Correlation between sagging and shear elasticity in pectin, gelatin and polyacrylamide gels

The relationship between the height of gels determined by a sag test and their elastic shear modulus (G′) has been both investigated experimentally and simulated using a finite element analysis for the inhomogeneous deformation of gels due to gravity. It was assumed in the simulations that gels can be modeled as incompressible linear elastic materials. General relationships between the sag of gels and their elastic modulus were obtained from the simulations for slip and no-slip conditions. The relationships were tested experimentally on pectin, gelatin and polyacrylamide gels with a range of concentrations and rigidities. The good agreement between the predictions and the results shows that these gels can be modeled accurately as incompressible elastic materials. A standard 150° SAG pectin gel, which sags 23.5% in the SAG test, has G′ moduli of 429 and 379 Pa under slip and no-slip conditions, respectively.     

Effect of surface roughness on slip flows in hydrophobic and hydrophilic microchannels by molecular dynamics simulation

The influences of surface roughness on the boundary conditions for a simple fluid flowing over hydrophobic and hydrophilic surfaces are investigated by molecular dynamics (MD) simulation. The degree of slip is found to decrease with surface roughness for both the hydrophobic and hydrophilic surfaces. The flow rates measured in hydrophobic channels are larger than those in hydrophilic channels with the presence of slip velocity at the walls. The simulation results of flow rate are correlated with the theoretical predictions according to the assumption of no slip boundary condition. The slip boundary condition also strongly depends on the shear rate near the surface. For hydrophobic surfaces, apparent fluid slips are observed on smooth and rough surfaces. For simple fluids flowing over a hydrophobic surface, the slip length increases linearly with shear rate for both the smooth and rough surfaces. Alternately, the slip length has a power law dependence on the shear rate for the cases of hydrophilic surfaces. It is observed that there is a no-slip boundary condition only when shear rate is low, and partial slip occurs when it exceeds a critical level.     

Biodegradable polymers from renewable sources: rheological characterization of hemicellulose-based hydrogels

Hemicellulose-based hydrogels were prepared by radical polymerization of 2-hydroxyethyl methacrylate or poly(ethylene glycol) dimethacrylate with oligomeric hydrosoluble hemicellulose modified with well-defined amounts of methacrylic functions. The polymerization reaction was carried out in water at 40 degrees C using a redox initiator system. The hydrogels were in general elastic, soft, and easily swellable in water. Their viscoelastic properties were determined by oscillatory shear measurements on 2 mm thick hydrogels under a slight compression to avoid slip, over the frequency range 10(-1) to 10(2). The rheological characterization indicated that the elastic response of the hydrogels was stronger than the viscous response, leading to the conclusion that the hydrogel systems displayed a predominantly solid-like behavior. The curves showed an increase in shear storage modulus with increasing cross-linking density. The nature of the synthetic comonomer in the hemicellulose-based hydrogels also influenced the shear storage modulus. Comparison of hemicellulose-based hydrogels with pure poly(2-hydroxyethyl methacrylate) hydrogels showed that their behaviors were rather similar, demonstrating that the synthetic procedure made it possible to prepare hemicellulose-based hydrogels with properties similar to those of pure poly(2-hydroxyethyl methacrylate) hydrogels.     

Tensile behavior of cortical bone: dependence of organic matrix material properties on bone mineral content

A porous composite model is developed to analyze the tensile mechanical properties of cortical bone. The effects of microporosity (volksman's canals, osteocyte lacunae) on the mechanical properties of bone tissue are taken into account. A simple shear lag theory, wherein tensile loads are transferred between overlapped mineral platelets by shearing of the organic matrix, is used to model the reinforcement provided by mineral platelets. It is assumed that the organic matrix is elastic in tension and elastic-perfectly plastic in shear until it fails. When organic matrix shear stresses at the ends of mineral platelets reach their yield values, the stress-strain curve of bone tissue starts to deviate from linear behavior. This is referred as the microscopic yield point. At the point where the stress-strain behavior of bone shows a sharp curvature, the organic phase reaches its shear yield stress value over the entire platelet. This is referred as the macroscopic yield point. It is assumed that after macroscopic yield, mineral platelets cannot contribute to the load bearing capacity of bone and that the mechanical behavior of cortical bone tissue is determined by the organic phase only. Bone fails when the principal stress of the organic matrix is reached. By assuming that mechanical properties of the organic matrix are dependent on bone mineral content below the macroscopic yield point, the model is used to predict the entire tensile mechanical behavior of cortical bone for different mineral contents. It is found that decreased shear yield stresses and organic matrix elastic moduli are required to explain the mechanical behavior of bones with lowered mineral contents. Under these conditions, the predicted values (elastic modulus, 0.002 yield stress and strain, and ultimate stress and strain) are within 15% of experimental data.     

Analysis of deformation and contraction in cylindrical crystals due to dispirations or dislocations.

Cylindrical crystal structures are common in biology. The shape changes and movements of cylindrical crystals are basic to the understanding of the contractile mechanisms in biological systems such as tobacco mosaic viruses and the tail sheath of T-even bacteriophages. It has been suggested that the concept of defects in crystal physics can be applied to study these contractile mechanisms. The defect believed to be responsible for the shape changes of cylindrical crystals is known as a dispiration. Dispirations are characterized by the shear displacement on the slip plane through a screw symmetry operation. The elastic field of a dispiration can be decomposed into its translational (dislocation) and rotational (disclination) components. The magnitude of the translational and rotational displacements in a cylindrical crystal has been related to the crystal structural parameters. The passage of a dispiration along a helical plane in a cylindrical crystal can induce one of two types of shape changes. In one type, only the disclination component of the dispiration contributes to contraction, whereas in the other type, both the disclination and dislocation components are responsible for the shape change. Estimates of the magnitude of contraction are made in terms of the dimensional and structural parameters of the cylindrical crystal. The reversal of the direction of helical slip results in extension instead of contraction of the cylindrical crystal. The local elastic deformation of a dispiration dipole situated on the helical plane of a cylindrical crystal is examined. It has been shown that, for the first type of deformation mentioned above, closed form solutions of the stress field can be obtained by superposing the stress fields of two dispiration dipoles with slip planes parallel and normal to the cylinder axis, respectively. The approximations of shallow shell theory are adopted in the analysis. Future problems of biological interests are identified.     

Low force decelerates L-selectin dissociation from P-selectin glycoprotein ligand-1 and endoglycan

Selectin-ligand interactions mediate the tethering and rolling of circulating leukocytes on vascular surfaces during inflammation and immune surveillance. To support rolling, these interactions are thought to have rapid off-rates that increase slowly as wall shear stress increases. However, the increase of off-rate with force, an intuitive characteristic named slip bonds, is at odds with a shear threshold requirement for selectin-mediated cell rolling. As shear drops below the threshold, fewer cells roll and those that do roll less stably and with higher velocity. We recently demonstrated a low force regime where the off-rate of P-selectin interacting with P-selectin glycoprotein ligand-1 (PSGL-1) decreased with increasing force. This counter-intuitive characteristic, named catch bonds, might partially explain the shear threshold phenomenon. Because L-selectin-mediated cell rolling exhibits a much more pronounced shear threshold, we used atomic force microscopy and flow chamber experiments to determine off-rates of L-selectin interacting with their physiological ligands and with an antibody. Catch bonds were observed at low forces for L-selectin-PSGL-1 interactions coinciding with the shear threshold range, whereas slip bonds were observed at higher forces. These catch-slip transitional bonds were also observed for L-selectin interacting with endoglycan, a newly identified PSGL-1-like ligand. By contrast, only slip bonds were observed for L-selectin-antibody interactions. These findings suggest that catch bonds contribute to the shear threshold for rolling and are a common characteristic of selectin-ligand interactions.     

Blood Flow, Slip, and Viscometry

The viscosity of blood, measured by the usual viscometers in which slip is not considered, is found to be flow dependent, varying markedly with shear rate, pressure gradient, and vessel diameter in the lower ranges of these factors. The study postulates, on grounds thought reasonable, that slip may be present in blood flow, as a function of the nature of the wall surfaces, shear stress at the wall, and relative cell volume (RCV) adjacent to the wall. It presumes that blood possesses a specific, flow-independent viscosity, and determines theoretically the viscosity indications of viscometers if blood slipped in the instruments. The study shows that if the slip function is of a certain plausible form, these viscosity indications would exhibit a flow dependence of much the same pattern as the actual indications supplied by the usual viscometers. The slip postulate permits, therefore, an interpretation of the “anomalous” flow behavior of blood, dispensing with the prevailing assumption of an ad hoc variability of its viscosity with flow factors. To the extent that viscometric data for blood may be representative of other non-newtonian fluids, the slip postulate may be applicable to these fluids.     

The material properties of bone-particle impregnated PMMA

The elastic Young's modulus and shear modulus of bone-particle impregnated polymethylmethacrylate (PMMA) has been measured experimentally at room temperature as a function of bone particle concentration. It was found that the moduli increased with increasing bone particle content. This increase was less than the stiffness increase predicted by higher-order composite theory [1, 2] under the assumption of perfect bonding between particles and matrix. It was concluded that a bond existed but that it was not a perfect bond.     

Catch bonds govern adhesion through L-selectin at threshold shear

Flow-enhanced cell adhesion is an unexplained phenomenon that might result from a transport-dependent increase in on-rates or a force-dependent decrease in off-rates of adhesive bonds. L-selectin requires a threshold shear to support leukocyte rolling on P-selectin glycoprotein ligand-1 (PSGL-1) and other vascular ligands. Low forces decrease L-selectin-PSGL-1 off-rates (catch bonds), whereas higher forces increase off-rates (slip bonds). We determined that a force-dependent decrease in off-rates dictated flow-enhanced rolling of L-selectin-bearing microspheres or neutrophils on PSGL-1. Catch bonds enabled increasing force to convert short-lived tethers into longer-lived tethers, which decreased rolling velocities and increased the regularity of rolling steps as shear rose from the threshold to an optimal value. As shear increased above the optimum, transitions to slip bonds shortened tether lifetimes, which increased rolling velocities and decreased rolling regularity. Thus, force-dependent alterations of bond lifetimes govern L-selectin-dependent cell adhesion below and above the shear optimum. These findings establish the first biological function for catch bonds as a mechanism for flow-enhanced cell adhesion.     

Blood low shear rate rheometry: influence of fibrinogen level and hematocrit on slip and migrational effects.

Red blood cell (RBC) aggregation is of prime importance in vivo and in vitro for low flow rates. It may be estimated by rheometrical measurements at low shear rates, but these are perturbed by slip and migrational effects which have already been highlighted in the past. These effects lead to a torque decay with time so that the true value of the stress at low shear rates may be greatly underestimated. Elevated aggregation being associated with different diseases, pathological blood samples show more pronounced perturbing effects and a strong time dependency in low shear rate rheometry. To test the dependence of slip and migrational effects on RBC aggregation, and particularly to determine the way in which they depend upon fibrinogen concentration ([Fb]), a home-made measuring system with roughened internal and external walls (170 microns roughness) was used to study low shear rate rheometry for RBC suspensions in PBS buffer containing albumin (at 50 g/l) and fibrinogen at various concentrations. The influences of hematocrit, shear rate, and fibrinogen concentration were investigated. Particular attention was paid to data acquisition at low shear rates (10(-3) s-1 to 3 x 10(-2) s-1). The combined influence of hematocrit and fibrinogen was investigated by adjusting hematocrit to 44 or 57% and fibrinogen concentration ([Fb]) to 3.0-4.5-6.5 g/l. Microscopic observations of the blood samples at rest were performed. They showed that different structures were formed according to fibrinogen concentration. The rheometrical measurements indicated that torque decay with shearing duration was strongly dependent on fibrinogen concentration and on shear rate at fixed hematocrit. Migrational and slip effects were more pronounced as shear rate decreased, fibrinogen concentration was raised, and hematocrit was lowered. The results have been explained on the basis of the expected microstructure of flowing blood in relation to the microscopic observations at rest.     

The relationship between muscle activation and shear elastic modulus of the sternocleidomastoid muscle during 3-D torque production

The sternocleidomastoid (SCM) is a primary neck torque generator, but the relationship between its muscle activation and shear elastic modulus during 3-D torque production is unknown. This study examined variations in neural control and shear elastic modulus of the SCM across various 3-D isometric torques. Our primary hypothesis was that the SCM would display similar preferred directions where muscle activity and shear elastic modulus were maximal during voluntary 3-D isometric torque production. Surface electromyography (EMG) and ultrasound shear wave elastography (SWE) data were collected from the SCM in 20 participants performing 3-D isometric target-matching at two different torque amplitudes. We used spherical statistics to compare the preferred directions calculated from the SWE and EMG data at 40% and 80% torque level during 3-D isometric torque production. We demonstrated a small but significant difference between EMG and SWE preferred directions, with the SWE preferred direction oriented more towards ipsilateral bending and less towards contralateral axial rotation than the preferred direction for the EMG data. We conclude that, although small differences exist, SCM shear elastic modulus is largely driven by activation during 3-D neck torques for healthy individuals.     

Simulation of direct shear tests on rooted and non-rooted soil using finite element analysis

The finite element (FE) method has been used in recent years to simulate overturning processes in trees and to better comprehend plant anchorage mechanics. We aimed at understanding the fundamental mechanisms of root-soil reinforcement by simulating direct shear of rooted and non-rooted soil. Two- (2D) and three-dimensional (3D) FE simulations of direct shear box tests were carried out using readily available software for routine strength assessment of the root-soil composite. Both rooted and non-rooted blocks of soil were modelled using a simplified model of root distribution and root material properties representative of real roots. Linear elastic behaviour was assumed for roots and the soil was modelled as an ideally plastic medium. FE analysis showed that direct shear tests were dependent on the material properties specified for both the soil and roots. 2D and 3D simulations of direct shear of non-rooted soil produced similar results and any differences between 2D and 3D simulations could be explained with regard to the spatial complexity of roots used in the root distribution model. The application of FE methods was verified through direct shear tests on soil with analogue roots and the results compared to in situ tests on rooted soil in field conditions.     

Utilizing scanning electron microscopy to observe the initiation and development of slip bands and fracture in a nickel based metallic glass

To gain a better understanding of the elastic/plastic deformation and fracture of metallic glasses, in situ bending of a nickel based metallic glass ribbon was observed utilizing scanning electron microscopy. The results verified that the formation of slip bands was the first observable indication of plastic deformation. The slip band formation was followed by a veined fracture and a rapid unstable fracture. It was also observed that the rapid fracture was arrested by the formation of box-like hinges in the material. It is believed that the failure of this metallic glass occurred in progressive stages of slip, veined fracture and rapid fracture.     

Bend propagation in flagella. I. Derivation of equations of motion and their simulation.

A set of nonlinear differential equations describing flagellar motion in an external viscous medium is derived. Because of the local nature of these equations and the use of a Crank-Nicolson-type forward time step, which is stable for large deltat, numerical solution of these equations on a digital computer is relatively fast. Stable bend initiation and propagation, without internal viscous resistance, is demonstrated for a flagellum containing a linear elastic bending resistance and an elastic shear resistance that depends on sliding. The elastic shear resistance is derived from a plausible structural model of the radial link system. The active shear force for the dynein system is specified by a history-dependent functional of curvature characterized by the parameters m0, a proportionality constant between the maximum active shear moment and curvature, and tau, a relaxation time which essentially determines the delay between curvature and active moment.     

Shear Elastic Modulus on Patellar Tendon Captured from Supersonic Shear Imaging: Correlation with Tangent Traction Modulus Computed from Material Testing System and Test–Retest Reliability

Characterization of the elastic properties of a tendon could enhance the diagnosis and treatment of tendon injuries. The purpose of this study was to examine the correlation between the shear elastic modulus on the patellar tendon captured from a Supersonic Shear Imaging (SSI) and the tangent traction modulus computed from a Material testing system (MTS) on 8 fresh patellar pig tendons (Experiment I). Test–retest reliability of the shear elastic modulus captured from the SSI was established in Experiment II on 22 patellar tendons of 11 healthy human subjects using the SSI. Spearman Correlation coefficients for the shear elastic modulus and tangent traction modulus ranged from 0.82 to 1.00 (all p<0.05) on the 8 tendons. The intra and inter-operator reliabilities were 0.98 (95% CI: 0.93–0.99) and 0.97 (95% CI: 0.93–0.98) respectively. The results from this study demonstrate that the shear elastic modulus of the patellar tendon measured by the SSI is related to the tangent traction modulus quantified by the MTS. The SSI shows good intra and inter-operator repeatability. Therefore, the present study shows that SSI can be used to assess elastic properties of a tendon.     

Evidence of changes in load sharing during isometric elbow flexion with ramped torque

This study aimed to: (1) test the repeatability of Supersonic Shear Imaging measures of muscle shear elastic modulus of four elbow flexor muscles during isometric elbow flexion with ramped torque; (2) determine the relationship between muscle shear elastic modulus and elbow torque for the four elbow flexor muscles, and (3) investigate changes in load sharing between synergist elbow flexor muscles with increases in elbow flexor torque. Ten subjects performed ten isometric elbow flexions consisting of linear torque ramps of 30-s from 0 to 40% of maximal voluntary contraction. The shear elastic modulus of each elbow flexor muscle (biceps brachii long head [BB(LH)], biceps brachii short head [BB(SH)], brachialis [BA], and brachoradialis [BR]) and of triceps brachii long head [TB] was measured twice with individual muscles recorded in separate trials in random order. A good repeatability of the shape of the changes in shear elastic modulus as a function of torque was found for each elbow flexor muscle (r-values: 0.85 to 0.94). Relationships between the shear elastic modulus and torque were best explained by a second order polynomial, except BA where a higher polynomial was required. Statistical analysis showed that BB(SH) and BB(LH) had an initial slow change at low torques followed by an increasing rate of increase in modulus with higher torques. In contrast, the BA shear elastic modulus increased rapidly at low forces, but plateaued at higher forces. These results suggest that changes in load sharing between synergist elbow flexors could partly explain the non-linear EMG-torque relationship classically reported for BB during isometric efforts.     

Atomistic simulation of dislocation interactions in a model crystal subjected to shear

The interaction of edge dislocations in a two-dimensional (2D) model crystal subjected to “simple shear” is studied using molecular statics simulations. An initial point defect is introduced in the model to trigger the dislocation activities in a controlled manner. We consider dislocations gliding towards one another on parallel slip planes separated by various distances. The overall load-displacement response of the crystal is obtained from the simulations, which can be correlated with the nano-scale atomistic mechanisms. Although the crystal is inherently anisotropic, the incipient dislocation plasticity is such that slip is parallel to the primary shear direction as clearly demonstrated in this work. It is also illustrated that dislocation annihilation, as well as dislocation encounter which leaves behind a point defect, can be unambiguously modeled. Throughout the deformation history, more dislocations capable of gliding in the crystal tend to generate a weaker mechanical response and more pronounced plasticity. The present study also offers mechanistic insight into experimentally observed small-scale crystal plasticity.     

Leukocyte Adhesion: What's the Catch?

A recent study shows that the leukocyte adhesion molecules known as selectins form 'catch' bonds, the dissociation rate of which decreases with increasing applied force. The ability of selectins to switch between catch and slip bonds, where dissociation increases with force, can explain the shear threshold effect, in which leukocyte adhesion goes through a maximum with increasing shear rate.     

Ab initio predictions of structural and elastic properties of struvite: contribution to urinary stone research

In the present work, we carried out density functional calculations of struvite--the main component of the so-called infectious urinary stones--to study its structural and elastic properties. Using a local density approximation and a generalised gradient approximation, we calculated the equilibrium structural parameters and elastic constants C(ijkl). At present, there is no experimental data for these elastic constants C (ijkl) for comparison. Besides the elastic constants, we also present the calculated macroscopic mechanical parameters, namely the bulk modulus (K), the shear modulus (G) and Young's modulus (E). The values of these moduli are found to be in good agreement with available experimental data. Our results imply that the mechanical stability of struvite is limited by the shear modulus, G. The study also explores the energy-band structure to understand the obtained values of the elastic constants.     

Red Blood Cell Shape and Fluctuations: Cytoskeleton Confinement and ATP Activity

We review recent theoretical work that analyzes experimental measurements of the shape and fluctuations of red blood cells. Particular emphasis is placed on the role of the cytoskeleton and cell elasticity and we contrast the situation of elastic cells with that of fluid-filled vesicles. In red blood cells (RBCs), the cytoskeleton consists of a two-dimensional network of spectrin proteins. Our analysis of the wave vector and frequency dependence of the fluctuation spectrum of RBCs indicates that the spectrin network acts as a confining potential that reduces the fluctuations of the lipid bilayer membrane. However, since the cytoskeleton is only sparsely connected to the bilayer, one cannot regard the composite cytoskeleton membrane as a polymerized object with a shear modulus. The sensitivity of RBC fluctuations and shapes to ATP concentration may reflect the transient defects induced in the cytoskeleton network by ATP.