Material properties of the human lumbar facet joint capsule

The human facet joint capsule is one of the structures in the lumbar spine that constrains motions of vertebrae during global spine loading (e.g., physiological flexion). Computational models of the spine have not been able to include accurate nonlinear and viscoelastic material properties, as they have not previously been measured. Capsules were tested using a uniaxial ramp-hold protocol or a haversine displacement protocol using a commercially available materials testing device. Plane strain was measured optically. Capsules were tested both parallel and perpendicular to the dominant orientation of the collagen fibers in the capsules. Viscoelastic material properties were determined. Parallel to the dominant orientation of the collagen fibers, the complex modulus of elasticity was E*=1.63MPa, with a storage modulus of E'=1.25MPa and a loss modulus of: E" =0.39MPa. The mean stress relaxation rates for static and dynamic loading were best fit with first-order polynomials: B(epsilon) = 0.1110epsilon-0.0733 and B(epsilon)= -0.1249epsilon + 0.0190, respectively. Perpendicular to the collagen fiber orientation, the viscous and elastic secant moduli were 1.81 and 1.00 MPa, respectively. The mean stress relaxation rate for static loading was best fit with a first-order polynomial: B (epsilon) = -0.04epsilon - 0.06. Capsule strength parallel and perpendicular to collagen fiber orientation was 1.90 and 0.95 MPa, respectively, and extensibility was 0.65 and 0.60, respectively. Poisson's ratio parallel and perpendicular to fiber orientation was 0.299 and 0.488, respectively. The elasticity moduli were nonlinear and anisotropic, and capsule strength was larger aligned parallel to the collagen fibers. The phase lag between stress and strain increased with haversine frequency, but the storage modulus remained large relative to the complex modulus. The stress relaxation rate was strain dependent parallel to the collagen fibers, but was strain independent perpendicularly.     

Mechanical properties of porcine femoral cortical bone measured by nanoindentation

This study uses a nanoindentation technique to examine variations in the local mechanical properties of porcine femoral cortical bone under hydrated conditions. Bone specimens from three age groups (6, 12 and 42 months), representing developing bone, ranging from young to mature animals, were tested on the longitudinal and transverse cross-sectional surfaces. Elastic modulus and hardness of individual lamellae within bone's microstructure: laminar bone, interstitial bone, and osteons, were measured. Both the elastic modulus and hardness increased with age. However, the magnitudes of these increases were different for each microstructural component. The longitudinal moduli were higher than the transverse moduli. Dehydrated samples were also tested to allow a comparison with hydrated samples and these resulted in higher moduli and hardness than the hydrated samples. Again, the degree of variation was different for each microstructural component. These results indicate that the developmental changes in bone have different rates of mechanical change within each microstructural component.     

Collagen fibril diameter distribution does not reflect changes in the mechanical properties of in vitro stress-deprived tendons

The purpose of this study was to determine if an association exists between the tensile properties and the collagen fibril diameter distribution in in vitro stress-deprived rat tail tendons. Rat tail tendons were paired into two groups of 21 day stress-deprived and 0 time controls and compared using transmission electron microscopy (n = 6) to measure collagen fibril diameter distribution and density, and mechanical testing (n =6) to determine ultimate stress and tensile modulus. There was a statistically significant decrease in both ultimate tensile strength (control: 17.95+/-3.99 MPa, stress-deprived: 6.79+/-3.91 MPa) and tensile modulus (control: 312.8+/-89.5 MPa, stress-deprived: 176.0+/-52.7 MPa) in the in vitro stress-deprived tendons compared to controls. However, there was no significant difference between control and stress-deprived tendons in the number of fibrils per tendon counted, mean fibril diameter, mean fibril density, or fibril size distribution. The results of this study demonstrate that the decrease in mechanical properties observed in in vitro stress-deprived rat tail tendons is not correlated with the collagen fibril diameter distribution and, therefore, the collagen fibril diameter distribution does not, by itself, dictate the decrease in mechanical properties observed in in vitro stress-deprived rat tail tendons.     

Mechanical properties of native and cross-linked type I collagen fibrils

Micromechanical bending experiments using atomic force microscopy were performed to study the mechanical properties of native and carbodiimide-cross-linked single collagen fibrils. Fibrils obtained from a suspension of insoluble collagen type I isolated from bovine Achilles tendon were deposited on a glass substrate containing microchannels. Force-displacement curves recorded at multiple positions along the collagen fibril were used to assess the bending modulus. By fitting the slope of the force-displacement curves recorded at ambient conditions to a model describing the bending of a rod, bending moduli ranging from 1.0 GPa to 3.9 GPa were determined. From a model for anisotropic materials, the shear modulus of the fibril is calculated to be 33 ± 2 MPa at ambient conditions. When fibrils are immersed in phosphate-buffered saline, their bending and shear modulus decrease to 0.07-0.17 GPa and 2.9 ± 0.3 MPa, respectively. The two orders of magnitude lower shear modulus compared with the Young's modulus confirms the mechanical anisotropy of the collagen single fibrils. Cross-linking the collagen fibrils with a water-soluble carbodiimide did not significantly affect the bending modulus. The shear modulus of these fibrils, however, changed to 74 ± 7 MPa at ambient conditions and to 3.4 ± 0.2 MPa in phosphate-buffered saline.     

The estimated elastic constants for a single bone osteonal lamella

Micromechanical estimates of the elastic constants for a single bone osteonal lamella and its substructures are reported. These estimates of elastic constants are accomplished at three distinct and organized hierarchical levels, that of a mineralized collagen fibril, a collagen fiber, and a single lamella. The smallest collagen structure is the collagen fibril whose diameter is the order of 20 nm. The next structural level is the collagen fiber with a diameter of the order of 80 nm. A lamella is a laminate structure, composed of multiple collagen fibers with embedded minerals and consists of several laminates. The thickness of one laminate in the lamella is approximately 130 nm. All collagen fibers in a laminate in the lamella are oriented in one direction. However, the laminates rotate relative to the adjacent laminates. In this work, all collagen fibers in a lamella are assumed to be aligned in the longitudinal direction. This kind of bone with all collagen fibers aligned in one direction is called a parallel fibered bone. The effective elastic constants for a parallel fibered bone are estimated by assuming periodic substructures. These results provide a database for estimating the anisotropic poroelastic constants of an osteon and also provide a database for building mathematical or computational models in bone micromechanics, such as bone damage mechanics and bone poroelasticity.     

Mechanical properties of rat thoracic and abdominal aortas

Mechanical properties of abdominal and thoracic arteries of 2mm in diameter were determined from adults Wistar rats. A tensile testing instrument was used to obtain stress/strain curves with arteries immersed in physiological buffer at 37 degrees C. A displacement was applied on all arteries with various frequencies (1-7.5Hz) and strains (5-60%). From each curve a Young modulus was obtained using a mathematical model based on a nonlinear soft tissue model. No influence of frequency on modulus was evidenced in the tested range. Abdominal aortas, which were found slightly thicker than thoracic aortas, were characterized by a higher modulus. Due to the interest of decellularized biological materials, we also used SDS/Triton treated arteries, and found that the chemical treatment increased modulus of thoracic arteries. Tensile tests were also performed on thoracic aortas in the longitudinal and transversal directions. Longitudinal moduli were found higher than transversal moduli and the difference could be related to the longitudinal orientation of collagen fibers. These data and mathematical model seem useful in the design of new vascular synthetic or biological prostheses for the field of tissue engineering.     

Dehomogenized Elastic Properties of Heterogeneous Layered Materials in AFM Indentation Experiments

Atomic force microscopy (AFM) is used to study mechanical properties of biological materials at submicron length scales. However, such samples are often structurally heterogeneous even at the local level, with different regions having distinct mechanical properties. Physical or chemical disruption can isolate individual structural elements but may alter the properties being measured. Therefore, to determine the micromechanical properties of intact heterogeneous multilayered samples indented by AFM, we propose the Hybrid Eshelby Decomposition (HED) analysis, which combines a modified homogenization theory and finite element modeling to extract layer-specific elastic moduli of composite structures from single indentations, utilizing knowledge of the component distribution to achieve solution uniqueness. Using finite element model-simulated indentation of layered samples with micron-scale thickness dimensions, biologically relevant elastic properties for incompressible soft tissues, and layer-specific heterogeneity of an order of magnitude or less, HED analysis recovered the prescribed modulus values typically within 10% error. Experimental validation using bilayer spin-coated polydimethylsiloxane samples also yielded self-consistent layer-specific modulus values whether arranged as stiff layer on soft substrate or soft layer on stiff substrate. We further examined a biophysical application by characterizing layer-specific microelastic properties of full-thickness mouse aortic wall tissue, demonstrating that the HED-extracted modulus of the tunica media was more than fivefold stiffer than the intima and not significantly different from direct indentation of exposed media tissue. Our results show that the elastic properties of surface and subsurface layers of microscale synthetic and biological samples can be simultaneously extracted from the composite material response to AFM indentation. HED analysis offers a robust approach to studying regional micromechanics of heterogeneous multilayered samples without destructively separating individual components before testing.     

Tensile experiments and SEM fractography on bovine subchondral bone

Subchondral bone undecalcified samples, extracted from bovine femoral heads, are subjected to a direct tensile load. The Young's modulus of each sample is determined from repeated tests within the elastic limit. In a last test, the tensile load is increased up to the specimen failure, determining the ultimate tensile strength. The investigation is performed on both dry and wet specimens. The measured Young's modulus for dry samples is 10.3+/-2.5GPa, while that of wet samples is 3.5+/-1.2GPa. The ultimate tensile strengths are 36+/-10 and 30+/-7.5MPa for dry and wet specimens, respectively. SEM micrographs of failure surfaces show characteristic lamellar bone structures, with lamellae composed of calcified collagen fibers. Rudimentary osteon-like structures are also observed. Failure surfaces of wet samples show a marked fiber pull-out, while delamination predominates in dry samples. The obtained results are interpreted on the basis of the deformation mechanisms typical of fiber-reinforced laminated composite materials.     

Mechanical properties of physiological and pathological models of collagen peptides investigated via steered molecular dynamics simulations

In this work we used molecular simulations to investigate the elastic properties of collagen single chain and triple helix with the aim of understanding its features starting from first principles. We analysed ideal collagen peptides, homotrimeric and heterotrimeric collagen type I and pathological models of collagen. Triple helices were found much more rigid than single chains, thus enlightening the important role of interchain stabilizing forces, like hydrophobic interaction and hydrogen bonds. We obtained Young's moduli close to 4.5GPa for the ideal model of collagen and for the physiological heterotrimer, while the physiological homotrimer presented a Young's modulus of 2.51GPa, that can be related to a mild form of Osteogenesis Imperfecta in which only the homotrimeric form of collagen type I is produced. Otherwise, the pathological model (presenting a glycine to alanine substitution) showed an elastic modulus of 4.32GPa, thus only slightly lower than the ideal model. This suggests that this mutation only slightly affects the mechanical properties of the collagen molecule, but possibly acts on an higher scale, such as the packing of collagen fibrils.     

Tensile damage and its effects on cortical bone

Plexiform bovine bone samples are repeatedly loaded in tension along their longitudinal axis. In order to induce damage in the bone tissue, bone samples are loaded past their yield point. Half of the bone samples from the damaged group were stored in saline to allow for viscoelastic recovery while the others were decalcified. Tensile tests were conducted on these samples to characterize the effects of damage on the mechanical behavior of the organic matrix (decalcified samples) as well as on bone tissue (stored in saline). The ultimate strain of the damaged decalcified bone is 29% higher compared to that of non-damaged decalcified (control) bone. The ultimate stresses as well as the elastic moduli are similar in both decalcified groups. This phenomenon is also observed in other collagenous tissue (tendon and ligament). This may suggest that damage in bone is caused by shear failure of the organic matrix; transverse separation of the collagen molecules or microfibrils from each other. In contrast, there is a trend towards lowered ultimate strains in damaged bone, which is soaked in saline, with respect to control bone samples (not damaged). The damaged bone tissue exhibits a bi-linear behavior in contrast to the mechanical behavior of non-damaged bone. The initial elastic modulus (below 55 MPa) and ultimate strength of damaged bone are similar to that in non-damaged bone.     

Mechanical properties of collagen fibrils

The formation of collagen fibers from staggered subfibrils still lacks a universally accepted model. Determining the mechanical properties of single collagen fibrils (diameter 50-200 nm) provides new insights into collagen structure. In this work, the reduced modulus of collagen was measured by nanoindentation using atomic force microscopy. For individual type 1 collagen fibrils from rat tail, the modulus was found to be in the range from 5 GPa to 11.5 GPa (in air and at room temperature). The hypothesis that collagen anisotropy is due to the subfibrils being aligned along the fibril axis is supported by nonuniform surface imprints performed by high load nanoindentation.     

The relationship of mechanical properties to morphology in patellar tendon autografts after posterior cruciate ligament replacement in sheep.

In a sheep model the posterior cruciate ligament (PCL) was replaced by a patellar tendon autograft (PTAG) using the central one-third of the ipsilateral patellar tendon (PT). The sheep were sacrificed at 16, 26, 52 and 104 weeks postoperation. The PTAG, and, as controls, the contralateral PCL and PT were harvested. These were examined using biomechanical testing as well as light and transmission electron microscopy, including immunohistological techniques. The material properties (maximum stress, elastic modulus) were compared to the morphological features. The cellular distribution, the distribution of glycosaminoglycans (GAGs), the collagen fibril diameter and the occurrence of Type III collagen were studied. Prior to transplantation, the PTAG was shown to be superior in maximum stress (57.2 +/- 5.5 MPa vs 41.3 +/- 1.9 MPa) and elastic modulus (368.8 +/- 49.3 MPa vs 172.3 +/- 14.6 MPa) to the PCL. The early decline in material properties of the PTAG (maximum stress 22% and elastic modulus 42% of the control) after free grafting paralleled a cell- and capillary-rich PTAG tissue with remnants of necrosis and a poorly organized extracellular matrix. Two years after implantation, with progressive alignment of the tissue matrix, maximum stress and elastic modulus acquired approximately 60 and 70% of the control, respectively. However, there was also an evidence of degenerative changes characterized by acellular areas, loss of the normal bundling pattern of collagen fibers and abnormal accumulation of GAGs. Ultrastructurally, there was a predominant shift to thin collagen fibrils in the PTAG compared to PCL and PT, both consisting of thick and thin collagen fibrils. Thin fibrils were demonstrated to be, in part, split thick fibrils as well as newly formed fibrils. Most of these thin fibrils revealed a positive reaction with antibodies to Type III collagen.     

How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study

This work consists of the validation of a novel approach to estimate the local anisotropic elastic constants of the bone extracellular matrix using nanoindentation. For this purpose, nanoindentation on two planes of material symmetry were analyzed and the resulting longitudinal elastic moduli compared to the moduli measured with a macroscopic tensile test. A combined lathe and tensile system was designed that allows machining and testing of cylindrical microspecimens of approximately 4mm in length and 300 microm in diameter. Three bovine specimens were tested in tension and their outer geometry and porosity assessed by synchrotron radiation microtomography. Based on the results of the traction test and the precise outer geometry, an apparent longitudinal Young's modulus was calculated. Results between 20.3 and 27.6 GPa were found that match with previously reported values for bovine compact bone. The same specimens were then characterized by nanoindentation on a transverse and longitudinal plane. A longitudinal Young's modulus for the bone matrix was then derived using the numerical scheme proposed by Swadener and Pharr and the fabric-elasticity relationship by Zysset and Curnier. Based on the matrix modulus and a power law effective volume fraction, an apparent longitudinal Young's modulus was predicted for each microspecimen. This alternative approach provided values between 19.9 and 30.0 GPa, demonstrating differences between 2% and 13% to the values provided by the initial tensile test. This study therefore raises confidence in our nanoindentation protocol of the bone extracellular matrix and supports the underlying hypotheses used to extract the anisotropic elastic constants.     

Biomechanical and mechanical behavior of the plantar fascia in macro and micro structures

Plantar fascia (PF) is a heterogeneous thickness structure across plantar foot. It is important significance to investigate the biomechanical behavior of the medial, middle and lateral PF regions. To investigate the non-uniform macro/micro structures of the different PF regions, the uniaxial tensile test of PF strips were performed to assess the mechanical behavior of PF. A scanning electron microscope (SEM) was used to visualize and measure the micro morphology of PF associated with collagen fibers. A three-dimensional foot finite element (FE) model was developed to quantify the tensile behavior of the internal PF. The elastic modulus of the lateral PF component (1560 MPa) was observed, followed by the medial (701 MPa), the central (1100 MPa) and the lateral (714 MPa) portions in the central component. Elongation of the central portion (0.192) was lower than the medial (0.223) and the lateral (0.227) portions. The corresponding SEM images showed that the fibers of the central portion were more densely packed and thicker compared to the ambilateral portions in the central component. While the FE model prediction also suggested that the greater elastic modulus of the central PF portion had lower strain (0.192) versus the ambilateral portions. Therefore, the lower elongation and greater elastic modulus at the central portion of PF would probably have a high risk of PF injury. The findings showed a relation between the mechanical tension and fibrous morphology of PF. This information would have a better understanding of the PF pathophysiology diseases related to tear and injury of PF.     

Elastic energy storage in unmineralized and mineralized extracellular matrices (ECMs): a comparison between molecular modeling and experimental measurements

In order to facilitate locomotion and limb movement many animals store energy elastically in their tendons. In the turkey, much of the force generated by the gastrocnemius muscle is stored as elastic energy during tendon deformation and not within the muscle. As limbs move, the tendons are strained causing the collagen fibers in the extracellular matrices to be strained. During growth, avian tendons mineralize in the portions distal to the muscle and show increased tensile strength, modulus, and energy stored per unit strain as a result. In this study the energy stored in unmineralized and mineralized collagen fibers was measured and compared to the amount of energy stored in molecular models. Elastic energy storage values calculated using the molecular model were slightly higher than those obtained from collagen fibers, but display the same increases in slope as the fiber data. We hypothesize that these increases in slope are due to a change from the stretching of flexible regions of the collagen molecule to the stretching of less flexible regions. The elastic modulus obtained from the unmineralized molecular model correlates well with elastic moduli of unmineralized collagen from other studies. This study demonstrates the potential importance of molecular modeling in the design of new biomaterials.     

Hyperelastic properties of human meniscal attachments

Meniscal attachments are ligamentous tissues anchoring the menisci to the underlying subchondral bone. Currently little is known about the behavior of meniscal attachments, with only a few studies quantitatively documenting their properties. The objective of this study was to quantify and compare the tensile mechanical properties of human meniscal attachments in the transverse direction, curve fit experimental Cauchy stress-stretch data to evaluate the hyperelastic behavior, and couple these results with previously obtained longitudinal data to generate a more complete constitutive model. Meniscal attachment specimens were tested using a uniaxial tension test with the collagen fibers oriented perpendicular to the loading axis. Tests were run until failure and load-optical displacement data was recorded for each test. The medial posterior attachment was shown to have a significantly greater elastic modulus (6.42±0.78 MPa) and ultimate stress (1.73±0.32 MPa) when compared to the other three attachments. The Mooney-Rivlin material model was selected as the best fit for the transverse data and used in conjunction with the longitudinal data. A novel computational approach to determining the transition point between the toe and linear regions is presented for the hyperelastic stress-stretch curves. Results from piece-wise non-linear longitudinal curve fitting correlate well with previous linear elastic and SEM findings. These data can be used to advance the design of meniscal replacements and improve knee joint finite element models.     

Assembly of type I collagen: fusion of fibril subunits and the influence of fibril diameter on mechanical properties.

Structural stability of the extracellular matrix is primarily a consequence of fibrillar collagen and the extent of cross-linking. The relationship between collagen self-assembly, consequent fibrillar shape and mechanical properties remains unclear. Our laboratory developed a model system for the preparation of self-assembled type I collagen fibers with fibrillar substructure mimicking the hierarchical structures of tendon. The present study evaluates the effects of pH and temperature during self-assembly on fibrillar structure, and relates the structural effects of these treatments on the uniaxial tensile mechanical properties of self-assembled collagen fibers. Results of the analysis of fibril diameter distributions and mechanical properties of the fibers formed under the different incubation conditions indicate that fibril diameters grow via the lateral fusion of discrete approximately 4 nm subunits, and that fibril diameter correlates positively with the low strain modulus. Fibril diameter did not correlate with either the ultimate tensile strength or the high strain elastic modulus, which suggests that lateral aggregation and consequently fibril diameter influences mechanical properties during small strain mechanical deformation. We hypothesize that self-assembly is mediated by the formation of fibrillar subunits that laterally and linearly fuse resulting in fibrillar growth. Lateral fusion appears important in generating resistance to deformation at low strain, while linear fusion leading to longer fibrils appears important in the ultimate mechanical properties at high strain.     

Quantitative electron microscope observations of the collagen fibrils in rat-tail tendon

An electron microscope study of collagen fibrils from fixed tail tendons of rats has revealed that from some time shortly after birth until maturity, the fibril diameters have a bimodal distribution. The “two” types of fibril are indistinguishable in both transverse and longitudinal section. Unfixed specimens of eight-week-old-tail tendon showed a similar bimodal distribution of diameters though the positions of the peak values compared to fixed specimens of an eight-week-old-tail tendon were shifted upwards by about 30%. It has also been shown quantitatively that the polar collagen fibrils are directed randomly “up” and “down” with respect to their neighbors. Whilst it has been suggested by others that anastomosis is a feature of collagen structure, the results presented here do not support this hypothesis. Fibrillar units ～ 140 Å in diameter have been observed and the possibilities that these are elastic fibers or the breakdown products of collagen fibrils have been considered.     

Evaluation of Stem Cell-to-Tenocyte Differentiation By Atomic Force Microscopy to Measure Cellular Elastic Moduli

In the present study, we evaluated whether stem cell-to-tenocyte differentiation could be evaluated via measurement of the mechanical properties of the cell. We used mechanical uniaxial cyclic stretching to induce the differentiation of human bone marrow mesenchymal stem cells into tenocytes. The cells were subjected to cyclic elongation of 10 or 15 % at a cyclic frequency of 1 Hz for 24 or 48 h, and differentiation was assessed by real-time PCR (rtPCR) determination of messenger RNA expression levels for four commonly used markers of stem cell-to-tenocyte differentiation: type I collagen, type III collagen, tenascin-C, and scleraxis. The rtPCR results showed that cells subjected to 10 % cyclic elongation for 24 or 48 h differentiated into tenocytes. Atomic force microscopy (AFM) was then used to measure the force curves around the cell nuclei, and the AFM data were used to calculate the elastic moduli of the cell surfaces. The elastic modulus values of the control (non-stretched) cells differed significantly from those of cells stretched at 10 % for 24 or 48 h (P < 0.01). Confocal fluorescence microscopic observations of actin stress fibers suggested that the change in elastic modulus was ascribable to the development of the cellular cytoskeleton during the differentiation process. Therefore, we conclude that the atomic force microscopic measurement of the elastic modulus of the cell surface can be used to evaluate stem cell-to-tenocyte differentiation.     

Site specificity of mechanical and structural properties of human fascia lata and their gender differences: A cadaveric study

The whole thigh muscles are covered with the fascia lata, which could have morphological and mechanical features that match the underlying muscles’ functions. In this study, we investigated the morphological and elastic properties of the human fascia lata taken from four (anterior, medial, lateral, and posterior) sites on the thigh of 17 legs of 12 cadavers (6 males and 6 females, 75–92 years). The thickness of the fascia lata was determined with a caliper. The interwoven collagen fiber’s directions were measured and classified into longitudinal, transverse, and diagonal in two opposing directions, relative to the thigh. Tensile strength test along the longitudinal and transverse directions was performed, and the stiffness, Young’s modulus, and hysteresis were determined. Fascia lata at the lateral site (0.8 ± 0.2 mm) was significantly thicker compared to other sites (0.2–0.3 mm). Fiber’s directions showed substantial variability among sites, and longitudinally directed fibers were higher in proportion (28–32%) than those in other directions (20–27%) at all sites except for the posterior site. The stiffness and Young’s modulus in the longitudinal direction (20–283 N/mm; 71.6–275.9 MPa, highest at the lateral site) were significantly higher than in the transverse direction (3–16 N/mm; 3.2–41.9 MPa, lowest at the lateral site). At the medial site, the proportion of the transversely directed fibers was higher in females than males, with higher stiffness and Young’s modulus thereof. The present study shows that the fascia lata possesses site- and gender-dependence of the morphological characteristics and elastic properties.