Dynamic mechanical response of bovine gray matter and white matter brain tissues under compression

Dynamic responses of brain tissues are needed for predicting traumatic brain injury (TBI). We modified a dynamic experimental technique for characterizing high strain-rate mechanical behavior of brain tissues. Using the setup, the gray and white matters from bovine brains were characterized under compression to large strains at five different strain rates ranging from 0.01 to 3000/s. The white matter was examined both along and perpendicular to the coronal section for anisotropy characterization. The results show that both brain tissue matters are highly strain-rate sensitive. Differences between the white matter and gray matter in their mechanical responses are recorded. The white matter shows insignificant anisotropy over all strain rates. These results will lead to rate-dependent material modeling for dynamic event simulations.     

Heterogeneous growth of plant tissues

KORN, R., 1993. Heterogeneous growth of plant tissues. Heterogeneous growth is defined as different rates or patterns of growth in adjacent tissue regions, in contrast to homogeneous growth where a region expresses a uniform rate or pattern of growth. Heterogeneous growth is inspected in a variety of plant tissues and the pattern of expansion is characterized for each. In the case of epidermal cell proliferation, different growth rates for cell plates and old walls lead to the feature of coordinated growth in which slow growth of the former is compensated for by a faster rate of the latter. Examples include leaf epidermal cells above veins growing differently from those above areole regions, and pairs of guard cells of stomata ceasing to expand before other epidermal cells. In the alga Coleochaete only marginal walls grow, and at different rates around the colony, to generate a fractal, stochastic type of coordinated growth. In the fern gametophyte there are complex gradients of differential growth rates. Epidermal cells of apices are often of mixed growth, as cells at the summit undergo two dimensional expansion while cells along the flanks express one dimensional expansion. Coordinated growth requires matched rates where the constraining effect of the slower growing region is compensated for by a faster rate in an encircling region compared to the average rate of the overall tissue. Mixed and differential growth patterns do not necessarily create constraints and so lead to smooth tissue expansion. Emergence of some constraints leads to breaking of symmetry and disruptive growth as in the appearance of new axes found in organs and epidermal derivatives. In planar development heterogeneous growth appears to be the rule, and homogeneous growth the exception.     

Growth,Anisotropy, and Residual Stresses in Arteries

A simple phenomenological theory of tissue growth is used in order to demonstrate that volumetric growth combined with material anisotropy can lead to accumulation of residual stresses in arteries. The theory is applied to growth of a cylindrical blood vessel with the anisotropy moduli derived from experiments. It is shown that bending resultants are developed in the ring cross-section of the artery. These resultants may cause the ring opening or closing after cutting the artery \textit {in vitro} as it is observed in experiments. It is emphasized that the mode of the arterial ring opening is affected by the parameters of anisotropy.     

Anisotropy of fibrous tissues in relation to the distribution of tensed and buckled fibers

Fibrous tissues are characterized by a much higher stiffness in tension than compression. This study uses microstructural modeling to analyze the material symmetry of fibrous tissues undergoing tension and compression, to better understand how material symmetry relates to the distribution of tensed and buckled fibers. The analysis is also used to determine whether the behavior predicted from a microstructural model can be identically described by phenomenological continuum models. The analysis confirms that in the case when all the fibers are in tension in the current configuration, the material symmetry of a fibrous tissue in the corresponding reference configuration is dictated by the symmetry of its fiber angular distribution in that configuration. However, if the strain field exhibits a mix of tensile and compressive principal normal strains, the fibrous tissue is represented by a material body which consists only of those fibers which are in tension; the material symmetry of this body may be deduced from the superposition of the planes of symmetry of the strain and the planes of symmetry of the angular fiber distribution. Thus the material symmetry is dictated by the symmetry of the angular distribution of only those fibers which are in tension. Examples are provided for various fiber angular distribution symmetries. In particular, it is found that a fibrous tissue with isotropic fiber angular distribution exhibits orthotropic symmetry when subjected to a mix of tensile and compressive principal normal strains, with the planes of symmetry normal to the principal directions of the strain. This anisotropy occurs even under infinitesimal strains and is distinct from the anisotropy induced from the finite rotation of fibers. It is also noted that fibrous materials are not stable under all strain states due to the inability of fibers to sustain compression along their axis; this instability can be overcome by the incorporation of a ground matrix. It is concluded that the material response predicted using a microstructural model of the fibers cannot be described exactly by phenomenological continuum models. These results are also applicable to nonbiological fiber-composite materials.     

Growth-induced buckling of an epithelial layer

We use a proof-of-concept experiment and two mathematical models to explore growth-induced tissue buckling, as may occur in colorectal crypt formation. Our experiment reveals how growth of a cultured epithelial monolayer on a thin flexible substrate can cause out-of-plane substrate deflections. We describe this system theoretically using a ‘bilayer’ model in which a growing cell layer adheres to a thin compressible elastic beam. We compare this with the ‘supported-monolayer’ model due to Edwards and Chapman (Bull Math Biol 69:1927–1942, 2007) for an incompressible expanding beam (representing crypt epithelium), which incorporates viscoelastic tethering to underlying stroma. We show that the bilayer model can exhibit buckling via parametric growth (in which the system passes through a sequence of equilibrium states, parameterised by the total beam length); in this case, non-uniformities in cell growth and variations in cell–substrate adhesion are predicted to have minimal effect on the shape of resulting buckled states. The supported-monolayer model reveals how competition between lateral supports and stromal adhesion influences the wavelength of buckled states (in parametric growth), and how non-equilibrium relaxation of tethering forces influences post-buckled shapes. This model also predicts that non-uniformities in growth patterns have a much weaker influence on buckled shapes than non-uniformities in material properties. Together, the experiment and models support the concept of patterning by growth-induced buckling and suggest that targeted softening of a growing cell layer provides greater control in shaping tissues than non-uniform growth.     

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.     

Migration-Directing Liquid Properties of Embryonic Amphibian Tissues

Deep ectoderm, mesoderm and endoderm excised from gastrulatingamphibian embryos spontaneously undergo liquid-like movementsin organ culture. Cell populations of these tissues on nonadhesivesubstrata will round up into spheres, spread over one anotherand segregate (sort out) from one another just as immiscibleliquid droplets do. In ordinary liquids, movements like theseare controlled by surface tensions; perhaps surface tensionsalso control the similar movements of liquid-like tissues. Onenecessary condition for tissue surface tension analysis is thatthe tissue must be able (just as ordinary liquids are able)to spontaneously relax internal stretching forces (shear stresses).When cellular aggregates of the germ layers were deformed bygentle compression between parallel glass plates, cells withinthe aggregates were initially stretched. However, the cellssoon returned to their original undistorted shapes. Thus, cellstretching forces were gradually relaxed by cell rearrangements.The in vitro spreading movements of the deep germ layers implythat the surface tension of ectoderm should be greater thanthe surface tension of mesoderm which should be greater thanthe surface tension of endoderm. Quantitative measurements oftissue surface tensions made by parallel plate compression confirmprecisely that relationship. Furthermore, the surface tensionsof these tissues remain constant regardless of the amount ofaggregate flattening—another necessary condition for validsurface tension measurements. These results demonstrate thatamphibian deep germ layers possess fundamental liquid propertieswhich are sufficient to direct their liquid-like rearrangementsin organ culture. Furthermore, I also report that one of theseproperties, surface tension, displays a preliminary correlationwith density of cell surface charge (assessed by electrophoreticmobility) and with the onset of in vivo mesodermal involution.     

Prediction of femoral head collapse in osteonecrosis

The femoral head deteriorates in osteonecrosis. As a consequence of that, the cortical shell of the femoral head can buckle into the cancellous bone supporting it. In order to examine the buckling scenario we performed numerical analysis of a realistic femoral head model. The analysis included a solution of the hip contact problem, which provided the contact pressure distribution, and subsequent buckling simulation based on the given contact pressure. The contact problem was solved iteratively by approximating the cartilage by a discrete set of unilateral linear springs. The buckling calculations were based on a finite element mesh with brick elements for the cancellous bone and shell elements for the cortical shell. Results of 144 simulations for a variety of geometrical, material, and loading parameters strengthen the buckling scenario. They, particularly, show that the normal cancellous bone serves as a strong supporting foundation for the cortical shell and prevents it from buckling. However, under the development of osteonecrosis the deteriorating cancellous bone is unable to prevent the cortical shell from buckling and the critical pressure decreases with the decreasing Young modulus of the cancellous bone. The local buckling of the cortical shell seems to be the driving force of the progressive fracturing of the femoral head leading to its entire collapse. The buckling analysis provides an additional criterion of the femoral head collapse, the critical contact pressure. The buckling scenario also suggests a new argument in speculating on the femoral head reinforcement. If the entire collapse of the femoral head starts with the buckling of the cortical shell then it is reasonable to place the reinforcement as close to the cortical shell as possible.     

The nonlinear material properties of liver tissue determined from no-slip uniaxial compression experiments

The mechanical response of soft tissue is commonly characterized from unconfined uniaxial compression experiments on cylindrical samples. However, friction between the sample and the compression platens is inevitable and hard to quantify. One alternative is to adhere the sample to the platens, which leads to a known no-slip boundary condition, but the resulting nonuniform state of stress in the sample makes it difficult to determine its material parameters. This paper presents an approach to extract the nonlinear material properties of soft tissue (such as liver) directly from no-slip experiments using a set of computationally determined correction factors. We assume that liver tissue is an isotropic, incompressible hyperelastic material characterized by the exponential form of strain energy function. The proposed approach is applied to data from experiments on bovine liver tissue. Results show that the apparent material properties, i.e., those determined from no-slip experiments ignoring the no-slip conditions, can differ from the true material properties by as much as 50% for the exponential material model. The proposed correction approach allows one to determine the true material parameters directly from no-slip experiments and can be easily extended to other forms of hyperelastic material models.     

Stress distribution in a circular membrane with a central fixation

Clinical interventions can change the mechanical environment of the tissues targeted for therapy. In order to design better procedures, it is important to understand cellular responses to altered mechanical stress. Rigid fixation is one example of a constraint imposed on living tissues as a result of implanted devices. This results in disturbed stress and strain fields, with potentially strong gradients. Herein, we numerically solve the governing nonlinear ordinary differential equation for the stress distribution in a finitely deformed anisotropic circular membrane with a concentric fixation by applying a zero-displacement condition at the inner circumference. Results show that rigid fixations yield distributions of stress and strain that are markedly different from tissue defects with traction-free boundaries. Moreover the material anisotropy plays a significant role in the manner the stress redistributes regardless of the size of fixation. The present study will contribute to the design of experiments to determine cellular reactions involved in the failure of interventional treatments.     

Site-specific effects of compression on macromolecular diffusion in articular cartilage

Articular cartilage is the connective tissue that lines joints and provides a smooth surface for joint motion. Because cartilage is avascular, molecular transport occurs primarily via diffusion or convection, and cartilage matrix structure and composition may affect diffusive transport. Because of the inhomogeneous compressive properties of articular cartilage, we hypothesized that compression would decrease macromolecular diffusivity and increase diffusional anisotropy in a site-specific manner that depends on local tissue strain. We used two fluorescence photobleaching methods, scanning microphotolysis and fluorescence imaging of continuous point photobleaching, to measure diffusion coefficients and diffusional anisotropy of 70 kDa dextran in cartilage during compression, and measured local tissue strain using texture correlation. For every 10% increase in normal strain, the fractional change in diffusivity decreased by 0.16 in all zones, and diffusional anisotropy increased 1.1-fold in the surface zone and 1.04-fold in the middle zone, and did not change in the deep zone. These results indicate that inhomogeneity in matrix structure and composition may significantly affect local diffusive transport in cartilage, particularly in response to mechanical loading. Our findings suggest that high strains in the surface zone significantly decrease diffusivity and increase anisotropy, which may decrease transport between cartilage and synovial fluid during compression.     

A Simple Phenomenological Theory of Tissue Growth

A simple phenomenological framework for modeling growth of living tissues is proposed. Growth is defined as a change of mass and configuration of the tissue. Tissue is considered as an open system where mass conservation is violated and the full-scale mass balance is applied. A possible structure of constitutive equations is discussed with reference tosimple growing materials. 'Thermoelastic' formulation of the simple growing material is specified. Within this framework traction free growth of cylindrical and spherical bodies is examined. It is shown that the theory accommodates the case where stresses are not generated in uniform volumetric growth. It is also found that surface growth corresponds to aboundary layersolution of the governing equations. This finding proves the ability of continuum mechanics to describe surface growth. The latter is contrary to the usual use of purely kinematical theories, which do not involve balance and constitutive equations, for treating surface growth.     

The influence of fiber orientation on the equilibrium properties of neutral and charged biphasic tissues

Constitutive models facilitate investigation into load bearing mechanisms of biological tissues and may aid attempts to engineer tissue replacements. In soft tissue models, a commonly made assumption is that collagen fibers can only bear tensile loads. Previous computational studies have demonstrated that radially aligned fibers stiffen a material in unconfined compression most by limiting lateral expansion while vertically aligned fibers buckle under the compressive loads. In this short communication, we show that in conjunction with swelling, these intuitive statements can be violated at small strains. Under such conditions, a tissue with fibers aligned parallel to the direction of load initially provides the greatest resistance to compression. The results are further put into the context of a Benninghoff architecture for articular cartilage. The predictions of this computational study demonstrate the effects of varying fiber orientations and an initial tare strain on the apparent material parameters obtained from unconfined compression tests of charged tissues.     

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.

     

Trabecular bone structure and strength - remodelling and repair

The strength of the spinal trabecular bone declines by a factor of 4-5 from the age of 20 to 80 years. At the same time, the volumetric (apparent) density declines by a factor of only 2. This discrepancy can be explained by the known power relationship between density and strength; this power relationship is based on the fact that trabecular bone is a porous material. To date, it has not been possible to determine or quantify the influence other factors may have in determining the strength of a loadbearing trabecular network. However, it is known that with age: 1) There is a loss of connectivity through osteoclastic perforations of horizontal struts. 2) There is an increase in anisotropy - again due to loss of horizontal struts, and perhaps also due to micro-modelling drift or to thickening of some vertical trabeculae. 3) The changes in the network can lead to the slenderness ratio between vertical and horizontal struts reaching a certain magnitude and thereby inducing buckling under compression. 4) Microdamage and microfractures will occur - mainly in these very loaded vertical struts. The microfractures will be repaired by microcallus formation, and these calluses will later be removed by the remodelling process. 5) Bone material quality will slightly change, leading to a decrease in collagen content and a relative increase in the degree of mineralisation. But, it is not known how these factors will influence the power relationship between density and strength. Nor is it known how different treatment regimens will affect the 'natural' power relationship: will the same curve be followed, but in the opposite direction? Or will the curve be less or more steep? Will the gain in bone strength be larger if treatment is started early - on the steep part of the curve? Furthermore, as trabecular bone can never be isolated in vivo, other factors need to be investigated: The interplay between the cortical shell and the trabecular network; transmission of load; the interplay between soft tissues (cartilage, connective tissue, muscle) and bone; the shock absorbing capacity of the discs; and the hydraulic effect of the bone marrow. In order to answer these questions, more in vitro and in vivo studies on human bone in relation to aging, to immobilisation, to exercise and in relation to different treatment regimens are needed.     

On the anisotropy and inhomogeneity of permeability in articular cartilage

Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is "directed" by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.     

Finite element simulation of skeletal muscular structures obtained from images of histological serial sections

In this study, we present a method for the three-dimensional reconstruction of objects obtained from histological serial sections (exemplified by those of a pennate striated skeletal muscle) and its application to the finite element method. A hyperelastic material model is used for modeling biological soft tissue. The reconstruction process relies on the direct construction of a volumetric mesh using an octree approach which leads to a stable finite element method. Stability can be expressed in the spectral matrix condition number. To visualize stress patterns within the underlying anatomy the simulation results are projected onto images of the histological scenario.     

Buckling of a growing tissue and the emergence of two-dimensional patterns

The process of biological growth and the associated generation of residual stress has previously been considered as a driving mechanism for tissue buckling and pattern selection in numerous areas of biology. Here, we develop a two-dimensional thin plate theory to simulate the growth of cultured intestinal epithelial cells on a deformable substrate, with the goal of elucidating how a tissue engineer might best recreate the regular array of invaginations (crypts of Lieberkühn) found in the wall of the mammalian intestine. We extend the standard von Kármán equations to incorporate inhomogeneity in the plate’s mechanical properties and surface stresses applied to the substrate by cell proliferation. We determine numerically the configurations of a homogeneous plate under uniform cell growth, and show how tethering to an underlying elastic foundation can be used to promote higher-order buckled configurations. We then examine the independent effects of localised softening of the substrate and spatial patterning of cellular growth, demonstrating that (within a two-dimensional framework, and contrary to the predictions of one-dimensional models) growth patterning constitutes a more viable mechanism for control of crypt distribution than does material inhomogeneity.     

Tissue-specific microdissection coupled with ProteinChip array technologies: applications in cancer research

Analysis of whole genomes to monitor specific changes in gene activation or changes in gene copy number due to perturbation has recently become possible using DNA chip technologies. It is now becoming apparent, however, that knowing the genetic sequence encoding a protein is not sufficient to predict the size or biological nature of a protein. This can be particularly important in cancer research where posttranslational modifications of a protein can specifically lead to the disease. To address this area, several proteomic tools have been developed. Currently the most widely used proteomics tool is two-dimensional polyacrylamide gel electrophoresis (2D-PAGE), which can display protein expression patterns to a high degree of resolution. However, 2D-PAGE can be time consuming; the analysis is complicated and, compared with DNA techniques, is not very sensitive. Although some of these problems can be alleviated by using high-quality homogeneous samples, such as those generated using microdissection techniques, the quantity of sample is often limited and may take several days to generate sufficient material for a single 2D-PAGE analysis. As an alternative to 2D-PAGE, a preliminary study using a new technique was used to generate protein expression patterns from either whole tissue extracts or microdissected material. Surface-enhanced laser desorption and ionization allows the retention of proteins on a solid-phase chromatographic surface or ProteinChip Array with direct detection of retained proteins by time-of-flight mass spectrometry. Using this system, we analyzed tumor and normal tissue from head and neck cancer and microdissected melanoma to determine differentially expressed proteins. In particular, comparisons of the protein expression patterns from microdissected normal and tumor tissues indicated several differences, highlighting the importance of extremely defined tissue lysates for protein profiling.