Effect of microgravity on the biomechanical properties of lumbar and caudal intervertebral discs in mice

Prolonged exposure to microgravity has shown to have deleterious effects on the human spine, indicated by low back pain during spaceflight and increased incidence of post-spaceflight herniated nucleus pulposus. We examined the effect of microgravity on biomechanical properties of lumbar and caudal discs from mice having been on 15-day shuttle mission STS-131. Sixteen C57BL/C mice (spaceflight group, n=8; ground-based control group, n=8) were sacrificed immediately after spaceflight. Physiological disc height (PDH) was measured in situ, and compressive creep tests were performed to parameterize biomechanical properties into endplate permeability (k), nuclear swelling pressure strain dependence (D), and annular viscoelasticity (G). For caudal discs, the spaceflight group exhibited 32% lower PDH, 70% lower D and crept more compared to the control mice (p=0.03). For lumbar discs, neither PDH nor D was significantly different between murine groups. Initial modulus, osmotic pressure, k and G for lumbar and caudal discs did not appear influenced by microgravity (p>0.05). Decreases in both PDH and D suggest prolonged microgravity effectively diminished biomechanical properties of caudal discs. By contrast, differences were not noted for lumbar discs. This potentially deleterious interaction between prolonged weightlessness and differential ranges of motion along the spine may underlie the increased cervical versus lumbar disc herniation rates observed among astronauts.     

Infant brain subjected to oscillatory loading: material differentiation,properties, and interface conditions

Past research into brain injury biomechanics has focussed on short duration impulsive events as opposed to the oscillatory loadings associated with Shaken Baby Syndrome (SBS). A series of 2D finite element models of an axial slice of the infant head were created to provide qualitative information on the behaviour of the brain during shaking. The test series explored variations in subarachnoid cerebrospinal fluid (CSF) representation, brain matter stiffness, dissipation, and nonlinearity, and differentiation of brain matter type. A new method of CSF modelling based on Reynolds lubrication theory was included to provide a more realistic brain–CSF interaction. The results indicate that solid CSF representation for this load regime misrepresents the phase lag of displacement, and that the volume of subarachnoid CSF, and inclusion of thickness variations due to gyri, are important to the resultant behavior. Stress concentrations in the deep brain are reduced by fluid redistribution and gyral contact, while inclusion of the pia mater significantly reduces cortex contact strains. These results provide direction for future modelling of SBS.     

Simulated-physiological loading conditions preserve biological and mechanical properties of caprine lumbar intervertebral discs in ex vivo culture

Low-back pain (LBP) is a common medical complaint and associated with high societal costs. Degeneration of the intervertebral disc (IVD) is assumed to be an important causal factor of LBP. IVDs are continuously mechanically loaded and both positive and negative effects have been attributed to different loading conditions.In order to study mechanical loading effects, degeneration-associated processes and/or potential regenerative therapies in IVDs, it is imperative to maintain the IVDs' structural integrity. While in vivo models provide comprehensive insight in IVD biology, an accompanying organ culture model can focus on a single factor, such as loading and may serve as a prescreening model to reduce life animal testing. In the current study we examined the feasibility of organ culture of caprine lumbar discs, with the hypothesis that a simulated-physiological load will optimally preserve IVD properties.Lumbar caprine IVDs (n = 175) were cultured in a bioreactor up to 21 days either without load, low dynamic load (LDL), or with simulated-physiological load (SPL). IVD stiffness was calculated from measurements of IVD loading and displacement. IVD nucleus, inner- and outer annulus were assessed for cell viability, cell density and gene expression. The extracellular matrix (ECM) was analyzed for water, glycosaminoglycan and total collagen content.IVD biomechanical properties did not change significantly with loading conditions. With SPL, cell viability, cell density and gene expression were preserved up to 21 days. Both unloaded and LDL resulted in decreased cell viability, cell density and significant changes in gene expression, yet no differences in ECM content were observed in any group.In conclusion, simulated-physiological loading preserved the native properties of caprine IVDs during a 21-day culture period. The characterization of caprine IVD response to culture in the LDCS under SPL conditions paves the way for controlled analysis of degeneration- and regeneration-associated processes in the future.     

Constitutive laws and failure models for compact bones subjected to dynamic loading

Many biological tissues, such as bones and ligaments, are fibrous. The geometrical structure of these tissues shows that they exhibit a similar hierarchy in their ultra- and macro-structures. The aim of this work is to develop a model to study the failure of fibrous structures subjected to dynamic loading. The important feature of this model is that it describes failure in terms of the loss of cohesion between fibres. We have developed a model based on the lamellar structure of compact bone with fibres oriented at 0, 45 and 90 degrees to the longitudinal axis of the bone and have studied the influence of the model parameters on the failure process. Bone porosity and joint stress force at failure were found to be the most significant parameters. Using least square resolution, we deduced a phenomenological model of the lamellar structure. Finally, experimental results were found to be comparable with our numerical model.     

Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression,flexion and axial rotation

A statistical factorial analysis approach was conducted on a poroelastic finite element model of a lumbar intervertebral disc to analyse the influence of six material parameters (permeabilities of annulus, nucleus, trabecular vertebral bone, cartilage endplate and Young's moduli of annulus and nucleus) on the displacement, fluid pore pressure and velocity fields. Three different loading modes were investigated: compression, flexion and axial rotation. Parameters were varied considering low and high levels in agreement with values found in the literature for both healthy and degenerated lumbar discs. Results indicated that annulus stiffness and cartilage endplate permeability have a strong effect on the overall fluid- and solid-phase responses in all loading conditions studied. Nucleus stiffness showed its main relevance in compression while annulus permeability influenced mainly the annular pressure field. This study confirms the permeability's central role in biphasic modelling and highlights for the lumbar disc which experiments of material property characterization should be performed. Moreover, such sensitivity study gives important guidelines in poroelastic material modelling and finite element disc validation.     

Calibration of hyperelastic material properties of the human lumbar intervertebral disc under fast dynamic compressive loads

Under fast dynamic loading conditions (e.g. high-energy impact), the load rate dependency of the intervertebral disc (IVD) material properties may play a crucial role in the biomechanics of spinal trauma. However, most finite element models (FEM) of dynamic spinal trauma uses material properties derived from quasi-static experiments, thus neglecting this load rate dependency. The aim of this study was to identify hyperelastic material properties that ensure a more biofidelic simulation of the IVD under a fast dynamic compressive load. A hyperelastic material law based on a first-order Mooney-Rivlin formulation was implemented in a detailed FEM of a L2-L3 functional spinal unit (FSU) to represent the mechanical behavior of the IVD. Bony structures were modeled using an elasto-plastic Johnson-Cook material law that simulates bone fracture while ligaments were governed by a viscoelastic material law. To mimic experimental studies performed in fast dynamic compression, a compressive loading velocity of 1 m/s was applied to the superior half of L2, while the inferior half of L3 was fixed. An exploratory technique was used to simulate dynamic compression of the FSU using 34 sets of hyperelastic material constants randomly selected using an optimal Latin hypercube algorithm and a set of material constants derived from quasi-static experiments. Selection or rejection of the sets of material constants was based on compressive stiffness and failure parameters criteria measured experimentally. The two simulations performed with calibrated hyperelastic constants resulted in nonlinear load-displacement curves with compressive stiffness (7335 and 7079 N/mm), load (12,488 and 12,473 N), displacement (1.95 and 2.09 mm) and energy at failure (13.5 and 14.7 J) in agreement with experimental results (6551 ± 2017 N/mm, 12,411 ± 829 N, 2.1 ± 0.2 mm and 13.0 ± 1.5 J respectively). The fracture pattern and location also agreed with experimental results. The simulation performed with constants derived from quasi-static experiments showed a failure energy (13.2 J) and a fracture pattern and location in agreement with experimental results, but a compressive stiffness (1580 N/mm), a failure load (5976 N) and a displacement to failure (4.8 mm) outside the experimental corridors. The proposed method offers an innovative way to calibrate the hyperelastic material properties of the IVD and to offer a more realistic simulation of the FSU in fast dynamic compression.     

Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method

The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.     

The influence of the material properties on the biomechanical behavior of the pelvic floor muscles during vaginal delivery

In this work, a finite element model intends to represent the effects that the passage of a fetal head can induce on the muscles of the pelvic floor, from a mechanical point of view.The finite element method is a valuable tool, that is contributing to the clarification of the mechanisms behind pelvic floor disorders related to vaginal deliveries, although some care is necessary in order to obtain correct results. The present work shows how the variation of the material parameters, used in the constitutive model, can affect the obtained results from a finite element simulation. The constitutive equation adopted in this work for the pelvic floor muscles is a modified form of the incompressible transversely isotropic hyperelastic model proposed earlier by Humphrey and Yin.Results for the pelvic floor strain and stresses obtained during the passage of the fetus head are presented. The results show the importance of the material parameters and the need for a correct constitutive model.     

A review of the biomechanical properties of bone as a material

Experimental studies on bone all reveal important difficulties in data interpretation. This paper proposes an analysis of experimental studies performed so far, with particular attention to the anisotropic characteristics of bone, its behaviour in the post-elastic phase, and its dependence on viscoelastic phenomena. Mechanical properties are also correlated with variables such as moisture, deformation rate during testing, density, variations in different regions of the bone, and the most relevant strength criteria are recalled. The investigation performed is also intended to provide an evaluation of the degree of refinement of biomechanical experimental data for use in a numerical approach to bone mechanics.     

Testing of a biomechanical model of the lumbar muscle force distribution using quasi-static loading exercises.

The study of lumbar muscle force distribution in response to externally applied loads is based on the introduction of biomechanical models of the lumbar region. The evaluation of such models requires the execution of loading exercises while monitoring the EMG activity of certain lumbar muscles. This work uses muscle activity maps as the major design tool of such exercises, provided that the subject is constrained to an upright erect posture. The maps describe the predicted muscle force for a given combination of externally applied bending moments. A series of shoulder adduction exercises were designed and the EMG signals of eight lumbar muscles were measured while subjects performed the exercises. The results show good agreement between the model predictions and the EMG measurements, especially when the load and the muscle were contralateral to one another.     

Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal,proteoglycan depleted and collagen degraded articular cartilage

Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (-64+/-28%) and a minor decrease of the fibril network modulus (-11+/-9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (-69+/-5%) and a decrease of the drained porous matrix modulus (-44+/-18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.     

Osmotic loading to determine the intrinsic material properties of guinea pig knee cartilage

Few methods exist to study cartilage mechanics in small animal joints due to the difficulties associated with handling small tissue samples. In this study, we apply an osmotic loading method to quantify the intrinsic material properties of articular cartilage in small animal joints. Cartilage samples were studied from the femoral condyle and tibial plateau of two-month old guinea pigs. Swelling strains were measured using confocal fluorescence scanning microscopy in samples subjected to osmotic loading. A histochemical staining method was developed and calibrated for quantification of negative fixed charge density in guinea pig cartilage. Site-matched swelling strain data and fixed charge density values were then used with a triphasic theoretical model for cartilage swelling to determine the uniaxial modulus of the cartilage solid matrix. Moduli obtained in this study (7.2 MPa femoral condyle; 10.8 MPa, tibial plateau) compare well with previously reported values for the tensile moduli of human and other animal cartilages determined from uniaxial tension experiments. This study provides the first available data for material properties and fixed charge density in cartilage from the guinea pig knee and suggests a promising method for tracking changes in cartilage mechanics in small animal models of degeneration.     

Evaluation of dynamic response and biomechanical properties of isolated blood vessels

In this study we present the experimental and mathematical model for a precise assessment of isolated blood vessels dynamic response under a sudden change of blood pressure. Only the end points within the time interval of the considered dynamic response of the blood vessel, or so-called “alternate steady states” of the processes, were usually considered in various studies. These studies do not provide an insight how the process variables change between these alternate steady states. Isolated blood vessels (rat abdominal aorta) were used to determine how the process dynamics can be described in detailed quantitative terms by mathematical parameters. The experimental model and mathematical procedures presented in this study describe precisely (at a high sensitivity level) the time history of the pressure and the diameter change in between alternate steady states, when an abrupt change of blood pressure occurs at the vessel outlet. Also, the experimental model and mathematical procedures were used to determine changes in the stress–strain law, caused by the action of L-arginine. The presented experimental design and mathematical model can be used for assessment of isolated blood vessel dynamic responses under different stimuli, such as drug effects, electrostimulation etc.     

Analysis and simulation of dynamic response behavior of Scots pine trees to wind loading

This paper presents an empirical approach for the decomposition, simulation, and reconstruction of wind-induced stem displacement of plantation-grown Scots pine trees. Results from singular spectrum analysis (SSA) allow a low-dimensional characterization of the complex and complicated tree motion patterns in response to non-destructive wind excitation. Since motion of the sample trees was dominated by sway in the first mode, the application of SSA on time series of sample trees’ stem displacement yielded characteristic and distinguishable non-oscillatory trend components, quasi-oscillatory sway, and noise, of which only the non-oscillatory components were correlated directly with wind characteristics. Although sway in the range of the dominant damped fundamental frequency dominated the measured stem displacement signals, it was almost decoupled from near-surface airflow. The ability to discriminate SSA-components is demonstrated based on correlation and spectral analysis. These SSA-components, as well as wind speed measured in the canopy space of the Scots pine forest, were used to train neural networks, which could then reasonably simulate tree response to wind excitation.     

Mechanical properties of soft human tissues under dynamic loading

The dynamic response of soft human tissues in hydrostatic compression and simple shear is studied using the Kolsky bar technique. We have made modifications to the technique that allow loading of a soft tissue specimen in hydrostatic compression or simple shear. The dynamic response of human tissues (from stomach, heart, liver, and lung of cadavers) is obtained, and analyzed to provide measures of dynamic bulk modulus and shear response for each tissue type. The dynamic bulk response of these tissues is easily described by a linear fit for the bulk modulus in this pressure range, whereas the dynamic shearing response of these tissues is strongly non-linear, showing a near exponential growth of the shear stress.     

Material properties of the placenta under dynamic loading conditions

Trauma during pregnancy especially occurring during car crashes leads to many foetal losses. Numerical modelling is widely used in car occupant safety issue and injury mechanisms analysis and is particularly adapted to the pregnant woman. Material modelling of the gravid uterus tissues is crucial for injury risk evaluation especially for the abruption placentae which is widely assumed as the leading cause of foetal loss. Experimental studies on placenta behaviour in tension are reported in the literature, but none in compression to the authors' knowledge. This lack of data is addressed in this study. To complement the already available experimental literature data on the placenta mechanical behaviour and characterise it in a compression loading condition, 80 indentation tests on fresh placentae are presented. Hyperelastic like mean experimental stress versus strain and corridors are exposed. The results of the experimental placenta indentations compared with the tensile literature results tend to show a quasi-symmetrical behaviour of the tissue. An inverse analysis using simple finite element models has permitted to propose parameters for an Ogden material model for the placenta which exhibits a realistic behaviour in both tension and compression.     

Cellular basis of the dynamic behavior of the imaginal thoracic discs during Drosophila metamorphosis

The eversion, migration, spreading, and fusion of the thoracic imaginal discs during metamorphosis of Drosophila are described using timed whole-mount preparations and several molecular markers. The leading edge of the migrating disc epithelia consists of two groups of cells, stalk cells (S cells) and specialized imaginal cells (I cells), that both express the gene puckered. With this and other markers, opening of the stalk, eversion of the discs, migration of the leading edges, and fusion of the imaginal epithelia can be visualized in detail. Fusion is initiated by S cells that migrate over the larval epithelium and constitute a bridge between two imaginal epithelia. S cells are subsequently lost and imaginal fusion is mediated by the I cells that remain at the site of fusion. The possible cellular basis of this process is discussed. Fusion along the dorsal midline of the notum from the mesothoracic wing discs occurs earlier than that of the prothoracic and metathoracic discs, which remain in a lateral position. For a relatively long period (30 h) the mesothoracic epithelium becomes attached to the head and abdomen, causing a temporary local discontinuity of the order of segments. Later the pro- and metathoracic discs intercalate between head and mesothorax and between abdomen and mesothorax, respectively, to reestablish the normal order.     

Mechanical behavior of bovine nasal cartilage under static and dynamic loading

Abnormal mechanical loading may trigger cartilage degeneration associated with osteoarthritis. Tissue response to load has been the subject of several in vitro studies. However, simple stimuli were often applied, not fully mimicking the complex in vivo conditions. Therefore, a rolling/plowing explant test system (RPETS) was developed to replicate the combined in vivo loading patterns. In this work we investigated the mechanical behavior of bovine nasal septum (BNS) cartilage, selected as tissue approximation for experiments with RPETS, under static and dynamic loading. Biphasic material properties were determined and compared with those of other cartilaginous tissues. Furthermore, dynamic loading in plowing modality was performed to determine dynamic response and experimental results were compared with analytical models and Finite Elements (FE) computations. Results showed that BNS cartilage can be modeled as a biphasic material with Young's modulus E=2.03±0.7 MPa, aggregate modulus H_A=2.35±0.7 MPa, Poisson's ratio ν=0.24±0.07, and constant hydraulic permeability k₀=3.0±1.3×10⁻¹⁵ m⁴ (N s)⁻¹. Furthermore, dynamic analysis showed that plowing induces macroscopic reactions in the tissue, proportionally to the applied loading force. The comparison among analytical, FE analysis and experimental results showed that predicted tangential forces and sample deformation lay in the range of variation of experimental results for one specific experimental condition. In conclusion, mechanical properties of BNS cartilage under both static and dynamic compression were assessed, showing that this tissue behave as a biphasic material and has a viscoelastic response to dynamic forces.     

Dependence of mechanical behavior of the murine tail disc on regional material properties: a parametric finite element study

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc's transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model-nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation-were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial 2200 s of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.     

Identification and characterisation of regional variations in the material properties of ureter according to microstructure

There are few previous studies on the elastic properties of ureter and most have been limited to essentially one-dimensional deformation measurements. The object of this study was, therefore, to identify regional variations in the multiaxial behaviour of rabbit ureter, subjected to in vitro inflation/extension testing under a physiological range of intraluminal pressures and longitudinal forces. A microstructure-motivated material model (via two- and four-fibre families in turn for elastin and collagen) was implemented and its capacity to mathematically characterise the experimental data contrasted favourably with that of the well-established phenomenological models, but it was compromised by parameter covariance. Extensive optimisation studies confirmed that the reduced model without contribution to the elastin and circumferential-fibre (collagen) families characterised the data equally well without over-parameterisation. In view of the fitted parameters, the ureteral tissue was stiffer longitudinally, justified by the preferential alignment of collagen along that axis and the lower ureter was stiffer than the upper ureter, justified by the histological observation of a thickest lamina propria, i.e. of highest collagen content, there. The lower ureter was less anisotropic than the upper ureter, possessing a comparatively larger amount of diagonally arranged collagen fibres in tunica mucosa, while having the usual amounts of longitudinally arranged fibres in tunica adventitia and of circumferentially arranged fibres in tunica muscularis. The present data may be used as inputs to mathematical models of the ureter, assessing regional and intramural stress distributions, through which it is hoped that an improved appreciation of ureteral function may be attained in both health and disease.