Microstructural Features of Non-Union of Human Humeral Shaft Fracture

Microstructures of non-unions of human humeral shaft fractures were investigated by using scanning electron microscopy, transmission electron microscopy, and X-ray microdiffraction. The non-union has a trabeculae structural framework similar to woven bone. Among the trabeculae are cavities that are subdivided into small chambers by thin plates of collagen fibrils. Some chambers are filled with variously shaped mineralized particles several micrometers in size. The collagen fibrils in both the trabeculae and the thin plates were only slightly mineralized by hydroxyapatite. Vesicles loaded with noncrystalline calcium phosphate (NCP) were observed in most mineralized particles, and brushite crystals with special morphology were seen to be embedded in some particles in irregular shapes. X-ray microdiffraction results indicated that the mineral phases in the non-unions were mainly NCP in addition to small amounts of hydroxyapatite and brushite. NCP deposition and insufficient mineralization of the collagen fibrils may be two important microstructural features of the non-unions of human humeral shaft fractures different from normally repaired bone callus.     

Mechanical interactions between collagen and proteoglycans: implications for the stability of lung tissue.

Collagen and elastin are thought to dominate the elasticity of the connective tissue including lung parenchyma. The glycosaminoglycans on the proteoglycans may also play a role because osmolarity of interstitial fluid can alter the repulsive forces on the negatively charged glycosaminoglycans, allowing them to collapse or inflate, which can affect the stretching and folding pattern of the fibers. Hence, we hypothesized that the elasticity of lung tissue arises primarily from 1) the topology of the collagen-elastin network and 2) the mechanical interaction between proteoglycans and fibers. We measured the quasi-static, uniaxial stress-strain curves of lung tissue sheets in hypotonic, normal, and hypertonic solutions. We found that the stress-strain curve was sensitive to osmolarity, but this sensitivity decreased after proteoglycan digestion. Images of immunofluorescently labeled collagen networks showed that the fibers follow the alveolar walls that form a hexagonal-like structure. Despite the large heterogeneity, the aspect ratio of the hexagons at 30% uniaxial strain increased linearly with osmolarity. We developed a two-dimensional hexagonal network model of the alveolar structure incorporating the mechanical properties of the collagen-elastin fibers and their interaction with proteoglycans. The model accounted for the stress-strain curves observed under all experimental conditions. The model also predicted how aspect ratio changed with osmolarity and strain, which allowed us to estimate the Young's modulus of a single alveolar wall and a collagen fiber. We therefore identify a novel and important role for the proteoglycans: they stabilize the collagen-elastin network of connective tissues and contribute to lung elasticity and alveolar stability at low to medium lung volumes.     

Biomechanical properties across trabeculae from the proximal femur of normal and ovariectomised sheep

The elastic behaviour of trabecular bone is a function not only of bone volume and architecture, but also of tissue material properties. Variation in tissue modulus can have a substantial effect on the biomechanical properties of trabecular bone. However, the nature of tissue property variation within a single trabecula is poorly understood. This study uses nanoindentation to determine the mechanical properties of bone tissue in individual trabeculae. Using an ovariectomised ovine model, the modulus and hardness distribution across trabeculae were measured. In both normal and ovariectomised bone, the modulus and hardness were found to increase towards the core of the trabeculae. Across the width of the trabeculae, the modulus was significantly less in the ovariectomised bone than in the control bone. However, in contrast to this hardness was found not to differ significantly between the two groups. This study provides valuable information on the variation of mechanical material properties in healthy and diseased trabecular bone tissue. The results of the current study will be useful in finite element modelling where more accurate values of trabecular bone modulus will enable the prediction of the macroscale behaviour of trabecular bone.     

Mechanical properties of mineralized collagen fibrils as influenced by demineralization

Dentin and bone derive their mechanical properties from a complex arrangement of collagen type-I fibrils reinforced with nanocrystalline apatite mineral in extra- and intrafibrillar compartments. While mechanical properties have been determined for the bulk of the mineralized tissue, information on the mechanics of the individual fibril is limited. Here, atomic force microscopy was used on individual collagen fibrils to study structural and mechanical changes during acid etching. The characteristic 67 nm periodicity of gap zones was not observed on the mineralized fibril, but became apparent and increasingly pronounced with continuous demineralization. AFM-nanoindentation showed a decrease in modulus from 1.5 GPa to 50 MPa during acid etching of individual collagen fibrils and revealed that the modulus profile followed the axial periodicity. The nanomechanical data, Raman spectroscopy and SAXS support the hypothesis that intrafibrillar mineral etches at a substantially slower rate than the extrafibrillar mineral. These findings are relevant for understanding the biomechanics and design principles of calcified tissues derived from collagen matrices.     

Uniaxial compression measurement device for investigation of the mechanical stability of biofilms.

The mechanical stability of biofilms is important for biotechnology, as sloughing of the biomass due to mechanical failure of the biofilm matrix can lead to severe interferences with biofilm processes. In cases of biofouling, biofilms have to be removed, in which case their mechanical stability must be overcome. The apparent modulus of elasticity and the yield strength as obtained from uniaxial compression experiments can be taken as parameters indicative for the mechanical stability of a biofilm. A film rheometer is presented which allows for the determination of these quantities, using model biofilms of Pseudomonas aeruginosa grown on membrane filters. The compressive stress-strain behaviour up to the point of failure is recorded at a compression speed of 1 microm s(-1). In accordance with the stress-strain curve, the investigated biofilm can be described as viscoelastic material, which demonstrates plastic flow properties. The extracellular polymeric substances (EPS), which keep biofilms together, form a temporary network of fluctuating junction points. Above the yield point, the gel structure fails and the system behaves as a highly viscous fluid. The apparent modulus of elasticity and the yield point are considered to be useful parameters for characterizing the mechanical properties of biofilms.     

Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments

Which of the elementary components (hydroxyapatite (HA) crystals, collagen, non-collagenous organic matter, water) do significantly contribute to the ultrastructural elastic stiffness magnitude and anisotropy of mineralized tissues; and how, i.e. through which shapes and assemblages (which micromechanical morphology)? We suggest answers to these questions by analyzing stiffness-volume fraction relationships of wet and dry tissue specimens in the framework of strain energy considerations. Radial stiffness values of both isotropic and anisotropic tissues are found to depend linearly to quadratically on only the mineral volume fraction. This suggests the isotropic contribution of HA to the ultrastructural stiffness. An energy-based analysis of the difference between the axial and radial stiffness values of anisotropic, collagen-rich tissues allows us to assess the collagen elasticity contribution, which is found to depend linearly on the extra-collagenous mineral concentration. These results suggest that collagen and hydroxyapatite are the elementary components governing the ultrastructural elastic stiffness magnitude and anisotropy of bone and mineralized tendons. The elastic stiffness of water and non-collagenous organic matter does not play a significant role. As for the morphological issue, we suggest that mineralized tissues are isotropic open crystal foams; and that these foams are reinforced unidirectionally by collagen molecules which are mechanically activated through tight links between these molecules and HA-crystals. The HA crystals are mechanically activated through stretching and bending in long bone tissues, they are predominantly stretched in mineralized tendons, and bent in hyperpycnotic tissues.     

Structure of alveolar bone during tooth eruption in the dog: preliminary findings

The structure of the alveolar bone during the tooth eruption in the young dog mandibles was investigated by microradiographic and polarized light techniques. Around the first erupting molar root a trabecular network of primary alveolar bone, less mineralized than the surrounding cortical one, was found. Numerous calcified spicules parallel one to others radiate out the spongiosa near the periodontal ligament. The collagen fiber bundles of the alveolar, woven, bone are continuous with the periodontal ligament ones. This finding indicates that the alveolar bone increases by ossification of the periodontal ligament. Therefore the latter is the forming alveolar bone substratum. The trabeculae of the occlused premolar alveolar bone are ticker and more mineralized. This modification of the occlused tooth alveolar bone could be related to the occlusal stresses.     

Passive tension in cardiac muscle: contribution of collagen, titin, microtubules, and intermediate filaments.

The passive tension-sarcomere length relation of rat cardiac muscle was investigated by studying passive (or not activated) single myocytes and trabeculae. The contribution of collagen, titin, microtubules, and intermediate filaments to tension and stiffness was investigated by measuring (1) the effects of KCl/KI extraction on both trabeculae and single myocytes, (2) the effect of trypsin digestion on single myocytes, and (3) the effect of colchicine on single myocytes. It was found that over the working range of sarcomeres in the heart (lengths approximately 1.9-2.2 microns), collagen and titin are the most important contributors to passive tension with titin dominating at the shorter end of the working range and collagen at longer lengths. Microtubules made a modest contribution to passive tension in some cells, but on average their contribution was not significant. Finally, intermediate filaments contributed about 10% to passive tension of trabeculae at sarcomere lengths from approximately 1.9 to 2.1 microns, and their contribution dropped to only a few percent at longer lengths. At physiological sarcomere lengths of the heart, cardiac titin developed much higher tensions (> 20-fold) than did skeletal muscle titin at comparable lengths. This might be related to the finding that cardiac titin has a molecular mass of 2.5 MDa, 0.3-0.5 MDa smaller than titin of mammalian skeletal muscle, which is predicted to result in a much shorter extensible titin segment in the I-band of cardiac muscle. Passive stress plotted versus the strain of the extensible titin segment showed that the stress-strain relationships are similar in cardiac and skeletal muscle. The difference in passive stress between cardiac and skeletal muscle at the sarcomere level predominantly resulted from much higher strains of the I-segment of cardiac titin at a given sarcomere length. By expressing a smaller titin isoform, without changing the properties of the molecule itself, cardiac muscle is able to develop significant levels of passive tension at physiological sarcomere lengths.     

Tensile testing of rodlike trabeculae excised from bovine femoral bone

Individual trabeculae, rodlike in form, were excised from bovine femora and tested in tension to obtain stress-strain plots. Tensile grips were constructed to permit such small specimens to be tested and to avoid slippage during the test. Data were collected for 38 specimens. The results of these tests show that rodlike trabeculae obtained from the femora of young bovine animals have an average Young's modulus in tension of approximately 1 GPa. This value is an order of magnitude lower than the corresponding value for cortical bone in the diaphysis of the femur.     

Microrheological Characterization of Collagen Systems: From Molecular Solutions to Fibrillar Gels

Collagen is the most abundant protein in the extracellular matrix (ECM), where its structural organization conveys mechanical information to cells. Using optical-tweezers-based microrheology, we investigated mechanical properties both of collagen molecules at a range of concentrations in acidic solution where fibrils cannot form and of gels of collagen fibrils formed at neutral pH, as well as the development of microscale mechanical heterogeneity during the self-assembly process. The frequency scaling of the complex shear modulus even at frequencies of ∼10 kHz was not able to resolve the flexibility of collagen molecules in acidic solution. In these solutions, molecular interactions cause significant transient elasticity, as we observed for 5 mg/ml solutions at frequencies above ∼200 Hz. We found the viscoelasticity of solutions of collagen molecules to be spatially homogeneous, in sharp contrast to the heterogeneity of self-assembled fibrillar collagen systems, whose elasticity varied by more than an order of magnitude and in power-law behavior at different locations within the sample. By probing changes in the complex shear modulus over 100-minute timescales as collagen self-assembled into fibrils, we conclude that microscale heterogeneity appears during early phases of fibrillar growth and continues to develop further during this growth phase. Experiments in which growing fibrils dislodge microspheres from an optical trap suggest that fibril growth is a force-generating process. These data contribute to understanding how heterogeneities develop during self-assembly, which in turn can help synthesis of new materials for cellular engineering.     

A new molecular model for collagen elasticity based on synchrotron X-ray scattering evidence.

Collagen is the most abundant structural protein in vertebrates. The specific shape of its stress-strain curve is crucial for the function of a number of organs. Although the macroscopic mechanical behavior of collagen is well known, there is still no explanation of the elastic process at the supramolecular level. We have performed in situ synchrotron x-ray scattering experiments, which show that the amount of lateral molecular order increases upon stretching of collagen fibers. In strain cycling experiments the relation between strain and diffuse equatorial scattering was found to be linear in the "heel" region of the stress-strain curve. A new molecular model for collagen elasticity is proposed, which, based on the existence of thermally activated molecular kinks, reproduces this linearity and gives a simple explanation for the form of the stress-strain curve of collagen.     

Elasticity of passive blood vessels: a new concept

The mechanical properties of passive blood vessels are generally thought to depend on the parallel arrangement of elastin and collagen with linear elasticity and collagen recruitment depending on vessel strain [hook-on (HO) model]. We evaluated an alternative model [serial element (SE) model] consisting of the series arrangement of an infinite number of elements, each containing elastin with a constant elastic modulus and collagen that switches stepwise from slack (zero stress) to fully rigid (infinite stiffness) on ongoing element strain. Both models were implemented with Weibull distributions for collagen recruitment strain (HO model) and collagen tightening strain (SE model). The models were tested in experiments on rat mesenteric small arteries. Strain-tension relations were obtained before and after two rounds of digestion by collagenase. Both models fitted the data prior to digestion. However, for the HO model, this required unrealistically low estimates for collagen recruitment or elastic modulus and unrealistically high estimates for distension of collagen fibers. Furthermore, the data after digestion were far better predicted by the SE model compared with the HO model. Finally, the SE model required one parameter less (collagen elastic modulus). Therefore, the SE model provides a valuable starting point for the understanding of vascular mechanics and remodeling of vessels.     

Two-dimensional tension tests in plant biomechanics--sweet cherry fruit skin as a model system

Splitting of fruits is a function of two-dimensional tension caused by different growth rates of tissues and turgor, especially water uptake shortly before harvest. In order to analyse the mechanical properties of spheroid plant material close to stress-strain conditions in vivo, a new hydraulic two-dimensional testing device was set up. Sweet cherry (Prunus avium L.) fruit skin was chosen as a model system. The recorded pressure-deflection curves were non-linear, with a considerable initial "lag phase" and a distinct increasing end part. Taking into account the special geometry, these curves could be modelled with a newly developed analytical approach based on linear elastic material behaviour. The results demonstrated good correlation if a modulus of elasticity ranging from 160 to 250 MPa for the cherry fruit skin was chosen. In addition, a mean strength value of 47 MPa was calculated based on the theory of thin shells and spheres. The results are compared with mechanical data found for fruits and other plant material. In order to test the theoretical approach, two- and one-dimensional tension tests were performed on packaging PE foil, revealing a mean modulus of 171 MPa in bi-axial tension, and 193 and 242 MPa in uni-axial tension, depending on the test speed. The results demonstrate that it seems to be feasible to use this method to analyse the two-dimensional stress-strain conditions of spheroid plant materials such as cherry fruit skins. It may be applied as a tool for crop testing to elucidate the mechanical basis of cracking susceptibility of fruits.     

Sensitivity analysis and parametric study of elastic properties of an unidirectional mineralized bone fibril-array using mean field methods

The key parameters determining the elastic properties of an unidirectional mineralized bone fibril-array decomposed in two further hierarchical levels are investigated using mean field methods. Modeling of the elastic properties of mineralized micro- and nanostructures requires accurate information about the underlying topology and the constituents’ material properties. These input data are still afflicted by great uncertainties and their influence on computed elastic constants of a bone fibril-array remains unclear. In this work, mean field methods are applied to model mineralized fibrils, the extra-fibrillar matrix and the resulting fibril-array. The isotropic or transverse isotropic elastic constants of these constituents are computed as a function of degree of mineralization, mineral distribution between fibrils and extra-fibrillar matrix, collagen stiffness and fibril volume fraction. The linear sensitivity of the elastic constants was assessed at a default set of the above parameters. The strain ratios between the constituents as well as the axial and transverse indentation moduli of the fibril-array were calculated for comparison with experiments. Results indicate that the degree of mineralization and the collagen stiffness dominate fibril-array elasticity. Interestingly, the stiffness of the extra-fibrillar matrix has a strong influence on transverse and shear moduli of the fibril-array. The axial strain of the intra-fibrillar mineral platelets is 30–90% of the applied fibril strain, depending on mineralization and collagen stiffness. The fibril-to-fibril-array strain ratio is essentially ~1. This study provides an improved insight in the parameters, which govern the fibril-array stiffness of mineralized tissues such as bone.     

Optical rheology of porcine sclera by birefringence imaging

Purpose

To investigate a relationship between birefringence and elasticity of porcine sclera ex vivo using polarization-sensitive optical coherence tomography (PS-OCT).

Methods

Elastic parameters and birefringence of 19 porcine eyes were measured. Four pieces of scleral strips which were parallel to the limbus, with a width of 4 mm, were dissected from the optic nerve head to the temporal side of each porcine eye. Birefringence of the sclera was measured with a prototype PS-OCT. The strain and force were measured with a uniaxial material tester as the sample was stretched with a speed of 1.8 mm/min after preconditioning. A derivative of the exponentially-fitted stress-strain curve at 0% strain was extracted as the tangent modulus. Power of exponential stress-strain function was also extracted from the fitting. To consider a net stiffness of sclera, structural stiffness was calculated as a product of tangent modulus and thickness. Correlations between birefringence and these elastic parameters were examined.

Results

Statistically significant correlations between birefringence and all of the elastic parameters were found at 2 central positions. Structural stiffness and power of exponential stress-strain function were correlated with birefringence at the position near the optic nerve head. No correlation was found at the position near the equator.

Conclusions

The evidence of correlations between birefringence and elasticity of sclera tested uniaxially was shown for the first time. This work may become a basis for in vivo measurement of scleral biomechanics using PS-OCT.     

Modelling the mechanical properties of single suspension-cultured tomato cells

BACKGROUND AND AIMS: The relationship between composition and structure of plant primary cell walls, and cell mechanical properties is not fully understood, partly because intrinsic properties of walls such as Young's modulus cannot be obtained readily. The aim of this work is to show that Young's modulus of walls of single suspension-cultured tomato cells can be determined by modelling force-deformation data. METHODS: The model simulates the compression of a cell between two flat surfaces, with the cell treated as a liquid-filled sphere with thin compressible walls. The cell wall and membrane were taken to be permeable, but the compression was so fast that water loss could be neglected in the simulations. Force-deformation data were obtained by compressing the cells in micromanipulation experiments. RESULTS:Good fits were obtained between the model and low-strain experimental data, using the modulus and initial inflation of the cell as adjustable parameters. The mean Young's modulus for 2-week-old cells was found to be 2.3 +/- 0.2 GPa at pH 5. This corresponds to an instantaneous bulk modulus of elasticity of approx. 7 MPa, similar to a value found by the pressure probe method. However, Young's modulus is a better parameter, as it should depend only on the composition and structure of the cell wall, not on bulk cell behaviour. This new method has been used to show that Young's modulus of cultured tomato cell walls is at its lowest at pH 4.5, the pH optimum for expansin activity. CONCLUSIONS:The linear elastic model is very suitable for estimating wall Young's modulus from micromanipulation experiments on single tomato cells. This is a powerful method for determining cell wall material properties.     

Neutron diffraction studies of collagen in fully mineralized bone

Neutron diffraction measurements have been made of the equatorial and meridional spacings of collagen in fully mineralized mature bovine bone and demineralized bone collagen, in both wet and dry conditions. The collagen equatorial spacing in wet mineralized bovine bone is 1.24 nm, substantially lower than the 1.53 nm value observed in wet demineralized bovine bone collagen. Corresponding spacings for dry bone and demineralized bone collagen are 1.16 nm and 1.12 nm, respectively. The collagen meridional long spacing in mineralized bovine bone is 63.6 nm wet and 63.4 nm dry. These data indicate that collagen in fully mineralized bovine bone is considerably more closely packed than had been assumed previously, with a packing density similar to that of the relatively crystalline collagens such as wet rat tail tendon. The data also suggest that less space is available for mineral within the collagen fibrils in bovine bone than had previously been assumed, and that the major portion of the mineral in this bone must be located outside the fibrils.     

Elastic energy storage in human articular cartilage: estimation of the elastic modulus for type II collagen and changes associated with osteoarthritis.

The viscoelastic mechanical properties of normal and osteoarthritic articular were analyzed based on data reported by Kempson [in: Adult Articular Cartilage (1973)] and Silver et al. (Connect. Tissue Res., 2001b). Results of the analysis of tensile elastic stress-strain curves suggest that the elastic modulus of cartilage from the superficial zone is approximately 7.0 GPa parallel and 2.21 GPa perpendicular to the cleavage line pattern. Collagen fibril lengths in the superficial zone were found to be approximately 1265 microm parallel and 668 microm perpendicular to the cleavage line direction. The values for the elastic modulus and fibril lengths decreased with increased extent of osteoarthritis. The elastic modulus of type II collagen parallel to the cleavage line pattern in the superficial zone approaches that of type I collagen in tendon, suggesting that elastic energy storage occurs in the superficial zone due to the tensile pre-tension that exists in this region. Decreases in the elastic modulus associated with osteoarthritis reflect decreased ability of cartilage to store elastic energy, which leads to cartilage fibrillation and fissure formation. We hypothesize that under normal physiological conditions, collagen fibrils in cartilage function to store elastic energy associated with weight bearing and locomotion. Enzymatic cleavage of cartilage proteoglycans and collagen observed in osteoarthritis may lead to fibrillation and fissure formation as a result of impaired energy storage capability of cartilage.     

A Quantitative Study of the Relationship between the Distribution of Different Types of Collagen and the Mechanical Behavior of Rabbit Medial Collateral Ligaments

The mechanical properties of ligaments are key contributors to the stability and function of musculoskeletal joints. Ligaments are generally composed of ground substance, collagen (mainly type I and III collagen), and minimal elastin fibers. However, no consensus has been reached about whether the distribution of different types of collagen correlates with the mechanical behaviors of ligaments. The main objective of this study was to determine whether the collagen type distribution is correlated with the mechanical properties of ligaments. Using axial tensile tests and picrosirius red staining-polarization observations, the mechanical behaviors and the ratios of the various types of collagen were investigated for twenty-four rabbit medial collateral ligaments from twenty-four rabbits of different ages, respectively. One-way analysis of variance was used in the comparison of the Young''s modulus in the linear region of the stress-strain curves and the ratios of type I and III collagen for the specimens (the mid-substance specimens of the ligaments) with different ages. A multiple linear regression was performed using the collagen contents (the ratios of type I and III collagen) and the Young''s modulus of the specimens. During the maturation of the ligaments, the type I collagen content increased, and the type III collagen content decreased. A significant and strong correlation () was identified by multiple linear regression between the collagen contents (i.e., the ratios of type I and type III collagen) and the mechanical properties of the specimens. The collagen content of ligaments might provide a new perspective for evaluating the linear modulus of global stress-strain curves for ligaments and open a new door for studying the mechanical behaviors and functions of connective tissues.     

Trabecular bone's mechanical properties are affected by its non-uniform mineral distribution

The bone remodeling process takes place at the surface of trabeculae and results in a non-uniform mineral distribution. This will affect the mechanical properties of cancellous bone, because the properties of bone tissue depend on its mineral content. We investigated how large this effect is by simulating several non-uniform mineral distributions in 3D finite element models of human trabecular bone and calculating the apparent stiffness of these models. In the ‘linear model’ we assumed a linear relation between mineral content and Young's modulus of the tissue. In the ‘exponential model’ we included an empirical exponential relation in the model. When the linear model was used the mineral distribution slightly changed the apparent stiffness, the difference varied between an 8% decrease and a 4% increase compared to the uniform model with the same BMD. The exponential model resulted in up to 20% increased apparent stiffness in the main load-bearing direction. A thin less mineralized surface layer (28 μm) and highly mineralized interstitial bone (mimicking mineralization resulting from anti-resorptive treatment) resulted in the highest stiffness. This could explain large reductions in fracture risk resulting from small increases in BMD. The non-uniform mineral distribution could also explain why bone tissue stiffness determined using nano-indentation is usually higher than finite element (FE)-determined stiffness. We conclude that the non-uniform mineral distribution in trabeculae does affect the mechanical properties of cancellous bone and that the tissue stiffness determined using FE-modeling could be improved by including detailed information about mineral distribution in trabeculae in the models.