Anisotropy of fibrous tissues in relation to the distribution of tensed and buckled fibers

Fibrous tissues are characterized by a much higher stiffness in tension than compression. This study uses microstructural modeling to analyze the material symmetry of fibrous tissues undergoing tension and compression, to better understand how material symmetry relates to the distribution of tensed and buckled fibers. The analysis is also used to determine whether the behavior predicted from a microstructural model can be identically described by phenomenological continuum models. The analysis confirms that in the case when all the fibers are in tension in the current configuration, the material symmetry of a fibrous tissue in the corresponding reference configuration is dictated by the symmetry of its fiber angular distribution in that configuration. However, if the strain field exhibits a mix of tensile and compressive principal normal strains, the fibrous tissue is represented by a material body which consists only of those fibers which are in tension; the material symmetry of this body may be deduced from the superposition of the planes of symmetry of the strain and the planes of symmetry of the angular fiber distribution. Thus the material symmetry is dictated by the symmetry of the angular distribution of only those fibers which are in tension. Examples are provided for various fiber angular distribution symmetries. In particular, it is found that a fibrous tissue with isotropic fiber angular distribution exhibits orthotropic symmetry when subjected to a mix of tensile and compressive principal normal strains, with the planes of symmetry normal to the principal directions of the strain. This anisotropy occurs even under infinitesimal strains and is distinct from the anisotropy induced from the finite rotation of fibers. It is also noted that fibrous materials are not stable under all strain states due to the inability of fibers to sustain compression along their axis; this instability can be overcome by the incorporation of a ground matrix. It is concluded that the material response predicted using a microstructural model of the fibers cannot be described exactly by phenomenological continuum models. These results are also applicable to nonbiological fiber-composite materials.     

Hindlimb unloading alters ligament healing.

We investigated the hypothesis that hindlimb unloading inhibits healing in fibrous connective tissue such as ligament. Male rats were assigned to 3- and 7-wk treatment groups with three subgroups each: sham control, ambulatory healing, and hindlimb-suspended healing. Ambulatory and suspended animals underwent surgical rupture of their medial collateral ligaments, whereas sham surgeries were performed on control animals. After 3 or 7 wk, mechanical and/or morphological properties were measured in ligament, muscle, and bone. During mechanical testing, most suspended ligaments failed in the scar region, indicating the greatest impairment was to ligament and not to bone-ligament insertion. Ligament testing revealed significant reductions in maximum force, ultimate stress, elastic modulus, and low-load properties in suspended animals. In addition, femoral mineral density, femoral strength, gastrocnemius mass, and tibialis anterior mass were significantly reduced. Microscopy revealed abnormal scar formation and cell distribution in suspended ligaments with extracellular matrix discontinuities and voids between misaligned, but well-formed, collagen fiber bundles. Hence, stress levels from ambulation appear unnecessary for formation of fiber bundles yet required for collagen to form structurally competent continuous fibers. Results support our hypothesis that hindlimb unloading impairs healing of fibrous connective tissue. In addition, this study provides compelling morphological evidence explaining the altered structure-function relationship in load-deprived healing connective tissue.     

The Effect of Static Stretch on Elastin Degradation in Arteries

Previously we have shown that gradual changes in the structure of elastin during an elastase treatment can lead to important transition stages in the mechanical behavior of arteries [1]. However, in vivo arteries are constantly being loaded due to systolic and diastolic pressures and so understanding the effects of loading on the enzymatic degradation of elastin in arteries is important. With biaxial tensile testing, we measured the mechanical behavior of porcine thoracic aortas digested with a mild solution of purified elastase (5 U/mL) in the presence of a static stretch. Arterial mechanical properties and biochemical composition were analyzed to assess the effects of mechanical stretch on elastin degradation. As elastin is being removed, the dimensions of the artery increase by more than 20% in both the longitude and circumference directions. Elastin assays indicate a faster rate of degradation when stretch was present during the digestion. A simple exponential decay fitting confirms the time constant for digestion with stretch (0.11±0.04 h⁻¹) is almost twice that of digestion without stretch (0.069±0.028 h⁻¹). The transition from J-shaped to S-shaped stress vs. strain behavior in the longitudinal direction generally occurs when elastin content is reduced by about 60%. Multiphoton image analysis confirms the removal/fragmentation of elastin and also shows that the collagen fibers are closely intertwined with the elastin lamellae in the medial layer. After removal of elastin, the collagen fibers are no longer constrained and become disordered. Release of amorphous elastin during the fragmentation of the lamellae layers is observed and provides insights into the process of elastin degradation. Overall this study reveals several interesting microstructural changes in the extracellular matrix that could explain the resulting mechanical behavior of arteries with elastin degradation.     

Degeneration affects the fiber reorientation of human annulus fibrosus under tensile load

The angled, lamellar structure of the annulus fibrosus is integral to its load-bearing function. Reorientation of this fiber structure with applied load may contribute to nonlinear mechanical behavior and to large increases in tensile modulus. Fiber reorientation has not yet been quantified for loaded non-degenerated and degenerated annulus fibrosus tissue. The objective of this study was to measure fiber reorientation and mechanical properties (toe- and linear-region modulus, transition strain, and Poisson's ratio) of loaded outer annulus fibrosus tissue using a new application of FFT image processing techniques. This method was validated for quantification of annulus fiber reorientation during loading in this study. We hypothesized that annulus fibrosus fibers would reorient under circumferential tensile load, and that fiber reorientation would be affine. Additionally, we hypothesized that degeneration would affect fiber reorientation, toe-region modulus and Poisson's ratio. Annulus fibrosus fibers were found to reorient toward the loading direction, and degeneration significantly decreased fiber reorientation (the fiber reorientation parameter, m(FFT)=-1.70 degrees /% strain for non-degenerated and -0.95 degrees /% strain for degenerated tissue). Toe-region modulus was significantly correlated with age (r=0.6). Paired t-tests showed no significant difference in the fiber reorientation parameter calculated experimentally with that calculated using an affine prediction. Thus, an affine prediction is a good approximation of fiber reorientation. The findings of this study add to the understanding of overall disc mechanical behavior and degeneration.     

Reticular meshwork of the spleen in rats studied by electron microscopy

The reticular meshwork of the rat spleen, which consists of both fibrous and cellular reticula, was investigated by transmission electron microscopy. The fibrous reticulum of the splenic pulp is composed of reticular fibers and basement membranes of the sinuses. These reticular fibers and basement membranes are continuous with each other. The reticular fibers are enfolded by reticular cells and are composed of two basic elements: 1) peripheral basal laminae of the reticular cells, and 2) central connective tissue spaces in which microfibrils, collagenous fibrils, elastic fibers, and unmyelinated adrenergic nerve fibers are present. The basement membranes of the sinuses are sandwiched between reticular cells and sinus endothelial cells and are composed of lamina-densalike material, microfibrils, collagenous fibrils, and elastic fibers. The presence of these connective tissue fibrous components indicates that there are connective tissue spaces in these basement membranes. The basement membrane is divided into three parts: the basal lamina of the reticular cell, the connective tissue space, and the basal lamina of the sinus endothelial cell. When the connective tissue space is very small or absent, the two basal laminae may fuse to form a single, thick basement membrane of the splenic sinus wall. The fibrous reticulum having these structures is responsible for support (collagenous fibrils) and rebounding (elastic fibers). The cells of the cellular reticulum--reticular cells and their cytoplasmic processes, which possess abundant contractile microfilaments, dense bodies, hemidesmosomes, basal laminae, and a well-developed, rough-surfaced endoplasmic reticulum, and Golgi complexes, which are characteristic of both fibroblasts and smooth muscle cells--are considered to be myofibroblasts. They may play roles in splenic contraction and in fibrogenesis of the fibrous reticulum. The contractile ability may be influenced by the unmyelinated adrenergic nerve fibers that pass through the reticular fibers. The three-dimensional reticular meshwork of the spleen consists of sustentacular fibrous reticulum and contractile myofibroblastic cellular reticulum. This meshwork not only supports the organ but also contributes to a contractile mechanism in circulation regulation, in collaboration with major contractile elements in the capsulo-trabecular system.     

全身纤维结缔组织网络中的界面流体传输现象

纤维结缔组织在身体中的作用是支撑、连接和分隔不同的组织和器官。最近,人体断肢解剖研究证实,一种定向纤维结缔组织组成了一种长程液体传输通路。其解剖位置有两种:皮肤传输通路(包括真皮、皮下组织和脂肪小叶间隔)和血管周围传输通路(静脉和动脉周围纤维结缔组织)。这种纤维通路的三维空间内部结构是一种纵向分布、相互连接的纤维丝,在每一根纤维丝及其周围水凝胶之间形成了一种固液界面区;纤维结缔组织中的液体能够通过这种界面区传输,命名为"生物界面流体传输通路";存在于各种组织和器官纤维基质中的液体,很可能并没有被束缚在"组织凝胶"中,而是在尚未明确的某种物理机制的作用下,朝向一定的方向传输。这些研究结果为理解纤维结缔组织的功能提供了一个新的视角。     

A biomechanical model for fibril recruitment: Evaluation in tendons and arteries

Simulations of soft tissue mechanobiological behaviour are increasingly important for clinical prediction of aneurysm, tendinopathy and other disorders. Mechanical behaviour at low stretches is governed by fibril straightening, transitioning into load-bearing at recruitment stretch, resulting in a tissue stiffening effect. Previous investigations have suggested theoretical relationships between stress-stretch measurements and recruitment probability density function (PDF) but not derived these rigorously nor evaluated these experimentally. Other work has proposed image-based methods for measurement of recruitment but made use of arbitrary fibril critical straightness parameters. The aim of this work was to provide a sound theoretical basis for estimating recruitment PDF from stress-stretch measurements and to evaluate this relationship using image-based methods, clearly motivating the choice of fibril critical straightness parameter in rat tail tendon and porcine artery. Rigorous derivation showed that the recruitment PDF may be estimated from the second stretch derivative of the first Piola-Kirchoff tissue stress. Image-based fibril recruitment identified the fibril straightness parameter that maximised Pearson correlation coefficients (PCC) with estimated PDFs. Using these critical straightness parameters the new method for estimating recruitment PDF showed a PCC with image-based measures of 0.915 and 0.933 for tendons and arteries respectively. This method may be used for accurate estimation of fibril recruitment PDF in mechanobiological simulation where fibril-level mechanical parameters are important for predicting cell behaviour.     

Fibrous framework of human skeletal muscles, fasciae and tendons

By means of scanning and transmissive electron microscopy, the construction of the fibrous framework of the human skeletal muscles, fasciae and tendons has been investigated and its morphofunctional analysis has been performed. The fibrous framework of the endomysium is presented as a complexly organized system of anastomosing fibers of the connective tissue, forming a net-like construction. The fibrous structures of the framework are united into a whole construction by connecting fibers and fibrils. Different types of structural interconnection of collagenous fibers with sarcolemma are revealed. The structure of the fibrous framework both in different muscles and within one muscle has certain peculiarities. The main constructive element of the fascial fibrous framework make large anastomosing collagenous fibers, their architectonics is stabilized by connective fibers and fibrils. The construction of the tendinous fibrous framework is characterized by a pronounced anisotropia of the largest collagenous fibers and a developed network of connective structures both on the surface and inside the collagenous fibers. Structural mechanisms, interconnecting muscles and tendons, are demonstrated. Presence of anastomoses between the fibrils in the composition of the collagenous fibers in the fascia and Achilles tendon are stated. Together with the peculiarities existing, the general principle of the structural organization of the fibrous framework of the muscle system is the net-like constructure dependent on presence of anastomoses and elements of the connective system between the fibrous structures. Depending on the organ's function, the construction of the network acquires certain specific morphological forms.     

A new method of estimating gauge length for porcine aortic valve test specimens

Porcine aortic valve (PAV) cusps are folded and wrinkled in the in vitro state. In the tensile testing of PAV specimens, estimating gauge length (the length at which a specimen starts to offer measurable resistance to load) is often difficult and subjective. We have therefore developed a new method for estimating the gauge length of such tissues. The method is based on the observation that the specimen's gauge length can be associated with a stationary point on the slope of its load-length curve if loaded from a wrinkled state, or a state of slight compression. We represented the load-length response of test specimens in the low-load, high-compliance region by a cubic function and determined the stationary point on the slope of the function using elementary calculus. The cubic function representation is fine-tuned by reducing or expanding an originally selected "test region" until the correlation coefficient of the cubic fit is maximized. The new method was applied to data obtained from the tensile testing of strips of heart valve tissue and was found to be objective, repeatable and robust.     

Cardiac mechanics at the cellular level.

The active mechanical properties of heart muscle are load, length, and time-dependent. The capability for investigating cardiac mechanisms at the cellular level may help to distinguish between those properties of the myocardium which arise from myocardial cells and those which arise from the tissue architecture and extracellular matrix of connective fibers. We present here, for the first time, a general approach for subjecting single heart cells to isometric, isotonic, afterloaded, or physiological loading sequences, while obtaining on-line measures of cell force and length. This approach has been implemented and tested on freshly dissociated, adult frog ventricular myocytes. Examples are presented for each of the four loading sequences.     

A composite micromechanical model for connective tissues: Part I--Theory.

A micromechanical model has been developed to study and predict the mechanical behavior of fibrous soft tissues. The model uses the theorems of least work and minimum potential energy to predict upper and lower bounds on material behavior based on the structure and properties of tissue components. The basic model consists of a composite of crimped collagen fibers embedded in an elastic glycosaminoglycan matrix. Upper and lower bound aggregation rules predict composite material behavior under the assumptions of uniform strain and uniform stress, respectively. Input parameters consist of the component material properties and the geometric configuration of the fibers. The model may be applied to a variety of connective tissue structures and is valuable in giving insight into material behavior and the nature of interactions between tissue components in various structures. Application of the model to rat tail tendon and cat knee joint capsule is described in a companion paper [2].     

Stretching of the back improves gait, mechanical sensitivity and connective tissue inflammation in a rodent model

The role played by nonspecialized connective tissues in chronic non-specific low back pain is not well understood. In a recent ultrasound study, human subjects with chronic low back pain had altered connective tissue structure compared to human subjects without low back pain, suggesting the presence of inflammation and/or fibrosis in the low back pain subjects. Mechanical input in the form of static tissue stretch has been shown in vitro and in vivo to have anti-inflammatory and anti-fibrotic effects. To better understand the pathophysiology of lumbar nonspecialized connective tissue as well as potential mechanisms underlying therapeutic effects of tissue stretch, we developed a carrageenan-induced inflammation model in the low back of a rodent. Induction of inflammation in the lumbar connective tissues resulted in altered gait, increased mechanical sensitivity of the tissues of the low back, and local macrophage infiltration. Mechanical input was then applied to this model as in vivo tissue stretch for 10 minutes twice a day for 12 days. In vivo tissue stretch mitigated the inflammation-induced changes leading to restored stride length and intrastep distance, decreased mechanical sensitivity of the back and reduced macrophage expression in the nonspecialized connective tissues of the low back. This study highlights the need for further investigation into the contribution of connective tissue to low back pain and the need for a better understanding of how interventions involving mechanical stretch could provide maximal therapeutic benefit. This tissue stretch research is relevant to body-based treatments such as yoga or massage, and to some stretch techniques used with physical therapy.     

A microstructurally driven model for pulmonary artery tissue

A new constitutive model for elastic, proximal pulmonary artery tissue is presented here, called the total crimped fiber model. This model is based on the material and microstructural properties of the two main, passive, load-bearing components of the artery wall, elastin, and collagen. Elastin matrix proteins are modeled with an orthotropic neo-Hookean material. High stretch behavior is governed by an orthotropic crimped fiber material modeled as a planar sinusoidal linear elastic beam, which represents collagen fiber deformations. Collagen-dependent artery orthotropy is defined by a structure tensor representing the effective orientation distribution of collagen fiber bundles. Therefore, every parameter of the total crimped fiber model is correlated with either a physiologic structure or geometry or is a mechanically measured material property of the composite tissue. Further, by incorporating elastin orthotropy, this model better represents the mechanics of arterial tissue deformation. These advancements result in a microstructural total crimped fiber model of pulmonary artery tissue mechanics, which demonstrates good quality of fit and flexibility for modeling varied mechanical behaviors encountered in disease states.     

Improved prediction of the collagen fiber architecture in the aortic heart valve

Living tissues show an adaptive response to mechanical loading by changing their internal structure and morphology. Understanding this response is essential for successful tissue engineering of load-bearing structures, such as the aortic valve. In this study, mechanically induced remodeling of the collagen architecture in the aortic valve was investigated. It was hypothesized that, in uniaxially loaded regions, the fibers aligned with the tensile principal stretch direction. For biaxial loading conditions, on the other hand, it was assumed that the collagen fibers aligned with directions situated between the principal stretch directions. This hypothesis has already been applied successfully to study collagen remodeling in arteries. The predicted fiber architecture represented a branching network and resembled the macroscopically visible collagen bundles in the native leaflet. In addition, the complex biaxial mechanical behavior of the native valve could be simulated qualitatively with the predicted fiber directions. The results of the present model might be used to gain further insight into the response of tissue engineered constructs during mechanical conditioning.     

白枕鹤的呼吸系统及其生态适应

白枕鹤的呼吸系统由喉头、气管、鸣管、肺及气囊组成。喉头有淋巴小结分布。气管在龙骨突起内盘旋,并随年龄而增长,软骨环逐渐骨化。鸣管由左右两个支气管特化而成,呈膜状扁管入肺。肺的长度约占躯干的1/2。气囊几遍布全身,高度发达。整个呼吸系统的结构,与其高空飞翔生活相适应。     

Stress and matrix‐responsive cytoskeletal remodeling in fibroblasts

In areolar “loose” connective tissue, fibroblasts remodel their cytoskeleton within minutes in response to static stretch resulting in increased cell body cross‐sectional area that relaxes the tissue to a lower state of resting tension. It remains unknown whether the loosely arranged collagen matrix, characteristic of areolar connective tissue, is required for this cytoskeletal response to occur. The purpose of this study was to evaluate cytoskeletal remodeling of fibroblasts in, and dissociated from, areolar and dense connective tissue in response to 2 h of static stretch in both native tissue and collagen gels of varying crosslinking. Rheometric testing indicated that the areolar connective tissue had a lower dynamic modulus and was more viscous than the dense connective tissue. In response to stretch, cells within the more compliant areolar connective tissue adopted a large “sheet‐like” morphology that was in contrast to the smaller dendritic morphology in the dense connective tissue. By adjusting the in vitro collagen crosslinking, and the resulting dynamic modulus, it was demonstrated that cells dissociated from dense connective tissue are capable of responding when seeded into a compliant matrix, while cells dissociated from areolar connective tissue can lose their ability to respond when their matrix becomes stiffer. This set of experiments indicated stretch‐induced fibroblast expansion was dependent on the distinct matrix material properties of areolar connective tissues as opposed to the cells' tissue of origin. These results also suggest that disease and pathological processes with increased crosslinks, such as diabetes and fibrosis, could impair fibroblast responsiveness in connective tissues. J. Cell. Physiol. 228: 50–57, 2013. © 2012 Wiley Periodicals, Inc.     

Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of?Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the microtubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22–44 s⁻¹, in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.     

Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the microtubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22–44 s⁻¹, in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.     

The abdominal muscle receptor organ in Astacus leptodactylus (Crustacea)

The structure of both the slow- and the fast-adapting abdominal muscle receptor organ of Astacus leptodactylus is described with particular reference to differences between the two systems. The receptors are composed of a thin muscle that extends from the front edge of one segment to the front edge of the following and a sensory cell connected with this muscle. In the zone where the sensory cells enter their respective muscle, muscle fibers are reduced (zone of relative muscle exclusion = ZRME) and partly replaced by connective tissue. The occurrence of dendritic processes of both the slow and the fast neurons is confined to this zone. The following differences between the two receptor types are established: (1) The fast receptor muscle reveals a smaller sarcomere length than the slow receptor muscle and a higher myosin/actin filament ratio. (2) Muscle fibers that pass the ZRME are always found at its periphery in the fast system, separated from dendritic processes by layers of connective tissue, while in the slow system muscle fibers frequently are intermingled with the sensory elements. (3) The ZRME of the slow receptor is 20-30% longer than that of the fast receptor. (4) The dendritic varicosities of the slow neuron, on an average, contain many more mitochondria than those of the fast neuron. (5) Dendritic processes (fine twigs as well as varicosities) are juxtaposed to the sarcolemma of the muscle fibers only in the slow system; in the fast system dendrites and muscle are spatially separated by connective tissue. It is assumed that these differences between the two receptor types are at least in part responsible for the different thresholds observed in physiological experiments.     

Sheep cardiac Purkinje fibers: Configurational changes during the cardiac cycle

Previous attempts to study the cytoarchitecture of cardiac Purkinje fibers with the scanning electron microscope (SEM) have been limited by the surrounding dense connective tissue. In this study the connective tissue was removed by treatment with 8N HCl, after adult sheep hearts were fixed in diastole or systole and tissue taken for SEM and transmission electron microscopy (TEM). In SEM, Purkinje fibers freely anastomosed in false tendons and formed a subendocardial plexus. In systole, medium and small-sized Purkinje fibers formed deep clefts not observed in diastole. The clefts are thought to be due to sarcolemmal folding and fiber buckling and may therefore affect conduction. The myofibrils beneath the laterally apposed sarcolemmas of adjacent Purkinje cells when fixed in systole were often observed as tightly curved arches in series. Similar configurations with expanded arches were observed in diastole. The formation of arches by myofibrils is unique to Purkinje fibers and is interpreted as the mechanism responsible for their compliance to stretch. The significance of contraction in producing the observed geometric changes in Purkinje fibers and the implications of their cytoarchitecture with respect to conduction are discussed.