Relationship between streaming potential and compressive stress in bovine intervertebral tissue

The intervertebral disc is formed by the nucleus pulposus (NP) and annulus fibrosus (AF), and intervertebral tissue contains a large amount of negatively charged proteoglycan. When this tissue becomes deformed, a streaming potential is induced by liquid flow with positive ions. The anisotropic property of the AF tissue is caused by the structural anisotropy of the solid phase and the liquid phase flowing into the tissue with the streaming potential. This study investigated the relationship between the streaming potential and applied stress in bovine intervertebral tissue while focusing on the anisotropy and loading location. Column-shaped specimens, 5.5 mm in diameter and 3 mm thick, were prepared from the tissue of the AF, NP and the annulus–nucleus transition region (AN). The loading direction of each specimen was oriented in the spinal axial direction, as well as in the circumferential and radial directions of the spine considering the anisotropic properties of the AF tissue. The streaming potential changed linearly with stress in all specimens. The linear coefficients k_e of the relationship between stress and streaming potential depended on the extracted positions. These coefficients were not affected by the anisotropy of the AF tissue. In addition, these coefficients were lower in AF than in NP specimens. Except in the NP specimen, the k_e values were higher under faster compression rate conditions. In cyclic compression loading the streaming potential changed linearly with compressive stress, regardless of differences in the tissue and load frequency.     

Elastic,permeability and swelling properties of human intervertebral disc tissues: A benchmark for tissue engineering

The aim of functional tissue engineering is to repair and replace tissues that have a biomechanical function, i.e., connective orthopaedic tissues. To do this, it is necessary to have accurate benchmarks for the elastic, permeability, and swelling (i.e., biphasic-swelling) properties of native tissues. However, in the case of the intervertebral disc, the biphasic-swelling properties of individual tissues reported in the literature exhibit great variation and even span several orders of magnitude. This variation is probably caused by differences in the testing protocols and the constitutive models used to analyze the data. Therefore, the objective of this study was to measure the human lumbar disc annulus fibrosus (AF), nucleus pulposus (NP), and cartilaginous endplates (CEP) biphasic-swelling properties using a consistent experimental protocol and analyses. The testing protocol was composed of a swelling period followed by multiple confined compression ramps. To analyze the confined compression data, the tissues were modeled using a biphasic-swelling model, which augments the standard biphasic model through the addition of a deformation-dependent osmotic pressure term. This model allows considering the swelling deformations and the contribution of osmotic pressure in the analysis of the experimental data. The swelling stretch was not different between the disc regions (AF: 1.28±0.16; NP: 1.73±0.74; CEP: 1.29±0.26), with a total average of 1.42. The aggregate modulus (Ha) of the extra-fibrillar matrix was higher in the CEP (390 kPa) compared to the NP (100 kPa) or AF (30 kPa). The permeability was very different across tissue regions, with the AF permeability (64 E⁻¹⁶ m⁴/N s) higher than the NP and CEP (~5.5 E⁻¹⁶ m⁴/N s). Additionally, a normalized time-constant (3000 s) for the stress relaxation was similar for all the disc tissues. The properties measured in this study are important as benchmarks for tissue engineering and for modeling the disc's mechanical behavior and transport.     

Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression

A 3D inhomogeneous finite-element model for charged hydrated soft tissues containing charged/uncharged solutes was developed and applied to analyze the mechanical, chemical, and electrical signals within the human intervertebral disc during an axial unconfined compression. The effects of tissue properties and boundary conditions on the physical signals and the transport of fluid and solute were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization and the effective (von Misses) solid stress were more pronounced in the annulus fibrosus (AF) region near the interface between AF and nucleus pulposus (NP). In NP, the distributions of the fluid pressure, effective stress, and electrical potential were more uniform than those in AF. The electrical signals were very sensitive to fixed charge density. Changes in material properties of NP (water content, fixed charge density, and modulus) affected fluid pressure, electrical potential, effective stress, and solute transport in the disc. This study is important for understanding disc biomechanics, disc nutrition, and disc mechanobiology.     

Penetration of cutting tool into cortical bone: Experimental and numerical investigation of anisotropic mechanical behaviour

An anisotropic mechanical behaviour of cortical bone and its intrinsic hierarchical microstructure act as protective mechanisms to prevent catastrophic failure due to natural loading conditions; however, they increase the extent of complexity of a penetration process in the case of orthopaedic surgery. Experimental results available in literature provide only limited information about processes in the vicinity of a tool–bone interaction zone. Also, available numerical models the bone-cutting process do not account for material anisotropy or the effect of damage mechanisms. In this study, both experimental and numerical studies were conducted to address these issues and to elucidate the effect of anisotropic mechanical behaviour of cortical bone tissue on penetration of a sharp cutting tool. First, a set of tool-penetration experiments was performed in directions parallel and perpendicular to bone axis. Also, these experiments included bone samples cut from four different cortices to evaluate the effect of spatial variability and material anisotropy on the penetration processes. Distinct deformation and damage mechanisms linked to different microstructure orientations were captured using a micro-lens high-speed camera. Then, a novel hybrid FE model employing a smoothed-particle-hydrodynamic domain embedded into a continuum FE one was developed based on the experimental configuration to characterise the anisotropic deformation and damage behaviour of cortical bone under a penetration process. The results of our study revealed a clear anisotropic material behaviour of the studied cortical bone tissue and the influence of the underlying microstructure. The proposed FE model reflected adequately the experimental results and demonstrated the need for the use of the anisotropic and damage material model to analyse cutting of the cortical-bone tissue.     

Effect of overload on changes in mechanical and structural properties of the annulus fibrosus of the intervertebral disc

The research focussed on analysing structural and mechanical properties in the intervertebral disc (IVD), caused by long-term cyclic loading. Spinal motion segments were divided into two groups: the control (C), and the group in which it was analysed the impact of posterior column in the load-bearing system of the spine—specimens with intact posterior column (IPC) and without posterior column (WPC). To evaluate the structural and mechanical changes, the specimens were tested with simulation of 100,000 compression-flexion load cycles after which it was performed macroscopic analysis. Mechanical properties of the annulus fibrosis (AF) from the anterior and posterior regions of the IVD were tested at the uniaxial tension test. The stiffness coefficient values were statistically 32% higher in the WPC group (110 N/mm) than in the IPC (79 N/mm). The dynamics of increase in this parameter does not correspond with the course of decrease in height loss. WPC segments revealed clear structural changes that mainly involve the posterior regions of the IVD (bulging and delamination with the effect of separation of collagen fibre bundles). Pathological changes also caused decreases in the value of stress in the AF. The greatest changes in the stress value about group C (7.43 ± 4.49 MPa) were observed in the front part of the fibrous ring, where this value was for IPC 4.49 ± 4.78 MPa and WPC 2.56 ± 1.01 MPa. The research indicates that the applied load model allows simulating damage that occurs in pathological IVD. And the posterior column’s presence affects this change’s dynamics, structural and mechanical properties of AF.

     

Modeling Soft Tissue Damage and Failure Using a Combined Particle/Continuum Approach

Biological soft tissues experience damage and failure as a result of injury, disease, or simply age; examples include torn ligaments and arterial dissections. Given the complexity of tissue geometry and material behavior, computational models are often essential for studying both damage and failure. Yet, because of the need to account for discontinuous phenomena such as crazing, tearing, and rupturing, continuum methods are limited. Therefore, we model soft tissue damage and failure using a particle/continuum approach. Specifically, we combine continuum damage theory with Smoothed Particle Hydrodynamics (SPH). Because SPH is a meshless particle method, and particle connectivity is determined solely through a neighbor list, discontinuities can be readily modeled by modifying this list. We show, for the first time, that an anisotropic hyperelastic constitutive model commonly employed for modeling soft tissue can be conveniently implemented within a SPH framework and that SPH results show excellent agreement with analytical solutions for uniaxial and biaxial extension as well as finite element solutions for clamped uniaxial extension in 2D and 3D. We further develop a simple algorithm that automatically detects damaged particles and disconnects the spatial domain along rupture lines in 2D and rupture surfaces in 3D. We demonstrate the utility of this approach by simulating damage and failure under clamped uniaxial extension and in a peeling experiment of virtual soft tissue samples. In conclusion, SPH in combination with continuum damage theory may provide an accurate and efficient framework for modeling damage and failure in soft tissues.     

Consistent trilayer biomechanical modeling of aortic valve leaflet tissue

Aortic valve tissue exhibits highly nonlinear, anisotropic, and heterogeneous material behavior due to its complex microstructure. A thorough understanding of these characteristics permits us to develop numerical models that can shed insight on the function of the aortic valve in health and disease. Herein, we take a closer look at consistently capturing the observed physical response of aortic valve tissue in a continuum mechanics framework. Such a treatment is the first step in developing comprehensive multiscale and multiphysics models.We highlight two important aspects of aortic valve tissue behavior: the role of the collagen fiber microstructure and the native prestressing. We propose a model that captures these two features as well as the heterogeneous layer-scale topology of the tissue. We find the model can reproduce the experimentally observed multiscale mechanical behavior in a manner that provides intuition on the underlying mechanics.     

The involvement of interleukin-1 and interleukin-4 in the response of human annulus fibrosus cells to cyclic tensile strain: an altered mechanotransduction pathway with degeneration

Introduction  

Recent evidence suggests that intervertebral disc (IVD) cells derived from degenerative tissue are unable to respond to physiologically relevant mechanical stimuli in the 'normal' anabolic manner, but instead respond by increasing matrix catabolism. Understanding the nature of the biological processes which allow disc cells to sense and respond to mechanical stimuli (a process termed 'mechanotransduction') is important to ascertain whether these signalling pathways differ with disease. The aim here was to investigate the involvement of interleukin (IL)-1 and IL-4 in the response of annulus fibrosus (AF) cells derived from nondegenerative and degenerative tissue to cyclic tensile strain to determine whether cytokine involvement differed with IVD degeneration.     

A homogenization model of the annulus fibrosus

The objective of this study was to use a homogenization model of the anisotropic mechanical behavior of annulus fibrosus (AF) to address some of the issues raised in structural finite element and fiber-reinforced strain energy models. Homogenization theory describes the effect of microstructure on macroscopic material properties by assuming the material is composed of repeating representative volume elements. We first developed the general homogenization model and then specifically prescribed the model to in-plane single lamella and multi-lamellae AF properties. We compared model predictions to experimentally measured AF properties and performed parametric studies. The predicted tensile moduli (E theta and E z) and their dependence on fiber volume fraction and fiber angle were consistent with measured values. However, the model prediction for shear modulus (G thetaz) was two orders of magnitude larger than directly measured values. The values of E theta and E z were strongly dependent on the model input for matrix modulus, much more so than the fiber modulus. These parametric analyses demonstrated the contribution of the matrix in AF load support, which may play a role when protoeglycans are decreased in disc degeneration, and will also be an important design factor in tissue engineering. We next compared the homogenization model to a 3-D structural finite element model and fiber-reinforced energy models. Similarities between the three model types provided confidence in the ability of these models to predict AF tissue mechanics. This study provides a direct comparison between the several types of AF models and will be useful for interpreting previous studies and elucidating AF structure-function relationships in disc degeneration and for functional tissue engineering.     

Simulation of bone tissue formation within a porous scaffold under dynamic compression

A computational model of mechanoregulation is proposed to predict bone tissue formation stimulated mechanically by overall dynamical compression within a porous polymeric scaffold rendered by micro-CT. Dynamic compressions of 0.5–5% at 0.0025–0.025 s⁻¹ were simulated. A force-controlled dynamic compression was also performed by imposing a ramp of force from 1 to 70 N. The model predicts homogeneous mature bone tissue formation under strain levels of 0.5–1% at strain rates of 0.0025–0.005 s⁻¹. Under higher levels of strain and strain rates, the scaffold shows heterogeneous mechanical behaviour which leads to the formation of a heterogeneous tissue with a mixture of mature bone and fibrous tissue. A fibrous tissue layer was also predicted under the force-controlled dynamic compression, although the same force magnitude was found promoting only mature bone during a strain-controlled compression. The model shows that the mechanical stimulation of bone tissue formation within a porous scaffold closely depends on the loading history and on the mechanical behaviour of the scaffold at local and global scales.     

A linear material model for fiber-induced anisotropy of the anulus fibrosus

The anulus fibrosus (AF) is a lamellar, fibrocartilaginous component of the intervertebral disc, which exhibits highly anisotropic behaviors in tension. These behaviors arise from the material's unique collagen structure. We have investigated the use of a linear, fiber-induced anisotropic model for the AF using a quadratic strain energy density formulation with an explicit representation of the collagen fiber populations. We have proposed a representative set of intrinsic material properties using independent datasets of the AF from the literature and appropriate thermodynamic constraints. The model was validated by comparing predictions with previous experimental data for AF behavior and its dependence on fiber angle. The model predicts that compressible effects may exist for the AF, and suggests that physical effects of the equivalent "matrix," "fiber," "fiber-matrix," and "fiber-fiber," interactions may be important contributors to the mechanical behavior of the AF.     

CNS Cell Distribution and Axon Orientation Determine Local Spinal Cord Mechanical Properties

Mechanical signaling plays an important role in cell physiology and pathology. Many cell types, including neurons and glial cells, respond to the mechanical properties of their environment. Yet, for spinal cord tissue, data on tissue stiffness are sparse. To investigate the regional and direction-dependent mechanical properties of spinal cord tissue at a spatial resolution relevant to individual cells, we conducted atomic force microscopy (AFM) indentation and tensile measurements on acutely isolated mouse spinal cord tissue sectioned along the three major anatomical planes, and correlated local mechanical properties with the underlying cellular structures. Stiffness maps revealed that gray matter is significantly stiffer than white matter irrespective of directionality (transverse, coronal, and sagittal planes) and force direction (compression or tension) (K_g= ∼130 Pa vs. K_w= ∼70 Pa); both matters stiffened with increasing strain. When all data were pooled for each plane, gray matter behaved like an isotropic material under compression; however, subregions of the gray matter were rather heterogeneous and anisotropic. For example, in sagittal sections the dorsal horn was significantly stiffer than the ventral horn. In contrast, white matter behaved transversely isotropic, with the elastic stiffness along the craniocaudal (i.e., longitudinal) axis being lower than perpendicular to it. The stiffness distributions we found under compression strongly correlated with the orientation of axons, the areas of cell nuclei, and cellular in plane proximity. Based on these morphological parameters, we developed a phenomenological model to estimate local mechanical properties of central nervous system (CNS) tissue. Our study may thus ultimately help predicting local tissue stiffness, and hence cell behavior in response to mechanical signaling under physiological and pathological conditions, purely based on histological data.     

Determination of mechanical stress distribution in Drosophila wing discs using photoelasticity

Morphogenesis, the process by which all complex biological structures are formed, is driven by an intricate interplay between genes, growth, as well as intra- and intercellular forces. While the expression of different genes changes the mechanical properties and shapes of cells, growth exerts forces in response to which tissues, organs and more complex structures are shaped. This is exemplified by a number of recent findings for instance in meristem formation in Arabidopsis and tracheal tube formation in Drosophila. However, growth not only generates forces, mechanical forces can also have an effect on growth rates, as is seen in mammalian tissues or bone growth. In fact, mechanical forces can influence the expression levels of patterning genes, allowing control of morphogenesis via mechanical feedback. In order to study the connections between mechanical stress, growth control and morphogenesis, information about the distribution of stress in a tissue is invaluable. Here, we applied stress-birefringence to the wing imaginal disc of Drosophila melanogaster, a commonly used model system for organ growth and patterning, in order to assess the stress distribution present in this tissue. For this purpose, stress-related differences in retardance are measured using a custom-built optical set-up. Applying this method, we found that the stresses are inhomogeneously distributed in the wing disc, with maximum compression in the centre of the wing pouch. This compression increases with wing disc size, showing that mechanical forces vary with the age of the tissue. These results are discussed in light of recent models proposing mechanical regulation of wing disc growth.     

Collagen fiber alignment does not explain mechanical anisotropy in fibroblast populated collagen gels

Many load-bearing soft tissues exhibit mechanical anisotropy. In order to understand the behavior of natural tissues and to create tissue engineered replacements, quantitative relationships must be developed between the tissue structures and their mechanical behavior. We used a novel collagen gel system to test the hypothesis that collagen fiber alignment is the primary mechanism for the mechanical anisotropy we have reported in structurally anisotropic gels. Loading constraints applied during culture were used to control the structural organization of the collagen fibers of fibroblast populated collagen gels. Gels constrained uniaxially during culture developed fiber alignment and a high degree of mechanical anisotropy, while gels constrained biaxially remained isotropic with randomly distributed collagen fibers. We hypothesized that the mechanical anisotropy that developed in these gels was due primarily to collagen fiber orientation. We tested this hypothesis using two mathematical models that incorporated measured collagen fiber orientations: a structural continuum model that assumes affine fiber kinematics and a network model that allows for nonaffine fiber kinematics. Collagen fiber mechanical properties were determined by fitting biaxial mechanical test data from isotropic collagen gels. The fiber properties of each isotropic gel were then used to predict the biaxial mechanical behavior of paired anisotropic gels. Both models accurately described the isotropic collagen gel behavior. However, the structural continuum model dramatically underestimated the level of mechanical anisotropy in aligned collagen gels despite incorporation of measured fiber orientations; when estimated remodeling-induced changes in collagen fiber length were included, the continuum model slightly overestimated mechanical anisotropy. The network model provided the closest match to experimental data from aligned collagen gels, but still did not fully explain the observed mechanics. Two different modeling approaches showed that the level of collagen fiber alignment in our uniaxially constrained gels cannot explain the high degree of mechanical anisotropy observed in these gels. Our modeling results suggest that remodeling-induced redistribution of collagen fiber lengths, nonaffine fiber kinematics, or some combination of these effects must also be considered in order to explain the dramatic mechanical anisotropy observed in this collagen gel model system.     

Damage accumulation location under cyclic loading in the lumbar disc shifts from inner annulus lamellae to peripheral annulus with increasing disc degeneration

It is difficult to study the breakdown of lumbar disc tissue over several years of exposure to bending and lifting by experimental methods. In our earlier published study we have shown how a finite element model of a healthy lumbar motion segment was used to predict the damage accumulation location and number of cyclic to failure under different loading conditions. The aim of the current study was to extend the continuum damage mechanics formulation to the degenerated discs and investigate the initiation and progression of mechanical damage. Healthy disc model was modified to represent degenerative discs (Thompson grade III and IV) by incorporating both geometrical and biochemical changes due to degeneration. Analyses predicted decrease in the number of cycles to failure with increasing severity of disc degeneration. The study showed that the damage initiated at the posterior inner annulus adjacent to the endplates and propagated outwards towards its periphery in healthy and grade III degenerated discs. The damage accumulated preferentially in the posterior region of the annulus. However in grade IV degenerated disc damage initiated at the posterior outer periphery of the annulus and propagated circumferentially. The finite element model predictions were consistent with the infrequent occurrence of rim lesions at early age but a much higher incidence in severely degenerated discs.     

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.     

Effect of non-uniform thickness of samples in stress relaxation tests under unconfined compression of samples of articular discs

A precise information of the biomechanical properties of soft tissues is required to develop a suitable simulation model, with which the distribution of stress and strain in the complex structures can be estimated. Many soft tissues have been mechanically characterized by stress relaxation tests under unconfined or confined compression. In general, full-thickness samples are extracted to reduce the damage in the tissue as much as possible. However, it is not guaranteed that these samples have a uniform thickness or, in other words, planar parallel faces. In particular, in the articular disc of the temporomandibular joint, many studies can be found testing full-thickness samples for which that thickness is known to be non-uniform, while making the assumption of uniaxial stress state to extract the mechanical properties from those tests. That inaccuracy may have a strong influence in some cases and needs a profound revision. The main goal of this work is to quantify the error committed in that assumption and the influence of the variation of thickness on that error in a particular test: stress relaxation tests under unconfined compression. Based on this error and defining an allowable tolerance, a criterion is established to reject samples depending on their aspect ratio.     

MRI-based experimentations of fingertip flat compression: Geometrical measurements and finite element inverse simulations to investigate material property parameters

Modeling human-object interactions is a necessary step in the ergonomic assessment of products. Fingertip finite element models can help investigating these interactions, if they are built based on realistic geometrical data and material properties. The aim of this study was to investigate the fingertip geometry and its mechanical response under compression, and to identify the parameters of a hyperelastic material property associated to the fingertip soft tissues.Fingertip compression tests in an MRI device were performed on 5 subjects at either 2 or 4 N and at 15° or 50°. The MRI images allowed to document both the internal and external fingertip dimensions and to build 5 subject-specific finite element models. Simulations reproducing the fingertip compression tests were run to obtain the material property parameters of the soft tissues.Results indicated that two ellipses in the sagittal and longitudinal plane could describe the external fingertip geometry. The internal geometries indicated an averaged maximal thickness of soft tissues of 6.4 ± 0.8 mm and a 4 ± 1 mm height for the phalanx bone. The averaged deflections under loading went from 1.8 ± 0.3 mm at 2 N, 50° to 3.1 ± 0.2 mm at 4 N, 15°. Finally, the following set of parameters for a second order hyperelastic law to model the fingertip soft tissues was proposed: C₀₁ = 0.59 ± 0.09 kPa and C₂₀ = 2.65 ± 0.88 kPa.These data should facilitate further efforts on fingertip finite element modeling.