Material characterization of the pig kidney in relation with the biomechanical analysis of renal trauma

The objective of this study was an investigation of the material properties of the fresh pig kidney and parametric characterization of its elastic and inelastic material behavior. The material investigation included density measurements, uniaxial as well as three-dimensional compression tests, tensile tests. and shear tests on the samples extracted from the fresh pig kidney. For comparison, density measurements on a number of soft synthetic materials were also performed. Compression tests on the radial and the tangential specimens from the cortex tissue were performed at various loading rates. Three-axial compression tests were performed on the cortex tissues placed in a compression chamber. Shear tests were performed by punching a cylinder into a slice of the cortex. Tensile tests were carried out on the outer capsule. For characterization of the material behavior, a non-linear theoretical simulation based on a two parameter Blatz model was used. For characterization of the time-dependent behavior of the pig kidney cortex, a four-parameter linear viscoelastic model was employed. From the present experimental and theoretical studies, a number of conclusions were derived: (1) The general behavior of the pig kidney cortex samples under compression showed the general non-linear features typical of the soft tissues; the stress strain diagram was composed of a very flat part at very low stress level to about 30% relative deformation which was followed by a steeply rising stiffening leading to the radial rupture of samples marked by a maximum nominal rupture strain of about 50%. (2) The uniaxial compression tests on the radial and the tangential samples from the cortex tissue showed an increase of the rupture stress with the increase in the loading rate, but a decrease in the related rupture strain. (3) The long-term uniaxial compression tests on the cortex specimens under sustained constant load showed an instantaneous deformation followed by a creep response which eventually approached an asymptote. (4) Simulation of the non-linear material behavior of the cortex tissue under uniaxial compression by the Blatz model gave two pairs of material parameters for the cortex in the radial and the tangential directions. Furthermore, fitting of the assumed four-parameter linear viscoelastic model with the experimental data resulted in the viscoelastic material parameters.     

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.     

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.     

Singular perturbation analysis of the nonlinear, flow-dependent compressive stress relaxation behavior of articular cartilage

The dominant mechanism giving rise to the viscoelastic response of articular cartilage during compression is the nonlinear diffusive interaction of the fluid and solid phases of the tissue as they flow relative to one another. The present study is concerned with the role of this interaction under uniaxial stress relaxation in compression. The model is a biphasic mixture of fluid and solid which incorporates the strain-dependent permeability found earlier from permeation experiments. When a ramp-displacement is imposed on the articular surface, simple, but accurate, asymptotic approximations are derived for the deformation and stress fields in the tissue for slow and moderately fast rates of compression. They are shown to agree very well with experiment and they provide a simple means for determining the material parameters. Moreover, they lead to important insights into the role of the flow-dependent viscoelastic nature of articular cartilage and other hydrated biological tissues.     

Biomechanical properties of the human umbilical cord

The umbilical cord is a complex and fascinating structure that connects the fetus to the placenta and encases the umbilical vessels. The response of its tissues to mechanical loading due to fetal movements and uterine contractions is not well understood. The aim of this study is the evaluation of the mechanical properties of the main components of the human umbilical cord. Fresh umbilical cord specimens were collected from neonates born at term of the gestation and submitted to compliance tests. Furthermore, uniaxial tensile and stress-relaxation tests were performed on samples of umbilical vein and Wharton's jelly. Both materials exhibited nonlinear stress-strain response with increasing strain, increasing the elastic modulus (E(high) about 10-20 times E(low)) and significant viscoelastic behavior. In addition, anisotropy of the vein was observed. Although the circumferential properties of the vein (mean E(high) about 2.4 MPa) were similar to those after birth, the longitudinal stiffness of both materials was higher (mean E(high) over 10 MPa) and comparable to that of the ligaments. These findings suggest a mechanism of protection acting against excessive elongations of the cord, which could cause undue restriction of the umbilical vessel area and interference with the fetal blood circulation.     

Determination of material models for arterial walls from uniaxial extension tests and histological structure

An approach is proposed that allows the determination of material models from uniaxial tests and histostructural data including fiber orientation of the tissue. A combination of neo-Hookean and Fung-type strain-energy functions is utilized, and inequality constraints imposed on the constitutive parameters are derived providing strict local convexity and preferred fiber orientations. It is shown how the Fung-type model gets a pseudo-structural aspect inherent in the phenomenological model; a correlation between the fiber structure and the parameters of the Fung-type model is explicitly provided. In order to apply the proposed approach, quasi-static uniaxial extension tests of preconditioned prepared strips from the intima, media and adventitia of a human aorta with non-atherosclerotic intimal thickening are acquired in axial and circumferential directions; structural information from histological analyses for each aortic tissue are documented. Data reveal a remarkable thickness, load-bearing capacity and stiffness of the intimal samples in comparison with the media and adventitia. Constitutive parameters for each aortic tissue layer are determined by solving the constrained problem using a penalty function method; a new approach for the estimation of appropriate start values is proposed. Finally, the predictivity and efficacy of the material models is shown by comparing model data with data from the uniaxial extension tests and histological image analyses.     

Mechanical characterisation of the human thoracic descending aorta: experiments and modelling

This work presents experiments and modelling aimed at characterising the passive mechanical behaviour of the human thoracic descending aorta. To this end, uniaxial tension and pressurisation tests on healthy samples corresponding to newborn, young and adult arteries are performed. Then, the tensile measurements are used to calibrate the material parameters of the Holzapfel constitutive model. This model is found to adequately adjust the material behaviour in a wide deformation range; in particular, it captures the progressive stiffness increase and the anisotropy due to the stretching of the collagen fibres. Finally, the assessment of these material parameters in the modelling of the pressurisation test is addressed. The implication of this study is the possibility to predict the mechanical response of the human thoracic descending aorta under generalised loading states like those that can occur in physiological conditions and/or in medical device applications.     

Magnetic resonance elastography in nonlinear viscoelastic materials under load

Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material’s rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy’s equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of \(4910.4 \pm 635.8\) Pa in unloaded state, the biased stiffness increases to 9767.5 \(\pm \,\)1949.9 Pa under a load of \(\approx \) 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

     

Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation

High-resolution architecture-based finite element models are commonly used for characterizing the mechanical behavior of cancellous bone. The vast majority of studies use homogeneous material properties to model trabecular tissue. The objectives of this study were to demonstrate that inhomogeneous finite element models that account for microcomputed tomography-measured tissue modulus variability more accurately predict the apparent stiffness of cancellous bone than homogeneous models, and to examine the sensitivity of an inhomogeneous model to the degree of tissue property variability. We tested five different material cases in finite element models of ten cancellous cubes in simulated uniaxial compression. Three of these cases were inhomogeneous and two were homogeneous. Four of these cases were unique to each specimen, and the remaining case had the same tissue modulus for all specimens. Results from all simulations were compared with measured elastic moduli from previous experiments. Tissue modulus variability for the most accurate of the three inhomogeneous models was then artificially increased to simulate the effects of non-linear CT-attenuation-modulus relationships. Uniqueness of individual models was more critical for model accuracy than level of inhomogeneity. Both homogeneous and inhomogeneous models that were unique to each specimen had at least 8% greater explanatory power for apparent modulus than models that applied the same material properties to all specimens. The explanatory power for apparent modulus of models with a tissue modulus coefficient of variation (COV) range of 21-31% was 13% greater than homogeneous models (COV=0). The results of this study indicate that inhomogenous finite element models that have tissue moduli unique to each specimen more accurately predict the elastic behavior of cancellous cubic specimens than models that have common tissue moduli between all specimens.     

Mechanical properties and microstructure of intraluminal thrombus from abdominal aortic aneurysm.

Accurate estimation of the wall stress distribution in an abdominal aortic aneurysm (AAA) may prove clinically useful by predicting when a particular aneurysm will rupture. Appropriate constitutive models for both the wall and the intraluminal thrombus (ILT) found in most AAA are necessary for this task. The purpose of this work was to determine the mechanical properties of ILT within AAA and to derive a more suitable constitutive model for this material. Uniaxial tensile testing was carried out on 50 specimens, including 14 longitudinally oriented and 14 circumferentially oriented specimens from the luminal region of the ILT, and 11 longitudinally oriented and 11 circumferentially oriented specimens from the medial region. A two-parameter, large-strain, hyperelastic constitutive model was developed and used to fit the uniaxial tensile testing data for determination of the material parameters. Maximum stiffness and strength were also determined from the data for each specimen. Scanning electron microscopy (SEM) was conducted to study the regional microstructural difference. Our results indicate that the microstructure of ILT differs between the luminal, medial, and abluminal regions, with the luminal region stronger and stiffer than the medial region. In all cases, the constitutive model fit the experimental data very well (R2>0.98). No significant difference was found for either of the two material parameters between longitudinal and circumferential directions, but a significant difference in material parameters, stiffness, and strength between the laminal and medial regions was determined (p<0.01). Therefore, our results suggest that ILT is an inhomogeneous and possibly isotropic material. The two-parameter, hyperelastic, isotropic, incompressible material model derived here for ILT can be easily incorporated into finite element models for simulation of wall stress distribution in AAA.     

Viscoelastic characterization of peripapillary sclera: material properties by quadrant in rabbit and monkey eyes

In this report we characterize the viscoelastic material properties of peripapillary sclera from the four quadrants surrounding the optic nerve head in both rabbit and monkey eyes. Scleral tensile specimens harvested from each quadrant were subjected to uniaxial stress relaxation and tensile ramp to failure tests. Linear viscoelastic theory, coupled with a spectral reduced relaxation function, was employed to characterize the viscoelastic properties of the tissues. We detected no differences in the stress-strain curves of specimens from the four quadrants surrounding the optic nerve head (ONH) below a strain of 4 percent in either the rabbit or monkey. While the peripapillary sclera from monkey eyes is significantly stiffer (both instantaneously and in equilibrium) and relaxes more slowly than that from rabbits, we detected no differences in the viscoelastic material properties (tested at strains of 0-1 percent) of sclera from the four quadrants surrounding the ONH within either species group.     

Modelling and simulation of porcine liver tissue indentation using finite element method and uniaxial stress–strain data

We hypothesize that both compression and elongation stress–strain data should be considered for modeling and simulation of soft tissue indentation. Uniaxial stress–strain data were obtained from in vitro loading experiments of porcine liver tissue. An axisymmetric finite element model was used to simulate liver tissue indentation with tissue material represented by hyperelastic models. The material parameters were derived from uniaxial stress–strain data of compressions, elongations, and combined compression and elongation of porcine liver samples. in vitro indentation tests were used to validate the finite element simulation. Stress–strain data from the simulation with material parameters derived from the combined compression and elongation data match the experimental data best. This is due to its better ability in modeling 3D deformation since the behavior of biological soft tissue under indentation is affected by both its compressive and tensile characteristics. The combined logarithmic and polynomial model is somewhat better than the 5-constant Mooney–Rivlin model as the constitutive model for this indentation simulation.     

The apparent viscoelastic behavior of articular cartilage--the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows

Articular cartilage was modeled rheologically as a biphasic poroviscoelastic material. A specific integral-type linear viscoelastic model was used to describe the constitutive relation of the collagen-proteoglycan matrix in shear. For bulk deformation, the matrix was assumed either to be linearly elastic, or viscoelastic with an identical reduced relaxation spectrum as in shear. The interstitial fluid was considered to be incompressible and inviscid. The creep and the rate-controlled stress-relaxation experiments on articular cartilage under confined compression were analyzed using this model. Using the material data available in the literature, it was concluded that both the interstitial fluid flow and the intrinsic matrix viscoelasticity contribute significantly to the apparent viscoelastic behavior of this tissue under confined compression.     

Biomechanics of single zonal chondrocytes

Articular cartilage has a distinct zonal architecture, and previous work has shown that chondrocytes from different zones exhibit variations in gene expression and biosynthesis. In this study, the material properties of single chondrocytes from the superficial and middle/deep zones of bovine distal metatarsal articular cartilage were determined using unconfined compression and digital videocapture. To determine the viscoelastic properties of zonal chondrocytes, unconfined creep compression experiments were performed and the resulting creep curves of individual cells were fit using a standard linear viscoelastic solid model. In the model, a fixed value of the Poisson's ratio was used, determined optically from direct compression of middle/deep chondrocytes. The two approaches used in this study yielded the following average material properties of single chondrocytes: Poisson's ratio of 0.26+/-0.08, instantaneous modulus of 1.06+/-0.82 kPa, relaxed modulus of 0.78+/-0.58 kPa, and apparent viscosity of 4.08+/-7.20 kPa s. Superficial zone chondrocytes were found to be significantly stiffer than middle/deep zone chondrocytes. Attachment time did not affect the stiffness of the cells. The zonal variation in viscoelastic properties may result from the distinct mechanical environments experienced by the cells in vivo. Identifying intrinsic differences in the biomechanics of superficial and middle/deep zone chondrocytes is an important component in understanding how biomechanics influence articular cartilage health and disease.     

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear,anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress–strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model?s nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean±95% confidence interval) of the disc?s nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc?s full nonlinear response in multiple loading scenarios.     

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.     

Material properties of the human calcaneal fat pad in compression: experiment and theory

The structural behaviour of the human heel pad has been studied extensively due to its ability to absorb shock, protect against excessive local stress, and reduce plantar pressures. However, the material properties of the tissue have not been adequately measured. These must be known in order to perform a finite element analysis of the effect of factors such as foot geometry and shoe/surface construction on heel pad function. Therefore, the purposes of this study were to (a) measure the viscoelastic behaviour of the fat pad in compression, and (b) to determine an appropriate constitutive equation to model the tissue. A series of unconfined compression tests were performed on 8 mm diameter cylinders of fat pad tissue, consisting of quasi-static, 175, 350 mm/s and stress-relaxation tests to 50% deformation. The tissue exhibited nonlinear, viscoelastic behaviour. No significant difference was found in the quasi-static behaviour between samples from different locations and orientations in the heel. The stress-relaxation tests were used to determine the time constant (τ₁=0.5 s), the 175 mm/s test to determine the relaxation coefficient (g₁=28), and the 350 mm/s compression test to determine the material constants (C₁₀₀=C₀₁₀=0.01, C₂₀₀=C₀₂₀=0.1 Pa) of a single-phase, hyperelastic, linear viscoelastic strain energy function (r²=0.98).     

Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential–axial and the radial–axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber–matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure–function, and to quantify the effect of degeneration. The biaxial stress–strain response was described well by the model (R ²?>?0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young’s modulus, provided an explanation for the low values in previously published axial direction Young’s modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.     

Nonlinear viscoelastic characterization of bovine trabecular bone

The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness–density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep–recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples (\(n = 19\)). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery’s nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep–recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening–softening behaviour with increasing stress.     

Constitutive model for brain tissue under finite compression

While advances in computational models of mechanical phenomena have made it possible to simulate dynamically complex problems in biomechanics, accurate material models for soft tissues, particularly brain tissue, have proven to be very challenging. Most studies in the literature on material properties of brain tissue are performed in shear loading and very few tackle the behavior of brain in compression. In this study, a viscoelastic constitutive model of bovine brain tissue under finite step-and-hold uniaxial compression with 10 s(-1) ramp rate and 20 s hold time has been developed. The assumption of quasi-linear viscoelasticity (QLV) was validated for strain levels of up to 35%. A generalized Rivlin model was used for the isochoric part of the deformation and it was shown that at least three terms (C(10), C(01) and C(11)) are needed to accurately capture the material behavior. Furthermore, for the volumetric deformation, a two parameter Ogden model was used and the extent of material incompressibility was studied. The hyperelastic material parameters were determined through extracting and fitting to two isochronous curves (0.06 s and 14 s) approximating the instantaneous and steady-state elastic responses. Viscoelastic relaxation was characterized at five decay rates (100, 10, 1, 0.1, 0 s(-1)) and the results in compression and their extrapolation to tension were compared against previous models.