Dynamic deformational loading results in selective application of mechanical stimulation in a layered, tissue-engineered cartilage construct

The application of dynamic physiologic loading to a bilayered chondrocyte-seeded agarose construct with a 2% (wt/vol) top layer and 3% (wt/vol) bottom layer was hypothesized to (1) improve overall construct properties and (2) result in a tissue that mimics the mechanical inhomogeneity of native cartilage. Dynamic loading over the 28 day culture period was found to significantly increase bulk mechanical and biochemical properties versus free-swelling culture. The initial depth-distribution of the compressive Young's modulus (EY) reflected the intrinsic properties of the gel in each layer and a similar trend to the native tissue, with a softer 2% gel layer and a much stiffer 3% gel layer. After 28 days in culture, free-swelling conditions maintained this general trend while loaded constructs possessed a reverse profile, with significant increases in EY observed only in the 2% gel. Histological analysis revealed preferential matrix formation in the 2% agarose layer, with matrix localized more pericellularly in the 3% agarose layer. Finite element modeling revealed that, prior to significant matrix elaboration, the 2% layer experiences increased mechanical stimuli (fluid flow and compressive strain) during loading that may enhance chondrocyte stimulation and nutrient transport in that layer, consistent with experimental observations. From these results, we conclude that due to the limitations in 3% agarose, the use of this type of bilayered construct to construct depth-dependent inhomogeneity similar to the native tissue is not likely to be successful under long-term culture conditions. Our study underscores the importance of other physical properties of the scaffold that may have a greater influence on interconnected tissue formation than intrinsic scaffold stiffness.     

The shear mechanical properties of diabetic and non-diabetic plantar soft tissue

Changes in the plantar soft tissue shear properties may contribute to ulceration in diabetic patients, however, little is known about these shear parameters. This study examines the elastic and viscoelastic shear behavior of both diabetic and non-diabetic plantar tissue. Previously compression tested plantar tissue specimens (n=54) at six relevant plantar locations (hallux, first, third, and fifth metatarsal heads, lateral midfoot, and calcaneus) from four cadaveric diabetic feet and five non-diabetic feet were utilized. Per in vivo data (i.e., combined deformation patterns of compression followed by shear), an initial static compressive strain (36-38%) was applied to the tissue followed by target shear strains of 50% and 85% of initial thickness. Triangle waves were used to quantify elastic parameters at both strain levels and a stress relaxation test (0.25 s ramp and 300 s hold) was used to quantify the viscoelastic parameters at the upper strain level. Several differences were found between test groups including a 52-62% increase in peak shear stress, a 63% increase in toe shear modulus, a 47% increase in final shear modulus, and a 67% increase in middle slope magnitude (sharper drop in relaxation) in the diabetic tissue. Beyond a 54% greater peak compressive stress in the third metatarsal compared to the lateral midfoot, there were no differences in shear properties between plantar locations. Notably, this study demonstrates that plantar soft tissue with diabetes is stiffer than healthy tissue, thereby compromising its ability to dissipate shear stresses borne by the foot that may increase ulceration risk.     

Viscoelastic shear properties of the corneal stroma

The cornea is a highly specialized transparent tissue which covers the front of the eye. It is a tough tissue responsible for refracting the light and protecting the sensitive internal contents of the eye. The biomechanical properties of the cornea are primarily derived from its extracellular matrix, the stroma. The majority of previous studies have used strip tensile and pressure inflation testing methods to determine material parameters of the corneal stroma. Since these techniques do not allow measurements of the shear properties, there is little information available on transverse shear modulus of the cornea. The primary objectives of the present study were to determine the viscoelastic behavior of the corneal stroma in shear and to investigate the effects of the compressive strain. A thorough knowledge of the shear properties is required for developing better material models for corneal biomechanics. In the present study, torsional shear experiments were conducted at different levels of compressive strain (0–30%) on porcine corneal buttons. First, the range of linear viscoelasticity was determined from strain sweep experiments. Then, frequency sweep experiments with a shear strain amplitude of 0.2% (which was within the region of linear viscoelasticity) were performed. The corneal stroma exhibited viscoelastic properties in shear. The shear storage modulus, G′, and shear loss modulus, G″, were reported as a function of tissue compression. It was found that although both of these parameters were dependent on frequency, shear strain amplitude, and compressive strain, the average shear storage and loss moduli varied from 2 to 8 kPa, and 0.3 to 1.2 kPa, respectively. Therefore, it can be concluded that the transverse shear modulus is of the same order of magnitude as the out-of-plane Young's modulus and is about three orders of magnitude lower than the in-plane Young's modulus.     

Mapping the depth dependence of shear properties in articular cartilage

Determining the depth dependence of the shear properties of articular cartilage is essential for understanding the structure-function relation in this tissue. Here, we measured spatial variations in the shear modulus G of bovine articular cartilage using a novel technique that combines shear testing, confocal imaging and force measurement. We found that G varied by up to two orders of magnitude across a single sample, exhibited a global minimum 50-250 microm below the articular surface in a region just below the superficial zone and was roughly constant at depths > 1000 microm (the "plateau region"). For plateau strains gamma(plateau) approximately 0.75% and overall compressive strains epsilon approximately 5%, G(min) and G(plateau) were approximately 70 and approximately 650 kPa, respectively. In addition, we found that the shear modulus profile depended strongly on the applied shear and axial strains. The greatest change in G occurred at the global minimum where the tissue was highly nonlinear, stiffening under increased shear strain, and weakening under increased compressive strain. Our results can be explained through a simple thought model describing the observed nonlinear behavior in terms of localized buckling of collagen fibers and suggest that compression may decrease the vulnerability of articular cartilage to shear-induced damage by lowering the effective strain on individual collagen fibrils.     

Dynamic mechanical properties of agarose gels modeled by a fractional derivative model

The complex modulus (E*) and elastic modulus (E') of agarose gels (2% to 4%) are measured with a dynamic mechanical analyzer in frequency sweep shear sandwich mode between 0.1 and 20 Hz. The data showed that E* and E' increase with frequency according to a power law which can be described by a fractional derivative model to characterize the dynamic viscoelasticity of the gel. The functions between the model parameters including storage modulus coefficient (H) and the power law exponent (beta) and the agarose concentration are established. A molecular basis for the application of the fractional derivative model to gel polymers is also discussed. Such an approach can be useful in tissue culture studies employing dynamic pressurization or for validation of magnetic resonance elastography.     

Simple shear testing of parallel-fibered planar soft tissues

The simple shear test may provide unique information regarding the material response of parallel-fibered soft tissues because it allows the elimination of the dominant fiber material response from the overall stresses. However, inhomogeneities in the strain field due to clamping and free edge effects have not been documented. The finite element method was used to study finite simple shear of simulated ligament material parallel to the fiber direction. The effects of aspect ratio, clamping prestrain, and bulk modulus were assessed using a transversely isotropic, hyperelastic material model. For certain geometries, there was a central area of uniform strain. An aspect ratio of 1:2 for the fiber to cross-fiber directions provided the largest region of uniform strain. The deformation was nearly isochoric for all bulk moduli indicating this test may be useful for isolating solid viscoelasticity from interstitial flow effects. Results suggest this test can be used to characterize the matrix properties for the type of materials examined in this study, and that planar measurements will suffice to characterize the strain. The test configuration may be useful for the study of matrix, fiber-matrix, and fiber-fiber material response in other types of parallel-fibered transversely isotropic soft tissues.     

Viscoelastic behavior of cellulose acetate in a mixed solvent system

The effect of increasing water composition on the rheological and microstructural behavior of a ternary cellulose acetate (CA)/N,N-dimethylacetamide (DMA)/water system is examined. Addition of water to the CA/DMA system results in enhanced steady shear viscosity and dynamic viscoelastic properties and ultimately to phase-separated gel formation. The changes in dynamic rheological behavior of the system during gelation correlate well with the combined solubility parameter (delta) and, in particular, the Hansen hydrogen-bonding solubility parameter index (delta(h)) of the solvent system, suggesting hydrogen-bonding interactions may be the major route initiating the sol-gel process. For all gels studied, the elastic modulus and the critical stress to yield shifts to higher values with increasing CA concentration and/or water content. In addition, the elastic modulus exhibits a power-law behavior with water content, with the same power-law exponent observed for gels containing different CA concentrations. Addition of water leads to formation of a denser gel network, as evidenced from direct visualization of the gel microstructure through confocal microscopy.     

Synthesis and mechanical properties of quaternary salts of chitosan-based films for food application

A novel method is described to synthesize quaternary salts of chitosan with dimethylsulfate and subsequently cast films. In an attempt to improve both mechanical and hydrophobic characteristics, the chitosan was previously modified by N-alkylation, introducing 4, 8 and 12 carbons moieties into the polymeric chain. Analysis by FTIR and solid-state CP-MAS (13)C NMR spectroscopy confirmed the success of both alkylation and quaternization processes. The average degree of quaternization of these N-methylated derivatives was calculated to be 35%. DMA measurements indicated that chitosan and its derivative films are typically brittle materials, exhibiting similar non-linear viscoelastic behaviors. The films of unmodified chitosan have a very small strain (approximately 2.8%), though they were the most resistant films (Young's modulus=2283 MPa; tensile strength >44.0 MPa). In general, the alkyl-chitosan derivatives appear to be more plastic than chitosan films but less resistant, e.g., for butyl chitosan: maximum strain=13.1%; tensile strength=13.4 MPa and Young's modulus=171 MPa. Conversely the quaternization reaction increased the hardness of the parent sample, viz. for quaternary salt of dodecyl chitosan: maximum strain=2.6%; tensile strength=38.3 MPa and Young's modulus=1792 MPa.     

Size-dependent rheology of type-I collagen networks

We investigate the system size-dependent rheological response of branched type I collagen gels. When subjected to a shear strain, the highly interconnected mesh dynamically reorients, resulting in overall stiffening of the network. When a continuous shear strain is applied to a collagen network, we observe that the local apparent modulus, in the strain-stiffening regime, is strongly dependent on the gel thickness. In addition, we demonstrate that the overall network failure is determined by the ratio of the gel thickness to the mesh size. These findings have broad implications for cell-matrix interactions, the interpretation of rheological tissue data, and the engineering of biomimetic scaffolds.     

Fluorescence photobleaching with spatial Fourier analysis: measurement of diffusion in light-scattering media.

A new method for the measurement of diffusion in thick samples is introduced, based upon the spatial Fourier analysis of Tsay and Jacobson (Biophys. J. 60: 360-368, 1991) for the video image analysis of fluorescence recovery after photobleaching (FRAP). In this approach, the diffusion coefficient is calculated from the decay of Fourier transform coefficients in successive fluorescence images. Previously, the application of FRAP in thick samples has been confounded by the optical effects of out-of-focus light and scattering and absorption by the sample. The theory of image formation is invoked to show that the decay rate is the same for both the observed fluorescence intensity and the true concentration distribution in the tissue. The method was tested in a series of macromolecular diffusion measurements in aqueous solution, in agarose gel, and in simulated tissue consisting of tumor cells (45% v/v) and blood cells (5% v/v) in an agarose gel. For a range of fluorescently labeled proteins (MW = 14 to 600 kD) and dextrans (MW = 4.4 to 147.8 kD), the diffusion coefficients in aqueous solution were comparable to previously published values. A comparison of the spatial Fourier analysis with a conventional direct photometric method revealed that even for the weakly scattering agarose sample, the conventional method gives a result that is inaccurate and dependent on sample thickness whereas the diffusion coefficient calculated by the spatial Fourier method agreed with published values and was independent of sample thickness. The diffusion coefficient of albumin in the simulated tissue samples, as determined by the spatial Fourier analysis, varied slightly with sample thickness.(ABSTRACT TRUNCATED AT 250 WORDS)     

Confined compression and torsion experiments on a pHEMA gel in various bath concentrations

The constitutive behaviour of cartilaginous tissue is the result of complex interaction between electrical, chemical and mechanical forces. Electrostatic interactions between fixed charges and mobile ions are usually accounted for by means of Donnan osmotic pressure. Recent experimental data show, however, that the shear modulus of articular cartilage depends on ionic concentration even if the strain is kept constant. Poisson–Boltzmann simulations suggest that this dependence is intrinsic to the double-layer around the proteoglycan chains. In order to verify this premise, this study measures whether—at a given strain—this ionic concentration–dependent shear modulus is present in a polymerized hydroxy-ethyl-methacrylate gel or not. A combined 1D confined compression and torque experiment is performed on a thin cylindrical hydrogel sample, which is brought in equilibrium with, respectively, 1, 0.1 and 0.03 M NaCl. The sample was placed in a chamber that consists of a stainless steel ring placed on a sintered glass filter, and on top a sintered glass piston. Stepwise ionic loading was cascaded by stepwise 1D compression, measuring the total stress after equilibration of the sample. In addition, a torque experiment was interweaved by applying a harmonic angular displacement and measuring the torque, revealing the relation between aggregate shear modulus and salt concentration at a given strain.     

In vivo liver tissue mechanical properties by Transient Elastography: comparison with Dynamic Mechanical Analysis

Understanding the mechanical properties of human liver is one of the most critical aspects of its numerical modeling for medical applications or impact biomechanics. Generally, model constitutive laws come from in vitro data. However, the elastic properties of liver may change significantly after death and with time. Furthermore, in vitro liver elastic properties reported in the literature have often not been compared quantitatively with in vivo liver mechanical properties on the same organ. In this study, both steps are investigated on porcine liver. The elastic property of the porcine liver, given by the shear modulus G, was measured by both Transient Elastography (TE) and Dynamic Mechanical Analysis (DMA). Shear modulus measurements were realized on in vivo and in vitro liver to compare the TE and DMA methods and to study the influence of testing conditions on the liver viscoelastic properties. In vitro results show that elastic properties obtained by TE and DMA are in agreement. Liver tissue in the frequency range from 0.1 to 4 Hz can be modeled by a two-mode relaxation model. Furthermore, results show that the liver is homogeneous, isotropic and more elastic than viscous. Finally, it is shown in this study that viscoelastic properties obtained by TE and DMA change significantly with post mortem time and with the boundary conditions.     

Electric birefringence imaging of electrokinetic agarose orientation.

Time-resolved and steady-state electric birefringence imaging with a slow-scan video camera is used to study orientation during DNA agarose gel electrophoresis. The hydrodynamically induced gel distortion is shown to be the major source of birefringence under electrophoresis running conditions and to generate a birefringence image that approximates the image of the DNA concentration gradient in the electric field direction. A fluid kinematic model is presented to describe the spatial distribution of steady-state birefringence and is verified with fluorescence measurements of DNA distribution. The stress-optic coefficient of 1% agarose gel is measured by mechanical compression and used to evaluate the magnitude of the induced strain on the gel during electrophoresis.     

Mechano-acoustic determination of Young's modulus of articular cartilage

The compressive stiffness of an elastic material is traditionally characterized by its Young's modulus. Young's modulus of articular cartilage can be directly measured using unconfined compression geometry by assuming the cartilage to be homogeneous and isotropic. In isotropic materials, Young's modulus can also be determined acoustically by the measurement of sound speed and density of the material. In the present study, acoustic and mechanical techniques, feasible for in vivo measurements, were investigated to quantify the static and dynamic compressive stiffness of bovine articular cartilage in situ. Ultrasound reflection from the cartilage surface, as well as the dynamic modulus were determined with the recently developed ultrasound indentation instrument and compared with the reference mechanical and ultrasound speed measurements in unconfined compression (n=72). In addition, the applicability of manual creep measurements with the ultrasound indentation instrument was evaluated both experimentally and numerically. Our experimental results indicated that the sound speed could predict 47% and 53% of the variation in the Young's modulus and dynamic modulus of cartilage, respectively. The dynamic modulus, as determined manually with the ultrasound indentation instrument, showed significant linear correlations with the reference Young's modulus (r(2)=0.445, p<0.01, n=70) and dynamic modulus (r(2)=0.779, p<0.01, n=70) of the cartilage. Numerical analyses indicated that the creep measurements, conducted manually with the ultrasound indentation instrument, were sensitive to changes in Young's modulus and permeability of the tissue, and were significantly influenced by the tissue thickness. We conclude that acoustic parameters, i.e. ultrasound speed and reflection, are indicative to the intrinsic mechanical properties of the articular cartilage. Ultrasound indentation instrument, when further developed, provides an applicable tool for the in vivo detection of cartilage mechano-acoustic properties. These techniques could promote the diagnostics of osteoarthrosis.     

Convergence behavior of high-resolution finite element models of trabecular bone

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.     

The development and characterization of anin vitro system to study strain-induced cell deformation in isolated chondrocytes

Summary A model system has been developed to investigate cell deformation of chondrocytesin vitro. Chondrocytes were isolated from bovine articular cartilage by enzymatic digestion and seeded in agarose (type VII) at a final concentration of 2 × 10⁶ cells·ml⁻¹ in 3% agarose. Mechanical evaluation of the system showed no change in the tangent modulus of agarose/chondrocyte cultures over a 6-d culture period. The resulting agarose/chondrocyte cultures were subjected to compressive strains ranging from 5–20%. Cell shape was assessed by measuring the dimensions of the cell both perpendicular (x) and parallel (y) to the axis of compression and deformation indices (I = y/x) calculated. Cell deformation increased with the level of strain applied for freshly isolated chondrocytes. The cultures were maintained in medium that inhibits or stimulates matrix production (DMEM and DMEM + 20% FCS, respectively) in order to assess the effect of cartilaginous matrix on chondrocyte deformation. Matrix elaborated by the cells markedly influenced levels of cell deformation, an increase in matrix leading to a decrease in cell deformation. Freshly isolated deep zone chondrocytes were found to deform significantly more than surface zone chondrocytes, although this effect was lost after 6 d in culture. The elaborated matrix also altered the recovery characteristics of the chondrocytes following constant compressive strain of 15% for 24 h. Cells that had elaborated matrix took several hours to return to unloaded shape, while cells without matrix returned to the unloaded shape instantly.     

Measurement of the dynamic shear modulus of mouse brain tissue in vivo by magnetic resonance elastography

In this study, the magnetic resonance (MR) elastography technique was used to estimate the dynamic shear modulus of mouse brain tissue in vivo. The technique allows visualization and measurement of mechanical shear waves excited by lateral vibration of the skull. Quantitative measurements of displacement in three dimensions during vibration at 1200 Hz were obtained by applying oscillatory magnetic field gradients at the same frequency during a MR imaging sequence. Contrast in the resulting phase images of the mouse brain is proportional to displacement. To obtain estimates of shear modulus, measured displacement fields were fitted to the shear wave equation. Validation of the procedure was performed on gel characterized by independent rheometry tests and on data from finite element simulations. Brain tissue is, in reality, viscoelastic and nonlinear. The current estimates of dynamic shear modulus are strictly relevant only to small oscillations at a specific frequency, but these estimates may be obtained at high frequencies (and thus high deformation rates), noninvasively throughout the brain. These data complement measurements of nonlinear viscoelastic properties obtained by others at slower rates, either ex vivo or invasively.     

The effect of finite compressive strain on chondrocyte viability in statically loaded bovine articular cartilage

Recent studies have reported that certain regimes of compressive loading of articular cartilage result in increased cell death in the superficial tangential zone (STZ). The objectives of this study were (1) to test the prevalent hypothesis that preferential cell death in the STZ results from excessive compressive strain in that zone, relative to the middle and deep zones, by determining whether cell death correlates with the magnitude of compressive strain and (2) to test the corollary hypothesis that the viability response of cells is uniform through the thickness of the articular layer when exposed to the same loading environment. Live cartilage explants were statically compressed by approximately 65% of their original thickness, either normal to the articular surface (axial loading) or parallel to it (transverse loading). Cell viability after 12 h was compared to the local strain distribution measured by digital image correlation. Results showed that the strain distribution in the axially loaded samples was highest in the STZ (77%) and lowest in the deep zone (55%), whereas the strain was uniformly distributed in the transversely loaded samples (64%). In contrast, axially and transversely loaded samples exhibited very similar profiles of cell death through the depth, with a preferential distribution in the STZ. Unloaded control samples showed negligible cell death. Thus, under prolonged static loading, depth-dependent variations in chondrocyte death did not correlate with the local depth-dependent compressive strain, and the prevalent hypothesis must be rejected. An alternative hypothesis, suggested by these results, is that superficial zone chondrocytes are more vulnerable to prolonged static loading than chondrocytes in the middle and deep zones.     

The influence of mechanical loading on isolated chondrocytes seeded in agarose constructs

Articular cartilage is subjected to dynamic compressive loading during normal activity which influences chondrocyte metabolism through various mechanotransduction pathways. A well characterised and reproducible model system, involving chondrocytes embedded in agarose gel, has been used to investigate the effects of mechanical compression on chondrocytes, isolated from full depth cartilage or separately from the superficial and deep zone tissue. The role of nitric oxide as a mediator of mechanical-induced effects has also been studied. Chondrocytes were isolated, separately, from full depth, superficial and deep zone cartilage and seeded in 3% agarose constructs. Dynamic compressive strain was applied to the constructs using a range of frequencies (0.3, 1 and 3 Hz). Glycosaminoglycan synthesis, cell proliferation and nitrite production were assessed. In further experiments, constructs were compressed in the presence of 1 mM L-NAME or 10 microM dexamethasone. Glycosaminoglycan synthesis by full depth chondrocytes was affected by compressive strain in a frequency dependent manner. Dynamic strain at all frequencies induced an increase in [3H]-thymidine incorporation. Glycosaminoglycan synthesis by deep zone cells was affected by the strain regimes in a similar fashion to full depth cells, while superficial cells exhibited a similar proliferative response to full depth cells. Dynamic compression inhibited nitrite production, the effect being reversed by L-NAME. Compression induced stimulation of [3H]-TdR incorporation was reversed by L-NAME. These studies demonstrate that glycosaminoglycan synthesis and proliferation are influenced by the dynamic strain regimes in a distinct manner. Indeed the data suggest that these processes occur in different chondrocyte sub-populations. It may be speculated that nitric oxide acts as a mediator of mechanotransduction processes affecting proliferation primarily in the superficial cell sub-population.     

Scaling analysis of the concentration dependence on elasticity of agarose gel

Since the critical exponent of the elastic modulus is related to the spatial dimension and the critical exponent of the correlation length, depending on the characteristics of elasticity, we experimentally evaluated both the elastic modulus of a sol-gel transition system and also the correlation length. We could determine the correlation length of agarose gel by the dynamic light scattering method; it was well described by the power law as a function of the deviation from the sol-gel transition point. Three scaling laws between the critical exponent of the correlation length (v) and that of the elastic shear modulus (t) were compared, and the critical exponent of the elastic modulus was described by the equation of de Gennes expression (t=1+v(d-2), where d is the spatial dimension). This result suggests that agarose fibers are stiff enough to show scalar elasticity.