Fiber Stretch Research Articles

Kinematics of cardiac growth: In vivo characterization of growth tensors and strains

Progressive growth and remodeling of the left ventricle are part of the natural history of chronic heart failure and strong clinical indicators for survival. Accompanied by changes in cardiac form and function, they manifest themselves in alterations of cardiac strains, fiber stretches, and muscle volume. Recent attempts to shed light on the mechanistic origin of heart failure utilize continuum theories of growth to predict the maladaptation of the heart in response to pressure or volume overload. However, despite a general consensus on the representation of growth through a second order tensor, the precise format of this growth tensor remains unknown. Here we show that infarct-induced cardiac dilation is associated with a chronic longitudinal growth, accompanied by a chronic thinning of the ventricular wall. In controlled in vivo experiments throughout a period of seven weeks, we found that the lateral left ventricular wall adjacent to the infarct grows longitudinally by more than 10%, thins by more than 25%, lengthens in fiber direction by more than 5%, and decreases its volume by more than 15%. Our results illustrate how a local loss of blood supply induces chronic alterations in structure and function in adjacent regions of the ventricular wall. We anticipate our findings to be the starting point for a series of in vivo studies to calibrate and validate constitutive models for cardiac growth. Ultimately, these models could be useful to guide the design of novel therapies, which allow us to control the progression of heart failure.

Fibre–matrix interaction in the human annulus fibrosus

Although the mechanical behaviour of the human annulus fibrosus has been extensively studied, the interaction between the collagen fibres and the ground matrix has not been well understood and is therefore ignored by most constitutive models. The objective of this study is to identify the significance of the fibre–matrix interaction in the human annulus fibrosus by careful investigation of the experimental data, the theoretical constitutive models, and the numerical simulation results in the literature. Based on the experimental results from biaxial and uniaxial tests, it is shown that the mechanical behaviour of the matrix can be well simulated by an incompressible neo-Hookean type model, but the effective stiffness of the matrix depends on fibre stretch ratio, which can only be explained by fibre–matrix interaction. Furthermore, we find that this interaction takes place anisotropically between the matrix and the fibres distributed in different proportions in different directions. The dependence of the tangent stiffness of the matrix on the first invariant of the deformation tensor can also be explained by this fibre orientation dispersion.

Fiber Stretch and Reorientation Modulates Mesenchymal Stem Cell Morphology and Fibrous Gene Expression on Oriented Nanofibrous Microenvironments

Because differentiation of mesenchymal stem cells (MSCs) is enacted through the integration of soluble signaling factors and physical cues, including substrate architecture and exogenous mechanical stimulation, it is important to understand how micropatterned biomaterials may be optimized to enhance differentiation for the formation of functional soft tissues. In this work, macroscopic strain applied to MSCs in an aligned nanofibrous microenvironment elicited cellular and nuclear deformations that varied depending on scaffold orientation. Reorientation of aligned, oriented MSCs corresponded at the microscopic scale with the affine approximation of their deformation based on macroscopic strains. Moreover, deformations at the subcellular scale corresponded with scaffold orientation, with changes in nuclear shape depending on the direction of substrate alignment. Notably, these deformations induced changes in gene expression that were also dependent on scaffold and cell orientations. These findings demonstrate that directional biases in substrate microstructure convey direction-dependent mechanosensitivity to MSCs and provide an experimental framework in which to explore the mechanistic underpinnings of this response.

Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential-axial and the radial-axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber-matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure-function, and to quantify the effect of degeneration. The biaxial stress-strain response was described well by the model (R (2)>0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young's modulus, provided an explanation for the low values in previously published axial direction Young's modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.

Non-uniform distribution of strain during stretch of relaxed skeletal muscle fibers from rat soleus muscle.

Tension and regional average sarcomere length (L(s)) behavior were examined during repeated stretches of single, permeabilized, relaxed muscle fibers isolated from the soleus muscles of rats. We tested the hypothesis that during stretches of single permeabilized fibers, the global fiber strain is distributed non-uniformly along the length of a relaxed fiber in a repeatable pattern. Each fiber was subjected to eight constant-velocity stretch and release cycles with a strain of 32% and strain rate of 54% s(-1). Stretch-release cycles were separated by a 4.5 min interval. Throughout each stretch-release cycle, sarcomere lengths were measured using a laser diffraction technique in which 20 contiguous sectors along the entire length of a fiber segment were scanned within 2 ms. The results revealed that: (1) the imposed length change was not distributed uniformly along the fiber, (2) the first stretch-release cycle differed from subsequent cycles in passive tension and in the distribution of global fiber strain, and (3) a characteristic "signature" for the L(s) response emerged after cycle 3. The findings support the conclusions that longitudinal heterogeneity exists in the passive stiffness of individual muscle fibers and that preconditioning of fibers with stretch-release cycles produces a stable pattern of sarcomere strains.

Fiber angle and aspect ratio influence the shear mechanics of oriented electrospun nanofibrous scaffolds

Fibrocartilages, including the knee meniscus and the annulus fibrosus (AF) of the intervertebral disc, play critical mechanical roles in load transmission across joints and their function is dependent upon well-defined structural hierarchies, organization, and composition. All, however, are compromised in the pathologic transformations associated with tissue degeneration. Tissue engineering strategies that address these key features, for example, aligned nanofibrous scaffolds seeded with mesenchymal stem cells (MSCs), represent a promising approach for the regeneration of these fibrous structures. While such engineered constructs can replicate native tissue structure and uniaxial tensile properties, the multidirectional loading encountered by these tissues in vivo necessitates that they function adequately in other loading modalities as well, including shear. As previous findings have shown that native tissue tensile and shear properties are dependent on fiber angle and sample aspect ratio, respectively, the objective of the present study was to evaluate the effects of a changing fiber angle and sample aspect ratio on the shear properties of aligned electrospun poly(ε-caprolactone) (PCL) scaffolds, and to determine how extracellular matrix deposition by resident MSCs modulates the measured shear response. Results show that fiber orientation and sample aspect ratio significantly influence the response of scaffolds in shear, and that measured shear strains can be predicted by finite element models. Furthermore, acellular PCL scaffolds possessed a relatively high shear modulus, 2–4 fold greater than native tissue, independent of fiber angle and aspect ratio. It was further noted that under testing conditions that engendered significant fiber stretch, the aggregate resistance to shear was higher, indicating a role for fiber stretch in the overall shear response. Finally, with time in culture, the shear modulus of MSC laden constructs increased, suggesting that deposited ECM contributes to the construct shear properties. Collectively, these findings show that aligned electrospun PCL scaffolds are a promising tool for engineering fibrocartilage tissues, and that the shear properties of both acellular and cell-seeded formulations can match or exceed native tissue benchmarks.

Effect of orientation and targeted extracellular matrix degradation on the shear mechanical properties of the annulus fibrosus

The intervertebral disc experiences combinations of compression, torsion, and bending that subject the disc substructures, particularly the annulus fibrosus (AF), to multidirectional loads and deformations. Combined tensile and shear loading is a particularly important loading paradigm, as compressive loads place the AF in circumferential hoop tension, and spine torsion or bending induces AF shear. Yet the anisotropy of AF mechanical properties in shear, as well as important structure-function mechanisms governing this response, are not well-understood. The objective of this study, therefore, was to investigate the effects of tissue orientation and enzymatic degradation of glycosaminoglycan (GAG) and elastin on AF shear mechanical properties. Significant anisotropy was found: the circumferential shear modulus, Gθz, was an order of magnitude greater than the radial shear modulus, Grθ. In the circumferential direction, prestrain significantly increased the shear modulus, suggesting an important role for collagen fiber stretch in shear properties for this orientation. While not significant and highly variable, ChABC treatment to remove GAG increased the circumferential shear modulus compared to PBS control (p=0.15). Together with the established literature for tensile loading of fiber-reinforced GAG-rich tissues, the trends for changes in shear modulus with ChABC treatment reflect complex, structure-function relationships between GAG and collagen that potentially occur over several hierarchical scales. Elastase digestion did not significantly affect shear modulus with respect to PBS control; further contributing to the notion that circumferential shear modulus is dominated by collagen fiber stretch. The results of this study highlight the complexity of the structure-function relationships that govern the mechanical response of the AF in radial and circumferential shear, and provide new and more accurate data for the validation of material models and tissue-engineered disc replacements.

Contribution of Stretch to the Change of Activation Properties of Muscle Fibers in the Diaphragm at the Transition from Fetal to Neonatal Life

The transition from fetal to postnatal life involves clearance of liquid from the lung and airways, and rapid formation of a functional residual capacity. Despite the importance of the diaphragm in this process, the impact of birth on the mechanical and functional activity of its muscle fibers is not known. This study determined the contractile characteristics of individual “skinned” diaphragm fibers from 70 days (0.47) gestation to after birth in sheep. Based on differential sensitivity to the divalent ions calcium (Ca2+) and strontium (Sr2+), all fibers in the fetal diaphragm were classified as “fast,” whereas fibers from the adult sheep diaphragm exhibited a “hybrid” phenotype where both “fast” and “slow” characteristics were present within each single fiber. Transition to the hybrid phenotype occurred at birth, was evident after only 40 min of spontaneous breathing, and could be induced by simple mechanical stretch of diaphragm fibers from near-term fetuses (∼147 days gestation). Both physical stretch of isolated fibers, and mechanical ventilation of the fetal diaphragm in situ, significantly increased sensitivity to Ca2+ and Sr2+, maximum force generating capacity, and decreased passive tension in near-term and preterm fetuses; however, only fibers from near-term fetuses showed a complete transition to a “hybrid” activation profile. These findings suggest that stretch associated with the transition from a liquid to air-filled lung at birth induces physical changes of proteins determining the activation and elastic properties of the diaphragm. These changes may allow the diaphragm to meet the increased mechanical demands of breathing immediately after birth.

Highly Oriented Crystalline PE Nanofibrils Produced by Electric‐Field‐Induced Stretching of Electrospun Wet Fibers

AbstractIn order to enhance the molecular orientation of electrospun nanofibers, a novel collection technique is proposed and applied to the spinning of polyethylene from high temperature solution. The technique makes use of a parallel‐electrode collector that acts before solidification of the fiber occurs. The resulting multiple‐necking morphology is composed of fine nanofibrils with very small diameter and narrow size distribution. The crystalline orientation of the nanofibrils was analyzed by TED. The formation mechanism of the nanofibrils is discussed. The strong elongational effect of the electric‐field‐induced stretching force in the parallel‐electrode collector is demonstrated by the orientational analysis and by observation of the multiple‐necking morphology. magnified image

Effects of Polymerization and Spinning Conditions on Mechanical Properties of PAN Precursor Fibers

PAN precursor fibers were produced via wet-spinning process, and effects of polymerization and spinning processes, especially the stretching process, were investigated on mechanical properties and micro-morphologies of precursor fibers. An increase in molecular weight, dope solid and densification and a decrease in surface defects were possible by controlling polymerization temperature, the number of heating rollers for densification and the jet stretch ratio, which improved the mechanical properties of precursor fibers. The curves for strength, modulus, tensile power and diameter as a function of stretch ratio can be divided into three stages: steady change area, little change area and sudden change area. With the increase of stretch ratio, the fiber diameter became smaller, the degree of crystallization increased and the structure of precursor fibers became compact and homogeneous, which resulted in the increase of strength, modulus and tensile power of precursor fibers. Empirical relationship between fiber strength and stretch ratio was studied by using the sub-cluster statistical theory. It was successfully predicted when the strengths were 0.8 GPa and 1.0 GPa under a certain technical condition, the corresponding stretch ratio of the fiber were 11.16 and 12.83 respectively.

Modelling skeletal muscle fibre orientation arrangement

Skeletal muscle tissues have complex geometries. In addition, the complex fibre orientation arrangement makes it quite difficult to create an accurate finite element muscle model. There are many possible ways to specify the complex fibre orientations in a finite element model, for example defining a local element coordinate system. In this paper, an alternative method using ABAQUS, which is combination of the finite element method and the non-uniform rational B-spline solid representation, is proposed to calculate the initial fibre orientations. The initial direction of each muscle fibre is specified as the tangent direction of the NURBS curve which the fibre lies on, and the directions of the deformed fibres are calculated from the initial fibre directions, the deformation gradients and the fibre stretch ratios. Several examples are presented to demonstrate the ability of the proposed method. Results show that the proposed method is able to characterise both the muscle complex fibre orientation arrangement and its complex mechanical response.

Effects of blebbistatin and Ca2+ concentration on force produced during stretch of skeletal muscle fibers

When activated muscle fibers are stretched at low speeds [≤ 2 optimal length (L(o))/s], force increases in two phases, marked by a change in slope [critical force (P(c))] that happens at a critical sarcomere length extension (L(c)). Some studies attribute P(c) to the number of attached cross bridges before stretch, while others attribute it to cross bridges in a pre-power-stroke state. In this study, we reinvestigated the mechanisms of forces produced during stretch by altering either the number of cross bridges attached to actin or the cross-bridge state before stretch. Two sets of experiments were performed: 1) activated fibers were stretched by 3% L(o) at speeds of 1.0, 2.0, and 3.0 L(o)/s in different pCa(2+) (4.5, 5.0, 5.5, 6.0), or 2) activated fibers were stretched by 3% L(o) at 2 L(o)/s in pCa(2+) 4.5 containing either 5 μM blebbistatin(+/-) or its inactive isomer (+/+). All stretches started at a sarcomere length (SL) of 2.5 μm. When fibers were activated at a pCa(2+) of 4.5, P(c) was 2.47 ± 0.11 maximal force developed before stretch (P(o)) and decreased with lower concentrations of Ca(2+). L(c) was not Ca(2+) dependent; the pooled experiments provided a L(c) of 14.34 ± 0.34 nm/half-sarcomere (HS). P(c) and L(c) did not change with velocities of stretch. Fibers activated in blebbistatin(+/-) showed a higher P(c) (2.94 ± 0.17 P(o)) and L(c) (16.30 ± 0.38 nm/HS) than control fibers (P(c) 2.31 ± 0.08 P(o); L(c) 14.05 ± 0.63 nm/HS). The results suggest that forces produced during stretch are caused by both the number of cross bridges attached to actin and the cross bridges in a pre-power-stroke state. Such cross bridges are stretched by large amplitudes before detaching from actin and contribute significantly to the force developed during stretch.

The effects of aponeurosis geometry on strain injury susceptibility explored with a 3D muscle model

In the musculoskeletal system, some muscles are injured more frequently than others. For example, the biceps femoris longhead (BFLH) is the most commonly injured hamstring muscle. It is thought that acute injuries result from large strains within the muscle tissue, but the mechanism behind this type of strain injury is still poorly understood. The purpose of this study was to build computational models to analyze the stretch distributions within the BFLH muscle and to explore the effects of aponeurosis geometry on the magnitude and location of peak stretches within the model. We created a three-dimensional finite element (FE) model of the BFLH based on magnetic resonance (MR) images. We also created a series of simplified models with a similar geometry to the MR-based model. We analyzed the stretches predicted by the MR-based model during lengthening contractions to determine the region of peak local fiber stretch. The peak along-fiber stretch was 1.64 and was located adjacent to the proximal myotendinous junction (MTJ). In contrast, the average along-fiber stretch across all the muscle tissue was 0.95. By analyzing the simple models, we found that varying the dimensions of the aponeuroses (width, length, and thickness) had a substantial impact on the location and magnitude of peak stretches within the muscle. Specifically, the difference in widths between the proximal and distal aponeurosis in the BFLH contributed most to the location and magnitude of peak stretch, as decreasing the proximal aponeurosis width by 80% increased peak average stretches along the proximal MTJ by greater than 60% while slightly decreasing stretches along the distal MTJ. These results suggest that the aponeurosis morphology of the BFLH plays a significant role in determining stretch distributions throughout the muscle. Furthermore, this study introduces the new hypothesis that aponeurosis widths may be important in determining muscle injury susceptibility.

A Simple Anisotropic Fiber Reinforced Hyperelastic Constitutive Model for Woven Composite Fabrics

Based on fiber reinforced continuum mechanics theory, a simple hyperelastic constitutive model is developed to characterize the anisotropic nonlinear material behaviour of woven composite fabrics under large deformation during forming. The strain energy function for the hyperelastic model is additively decomposed into two parts nominally representing the tensile energy from weft and warp yarn fiber stretches and shearing energy from fiber-fiber interaction between weft and warp yarns, respectively. The proposed material characterization approach is demonstrated on a balanced plain weave composite fabric. The equivalent material parameters in the hyperelastic constitutive model are obtained by matching experimental load-displacement data of uni-axial tensile and picture frame tests on the woven composite fabric. The development of this anisotropic fiber reinforced hyperelastic model is critical to the numerical simulation and optimization of woven composites forming.

How Mechanical Forces Can Switch On and Off Protein and Cell Binding Sites

How do cells sense whether proteins are stretched or relaxed? While mounting evidence exists that cells and tissues sense mechanical stimuli and convert them into biochemical signals, knowledge about the underpinning mechanisms is sparse. A multitude of structural mechanisms have evolved among extracellular and cytoplasmic proteins that are part of force-bearing protein networks, each enabling distinct modes of mechano-chemical signal conversion. The structural motives include designs by which force can destroy recognitions sites, or alternatively open up cryptic sites that can then recruit other proteins in a force-upregulated manner. Here we will discuss how the stretching of fibronectin fibers, which form the most extensible protein fibers known so far, can activate or destroy protein and cell binding sites over a wide range of mechanical strains. Stretching of fibronectin fibers thus not only increases their Young's moduli, over orders of magnitude until they rupture when stretched to a few MPa, but their biochemical display is altered in intricate ways as well. Deciphering the underlying engineering design principles by which extracellular matrix proteins can serve as mechano-chemical signalling switches is not only essential to learn how cells sense and respond to mechanical forces, and probe the physical properties of their environments. It has far reaching implications in tissue engineering, systems biology and medicine.

Reversal of the Myosin Power Stroke Induced by Fast Stretching of Intact Skeletal Muscle Fibers

Force generation and movement in skeletal muscle result from a cyclical interaction of overlapping myosin and actin filaments that permits the free energy of ATP hydrolysis to be converted into mechanical work. The rapid force recovery that occurs after a step release imposed on a muscle is thought to result from a synchronized tilting of myosin lever arms toward a position of lower free energy (the power stroke). We investigated the power stroke mechanism in intact muscle fibers of Rana esculenta using a fast stretch to detach forcibly cross-bridges. Stretches were applied either with or without a conditioning step release. Cross-bridge rupture tension was not significantly influenced by the release, whereas sarcomere elongation at the rupture point increased immediately after the release and returned to the prerelease condition within 15–20 ms, following a slower time course compared to the recovery of tension. These observations suggest that the rupture force of a bridge is unaltered by a conditioning release, but rupture must first be preceded by a power stroke reversal, which restores the prepower stroke state. The sarcomere extension at the rupture point indicates both the extent of this power stroke reversal and the time course of strained bridge replenishment.

Single-molecule force spectroscopy reveals a highly compliant helical folding for the 30-nm chromatin fiber

The compaction of eukaryotic DNA into chromatin has been implicated in the regulation of all DNA processes. To unravel the higher-order folding of chromatin, we used magnetic tweezers and probed the mechanical properties of single 197-bp repeat length arrays of 25 nucleosomes. At forces up to 4 pN, the 30-nm fiber stretches like a Hookian spring, resulting in a three-fold extension. Together with a high nucleosome-nucleosome stacking energy, this points to a solenoid as the underlying topology of the 30-nm fiber. Unexpectedly, linker histones do not affect the length or stiffness of the fiber but stabilize its folding. Fibers with a nucleosome repeat length of 167 bp are stiffer, consistent with a two-start helical arrangement. The observed high compliance causes extensive thermal breathing, which forms a physical basis for the balance between DNA condensation and accessibility.

Acute Renal Failure and Mechanical Ventilation: Reality or Myth?

Acute Renal Failure and Mechanical Ventilation: Reality or Myth?

A 3D skeletal muscle model coupled with active contraction of muscle fibres and hyperelastic behaviour

This paper presents a three-dimensional finite element model of skeletal muscle which was developed to simulate active and passive non-linear mechanical behaviours of the muscle during lengthening or shortening under either quasi-static or dynamic condition. Constitutive relation of the muscle was determined by using a strain energy approach, while active contraction behaviour of the muscle fibre was simulated by establishing a numerical algorithm based on the concept of the Hill's three-element muscle model. The proposed numerical algorithm could be used to predict concentric, eccentric, isometric and isotonic contraction behaviours of the muscle. The proposed numerical algorithm and constitutive model for the muscle were derived and implemented into a non-linear large deformation finite element programme ABAQUS by using user-defined material subroutines. A number of scenarios have been used to demonstrate capability of the model for simulating both quasi-static and dynamic response of the muscle. Validation of the proposed model has been performed by comparing the simulated results with the experimental ones of frog gastrocenemius muscle deformation. The effects of the fusiform muscle geometry and fibre orientation on the stress and fibre stretch distributions of frog muscle during isotonic contraction have also been investigated by using the proposed model. The predictability of the present model for dynamic response of the muscle has been demonstrated by simulating the extension of a squid tentacle during a strike to catch prey.

Modelling the growth and stabilization of cerebral aneurysms

Experimental and theoretical guidance is needed to understand how the collagen fabric evolves during the development of aneurysms. In this paper, we model the development of an aneurysm as a cylindrical/spherical membrane subject to 1D enlargement; these conceptual models reflect the development of fusiform and saccular cerebral aneurysms. The mechanical response is attributed to the elastin and collagen. We introduce variables which define the elastin and collagen fibre concentration; these evolve to simulate growth/atrophy of the constituents. A hypothetical aneurysm model is analysed: collagen stretch is constant, elastin degrades and collagen fibre concentration can adapt to maintain mechanical equilibrium. An analytic expression for the rate of evolution of the fibre concentration is derived. The functional form is dependent on (i) the current collagen fibre concentration, (ii) the deviations in the collagen fibre stretch from the attachment stretch, (iii) the rate of change of fibre stretch, (iv) the rate of loss of elastin and (v) the ratio of load borne by elastinous and collagenous constituents. Finally, numerical examples of aneurysm development are considered. Suitable candidates for the fibre concentration evolution equations are identified that yield stabilization of the aneurysm even when there is complete loss of elastin. This theoretical analysis provides the basis for the development of physiologically realistic models of aneurysm development.