Stretch Regime Research Articles

Analysis of the compressible, isotropic, neo-Hookean hyperelastic model

The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.

Interfacial friction and substrate deformation mediate long-range signal propagation in tissues.

Tissue layers can generally slide at the interface, accompanied by the dissipation due to friction. Nevertheless, it remains elusive how force could propagate in a tissue with such interfacial friction. Here, we elaborate the force dynamics in a prototypical multilayer system in which an epithelial monolayer was cultivated upon an elastic substrate in contact with a hard surface, and discover a novel mechanism of pronounced force propagation over a long distance due to interfacial dynamics between substrate layers. We derived an analytical model for the dynamics of the elastic substrate under the shear stress provided by the cell layer at the surface boundary and the friction at bottom. The model reveals that sliding between substrate layers leads to an expanding stretch regime from a shear regime of substrate deformation in time and space. The regime boundary propagating diffusively with a speed depending on the stiffness, thickness, and slipperiness of the substrate, is a robust nature of a deformed elastic sheet with interfacial friction. These results shed new light on force propagation in tissues and our model could serve as a basis for studies of such propagation in a more complex tissue environment.

A survey of pathways for mechano-electric coupling in the atria

Mechano-electric coupling (MEC) in atrial tissue has received sparse investigation to date, despite the well-known association between chronic atrial dilation and atrial fibrillation (AF). Of note, no fewer than six different mechanisms pertaining to stretch-activated channels, cellular capacitance and geometric effects have been identified in the literature as potential players. In this mini review, we briefly survey each of these pathways to MEC. We then perform computational simulations using single cell and tissue models in presence of various stretch regimes and MEC pathways. This allows us to assess the relative significance of each pathway in determining action potential duration, conduction velocity and rotor stability. For chronic atrial stretch, we find that stretch-induced alterations in membrane capacitance decrease conduction velocity and increase action potential duration, in agreement with experimental findings. In the presence of time-dependent passive atrial stretch, stretch-activated channels play the largest role, leading to after-depolarizations and rotor hypermeandering. These findings suggest that physiological atrial stretches, such as passive stretch during the atrial reservoir phase, may play an important part in the mechanisms of atrial arrhythmogenesis.

The geometrical shape of mesenchymal stromal cells measured by quantitative shape descriptors is determined by the stiffness of the biomaterial and by cyclic tensile forces.

Controlling mesenchymal stromal cell (MSC) shape is a novel method for investigating and directing MSC behaviour in vitro. it was hypothesized that specifigc MSC shapes can be generated by using stiffness-defined biomaterial surfaces and by applying cyclic tensile forces. Biomaterials used were thin and thick silicone sheets, fibronectin coating, and compacted collagen type I sheets. The MSC morphology was quantified by shape descriptors describing dimensions and membrane protrusions. Nanoscale stiffness was measured by atomic force microscopy and the expression of smooth muscle cell (SMC) marker genes (ACTA2, TAGLN, CNN1) by quantitative reverse-transcription polymerase chain reaction. Cyclic stretch was applied with 2.5% or 5% amplitudes. Attachment to biomaterials with a higher stiffness yielded more elongated MSCs with fewer membrane protrusions compared with biomaterials with a lower stiffness. For cyclic stretch, compacted collagen sheets were selected, which were associated with the most elongated MSC shape across all investigated biomaterials. As expected, cyclic stretch elongated MSCs during stretch. One hour after cessation of stretch, however, MSC shape was rounder again, suggesting loss of stretch-induced shape. Different shape descriptor values obtained by different stretch regimes correlated significantly with the expression levels of SMC marker genes. Values of approximately 0.4 for roundness and 3.4 for aspect ratio were critical for the highest expression levels of ACTA2 and CNN1. Thus, specific shape descriptor values, which can be generated using biomaterial-associated stiffness and tensile forces, can serve as a template for the induction of specific gene expression levels in MSC. Copyright © 2017 John Wiley & Sons, Ltd.

Selective enzymatic removal of elastin and collagen from human abdominal aortas: Uniaxial mechanical response and constitutive modeling

The ability to selectively remove the structurally most relevant components of arterial wall tissues such as collagen and elastin enables ex vivo biomechanical testing of the remaining tissues, with the aim of assessing their individual mechanical contributions. Resulting passive material parameters can be utilized in mathematical models of the cardiovascular system. Using eighteen wall specimens fromnon-atherosclerotic human abdominal aortas (55±11years; 9female, 9male), we tested enzymatic approaches for the selective digestion of collagen and elastin, focusing on their application to human abdominal aortic wall tissues from different patients with varying sample morphologies. The study resulted in an improved protocol for elastin removal, showing how the enzymatic process is affected by inadequate addition of trypsin inhibitor. We applied the resulting protocol to circumferential and axial specimens from the media and the adventitia, and performed cyclic uniaxial extension tests in the physiological and supra-physiological loading domain. The collagenase-treated samples showed a (linear) response without distinct softening behavior, while the elastase-treated samples exhibited a nonlinear, anisotropic response with pronounced remanent deformations (continuous softening), presumably caused by some sliding of collagen fibers within the damaged regions of the collagen network. In addition, our data showed that the stiffness in the initial linear stress–stretch regime at low loads is lower in elastin-free tissue compared to control samples (i.e. collagen uncrimping requires less force than the stretching of elastin), experimentally confirming that elastin is responsible for the initial stiffness in elastic arteries. Utilizing a continuum mechanical description to mathematically capture the experimental results we concluded that the inclusion of a damage model for the non-collagenous matrix material is, in general, not necessary. To model the softening behavior, continuous damage was included in the fibers by adding a damage variable which led to remanent strains through the consideration of damage.

Flow-enhanced nucleation of poly(1-butene): Model application to short-term and continuous shear and extensional flow

A modeling framework for flow-enhanced nucleation of polymers is applied to a broad set of data from literature. Creation of flow-induced pointlike nuclei is coupled to chain stretch of the high-molecular weight tail of the material, calculated with a rheological constitutive model. As the flow-induced nuclei grow, the crystalline volume fraction increases and with it the viscosity of the material. This is accounted for by describing the material as a suspension of spheres in a viscoelastic matrix. Calculations are compared with a broad set of experimental data from literature on three grades of poly(1-butene). First, a parameter set is determined by fitting model results to flow-induced nucleation densities from short-term shear experiments. Next, this parameter set is used to validate the framework in continuous flow experiments in which viscosity is monitored during a constant flow rate. In this way, we demonstrate the approach is applicable to not only short-term shear but also continuous flow. It was observed in experiments that for continuous extensional flow, the viscosity shows an upturn at a constant strain, the value of which is independent of strain rate. We hypothesize that this upturn is related to long chains entering the chain stretch regime, as a result of the extension rate exceeding the inverse of the Rouse time of the longest chains.

DNA conformation in nanochannels: Monte Carlo simulation studies using a primitive DNA model

We have performed canonical ensemble Monte Carlo simulations of a primitive DNA model to study the conformation of 2.56 ~ 21.8 μm long DNA molecules confined in nanochannels at various ionic concentrations with the comparison of our previous experimental findings. In the model, the DNA molecule is represented as a chain of charged hard spheres connected by fixed bond length and the nanochannels as planar hard walls. System potentials consist of explicit electrostatic potential along with short-ranged hard-sphere and angle potentials. Our primitive model system provides valuable insight into the DNA conformation, which cannot be easily obtained from experiments or theories. First, the visualization and statistical analysis of DNA molecules in various channel dimensions and ionic strengths verified the formation of locally coiled structures such as backfolding or hairpin and their significance even in highly stretched states. Although the folding events mostly occur within the region of ~0.5 μm from both chain ends, significant portion of the events still take place in the middle region. Second, our study also showed that two controlling factors such as channel dimension and ionic strength widely used in stretching DNA molecules have different influence on the local DNA structure. Ionic strength changes local correlation between neighboring monomers by controlling the strength of electrostatic interaction (and thus the persistence length of DNA), which leads to more coiled local conformation. On the other hand, channel dimension controls the overall stretch by applying the geometric constraint to the non-local DNA conformation instead of directly affecting local correlation. Third, the molecular weight dependence of DNA stretch was observed especially in low stretch regime, which is mainly due to the fact that low stretch modes observed in short DNA molecules are not readily accessible to much longer DNA molecules, resulting in the increase in the stretch of longer DNA molecules.

The Effect of Dynamical Strain on the Maturation of Collagen-Based Cell-Containing Scaffolds for Vascular Tissue Engineering

Diseases occurring to blood vessel are preferentially solved by replacing the vessel by an autologous graft. When it is not available, a synthetic graft is used which has low patency rates for small diameter (<6 mm) vessels. Tissue engineering of blood vessel aims to improve the performance of vascular substitutes. Bioreactors are used in vascular tissue engineering to mimic the mechanical and biochemical environment of blood vessel. A 2D bioreactor was custom made in order to impose a dynamical strain to silicone membrane receiving the collagen cell-based construct. Collagen gels with vascular smooth muscle cells cultured inside were subdued to maturation under dynamical uniaxial stretch regimes at 1Hz for 48 hours. The percentage of deformation encountered by the silicone membrane was measured by ImageJ. Collagen fibrils and porcine smooth muscle cells (PSMC) orientations were assessed by scanning electron microscopy (SEM). Results show that the study of mechanical conditioning on cell activity is an important issue for enhancing the alignment of collagen fibrils.

Thermo-electro-mechanical instability of dielectric elastomers

We here propose a new method to analyze the thermo-electro-mechanical instability ofdielectric elastomers. The equilibrium equations in this thermodynamic system at differenttemperatures are initially established. We then obtained the critical nominal electric fieldand the critical stretch under various mechanical and thermal loads, involving the effects ofdifferent stretch regimes on the system stability, i.e. the equal-biaxial stretch, theunequal-biaxial stretch and the thickness elongation. Finally, numerical results showed thatas the temperature increases, the critical nominal electric field and the stretchof the dielectric elastomer are strengthened, which consequently stabilize thesystem. The results provide guidance to the design and synthesis of dielectricelastomer-based devices, especially for those operating at various temperatures.

Strain history and TGF-β1 induce urinary bladder wall smooth muscle remodeling and elastogenesis

Mechanical cues that trigger pathological remodeling in smooth muscle tissues remain largely unknown and are thought to be pivotal triggers for strain-induced remodeling. Thus, an understanding of the effects mechanical stimulation is important to elucidate underlying mechanisms of disease states and in the development of methods for smooth muscle tissue regeneration. For example, the urinary bladder wall (UBW) adaptation to spinal cord injury (SCI) includes extensive hypertrophy as well as increased collagen and elastin, all of which profoundly alter its mechanical response. In addition, the pro-fibrotic growth factor TGF-β1 is upregulated in pathologies of other smooth muscle tissues and may contribute to pathological remodeling outcomes. In the present study, we utilized an ex vivo organ culture system to investigate the response of UBW tissue under various strain-based mechanical stimuli and exogenous TGF-β1 to assess extracellular matrix (ECM) synthesis, mechanical responses, and bladder smooth muscle cell (BSMC) phenotype. Results indicated that a 0.5-Hz strain frequency triangular waveform stimulation at 15% strain resulted in fibrillar elastin production, collagen turnover, and a more compliant ECM. Further, this stretch regime induced changes in cell phenotype while the addition of TGF-β1 altered this phenotype. This phenotypic shift was further confirmed by passive strip biomechanical testing, whereby the bladder groups treated with TGF-β1 were more compliant than all other groups. TGF-β1 increased soluble collagen production in the cultured bladders. Overall, the 0.5-Hz strain-induced remodeling caused increased compliance due to elastogenesis, similar to that seen in early SCI bladders. Thus, organ culture of bladder strips can be used as an experimental model to examine ECM remodeling and cellular phenotypic shift and potentially elucidate BMSCs ability to produce fibrillar elastin using mechanical stretch either alone or in combination with growth factors.

Real-time PCR analysis of mechanical strain and BMPs in human periosteal cells: an in vitro model of entheseal stress

Background and objectivesEnthesitis with new cartilage and bone formation, which leads to joint ankylosis, is a hallmark of spondyloarthritis (SpA). Ankylosis is thought to occur initially in entheseal sites, however,...

Stable and Metastable States of Human Amylin in Solution

Patients with type II diabetes exhibit fibrillar deposits of human amylin protein in the pancreas. It has been proposed that amylin oligomers arising along the aggregation or fibril-formation pathways are important in the genesis of the disease. In a step toward understanding these aggregation pathways, in this work we report the conformational preferences of human amylin monomer in solution using molecular simulations and infrared experiments. In particular, we identify a stable conformer that could play a key role in aggregation. We find that amylin adopts three stable conformations: one with an α-helical segment comprising residues 9–17 and a short antiparallel β-sheet comprising residues 24–28 and 31–35; one with an extended antiparallel β-hairpin with the turn region comprising residues 20–23; and one with no particular structure. Using detailed calculations, we determine the relative stability of these various conformations, finding that the β-hairpin conformation is the most stable, followed by the α-helical conformation, and then the unstructured coil. To test our predicted structure, we calculate its infrared spectrum in the amide I stretch regime, which is sensitive to secondary structure through vibrational couplings and linewidths, and compare it to experiment. We find that theoretically predicted spectra are in good agreement with the experimental line shapes presented herein. The implications of the monomer secondary structures on its aggregation pathway and on its interaction with cell membranes are discussed.

Solution Structures of Rat Amylin Peptide: Simulation, Theory, and Experiment

Amyloid deposits of amylin in the pancreas are an important characteristic feature found in patients with Type-2 diabetes. The aggregate has been considered important in the disease pathology and has been studied extensively. However, the secondary structures of the individual peptide have not been clearly identified. In this work, we present detailed solution structures of rat amylin using a combination of Monte Carlo and molecular dynamics simulations. A new Monte Carlo method is presented to determine the free energy of distinct biomolecular conformations. Both folded and random-coil conformations of rat amylin are observed in water and their relative stability is examined in detail. The former contains an α-helical segment comprised of residues 7–17. We find that at room temperature the folded structure is more stable, whereas at higher temperatures the random-coil structure predominates. From the configurations and weights we calculate the α-carbon NMR chemical shifts, with results that are in reasonable agreement with experiments of others. We also calculate the infrared spectrum in the amide I stretch regime, and the results are in fair agreement with the experimental line shape presented herein.

Response to Letter by Marossezky et al

Response: The letter by Marossezky et al takes issue with the design of our recent randomized trial of splinting early after stroke,1 suggesting that our findings failed to show that “routine splinting soon after stroke should be discontinued.” They believe that we did not define “contracture.” We take this opportunity to clarify that we use the term contracture to refer to a reduction in the slack length or compliance of the relaxed muscle.2 Clinically, contracture manifests as a loss of range of motion or an increased resistance to passive movement.3 Much of our article refers to muscle extensibility to make clear …

Regulation of cyclic longitudinal mechanical stretch on proliferation of human bone marrow mesenchymal stem cells.

Mechanical stimulation is critical to both physiological and pathological states of living cells. Although a great deal of research has been done on biological and biochemical regulation of the behavior of bone marrow mesenchymal stem cells (MSCs), the influence of biomechanical factors on their behavior is still not fully documented. In this study, we investigated the modulation of mechanical stretch magnitude, frequency, and duration on the human marrow mesenchymal stem cells (hMSCs) proliferation by an in vitro model system using a mechanical stretch loading apparatus, and optimized the stretch regime for the proliferation of hMSCs. We applied 3-(4,5-dimethylthiazol-2-yl)- 2,5-diphenyl tetrasodium bromide (MTT) assay to estimate the overall proliferative effects of the stretch on hMSCs. We found that fibronectin coating increased adhesion to silicone chamber surface, however, it did not show significant effect on proliferation of hMSCs. A frequency of 1 Hz was more effective in stimulating hMSCs proliferation. At 1 Hz, 5% strain for 15, 30, 60 min, the significant increase of hMSCs proliferation was observed. Proliferation was enhanced at 1 Hz, 10% strain for 15, 30 min, while decreased for 60 min. At 1 Hz, 15% strain, 15 min stretch resulted in the decrease of proliferation, and 30 min and 60 min stretch showed an increased proliferation. Long time (12 and 24 h) strain application blocked the proliferation. These results indicate that mechanical stretch plays an important role in hMSCs growth and proliferation; an appropriate mechanical stretch regime could be a novel approach to promoting proliferation of hMSCs in vitro.

A Pilot Randomized Controlled Trial of a Daily Muscle Stretch Regime to Prevent Contractures in the Arm after Stroke

A Pilot Randomized Controlled Trial of a Daily Muscle Stretch Regime to Prevent Contractures in the Arm after Stroke

A pilot randomized controlled trial of a daily muscle stretch regime to prevent contractures in the arm after stroke

To evaluate the feasibility and effects of daily stretch positioning for prevention of contractures in stroke patients without arm function. Randomized controlled pilot study. Stroke rehabilitation ward, U.K. Twenty-five subjects drawn from an initial pool of 126 presenting with loss of arm function, all within four weeks of stroke. In addition to usual care, subjects in the experimental group (n=13) were prescribed two 30-min stretches for wrist and finger flexors and two 30-min stretches targeting shoulder adductors and internal rotators, per day for up to 12 weeks post stroke. Stretches were carried out by therapists and nursing staff. Passive range of wrist extension and shoulder external rotation to standard force or to pain at four, eight and twelve weeks after stroke. Compliance was variable. Frequency of positioning was fair from four to eight weeks post stroke but declined after that. Mean (SD) frequency of stretch positions completed between four and eight weeks was 36.5 (13.0) for the wrist, 31.2 (14.1) for the shoulder, out of 56 prescribed. There were no significant effects of treatment. By eight weeks post stroke the mean range of wrist extension and shoulder external rotation lost on the affected side in both groups was approximately 30 degrees. The stretch treatment was not well tolerated over many weeks. Statistical power was low due to the large degree of variability of range of motion and small sample size. The regime tested cannot be recommended as a workable treatment to prevent contractures.

Structural Studies of Locally Strained Diffusion Flames

Numerical analysis is performed on the H2/N2-air laminar counterflow diffusion flames affected by positive or negative stretch rate induced by locally sucking flow from fuel and air sides. Adjusting the suction velocity leads to the formation of three typical flame shapes, flat, or with concave or convex curvature. Numerical computations taking into account detailed chemical kinetics and multicomponent diffusion clarify the effects of negative stretch rate on the flame structure and characteristics. In addition, the effect of a preferential diffusion in relation to the flame curvature under the negative stretch regime is discussed. The results show that (1) Temperature increases with decreasing the stretch rate, and the tendency remains even in the regime of negative stretch rate. (2) H2 concentration due to the preferential diffusion and excess enthalpy due to the non-unity Lewis number effect become relatively significant with decreasing stretch rate. This is one of the reasons for (1). (3) Temperature increase due to the negative stretch rate depends on the flame curvature. (4) The maximum flame temperature cannot be rationalized by the local stretch rate, and changes over a wide range depending on the preferential diffusion in relation to flame curvature.

Local equilibrium temperature as a measure of stretch and preferential diffusion effects in counterflow H 2/air premixed flames

The effects of stretch and preferential diffusion on the structure and extinction of hydrogen-air premixed flames are investigated numerically. A symmetric double-flame configuration in a counterflow is adopted as a model problem. A local total enthalpy and enthalpies of formation of local mixture and corresponding equilibrium composition are discussed in conjunction with the energy status of local mixtures. Based on these, a local adiabatic equilibrium temperature is proposed as a measure of energy loss and gain caused by preferential diffusion, flame stretch, and reaction incompleteness. Results show that the extinction mechanism of hydrogen-air premixed flames can be explained based on the reaction incompleteness and energy loss and gain. The reaction incompleteness can be quantified by the difference between flame temperature and local equilibrium temperature and the energy gain by the difference in local equilibrium temperatures between free stream and burned gas. The effects of stretch on reaction incompleteness and energy gain are also discussed. It has been found for the symmetric counterflow flames that lean hydrogen flames have energy gain through preferential diffusion: however, continuous increase in reaction incompleteness with stretch causes extinction. While for rich mixtures, even though reaction incompleteness nearly levels off in the high stretch regime, energy loss by preferential diffusion leads to extinction.

The induction of c-fos and c-jun in the stretched latissimus dorsi muscle of the rabbit: responses to duration, degree and re-application of the stretch stimulus.

The mRNA levels of the proto-oncogenes c-fos and c-jun were measured in the rabbit latissimus dorsi (LD) muscle in response to the application of various stretch regimes in vivo. It was shown that it was necessary for the stretch to be applied continuously over 1 h in order to achieve full induction of c-fos and c-jun mRNA at 1 h. In addition, a correlation was demonstrated between the degree of stretch imposed on the LD and the induced levels of c-fos and c-jun mRNA. Moreover, a second induction of these genes occurred when the LD was subjected to a second stretch stimulus. The magnitude and time course of the second response depended on the precise timing of the second stimulus in relation to the initial induction.