Sinusoidal Strain Research Articles

Characterization of the Flexcell™ Uniflex™ cyclic strain culture system with U937 macrophage-like cells

Mechanical forces alter many cell functions in a variety of cell types. It has been recognized that stimulation of cells in culture may be more representative of some physiologic conditions. Although there are commercially available systems for the study of cells cultured in a mechanical environment, very little has been documented on the validation techniques for these devices. In this study, Flexcell's™ recently introduced Uniflex™ cyclic strain system was programmed to apply 10% longitudinal sinusoidal strain (0.25 Hz) for 48 h to U937 cells cultured on Uniflex™ plates. Image analysis was employed to characterize the actual strain field. For a chosen amplitude of 10% the applied strain was highly reproducible and relatively uniform (10.6±0.2%) in a central rectangular region of the membrane (dimensions of 9.2±2×13.6±0.8 mm 2). The strain increased the release of IL-6, esterase and acid phosphatase activity ( p<0.05) from adherent U937 cells. Cells also displayed altered morphology, aligning and lengthening with the direction of strain, whereas static cells maintained a round appearance showing no preferred orientation. These data indicate that cyclic mechanical strain applied by the Uniflex™ strain system modulates U937 cell function leading to selective increases in enzymatic activities as well as orientation in a favored direction.

A comparison of some models for describing polymer crystallization at low deformation rates

There is now in the literature a number of mathematical models of the effects of flow on crystallization of polymers, and here we compare the performance of various models in slow simple shearing and sinusoidal strain (oscillatory) flows. We compare the model predictions to the experiments of Wassner and Maier [E. Wassner, R.-D. Maier, Shear-induced crystallization of polypropylene melts. in: D.M. Binding, et al. (Ed.), Proceedings of the XIII International Congress on Rheology, Cambridge, 2000, pp. 1–183] on isotactic polypropylene. Both the Kolmogorov [A.N. Kolmogorov, On the statistics of the crystallization process on metals. Bull. Akad. Sci. USSR, Class Sci., Math. Nat. 1 (1937) 355–359] and Nakamura et al. [K. Nakamura, T. Watanabe, K. Katayama, T. Amano, Some aspects of non-isothermal crystallization of polymers I, J. Appl. Polym. Sci. 16 (1972) 1077–1091] crystallinity formulations are discussed, and the advantages of the former are emphasized. For the cases considered, we see that strain-based crystallinity enhancement formulations appear to give results close to the experiments at the low flow rates which were studied, although they have some drawbacks. Several other ideas also lead to acceptable results; a new formulation based on both strain and strain-rate appears to give the best overall fit.

Low‐shrinkage dental restorative composite: Modeling viscoelastic behavior during setting

Much attention has been directed toward developing dental direct restorative composites that generate less shrinkage stress during setting. The aim of this study was to explore the viscoelastic behavior of a new class of low-shrinkage dental restorative composite during setting. The setting behavior of an experimental oxirane composite has been investigated by analyzing stress-strain data with two-parametric mechanical models. Experimental data were obtained from a dynamic test method, in which the setting light-activated composite was continuously subjected to sinusoidal strain cycles. The material parameters and the model's predictive capacity were analyzed with validated modeling procedures. The light-activated oxirane composite exhibited shrinkage delay and low polymerization shrinkage strain and stresses when compared with conventional light-activated composite. Noise in the stress data restricted the predictive ability of the Maxwell model to the elastic modulus development of the composite only. Evaluation tests of their potential as restorative material are required, to examine if the biocompatibility and mechanical properties after setting of oxirane composites are acceptable for dental use.

Strain Rate Sensitivity of Superplastic Inconel 718

The strain rate sensitivity, m, of a superplastic-quality (SPF) INCONEL 718 alloy has been measured in the temperature and strain rate ranges of 925–1000°C and 10−4–10−2 s−1 using both the classical method of instantaneous strain rate changes and a new method based on the continuous response to a sinusoidal strain rate input. The novel method furnishes continuous information from the whole stress–strain curve on the dependence of m on strain rate transients.In agreement with other recent studies, our results show that the maximum m values of the 718 alloy, although interesting enough for industrial superplastic forming, are lower than those shown by other superplastic materials for typical aeronautical application. A texture analysis indicates that crystallographic slip does not merely act here as an accommodation mechanism for grain boundary sliding. It significantly contributes to the total plastic strain, being thus responsible for the relatively low values observed for the strain rate sensitivity m.

Bi2Te3: Structural Modulations in Epitaxially Grown Superlattices and Bulk Materials

ABSTRACTMultiquantum well structures of Bi2Te3 are predicted to show an enhancement of the thermoelectric figure of merit ZT. Electron-conducting Bi2Te3 thin films and superlattices (SL) with a period of 12 nm were epitaxially grown on BaF2 substrates by molecular beam epitaxy. The microstructure was investigated by transmission electron microscopy. The SL could be imaged with strong contrast yielding a period of 12.0±0.5 nm. The SL is slightly bent with an amplitude of 30 nm and a wave length of 400 nm. Threading dislocations were found with a density of 2·109 cm−2. The SL interfaces are strongly bent close to threading dislocations, undisturbed regions have a maximum lateral size of 500 nm. A structural modulation (nns) with a wave length of 10 nm was found in Bi2Te3 thin films, superlattices and bulk materials. The structural modulation is found to be of general character for Bi2Te3 materials and is superimposed to the average structure. It was analysed in detail by stereomicroscopy in bulk material yielding a pure structural modulation with a displacement vector parallel to [5,-5,1] and a wave vector parallel to (1,0,10). The investigations showed the presence of none, one or two (nns). The number of (nns) and thereby the thermoelectric properties might be controlled by the growth parameters. Phonons should be scattered on the sinusoidal strain field of the (nns) yielding (i) a significantly decreased thermal conductivity, (ii) a reduced dimensionality and (iii) anisotropic transport coefficients in the basal plane.

Demodulation of extrinsic Fabry-Pe´rot interferometric sensors for vibration testing using neural networks

Strain level measurement on a periodically actuated and instrumented structure can provide information about the health of that structure. A simple demodulation system employing artificial neural networks (ANNs) is analyzed for an extrinsic Fabry-Perot interferometric (EFPI) strain sensor. The harmonic content of the nonlinear sensor output for the sinusoidal strain case is used to predict the maximum strain level. Implementations of the demodulation system are demonstrated for both simulated and experimental data using back-propagation neural networks. The simulation uses the theoretical response of the EFPI sensor and the experiment uses an EFPI-instrumented smart composite beam to obtain training and testing data. Excitation is provided by a piezoelectric actuator operating from 50 Hz to 1 kHz. System performance is compared for two-stage and single-stage networks and for differing types of data preprocessing. The ANN systems successfully extract the signal harmonics and predict the peak strain levels. Data preprocessing using principal component analysis produces the best accuracy. The architecture of an EFPI-based health monitoring system is proposed.

Viscoelastic properties of the human medial collateral ligament under longitudinal, transverse and shear loading

Ligament viscoelasticity controls viscous dissipation of energy and thus the potential for injury or catastrophic failure. Viscoelasticity under different loading conditions is likely related to the organization and anisotropy of the tissue. The objective of this study was to quantify the strain- and frequency-dependent viscoelastic behavior of the human medial collateral ligament (MCL) in tension along its longitudinal and transverse directions, and under shear along the fiber direction. The overall hypothesis was that human MCL would exhibit direction-dependent viscoelastic behavior, reflecting the composite structural organization of the tissue. Incremental stress relaxation testing was performed, followed by the application of small sinusoidal strain oscillations at three different equilibrium strain levels. The peak and equilibrium stress–strain curves for the longitudinal, transverse and shear tests demonstrate that the instantaneous and long-time stress–strain response of the tissue differs significantly between loading conditions of along-fiber stretch, cross-fiber stretch and along-fiber shear. The reduced relaxation curves demonstrated at least two relaxation times for all three test modes. Relaxation resulted in stresses that were 60–80% of the initial stress after 1000 s. Incremental stress relaxation proceeded faster at the lowest strain level for all three test configurations. Dynamic stiffness varied greatly with test mode and equilibrium strain level, and showed a modest but significant increase with frequency of applied strain oscillations for longitudinal and shear tests. Phase angle was unaffected by strain level (with exception of lowest strain level for longitudinal samples) but showed a significant increase with increasing strain oscillation frequency. There was no effect of test type on the phase angle. The increase in phase and thus energy dissipation at higher frequencies may protect the tissue from injury at faster loading rates. Results suggest that the long-time relaxation behavior and the short-time dynamic energy dissipation of ligament may be governed by different viscoelastic mechanisms, yet these mechanisms may affect tissue viscoelasticity similarly under different loading configurations.

Shear properties of the temporomandibular joint disc in relation to compressive and shear strain.

Shear stress can result in fatigue, damage, and irreversible deformation of the temporomandibular joint disc. Insight into the dynamic shear properties of the disc may give insight into the mechanism inducing tissue failure due to shear. We tested the hypothesis that the dynamic shear properties of the disc depend on the amount of shear and compressive strain. Twenty-four porcine discs were used for dynamic shear tests. The specimens were clamped between the plates of a loading apparatus under compressive strains of 5%, 10%, and 15%. Dynamic shear was applied to the specimen by a sinusoidal strain of, respectively, 0.5%, 1.0%, and 1.5%. Both the dynamic elasticity and viscosity were proportional to compressive strain and inversely proportional to shear strain. These shear characteristics suggest a significant role of compressive and shear strain on the internal friction of the disc.

IN VITRO ACCELERATED CALCIFICATION TESTER FOR BIOMATERI-ALS USING REAL BLOOD

Purpose: Our previous studies of a polymer heart valve through animal experiments and numerical simulation indicated that mechanical tensile strain is one of the keys to induce calcification. Therefore, we have developed an in vitro accelerated fatigue tester for further analysis of calcification mechanism using real blood. Methods: A segmented-poly-urethane was selected as a test subject. Firstly, some polymer specimens were pre-fatigued under a cyclic sinusoidal tensile strain of 525% at a frequency of 20Hz for 20 days, which is equivalent to 400-days fatigue in a physiologic environment. This pre-fatigued specimen and a virgin specimen with the identical dimension and material were installed into each blood chamber. It was made by a flexible polyurethane with a blood volume of 50ml. Prior to blood compatibility tests, all components were sterilized. Accelerated cyclic strain of 5±5% was acted to both the specimens for 6 hours in a fresh heparinized porcine blood. Results: The comparative tests were conducted 3 times. Then, influence of the pre-fatigue on blood compatibility including calcification was investigated. In all three cases, deposit was only found on the surfaces of pre-fatigued specimens. On the contrary, no deposit was found on the surfaces of virgin specimens. Scanning electron microscopic views showed crystal-like formation of the pre-fatigued surfaces. Moreover, energy dispersive X-ray analysis revealed that the components of deposit included Calcium and Phosphorus. As these in vitro results are quite similar to a typical calcification observed in vivo, effectiveness of our new tester was demonstrated.

The Payne effect in finite viscoelasticity: constitutive modelling based on fractional derivatives and intrinsic time scales

As we know from experimental testing, the stiffness behaviour of carbon black-filled elastomers under dynamic deformations is weakly dependent on the frequency of deformation but strongly dependent on the amplitude. Increasing strain amplitudes lead to a decrease in the dynamic stiffness, which is known as the Payne effect. In this essay, we develop a constitutive approach of finite viscoelasticity to represent the Payne effect in the context of continuum mechanics. The starting point for the constitutive model resulting from this development is the theory of finite linear viscoelasticity for incompressible materials, where the free energy is assumed to be a linear functional of the relative Piola strain tensor. Motivated by the weak frequency dependence of the dynamic stiffness of reinforced rubber, the memory kernel of the free energy functional is of the Mittag Leffler type. We demonstrate that the model is compatible with the Second Law of Thermodynamics and equal to a fractional differential equation between the overstress of the Second Piola Kirchhoff type and the Piola strain tensor. In order to represent the dependence of the dynamic stiffness on the amplitude of strain, we replace the physical time by an intrinsic time variable. The temporal evolution of the intrinsic time is driven by an internal variable, which is a measure for the current state of the material's microstructure. The material constants of the model are estimated using a stochastic identification algorithm of the Monte Carlo type. We demonstrate that the constitutive approach pursued here represents the combined frequency and amplitude dependence of filler-reinforced rubber. In comparison with the micromechanical Kraus model developed for sinusoidal strains, the theory set out in this essay allows the representation of the stress response under arbitrary loading histories.

Vibration Control by Magnetostrictive Actuator Coupled with Negative Inductance Circuits

The stiffness of magnetostrictive materials can be controlled by the feedback action of the negative inductance circuits connected to the coils surrounding them. The effect is analogous to that of piezoelectric materials whose stiffness can be controlled by the negative capacitance circuits connected to them. The applied sinusoidal strain of the central rod in a magnetostrictive actuator induces the sinusoidal electric current in the surrounding coil. The current is increased or decreased by the feedback from the circuits, resulting in the corresponding increase or decrease in the strain under the fixed applied stress. The apparent dynamic elastic coefficient is thus arbitrarily controlled. If the actuator is placed between a shaker and a heavy mass, the resonant frequency of the system decreases or increases depending on the type of the negative inductance circuit. The transmissibility of vibration through the actuator is thus controlled in the respective frequency range.

Tissue engineered composite of a woven fabric scaffold with tendon cells, response on mechanical simulation in vitro

In reconstructive surgery, complications of implanted textiles are often associated with mechanical and structural incompatibility between implant and host tissue. Ingrowing cells and maturation of an extracellular matrix form together with the textile a vital/avital composite and by this change mechanical properties of the textile implant. Thus, a profound understanding is required to consider these effects in the design of the implant. Mechanical stimulation in tissue engineering is proposed as a viable experimental technique to investigate structure-properties relations to design vital/avital composites. Therefore, the aim of this study was to investigate the effects of cyclic mechanical stimulation (2% sinusoidal strain, 1 h at 0.5 Hz stimulation followed by 6 h recreation phase at 0.01 Hz) on a vital/avitat composite that consists of a woven fabric as scaffold and confluent tendon fibroblasts as the vital matrix. The force response during the exertion phase could be correlated to dynamic orientation of f-actin filaments in the cytosceleton.

The response of a propane-air counter-flow diffusion flame subjected to a transient flow field

OH planar laser-induced fluorescence (PLIF) and particle image velocimetry have been used to study the frequency response of laminar C 3H 8-air counterflow diffusion flames to assess the adequacy of the steady-flamelet models. Particle image velocimetry was used to determine the flame strain rate, while OH PLIF was used both to measure temperature at the flame front, using the two-line PLIF technique, and the reaction-zone width. Both measurements demonstrate that the frequency response of flames subjected to a time-varying flow field is diffusion-limited. At the 30-Hz and 50-Hz forcing frequencies, the maximum reaction-zone temperature and width were found to respond quasi-steadily. However, at higher forcing frequencies-i.e., 100 and 200 Hz-transient behavior is evident from the phase relationship between the imposed sinusoidal strain rate and the resulting peak temperature and reaction-zone width. The measured values of the OH-field widths were well fit by an offset sine function. In all cases when the oscillation amplitude is normalized by the cycle mean strain rate and plotted against the non-dimensional flow field frequency, the results collapse onto a single line having a steep negative slope.

Effects of broad frequency vibration on cultured osteoblasts

Bone is subjected in vivo to both high amplitude, low frequency strain, incurred by locomotion, and to low amplitude, broad frequency strain. The biological effects of low amplitude, broad frequency strain are poorly understood. To evaluate the effects of low amplitude strains ranging in frequency from 0 to 50 Hz on osteoblastic function, we seeded MC3T3-E1 cells into collagen gels and applied the following loading protocols for 3 min per day for either 3 or 7 days: (1) sinusoidal strain at 3 Hz, with 0–3000 μstrain peak-to-peak followed by 0.33 s resting time, (2) “broad frequency vibration” of low amplitude strain (standard deviation of 300 μstrain) including frequency components from 0 to 50 Hz, and (3) sinusoidal strain combined with broad frequency vibration ( S+ V). The cells were harvested on day 4 or 8. We found that the S+ V stimulation significantly repressed cell proliferation by day 8. Osteocalcin mRNA was up-regulated 2.6-fold after 7 days of S+ V stimulation, and MMP-9 mRNA was elevated 1.3-fold after 3 days of vibration alone. Sinusoidal stimulation alone did not affect the cell responses. No differences due to loading were observed in alkaline phosphatase activity and in mRNA levels of type I collagen, osteopontin, connexin 43, MMPs-1A, -3, -13. These results suggest that osteoblasts are more sensitive to low amplitude, broad frequency strain, and this kind of strain could sensitize osteoblasts to high amplitude, low frequency strain. This suggestion implies a potential contribution of stochastic resonance to the mechanical sensitivity of osteoblasts.

Strain-field domain structure in Bi 2Te 3 thermoelectric materials

A strain-field domain structure and a large number of precipitates have been observed in Bi 2Te 3 n- and p-type thermoelectric materials by transmission electron (TEM) microscopy analysis. The microstructure can be understood as an average unstrained structure plus a sinusoidal strain field. The displacement field of this strain field is generated by dislocations, mostly dipoles that are about 5 nm apart. These domains have a periodicity of 10 nm and lie parallel to the crystallographic (1,0,10) planes. The Burgers-vector of the dislocations within the domains is b =1/2[2,1,w] with w=0.16. These domains might originate from the strain field and motion of precipitates with a size of approximately 2–4 nm, which lie in (−1,0,5) crystallographic planes.

腐食疲労の除荷過程における電流応答に及ぼすき裂閉口の影響

Response current to strain for iron electrode polarized at a potential of about 200 mV less than the pitting potential was measured in a sodium borate and boric acid buffer solution of pH 8.39 containing 5 mol/m3 chloride ions. The different types of strain waveforms (triangular, trapezoidal and negative saw teeth) were employed to clarify the current decay behaviors in the unloading cycle. Rapid current decay during the unloading cycle was observed for sinusoidal and triangular strains. For the response current induced by the trapezoidal strain, it was observed that current decay came to an end during the holding period at the maximum strain. Current flow was not observed during the unloading cycle after the current decay finished. It was detected from the negative saw teeth strain waveforms that current decay came to an end during the unloading cycle was under way. It suggested that there was an existence of certain strain value where the current decay stopped during the unloading cycle. The response current in the negative saw teeth waveform was calculated, assuming that the current decay was caused by not only the repassivation process at the crack tip but also the reduction of active fresh surface area which was introduced in the preceding loading cycle. The calculated results agreed well with the experimental results. Moreover, response current in the two cyclic strain waveforms was calculated. One was a triangular strain waveform with strain rate kept constant, the other was a sinusoidal strain waveform with strain rate changing continuously. It was confirmed that the changing in the fresh surface area influenced to the current response induced by the cyclic strain.

The efficiency of an asynchronous flight muscle from a beetle.

Mechanical power output and metabolic power input were measured from an asynchronous flight muscle, the basalar muscle of the beetle Cotinus mutabilis. Mechanical power output was determined using the work loop technique and metabolic power input by monitoring CO(2) production or both CO(2) production and O(2) consumption. At 35 degrees C, and with conditions that maximized power output (60 Hz sinusoidal strain, optimal muscle length and strain amplitude, 60 Hz stimulation frequency), the peak mechanical power output during a 10 s burst was approximately 140 W kg(-1), the respiratory coefficient 0.83 and the muscle efficiency 14-16 %. The stimulus intensity used was the minimal required to achieve a maximal isometric tetanus. Increasing or decreasing the stimulus intensity from this level changed mechanical power output but not efficiency, indicating that the efficiency measurements were not contaminated by excitation of muscles adjacent to that from which the mechanical recordings were made. The CO(2) produced during an isometric tetanus was approximately half that during a bout of similar stimulation but with imposed sinusoidal strain and work output, suggesting that up to 50 % of the energy input may go to muscle activation costs. Reducing the stimulus frequency to 30 Hz from its usual value of 60 Hz reduced mechanical power output but had no significant effect on efficiency. Increasing the frequency of the sinusoidal strain from 60 to 90 Hz reduced power output but not CO(2) consumption; hence, there was a decline in efficiency. The respiratory coefficient was the same for 10 s and 30 s bursts of activity, suggesting that there was no major change in the fuel used over this time range. The mass-specific mechanical power output and the efficiency of the beetle muscle were each 2-3 times greater than values measured in previous studies, using similar techniques, from locust flight muscles, which are synchronous muscles. These results support the hypothesis that asynchronous flight muscles have evolved in several major insect taxa because they can provide greater power output and are more efficient than are synchronous muscles for operation at the high frequencies of insect flight.

Effect of mechanical perturbation on the release of PGE(2) by macrophages in vitro.

Macrophages play numerous roles in both physiologic and pathologic processes. Along with fibroblasts, they comprise the synovial tissue that forms the lining of musculoskeletal joint capsules and bursae, and they often envelop implants. During the process of phagocytosing prosthesis-related particles, macrophages in peri-implant tissue release inflammatory mediators. Little is known, however, about the response of these cells to mechanical perturbation, which often is a component of the physical environment of the cell. Mouse peritoneal macrophages were grown on a flexible membrane in vitro and a dynamic 1-Hz spatially uniform sinusoidal strain pattern imparted to the elastomeric substrate. The effect of mechanical strain on prostaglandin (PG) E(2) release was evaluated using cells that were activated by lipopolysaccharide (LPS) as well as by those that were not. The results are compared with the levels of PGE(2) stimulated by metallic particles. Strain magnitudes of 4 and 8% applied for 1 h resulted in almost a twofold increase in the release of PGE(2) from LPS-stimulated cells (p < 0.05) and nonstimulated macrophages (p < 0.07), compared with nonperturbated controls. No release was elicited by a challenge of metal particles. These findings demonstrate for the first time an effect of mechanical force on the release of an inflammatory mediator by macrophages. This response may help to explain the macrophage-mediated processes underlying the osteolysis associated with loose prostheses in bone and suggests a mechanism for the inflammation of synovial tissues by excessive mechanical strain.

Tissue Shear Deformation Stimulates Proteoglycan and Protein Biosynthesis in Bovine Cartilage Explants

Chondrocytes are known to sense and respond to mechanical and physicochemical stimuli by multiple regulatory pathways, including upstream signaling, transcription, translation, posttranslational modifications, and vesicular transport. Due to the complexity of identifying the biophysical phenomena that occur during cartilage loading in vivo, the regulatory mechanisms that govern chondrocyte mechanotransduction are not fully understood. Recent studies have shown that fluid flow during dynamic compression of cartilage explants can stimulate proteoglycan and protein synthesis. In this study, we examined the effect of deformations of cell and extracellular matrix on chondrocyte biosynthesis. We used tissue shear loading, since tissue shear causes little volumetric deformation and can thereby decouple fluid flow from cell and matrix deformation. Shear loading was applied over a wide range of frequencies, 0.01–1.0 Hz, using 1–3% sinusoidal shear strain amplitudes, and the resulting proteoglycan and protein syntheses were measured using radiolabel incorporation. In addition, quantitative autoradiography was used to investigate spatial variations in matrix biosynthesis and to correlate these variations with the spatial profiles of biophysical stimuli. Our data show that tissue shear loading at 1–3% strain amplitude stimulated the synthesis of protein by ∼50% and proteoglycans by ∼25% at frequencies between 0.01 and 1.0 Hz. The relatively uniform patterns of biosynthesis in the radial and vertical directions within cylindrical explants revealed by autoradiography suggest that the stimulatory effect was associated with the relatively uniform deformation caused by simple shear loading. These results suggest that chondrocytes can respond to tissue shear stress-initiated pathways for the production of collagen and proteoglycan, which include deformation of cells and pericellular matrix, even in the absence of macroscopic tissue-level fluid flow.

Proper ferroelastic phase transitions in thin epitaxial films with symmetry-conserving and symmetry-breaking misfit strains

We study how the ferroelastic domain structure sets in in an epitaxial film of a material with second order proper ferroelastic transition. The domain structures considered are similar to either $a_{1}/a_{2}/a_{1}/a_{2}$ or $c/a/c/a$ structures in perovskite ferroelectrics. If the "extrinsic" misfit strain, not associated with the transition, does not break the symmetry of the high-temperature phase, the phase transition in the film occurs at somewhat lower temperature compared to the bulk. The loss of stability then occurs with respect to a sinusoidal strain wave, which evolves into the domain structure with practically the same geometry and approximately the same period. In the presence of the symmetry-breaking component of the misfit strain ("extrinsic" misfit) the character of the phase transition is qualitatively different. In this case it is a {\em topological} transition between single-domain and multi-domain states, which starts from a low density of the domain walls.