of two focused quasi-CW ultrasound beams of slightly different frequencies. The propagation of such shear waves within a viscoelastic medium is known to be affected by the dispersive effects of viscosity. Specifically, a low-frequency (LF) spectral component was shown to arise with increased viscosities and higher modulation frequencies and appear as a ‘slow’ wave at the end of the shear waveform. In this paper, the shear dispersion characteristics are studied based on the Pseudo–Wigner–Ville distribution (PWVD) in the time–frequency domain. The ridges of the PWVD are then extracted and used to calculate the frequency-dependent shear speed, by identifying the LF dispersive component both in time and frequency. Using numerical simulations, it is shown that this way of estimating the shear dispersion is more efficient and robust than the conventional phase-delay Fourier method. Thus, more accurate estimates of the local shear modulus and viscosity of the propagating medium could be achieved. The effects of noise on the proposed method are also discussed.

Microscopic heterogeneity in viscoelastic properties of molecular assembled systems

An important step in understanding molecular assembled systems is to examine the structure and physical properties at various length scales and clarify the correlation between them. However, while the structures of these systems have been extensively studied from nanoscopic to macroscopic scales, their viscoelastic properties have been often limited to bulk rheological measurements. By using optical tweezers and particle tracking, we here show the local viscoelastic properties and their spatial distributions for the following systems: worm-like micelle solution, supramolecular hydrogel and lyotropic liquid crystal, which are formed by self-assembly of amphiphilic molecules in water. We found that all systems studied possessed a spatial heterogeneity in their viscoelastic properties and this was originated from the heterogeneous structures. It is interesting to note that there is the heterogeneity with the characteristic length scale of sub-micrometer or micrometer scale, thereby structures, although the systems are formed by molecules with nanometer size. The findings of these studies should lead to a better understanding of the dynamics of such systems.

Characterization of Changes to the Mechanical Properties of Arteries due to Cold Storage Using Nanoindentation Tests

Understanding the effect of cold storage on arterial tissues is essential in various clinical and experimental practices. Cold storage techniques could significantly affect the post-cryosurgical or post-cryopreservation mechanical behavior of arteries. Previously, arteries were considered homogenous and elastic and the changes in material properties due to cold storage were inconclusive. In this study, using a custom-made nanoindentation device, changes to the local viscoelastic properties of porcine thoracic aorta wall due to three common storage temperatures (+4, -20, and -80 °C) within 24 h, 48 h, 1 week, and 3 weeks were characterized. The changes to both elastic and relaxation behaviors were investigated considering the multilayer, heterogeneous nature of the aortic wall. The results showed that the average instantaneous Young's modulus (E) of +4 °C storage samples decreased while their permanent average relaxation amplitude (G (∞)) increased and after 48 h these changes became significant (10 and 13% for E and G (∞), respectively). Generally, in freezer storage, E increased and G (∞) showed no significant change. In prolonged preservation (>1 week), the results of -20 °C showed significant increase in E (20% after 3 weeks) while this increase for -80 °C was not significant, making it a better choice for tissue cold storage applications.

Viscoelasticity of pore-spanning polymer membranes derived from giant polymersomes

We show how the viscoelastic properties of membranes formed from poly(butadiene)-block-poly(ethylene oxide) (PB130-b-PEO66) block copolymers can be locally accessed by atomic force microscopy. Polymer membranes are spread on microstructured porous silicon substrates from PB130-b-PEO66 vesicles by decreasing the osmotic pressure of the solution. Local viscoelastic properties of the pore-spanning polymer membranes were obtained from site-specific indentation experiments. Elastic moduli of these membranes were in the order of few MPa, while the elastic moduli of cross-linked membranes considerably increased to few GPa. Furthermore, the energy dissipation and velocity dependence of the hysteresis between indentation and relaxation were quantified and compared with a modified Kelvin–Voigt model. Relaxation times were in the order of hundreds of milliseconds explaining why the stiffness of the membrane increases with increasing indentation velocity.

レーザーパーティクルトラッキング法を用いた動的粘弾性測定装置の製作

An apparatus for dynamic viscoelasticity measurements was developed using laser particle tracking method (LPT). LPT measures the position of micron-sized probe particles embedded in the material. The power spectrum density (PSD) is calculated from the displacement of the probe particle due to Brownian motion, and then the complex modulus is determined from PSD. This method is useful for studying viscoelastic properties at high frequency region in addition to investigating local viscoelastic properties of materials. The apparatus was calibrated with pure water and ethyleneglycol. The complex shear modulus for aqueous solution of wormlike micelles in high frequency regime was measured. The complex shear modulus obtained by LPT showed a good agreement with the results obtained by a conventional rheometer and the flow birefringence measurement, indicating the reliability of the apparatus.

Structural and micromechanical characterization of type I collagen gels

In this paper we report a study where we use a novel optical tweezers technique to measure the local viscoelastic properties of type I collagen solutions spanning the sol-to-gel transition. We use phase contrast optical microscopy to reveal dense and sparse regions of the rigid fibril networks, and find that the spatial variations in the mechanical properties of the collagen gels closely follow the structural properties. Within the dense phase of the connected network in the gel samples, there are regions that exhibit drastically different viscoelastic properties. Within the sparse regions of the gel samples, no evidence of elasticity is found. In type I collagen gels, we find a high degree of structural inhomogeneity. The inhomogeneity in the structural properties of collagen gels and the corresponding viscoelastic properties provide benchmark measurements for the behavior of desirable biological materials, or tissue equivalents.

In Situ Characterization of Differences in the Viscoelastic Response of Individual Gram-Negative and Gram-Positive Bacterial Cells

We used a novel atomic force microscopy (AFM)-based technique to compare the local viscoelastic properties of individual gram-negative (Escherichia coli) and gram-positive (Bacillus subtilis) bacterial cells. We found that the viscoelastic properties of the bacterial cells are well described by a three-component mechanical model that combines an instantaneous elastic response and a delayed elastic response. These experiments have allowed us to investigate the relationship between the viscoelastic properties and the structure and composition of the cell envelope. In addition, this is the first report in which the mechanical role of Lpp, the major peptidoglycan-associated lipoprotein and one of the most abundant outer membrane proteins in E. coli cells, has been quantified. We expect that our findings will be helpful in increasing the understanding of the structure-property relationships of bacterial cell envelopes.

Particle tracking microrheology of gel-forming amyloid fibril networks

Microrheology is a technique that is increasingly used to investigate the local viscoelastic properties of complex fluids non-invasively, by tracking the motion of micron-sized probe spheres. In this work, passive Particle Tracking Microrheology (PTM) is used to study network formation in the milk protein beta-lactoglobulin at 80 degrees C and pH 2. In these conditions the protein aggregates to form thread-like structures known as amyloid fibrils, which can further aggregate into elastic networks. Using PTM, gels were observed to form at significantly lower concentrations than determined by bulk rheometry, where the oscillatory shear forces may disrupt either fibril or network formation. During incubation, the Mean Square Displacement (MSD) of the probe particles exhibited time-cure superposition, allowing the critical relaxation exponent to be calculated as approximately 0.63, consistent with other biopolymer gels. Combined with the gel-like appearance of the complex modulus at long incubation times, this confirms that a true gel is forming, with physical or chemical crosslinks forming between the fibrils, refining the conclusions of other workers in the field.

Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography

The emergence of ultrafast frame rates in ultrasonic imaging has been recently made possible by the development of new imaging modalities such as transient elastography. Data acquisition rates reaching more than thousands of images per second enable the real-time visualization of shear mechanical waves propagating in biological tissues, which convey information about local viscoelastic properties of tissues. The first proposed approach for reaching such ultrafast frame rates consists of transmitting plane waves into the medium. However, because the beamforming process is then restricted to the receive mode, the echographic images obtained in the ultrafast mode suffer from a low quality in terms of resolution and contrast and affect the robustness of the transient elastography mode. It is here proposed to improve the beamforming process by using a coherent recombination of compounded plane-wave transmissions to recover high-quality echographic images without degrading the high frame rate capabilities. A theoretical model is derived for the comparison between the proposed method and the conventional B-mode imaging in terms of contrast, signal-to-noise ratio, and resolution. Our model predicts that a significantly smaller number of insonifications, 10 times lower, is sufficient to reach an image quality comparable to conventional B-mode. Theoretical predictions are confirmed by in vitro experiments performed in tissue-mimicking phantoms. Such results raise the appeal of coherent compounds for use with standard imaging modes such as B-mode or color flow. Moreover, in the context of transient elastography, ultrafast frame rates can be preserved while increasing the image quality compared with flat insonifications. Improvements on the transient elastography mode are presented and discussed.

Effects of Static and Dynamic Forces on Surface Viscoelastic Response of Polymer Films in Scanning Viscoelasticity Microscopy

Scanning force microscopy with force-modulation mode enables one to gain direct insights into local viscoelastic properties at polymer surfaces. Changing modulation condition such as dynamic amplitude and frequency in addition to static normal force, surface viscoelastic response of polystyrene (PS) film was studied. If dynamic and/or static forces were/was ill-chosen, non-linearity of viscoelastic response became dominant, resulting in hole formation at the surface. On the contrary, if they were appropriately adjusted, linear viscoelastic measurement could be realized in the frequency range from 10 Hz to 4 kHz. This leads to traditional rheological analysis even at the surface.

Bubble-based acoustic radiation force using chirp insonation to reduce standing wave effects

Bubble-based acoustic radiation force can measure local viscoelastic properties of tissue. High intensity acoustic waves applied to laser-generated bubbles induce displacements inversely proportional to local Young’s modulus. In certain instances, long pulse durations are desirable but are susceptible to standing wave artifacts, which corrupt displacement measurements. Chirp pulse acoustic radiation force was investigated as a method to reduce standing wave artifacts. Chirp pulses with linear frequency sweep magnitudes of 100, 200 and 300 kHz centered around 1.5 MHz were applied to glass beads within gelatin phantoms and laser-generated bubbles within porcine lenses. The ultrasound transducer was translated axially to vary standing wave conditions, while comparing displacements using chirp pulses and 1.5 MHz tone burst pulses of the same duration and peak rarefactional pressure. Results demonstrated significant reduction in standing wave effects using chirp pulses, with displacement proportional to acoustic intensity and bubble size. (E-mail: terpeldi@umich.edu)

Probing Single-Cell Micromechanics In Vivo: The Microrheology of C. elegans Developing Embryos

Cells are not directly accessible in vivo and therefore their mechanical properties cannot be measured by methods that require a direct contact between probe and cell. Here, we introduce a novel in vivo assay based on particle tracking microrheology whereby the extent and time-lag dependence of the mean squared displacements of thermally excited nanoparticles embedded within the cytoplasm of developing embryos reflect local viscoelastic properties. As a proof of principle, we probe local viscoelastic properties of the cytoplasm of developing Caenorhabditis elegans embryos. Our results indicate that unlike differentiated cells, the cytoplasm of these embryos does not exhibit measurable elasticity, but is highly viscous. Furthermore, the viscosity of the cytoplasm does not vary along the anterior-posterior axis of the embryo during the first cell division. These results support the hypothesis that the asymmetric positioning of the mitotic spindle stems from an asymmetric distribution of elementary force generators as opposed to asymmetric viscosity of the cytoplasm.

Measuring local viscoelastic properties of complex materials with tapping mode atomic force microscopy

Tapping mode atomic force microscopy is a technique to measure the topography and properties of surfaces involving a micro-cantilever with a tip at one end that is excited into an oscillation near its resonance frequency. The phase lag between the excitation signal and the observed oscillation is sensitive to local mechanical properties under certain experimental conditions. We have found that by using silicon as an internal standard reference surface we can unambiguously relate the phase lag to local viscoelastic properties of a polymeric material. A model describing this relation has been built, validated with experimental data and finally inverted such that it can be used to determine local properties. This allows us to measure high frequency local viscoelastic properties on length scales as small as several nanometers. This technique works well for relatively compliant polymer surfaces with a shear modulus less than about 1GPa.

Linear and Nonlinear Viscoelasticity of a Model Unentangled Polymer Melt: Molecular Dynamics and Rouse Modes Analysis

AbstractSummary: Using molecular dynamics simulations, we determine the linear and nonlinear viscoelastic properties of a model polymer melt in the unentangled regime. Several approaches are compared for the computation of linear moduli and viscosity, including Green‐Kubo and nonequilibrium molecular dynamics (NEMD). An alternative approach, based on the use of the Rouse modes, is also discussed. This approach could be used to assess local viscoelastic properties in inhomogeneous systems. We also focus on the contributions of different interactions to the viscoelastic moduli and explain the microscopic mechanisms involved in the mechanical response of the melt to external solicitation. magnified image

Local Dynamics and Viscoelastic Properties of Vulcanisates Based on Butadiene–acrylonitrile Rubbers

Local Dynamics and Viscoelastic Properties of Vulcanisates Based on Butadiene–acrylonitrile Rubbers

Cell Motility and Local Viscoelasticity of Fibroblasts

Viscoelastic changes of the lamellipodial actin cytoskeleton are a fundamental element of cell motility. Thus, the correlation between the local viscoelastic properties of the lamellipodium (including the transitional region to the cell body) and the speed of lamellipodial extension is studied for normal and malignantly transformed fibroblasts. Using our atomic force microscopy-based microrheology technique, we found different mechanical properties between the lamellipodia of malignantly transformed fibroblasts (H-ras transformed and SV-T2 fibroblasts) and normal fibroblasts (BALB 3T3 fibroblasts). The average elastic constants, K, in the leading edge of SV-T2 fibroblasts (0.48 ± 0.51 kPa) and of H-ras transformed fibroblasts (0.42 ± 0.35 kPa) are significantly lower than that of BALB 3T3 fibroblasts (1.01 ± 0.40 kPa). The analysis of time-lapse phase contrast images shows that the decrease in the elastic constant, K, for malignantly transformed fibroblasts is correlated with the enhanced motility of the lamellipodium. The measured mean speeds are 6.1 ± 4.5 μ m/h for BALB 3T3 fibroblasts, 13.1 ± 5.2 μm/h for SV-T2 fibroblasts, and 26.2 ± 11.5 μm/h for H-ras fibroblasts. Furthermore, the elastic constant, K, increases toward the cell body in many instances which coincide with an increase in actin filament density toward the cell body. The correlation between the enhanced motility and the decrease in viscoelastic moduli supports the Elastic Brownian Ratchet model for driving lamellipodia extension.