Mechanical properties of brain tissue in tension

This paper contains experimental results of in vitro, uniaxial tension of swine brain tissue in finite deformation as well as proposes a new hyper-viscoelastic constitutive model for the brain tissue. The experimental results obtained for two loading velocities, corresponding to strain rates of 0.64 and 0.64 x 10(-2)s(-1), are presented. We believe that these are the first ever experiments of this kind. The applied strain rates were similar to those applied in our previous study, focused on explaining brain tissue properties in compression. The stress-strain curves are convex downward for all extension rates. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. Swine brain tissue was found to be considerably softer in extension than in compression. Previously proposed in the literature brain tissue constitutive models, developed based on experimental data collected in compression are shown to be inadequate to explain tissue behaviour in tension. A new, non-linear, viscoelastic model based on the generalisation of the Ogden strain energy hyper-elastic constitutive equation is proposed. The new model accounts well for brain tissue deformation behaviour in both tension and compression (natural strain in <-0.3,0.2>) for strain rates ranging over five orders of magnitude.     

Mechanical behaviour of bio-inspired brittle-matrix nanocomposites under different strain rates using molecular dynamics

We study the generic mechanical behaviour of ceramic–ceramic nanocomposites inspired from biological materials. The nanocomposite models considered in our study are the regularly and stairwise staggered arrangements of stiff brittle platelets embedded in compliant brittle matrix. Molecular dynamics simulations are carried out to investigate the effect of strain rate on these nanocomposites. The variation in stress–strain behaviour and mechanical properties are analysed. The evolution of deformation processes is also investigated. Our results show the existence of different strain rate regimes separated by critical strain rate. Deformation mechanisms such as matrix cracking, crack bridging, interfacial debonding and hence platelet pullout are observed at lower strain rates. Amorphous deformation and direct debonding without matrix cracking are observed at higher strain rates.     

Do changes in the mechanical properties of articular cartilage promote catabolic destruction of cartilage and osteoarthritis?

Osteoarthritis (OA) is a joint disease characterized by cartilage degeneration, a thickening of subchondral bone, and formation of marginal osteophytes. Previous mechanical characterization of cartilage in our laboratory suggests that energy storage and dissipation is reduced in osteoarthritis as the extent of fibrillation and fissure formation increases. It is not clear whether the loss of energy storage and dissipation characteristics is a result of biochemical and/or biophysical changes that occur to hyaline cartilage in joints. The purpose of this study is to present data, on the strain rate dependence of the elastic and viscous behaviors of cartilage, in order to further characterize changes that occur in the mechanical properties that are associated with OA. We have previously hypothesized that the changes seen in the mechanical properties of cartilage may be due to altered mechanochemical transduction by chondrocytes. Results of incremental tensile stress-strain tests at strain rates between 100%/min and 10,000%/min conducted on OA cartilage indicate that the slope of the elastic stress-strain curve increases with increasing strain rate, unlike the reported behavior of skin and self-assembled collagen fibers. It is suggested that the strain-rate dependence of the elastic stress-strain curve is due to the presence of large quantities of proteoglycans (PGs), which protect articular cartilage by increasing the apparent stiffness. The increased apparent stiffness of articular cartilage at high strain rates may limit the stresses borne and prolong the onset of OA. It is further hypothesized that increased compressive loading of chondrocytes in the intermediate zone of articular cartilage occurs as a result of normal wear to the superficial zone or from excessive impact loading. Once the superficial zone of articular cartilage is worn away, the tension is decreased throughout all cartilage zones leading to increased chondrocyte compressive loading and up-regulation of mechanochemical transduction processes that elaborate catabolic enzymes.     

The mechanical properties of rat spinal cord in vitro

Freshly excised rat spinal cords were tested in uniaxial tension, in vitro, at strain rates ranging from 0.002 to 0.2 s-1. Stress relaxation tests were performed for a range of strains from 2% to 5%, with the relaxation behaviour being recorded for a period of at least 30 min. Samples exhibited a characteristic "J" shaped non-linear stress-strain response, with stiffness increasing with applied strain. The cords were labelled with rows of small markers and the uniaxial tension tests were recorded via video. Subsequent image analysis enabled the distribution of strain on the cord surface to be determined. Viscoelastic models were developed to model the mechanical behaviour of the specimens and were found to adequately describe the material behaviour.     

Inertia effects on characterization of dynamic response of brain tissue

Modeling and simulation of traumatic brain injury (TBI) resulted from collision or blast loading requires characterization of mechanical response over a wide range of loading rates under valid testing conditions. In this study, mechanical response of fresh bovine brain tissue was studied using the two modified Kolsky bar techniques. Radial deformation behavior of annular specimens, which are typically used to characterize the dynamic uniaxial compressive response of biological tissues, was examined using a modified Kolsky bar and a high speed camera to collect images while the specimen deforms at an axial strain rate of 2000s(-1). The high-speed images revealed inhomogeneous specimen deformation possibly brought about by radial inertia and causing a multi-axial stress state. To acquire valid stress-strain results that can be used to produce constitutive behavior of the soft materials, a novel torsion technique was developed to obtain pure shear response at dynamic loading rates. Experimental results show clear differences in the material response using the two methods. These results indicate that the previously demonstrated annular specimen geometry aimed at reducing inertia induced stress components for high rate soft materials uniaxial-compressive testing may still possess a significant component of radial inertia induced radial stress which consequently caused the observed inhomogeneous deformation in brain tissue test samples.     

The measurement and modelling of the mechanical properties of human skin in vivo--I. The measurement

The mechanical properties of human skin in vivo are studied by means of uniaxial strain measurements. In order to obtain a stress-strain relationship which is independent of the in vivo measuring configuration, values for the effective width and effective length of the loaded skin strip have to be known. By variation of tab width and tab distance in a few series of experiments on the same subject, these effective values are found. In order to obtain a time independent stress-strain relationship a correction procedure is introduced. In this procedure the time dependent (viscoelastic) effects are described and subtracted from the total response.     

Control of sweating in man after work-induced thermal load and symmetrically applied cooling

To examine the compensatory effects of work-induced thermal load and symmetrically applied local cooling on local sweat rates, two kinds of experiment were carried out on eight male subjects in a climatic chamber: 1) Experiments at 36 degrees C ambient temperature with a work load of about 25 W by the right leg. 2) Experiments at 36 degrees C ambient temperature with a work load of about 25 W by the right leg as in 1., but with additional compensatory cooling of the left leg controlled throughout by heat balance calculations at 75-85 W, equal to the heat produced in the working leg, the necessary air temperature being dependent on local sweat rate. Work load without cooling brought about a significant increase in core temperatures, metabolism, heart rate and local sweat rates. With unchanged local skin temperatures local sweat rate increase was higher in the working leg. Therefore the existence of muscle thermoreceptors should be assumed, the afferent information from which is processed and weighted in a different way to that provided by skin receptors. Work load combined with additional cooling reduced local and mean skin temperatures and heart rate, but had no significant influence on core temperature or metabolism. However, local sweat rate was generally lower in both thighs, with a major reduction in the cooled leg confirming control of local sweat rate by local temperature.(ABSTRACT TRUNCATED AT 250 WORDS)     

Three-dimensional Orthotropic Viscoelastic Finite Element Model of a Human Ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only.

A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.     

Compression behavior of porcine spinal cord white matter

Spinal cord injury often results from a compressive load; however, the compression behavior of spinal cord white matter has not been clearly established. Quantifying the compression behavior is important for advancing our understanding of spinal cord injury mechanics and facilitating the use of finite element models to study injury. The objective of this study was to characterize the unconfined compression behavior of isolated white matter segments and determine the constitutive model which best captured the stress-strain behavior. Spinal cord white matter samples were harvested immediately following sacrifice from juvenile Yorkshire pigs (n=104). The samples were compressed to 40% strain at four strain rates (0.005, 0.05, 0.5, and 5.0/s) and allowed to relax for 60s. The effects of preload, peak strain, sample aspect ratio, and time post mortem on peak stress, and constitutive model parameters were also examined. Strain rate had a significant effect on peak stress (p<0.001). A first-order Ogden model best captured the loading response of spinal cord white matter (R(2)=0.99) and a viscoelastic material model combining a first-order Ogden model with a 3-term Prony series effectively captured the effect of strain rate and the relaxation response. This study showed spinal cord white matter to be less stiff than previously estimated by inverse finite element methods, which will have a significant effect on finite element model predictions of the magnitude and distribution of stresses and strains in the spinal cord. This study is the first to quantify the unconfined compression response of spinal cord white matter.     

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin

The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.     

Dynamic response of the isolated passive rat diaphragm strip.

To further our understanding of the mechanisms underlying chest wall mechanics, we investigated the dynamic response of the isolated passive rat diaphragm strip. Stress adaptation of the tissue was measured from 0.05 to 60 s after subjecting the strips to strain steps of normalized strain amplitudes from 0.005 to 0.04. The tissue resistance (R), elastance (E), and hysteresivity (eta) were measured in the same range of amplitudes by sinusoidally straining the strip at frequencies from 0.03125 to 10 Hz. The stress (T) depended exponentially on the strain (epsilon) and relaxed and recovered linearly with the logarithm of time. E increased linearly with the logarithm of frequency and decreased with increasing amplitude. R fell hyperbolically with frequency and showed an amplitude dependence similar to that of E. To interpret the strong nonlinear behavior, we extended the viscoelastic model of Hildebrandt (J. Appl. Physiol. 28: 365-372, 1970) to include an exponential stress-strain relationship. Accordingly, the step response was described by T - Tr = Tr(e alpha delta epsilon - 1)(1 - gamma log t), where delta epsilon is the strain amplitude, Tr is the initial operating stress, alpha is a measure of the stress-strain nonlinearity, and gamma is the rate of stress adaptation. The oscillatory response of the model was computed by applying Fung's quasi-linear viscoelastic theory. This quasi-linear viscoelastic model fitted the step and oscillatory data fairly well but only if alpha depended negatively on delta epsilon, as might be expected in a plastic material.     

The structure and mechanical design of rhinoceros dermal armour.

The collagenous dermis of the white rhinoceros forms a thick, protective armour that is highly specialized in its structure and material properties compared with other mammalian skin. Rhinoceros skin is three times thicker than predicted allometrically, and it contains a dense and highly ordered three-dimensional array of relatively straight and highly crosslinked collagen fibres. The skin of the back and flanks exhibits a steep stress-strain curve with very little 'toe' region, a high elastic modulus (240 MPa), a high tensile strength (30 MPa), a low breaking strain (0.24) and high breaking energy (3 MJm-3) and work of fracture (78 kJm-2). By comparison, the belly skin is somewhat less stiff, weaker, and more extensible. In compression, rhinoceros skin withstands average stresses and strains of 170 MPa and 0.7, respectively, before yielding. As a biological material, rhinoceros dorsolateral skin has properties that are intermediate between those of 'normal' mammalian skin and tendons. This study shows that the dermal armour of the rhinoceros is very well adapted to resist blows from the horns of conspecifics, as might occur during aggressive behaviour, due to specialized material properties as well as its great thickness.     

Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure

It is difficult to define the 'physiological' mechanical properties of bone. Traumatic failures in-vivo are more likely to be orders of magnitude faster than the quasistatic tests usually employed in-vitro. We have reported recently [Hansen, U., Zioupos, P., Simpson, R., Currey, J.D., Hynd, D., 2008. The effect of strain rate on the mechanical properties of human cortical bone. Journal of Biomechanical Engineering/Transactions of the ASME 130, 011011-1-8] results from tests on specimens of human femoral cortical bone loaded in tension at strain rates (epsilon ) ranging from low (0.08s(-1)) to high (18s(-1)). Across this strain rate range the modulus of elasticity generally increased, stress at yield and failure and strain at failure decreased for rates higher than 1s(-1), while strain at yield was invariant for most strain rates and only decreased at rates higher than 10s(-1). The results showed that strain rate has a stronger effect on post-yield deformation than on initiation of macroscopic yielding. In general, specimens loaded at high strain rates were brittle, while those loaded at low strain rates were much tougher. Here, a post-test examination of the microcracking damage reveals that microcracking was inversely related to the strain rate. Specimens loaded at low strain rates showed considerable post-yield strain and also much more microcracking. Partial correlation and regression analysis suggested that the development of post-yield strain was a function of the amount of microcracking incurred (the cause), rather than being a direct result of the strain rate (the excitation). Presumably low strain rates allow time for microcracking to develop, which increases the compliance of the specimen, making them tougher. This behaviour confirms a more general rule that the degree to which bone is brittle or tough depends on the amount of microcracking damage it is able to sustain. More importantly, the key to bone toughness is its ability to avoid a ductile-to-brittle transition for as long as possible during the deformation. The key to bone's brittleness, on the other hand, is the strain and damage localisation early on in the process, which leads to low post-yield strains and low-energy absorption to failure.     

Inelastic strain accumulation in cortical bone during rapid transient tensile loading

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of +/- 420 MPa/s. Loads were reversed at pre selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.     

A finite deformation theory for cartilage and other soft hydrated connective tissues--I. Equilibrium results

The determination of valid stress-strain relations for articular cartilage under finite deformation conditions is a prerequisite for constructing models for synovial joint lubrication. Under physiological conditions of high strain rates and/or high stresses in the joint, large strains occur in cartilage. A finite deformation theory valid for describing cartilage, as well as other soft hydrated connective tissues under large loads, has been developed. This theory is based on the choice of a specific Helmholtz energy function which satisfies the generalized Coleman-Noll (GCN0) condition and the Baker-Ericksen (B-E) inequalities established in finite elasticity theory. In addition, the finite deformation biphasic theory includes the effects of strain-dependent porosity and permeability. These nonlinear effects are essential for properly describing the biomechanical behavior of articular cartilage, even when strain rates are low and strains are infinitesimal. The finite deformation theory describes the large strain behavior of cartilage observed in one-dimensional confined compression experiments at equilibrium, and it reduces to the linear biphasic theory under infinitesimal strain and slow strain rate conditions. Using this theory, we have determined the material coefficients of both human and bovine articular cartilages under large strain conditions at equilibrium. The theory compares very well with experimental results.     

Evaluation of the influence of strain rate on Colles' fracture load

Colles' fracture, a transverse fracture of the distal radius bone, is one of the most frequently observed osteoporotic fractures resulting from low energy or traumatic events, associated with low and high strain rates, respectively. Although experimental studies on Colles' fracture were carried out at various loading rates ranging from static to impact loadings, there is no systematic study in the literature that isolates the influence of strain rate on Colles' fracture load. In order to provide a better understanding of fracture risk, the current study combines experimental material property measurements under varying strain rates with computational modeling and presents new information on the effect of strain rate on Colles' fracture. The simulation results showed that Colles' fracture load decreased with increasing strain rate with a steeper change in lower strain rates. Specifically, strain rate values (0.29s(-1)) associated with controlled falling without fracture corresponded to a 3.7% reduction in the fracture load. On the other hand, the reduction in the fracture load was 34% for strain rate of 3.7s(-1) reported in fracture inducing impact cadaver experiments. Further increase in the strain rate up to 18s(-1) led to an additional 22% reduction. The most drastic reduction in fracture load occurs at strain rates corresponding to the transition from controlled to impact falling. These results are particularly important for the improvement of fracture risk assessment in the elderly because they identify a critical range of loading rates (10-50mm/s) that can dramatically increase the risk of Colles' fracture.     

Characterization of human passive muscles for impact loads using genetic algorithm and inverse finite element methods

The objective of this study is to identify the dynamic material properties of human passive muscle tissues for the strain rates relevant to automobile crashes. A novel methodology involving genetic algorithm (GA) and finite element method is implemented to estimate the material parameters by inverse mapping the impact test data. Isolated unconfined impact tests for average strain rates ranging from 136 s⁻¹ to 262 s⁻¹ are performed on muscle tissues. Passive muscle tissues are modelled as isotropic, linear and viscoelastic material using three-element Zener model available in PAMCRASH^TM explicit finite element software. In the GA based identification process, fitness values are calculated by comparing the estimated finite element forces with the measured experimental forces. Linear viscoelastic material parameters (bulk modulus, short term shear modulus and long term shear modulus) are thus identified at strain rates 136 s⁻¹, 183 s⁻¹ and 262 s⁻¹ for modelling muscles. Extracted optimal parameters from this study are comparable with reported parameters in literature. Bulk modulus and short term shear modulus are found to be more influential in predicting the stress-strain response than long term shear modulus for the considered strain rates. Variations within the set of parameters identified at different strain rates indicate the need for new or improved material model, which is capable of capturing the strain rate dependency of passive muscle response with single set of material parameters for wide range of strain rates.     

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

Interbody fusion device subsidence has been reported clinically. An enhanced understanding of the mechanical behaviour of the surrounding bone would allow for accurate predictions of vertebral subsidence. The multiaxial inelastic behaviour of trabecular bone is investigated at a microscale and macroscale level. The post-yield behaviour of trabecular bone under hydrostatic and confined compression is investigated using microcomputed tomography-derived microstructural models, elucidating a mechanism of pressure-dependent yielding at the macroscopic level. Specifically, microstructural trabecular simulations predict a distinctive yield point in the apparent stress–strain curve under uniaxial, confined and hydrostatic compression. Such distinctive apparent stress–strain behaviour results from localised stress concentrations and material yielding in the trabecular microstructure. This phenomenon is shown to be independent of the plasticity formulation employed at a trabecular level. The distinctive response can be accurately captured by a continuum model using a crushable foam plasticity formulation in which pressure-dependent yielding occurs. Vertebral device subsidence experiments are also performed, providing measurements of the trabecular plastic zone. It is demonstrated that a pressure-dependent plasticity formulation must be used for continuum level macroscale models of trabecular bone in order to replicate the experimental observations, further supporting the microscale investigations. Using a crushable foam plasticity formulation in the simulation of vertebral subsidence, it is shown that the predicted subsidence force and plastic zone size correspond closely with the experimental measurements. In contrast, the use of von Mises, Drucker–Prager and Hill plasticity formulations for continuum trabecular bone models lead to over prediction of the subsidence force and plastic zone.     

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.