The mechanical properties of neonatal rat spinal cord in vitro,and comparisons with adult

A number of studies have investigated the mechanical properties of adult spinal cord under tension, however it is not known whether age has an effect on these properties. This is of interest to those aiming to understand the clinical differences between adults and children with spinal cord injury (e.g. severity and recovery), and those developing experimental or computational models for paediatric spinal cord injury. Entire spinal cords were freshly harvested from neonatal rats (14 days) and tested in vitro under uniaxial tension at a range of strain rates (0.2, 0.02, 0.002/s) to a range of strains (2%, 3.5%, 5%), with relaxation responses being recorded for 15 min. These mechanical properties were compared to previously reported data from similar experiments on adult rat spinal cords, and the peak stress and the stress after 15 min of relaxation were found to be significantly higher for spinal cords from adults than neonates (p<0.001). A non-linear viscoelastic model was developed and was observed to adequately predict the mechanical behaviour of this tissue. The model developed in this study may be of use in computational models of paediatric spinal cord. The significant differences between adult and neonatal spinal cord properties may explain the higher initial severity of spinal cord injury in children and may have implications for the development of experimental animal models for paediatric spinal cord injury, specifically for those aiming to match the injury severity with adult experimental models.     

猪眼角膜的生物力学特性

对猪眼角膜进行了有系统的单轴拉伸实验,通过实验来确定其极限强度,断裂能、显著非线性的应力-应变关系和滞后环.在不同的应变水平下进行了应为松弛实验并确定了连续松弛谱的各参数.从极限强度、断裂能和应力松弛来看,角膜的纵向和横向之间无重大的差异,据此,各向同性假定可用于初步的角膜力学模型.     

Nonlinear tensile properties of bovine articular cartilage and their variation with age and depth

Tensile stiffness of articular cartilage is much greater than its compressive stiffness and plays an essential role even in compressive properties by increasing transient fluid pressures during physiological loading. Recent studies of nonlinear properties of articular cartilage in compression revealed several physiologically pertinent nonlinear behaviors, all of which required that cartilage tensile stiffness increase significantly with stretch. We therefore performed sequences of uniaxial tension tests on fresh bovine articular cartilage slices using a protocol that allowed several hours to attain equilibrium and measured longitudinal and transverse tissue strain. By testing bovine cartilage from different ages (6 months to 6 years) we found that equilibrium and transient tensile modulus increased significantly with maturation and age, from 0 to 15 MPa at equilibrium and from 10 to 28 MPa transiently. Our results indicate that cartilage stiffens with age in a manner similar to other highly hydrated connective tissues, possibly due to age-dependent content of enzymatic and nonenzymatic collagen cross links. The long relaxation period used in our tests (5-10 hours) was necessary in order to attain equilibrium and avoid a very significant overestimation of equilibrium modulus that occurs when much shorter times are used (15-30 minutes). We also found that equilibrium and transient tensile modulus increased nonlinearly when cartilage is stretched from 0 to 10% strain without any previous tare load. Although our results estimate a nonlinear increase in tensile stiffness with stretch that is an order of magnitude lower than that required to predict nonlinear properties in compression, they are in agreement with previous results from other uniaxial tension tests of collagenous materials. We therefore speculate that biaxial tensile moduli may be much higher and thereby more compatible with observed nonlinear compressive properties.     

Viscoelastic properties of passive skeletal muscle in compression—Cyclic behaviour

Skeletal muscle relaxation behaviour in compression has been previously reported, but the anisotropic behaviour at higher loading rates remains poorly understood. In this paper, uniaxial unconfined cyclic compression tests were performed on fresh porcine muscle samples at various fibre orientations to determine muscle viscoelastic behaviour. Mean compression level of 25% was applied and cycles of 2% and 10% amplitude were performed at 0.2–80 Hz. Under cycles of low frequency and amplitude, linear viscoelastic cyclic relaxation was observed. Fibre/cross-fibre results were qualitatively similar, but the cross-fibre direction was stiffer (ratio of 1.2). In higher amplitude tests nonlinear viscoelastic behaviour with a frequency dependent increase in the stress cycles amplitude was found (factor of 4.1 from 0.2 to 80 Hz).The predictive capability of an anisotropic quasi-linear viscoelastic model previously fitted to stress-relaxation data from similar tissue samples was investigated. Good qualitative results were obtained for low amplitude cycles but differences were observed in the stress cycle amplitudes (errors of 7.5% and 31.8%, respectively, in the fibre/cross-fibre directions). At higher amplitudes significant qualitative and quantitative differences were evident. A nonlinear model formulation was therefore developed which provided a good fit and predictions to high amplitude low frequency cyclic tests performed in the fibre/cross-fibre directions. However, this model gave a poorer fit to high frequency cyclic tests and to relaxation tests. Neither model adequately predicts the stiffness increase observed at frequencies above 5 Hz.Together with data previously presented, the experimental data presented here provide a unique dataset for validation of future constitutive models for skeletal muscle in compression.     

Effect of temperature on the biaxial mechanics of excised lung parenchyma of the dog.

The influence of temperature on the mechanical properties of excised saline-filled lung parenchyma of the dog was studied at low lung volume. The motivation of this study was to determine whether lung tissue material without the influence of surface tension undergoes a phase transition in the 20-40 degrees C range, as does synthetic elastin studied by Urry in 1984-1986. Dynamic biaxial and uniaxial tensile tests were done, and strain vs. Lagrangian stress curves were recorded during slow cooling and heating between 40 and 10 degrees C. To emphasize the effects of elastin, strains (defined as stretch ratio minus one) were kept below 30%. A slight decrease in compliance occurred with cooling over the entire temperature range. This effect may be attributed to collagen. It was accompanied by a gradual increase in length as the tissue cooled, an effect that may be attributed to elastin. This process was partially reversible with reheating. However, this effect is in contrast with the sudden drastic change in mechanical properties of synthetic elastin described by Urry. Hysteresis, creep, and stress relaxation were small at these low strains. Possible causes of these effects are discussed.     

Local movement in stimulated frog sartorius muscle

Local movement was recorded in tetanically contracting frog sartorius muscle to estimate the nonuniformity in the distribution of compliance in the muscle preparation and the compliance that resides in the attachments of the preparation to the measuring apparatus. The stimulated muscle was also subjected to rapid length changes, and the local movements and tension responses were recorded. The results indicate that during tension development at resting length the central region of the muscle shortens at the expense of the ends. After stimulation the "shoulder" in the tension, which divided the relaxation into a slow decline and a subsequent, rather exponential decay toward zero, was accompanied by an abrupt increase in local movement. We also examined the temperature sensitivity of the two phases of relaxation. The results are consistent with the view that the decrease in tension during relaxation depends on mechanical conditions. The local movement brought about by the imposed length changes indicates that the peak value of the relative length change of the uniformly acting part was approximately 20% less than the relative length change of the whole preparation. From these observations, corrections were obtained for the compliance data derived from the tension responses. These corrections allow a comparison with data in the literature obtained from single fiber preparations. The implications for the stiffness measured during the tension responses are discussed.     

Tensile and compressive behaviour of the bovine periodontal ligament

The mechanical response of the bovine periodontal ligament (PDL) subjected to uniaxial tension and compression is reported. Several sections normal to the longitudinal axis of bovine incisors and molars were extracted from different depths. Specimens with dimensions 10 x 5 x 2 mm including dentine, PDL and alveolar bone were obtained from these sections. Scanning electron microscopy suggested a strong similarity between the bovine PDL and the human PDL microstructure described in the literature. The prepared specimens were tested in a custom made uniaxial testing machine. They were clamped on their bone and dentine extremities and immersed in a saline solution at 37 degrees C. Stress-strain curves indicated that the PDL is characterized by a non-linear and time-dependent mechanical behaviour with the typical features of collagenous soft tissues. The curves exhibited hysteresis and preconditioning effects. The mechanical parameters evaluated in tension were maximum tangent modulus, strength, maximizer strain and strain energy density. For the molars, all these parameters increased with depth except for the apical region. For the incisors, all parameters increased with depth except ultimate strain which decreased. It was assumed that collagen fibre density and orientation were responsible for these findings.     

The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet

We have recently demonstrated that the mitral valve anterior leaflet (MVAL) exhibited minimal hysteresis, no strain rate sensitivity, stress relaxation but not creep (Grashow et al., 2006, Ann Biomed Eng., 34(2), pp. 315-325; Grashow et al., 2006, Ann Biomed. Eng., 34(10), pp. 1509-1518). However, the underlying structural basis for this unique quasi-elastic mechanical behavior is presently unknown. As collagen is the major structural component of the MVAL, we investigated the relation between collagen fibril kinematics (rotation and stretch) and tissue-level mechanical properties in the MVAL under biaxial loading using small angle X-ray scattering. A novel device was developed and utilized to perform simultaneous measurements of tissue level forces and strain under a planar biaxial loading state. Collagen fibril D-period strain (epsilonD) and the fibrillar angular distribution were measured under equibiaxial tension, creep, and stress relaxation to a peak tension of 90 N/m. Results indicated that, under equibiaxial tension, collagen fibril straining did not initiate until the end of the nonlinear region of the tissue-level stress-strain curve. At higher tissue tension levels, epsilonD increased linearly with increasing tension. Changes in the angular distribution of the collagen fibrils mainly occurred in the tissue toe region. Using epsilonD, the tangent modulus of collagen fibrils was estimated to be 95.5+/-25.5 MPa, which was approximately 27 times higher than the tissue tensile tangent modulus of 3.58+/-1.83 MPa. In creep tests performed at 90 N/m equibiaxial tension for 60 min, both tissue strain and epsilonD remained constant with no observable changes over the test length. In contrast, in stress relaxation tests performed for 90 min epsilonD was found to rapidly decrease in the first 10 min followed by a slower decay rate for the remainder of the test. Using a single exponential model, the time constant for the reduction in collagen fibril strain was 8.3 min, which was smaller than the tissue-level stress relaxation time constants of 22.0 and 16.9 min in the circumferential and radial directions, respectively. Moreover, there was no change in the fibril angular distribution under both creep and stress relaxation over the test period. Our results suggest that (1) the MVAL collagen fibrils do not exhibit intrinsic viscoelastic behavior, (2) tissue relaxation results from the removal of stress from the fibrils, possibly by a slipping mechanism modulated by noncollagenous components (e.g. proteoglycans), and (3) the lack of creep but the occurrence of stress relaxation suggests a "load-locking" behavior under maintained loading conditions. These unique mechanical characteristics are likely necessary for normal valvular function.     

Age-dependent changes in the mechanical properties of tail tendons in TGF-beta inducible early gene-1 knockout mice.

The purpose of this study is to investigate age-dependent changes in the architecture and mechanical properties of tendon in TGF-beta inducible early gene-1 (TIEG) knockout mice. Wild-type and TIEG knockout mice, aged 1, 2, and 15 mo, were used. The mechanical properties of tail tendons isolated from these mice were determined using uniaxial tensile ramp (0.05 mm/s) and relaxation (5 mm/s) tests, with a strain of 10%. Mechanical parameters (Young's modulus from the ramp test; fast and static stresses from the relaxation test) were measured and recorded. The structure of the tail tendon fascicle was characterized by transmission electron microscopy. The results of the mechanical testing revealed no significant difference between the knockout and wild-type groups at 1 or 15 mo of age. However, the fascicles of the knockout mice at 3 mo of age exhibited decreased fast and static stresses compared with those of the wild-type mice. Electron microscopy revealed an increase in fibril size in the knockout mouse tendons relative to wild-type controls at 1 and 3 mo of age. These data indicate an important role for TIEG in tendon microarchitecture and strength in adult mice.     

A model for the compressible,viscoelastic behavior of human amnion addressing tissue variability through a single parameter

A viscoelastic, compressible model is proposed to rationalize the recently reported response of human amnion in multiaxial relaxation and creep experiments. The theory includes two viscoelastic contributions responsible for the short- and long-term time-dependent response of the material. These two contributions can be related to physical processes: water flow through the tissue and dissipative characteristics of the collagen fibers, respectively. An accurate agreement of the model with the mean tension and kinematic response of amnion in uniaxial relaxation tests was achieved. By variation of a single linear factor that accounts for the variability among tissue samples, the model provides very sound predictions not only of the uniaxial relaxation but also of the uniaxial creep and strip-biaxial relaxation behavior of individual samples. This suggests that a wide range of viscoelastic behaviors due to patient-specific variations in tissue composition can be represented by the model without the need of recalibration and parameter identification.     

Determination of material parameters of the two-dimensional Holzapfel–Weizsäcker type model based on uniaxial extension data of arterial walls

Soft tissues are anisotropic materials yet a majority of mechanical property tests have been uniaxial, which often failed to recapitulate the tensile response in other directions. This paper aims to study the feasibility of determining material parameters of anisotropic tissues by uniaxial extension with a minimal loss of anisotropic information. We assumed that by preselecting a certain constitutive model, we could give the constitutive parameters based on uniaxial extension data from orthogonal strip samples. In our study, the Holzapfel–Weizsäcker type strain energy density function (H–W model) was used to determine the material parameters of arterial walls from two fresh donation bodies. The key points we applied were the relationships between strain components in uniaxial tensile tests and the methods of stochastic optimisation. Further numerical experiments were taken. The estimate–effect ratio, defined by the number of data with the precision of estimation less than 0.5% over whole size of data, was calculated to demonstrate the feasibility of our method. The material parameters for Chinese aorta and pulmonary artery were given with the maximum root mean square (RMS) errors 0.042, and the minimal estimate–effect ratio in numerical experiments was 90.79%. Our results suggest that the constitutive parameters of arterial walls can be determined from uniaxial extension data, given the passive mechanical behaviour governed by H–W model. This method may apply to other tissues using different constitutive models.     

Stress relaxation behaviour of trabecular bone specimens

The present study defines several conditions under which stress relaxation tests can be performed and investigates the viscoelastic behaviour of trabecular bone in compression through a series of stress relaxation tests at three strain levels and in three loading directions of each cubic specimen. A visoelastic model is proposed to characterize the behaviour of trabecular bone and a spectrum of relaxation times is determined. Trabecular bone from the femoral head is non-linearly viscoelastic and displays anisotropic behaviour, which cannot be more symmetric elastically than orthotropic.     

The development of an improved physical surrogate model of the human spinal cord—Tension and transverse compression

To prevent spinal cord injury, optimize treatments for it, and better understand spinal cord pathologies such as spondylotic myelopathy, the interaction between the spinal column and the spinal cord during injury and pathology must be understood. The spinal cord is a complex and very soft tissue that changes properties rapidly after death and is difficult to model. Our objective was to develop a physical surrogate spinal cord with material properties closely corresponding to the in vivo human spinal cord that would be suitable for studying spinal cord injury under a variety of injurious conditions. Appropriate target material properties were identified from published studies and several candidate surrogate materials were screened, under uniaxial tension, in a materials testing machine. QM Skin 30, a silicone elastomer, was identified as the most appropriate material. Spinal cords manufactured from QM Skin 30 were tested under uniaxial tension and transverse compression. Rectangular specimens of QM Skin 30 were also tested under uniform compression. QM Skin 30 produced surrogate cords with a Young's modulus in tension and compression approximately matching values reported for in vivo animal spinal cords (0.25 and 0.20 MPa, respectively). The tensile and compressive Young's modulus and the behavior of the surrogate cord simulated the nonlinear behavior of the in vivo spinal cord.     

Validation of a pressure diameter method for determining modulus and strain of collagen engagement for long branches of bovine pulmonary arteries

Recent studies have shown that capacitance measurements of large arteries provide better prognosis and diagnosis than tests of resistance alone in pulmonary hypertension (Mahapatra et al., 2006, "Relationship of Pulmonary Arterial Capacitance and Mortality in Idiopathic Pulmonary Arterial Hypertension," J. Am. Coll. Cardiol., 47(4), pp. 799-803; Reuben, 1971, "Compliance of the Human Pulmonary Arterial System in Disease," Circ. Res., 29, pp. 40-50]. Decreased arterial capacitance causes increased load to the heart and is the direct result of increased stiffness and elastic modulus of the arterial wall. Here, we validate a pressure-diameter (PD) method for comparing the elastic modulus and collagen engagement for post-hilar pulmonary arteries with a large range of arterial diameter. The tissue mechanics of the post-hilar arteries are not well-characterized in pulmonary hypertension. It is believed that future studies with this method will provide useful insight into the role of passive tissue mechanics of these arteries in the pathophysiology of pulmonary hypertension, eventually improving clinical diagnosis, prognosis, and treatment. Post-hilar pulmonary arteries, excised from healthy and hypertensive calves and healthy cows, were inflated over a range of 0 [mm Hg] to 110 [mm Hg] in an isolated tissue bath. Internal pressure was recorded with an electric pressure catheter. Artery diameter and longitudinal stretch were recorded photographically. Stress-strain data curves were extracted using Lame's law of thick-walled tubes. Radial strips were removed from each section and tested in a uniaxial (MTS) tester for validation. Both the elastic modulus and collagen engagement strain were similar to results obtained by more traditional means. The average difference between measured values of the two methods for collagen engagement strain was 3.3% of the average value of the engagement strain. The average difference between the measured values of the two methods for modulus of elasticity was 7.4% of the average value of the modulus. The maximum, theoretical, relative error for the stress determined with the PD method was calculated at 20.3%. The PD method proved to be a suitable replacement for uniaxial strain tests in comparing collagen engagement strains. The method allowed faster testing of tissues of multiple diameters, while removing the effect of end conditions. The PD method will be of further utility in continued study of tissue mechanics in pulmonary hypertension studies.     

The measurement of the variation in the surface strains of Achilles tendon grafts using imaging techniques

Uniaxial tensile tests are commonly used to characterize the structural and material properties of tendons and ligaments. During these tests, the stress and strain distributions applied to the specimen are assumed to be uniform. However, few studies have investigated the strain distributions throughout the tissue. The purpose of this study was to use imaging techniques to measure the strains around the circumference of 11 mm wide Achilles tendon grafts during a uniaxial tensile test. Pairs of radiopaque beads with a diameter of 2mm were affixed around the mid-substance of the tendon in four different locations. The motion of the beads was recorded using a cine fluoroscope. This system was shown to measure the displacement of the beads with an accuracy of 0.02 mm. During the uniaxial tensile test, large variations in local tissue strains were observed. At 10 MPa of applied stress, the local tissue strain varied from an average of 2.5-8.7%, an increase in strain of more than three times. As a result of these large variations, the modulus calculated from the stress-strain data varied from an average of 217 to 897 MPa, an increase of approximately 4 times. Furthermore, these data suggest that underestimates of the elastic modulus may result if a uniform strain distribution is assumed. These results indicate that during uniaxial tensile tests, the assumption of uniform stress and strain distributions should be carefully considered and small, uniform specimens should be used when measuring the material properties of soft tissues.     

Viscoelastic behaviour and failure of bovine cancellous bone under constant strain rate

A programme has been established to characterize the long-term behaviour of cancellous bone. Fresh bovine cancellous specimens of dimensions 10 x 10 x 10 mm3 and 10 x 40 x 3.6 mm3 were manufactured and used within the testing programme. Results published in the literature indicate that the long-term behaviour of cancellous bone is well described by a power law, which is a very similar response of typical polymers. So far, dynamic mechanical tests (DMA) in three-point bending, under frequencies between 0.01 and 100 Hz at room temperature, confirmed the published results in a qualitative way. Nevertheless, the measured dimensionless damping, tan delta, was slightly higher than the values reported in the literature for the compact bone. The relaxation curves were obtained from dynamic tests and confirmed that bone relaxation modulus can be described by a power law function of time. Tests under constant compression strain rate were performed at four different strain rates: 0.15/s, 0.015/s, 0.0015/s and 0.00015/s and strain rate dependent behaviour was observed. An average elastic bending modulus of 300 MPa was obtained.     

A comparison of uniaxial and biaxial mechanical properties of the annulus fibrosus: a porcine model

The annulus fibrosus of the intervertebral disk experiences multidirectional tension in vivo, yet the majority of mechanical property testing has been uniaxial. Therefore, our understanding of how this complex multilayered tissue responds to loading may be deficient. This study aimed to determine the mechanical properties of porcine annular samples under uniaxial and biaxial tensile loading. Two-layer annulus samples were isolated from porcine disks from four locations: anterior superficial, anterior deep, posterior superficial, and posterior deep. These tissues were then subjected to three deformation conditions each to a maximal stretch ratio of 1.23: uniaxial, constrained uniaxial, and biaxial. Uniaxial deformation was applied in the circumferential direction, while biaxial deformation was applied simultaneously in the circumferential and compressive directions. Constrained uniaxial consisted of a stretch ratio of 1.23 in the circumferential direction while holding the tissue stationary in the axial direction. The maximal stress and stress-stretch ratio (S-S) moduli determined from the biaxial tests were significantly higher than those observed during both the uniaxial tests (maximal stress, 97.1% higher during biaxial; p=0.002; S-S moduli, 117.9% higher during biaxial; p=0.0004) and the constrained uniaxial tests (maximal stress, 46.8% higher during biaxial; S-S moduli, 82.9% higher during biaxial). These findings suggest that the annulus is subjected to higher stresses in vivo when under multidirectional tension.     

Effect of freezing and thawing on the biomechanical characteristics of porcine ocular tissues

PurposeTo evaluate the effect of freezing and thawing on the biomechanical properties of ex-vivo porcine ocular tissue.MethodsThirty-six porcine eyes (18 pairs) were obtained fresh from a local abattoir and split into two groups of nine pairs to study the effect of storage at −20 °C and −80 °C. A randomly-selected eye from each pair (Control Group, CG) was tested fresh while the fellow eyes were frozen for 14 days, either at −20 °C and −80 °C (Frozen Group, FG) before thawing and testing. Seventy-two strips were extracted from the corneas and scleras of eye globes and subjected to uniaxial tension tests under loads up to 1.0 N. Following five preconditioning cycles, the load and elongation data obtained experimentally were analysed to derive the tissue’s stress-strain and tangent modulus-strain behaviour.ResultsCorneal tissue subjected to freezing at −20 °C exhibited significant increases in tangent modulus (mechanical stiffness) by 13 ± 17% (p = 0.003) at 1% strain and 14 ± 12% (p < 0.001) at 2% strain. In contrast, the increases in corneal stiffness at −80 °C were insignificant (6 ± 14%, p = 0.099 at 1% strain, 6 ± 15%, p = 0.091 at 2% strain). The corresponding increases in tangent modulus in the sclera were all insignificant (for −20 °C: 4 ± 14%, p = 0.265 at 1% strain, 3 ± 9%, p = 0.186 at 2% strain; for −80 °C: 3 ± 18%, p = 0.537 at 1% strain and 3 ± 18%, p = 0.491 at 2% strain).ConclusionsThe study provided evidence that freezing and thawing led to insignificant changes in ocular tissue stiffness except in corneal tissue that was frozen at −20 °C.     

Comparison of cellular strain with applied substrate strain in vitro

Strain magnitudes within tenocytes undergoing substrate tensile strain are not well defined. It was hypothesized that strain magnitudes at the cellular level would reflect those of the applied substrate (equibiaxial or uniaxial) strain. A vacuum-operated device was used to apply equibiaxial or uniaxial tension to a flexible substrate upon which tenocytes were cultured in monolayer. Images of tenocytes labeled with Fura-2, to detect free intracellular calcium ions, and MitoFluor Green, to detect mitochondria, were taken prior to strain and for 20 min during application of static strain. A custom-written, texture correlation program computed strain magnitudes in the cell based on the change in pixel pattern displacements between images of non-strained and strained cells. On average, cellular strain was approximately 37+/-8% and 63+/-11% of the applied equibiaxial and uniaxial substrate strain, respectively. The largest cell strains were detected in cells oriented parallel to the direction of applied uniaxial tensile strain. However, strain magnitudes within a cell were heterogeneous. The variance in strain magnitude within and among tenocytes is dependent on cell orientation, cell stiffness, cytoskeleton organization, subcellular organelles, or placement and type of cell-substrate contacts. Results of the present study indicate that cultured tenocytes experience a moderate fraction of the applied substrate strain.