Poroelasticity of cartilage at the nanoscale

Atomic-force-microscopy-based oscillatory loading was used in conjunction with finite element modeling to quantify and predict the frequency-dependent mechanical properties of the superficial zone of young bovine articular cartilage at deformation amplitudes, δ, of ∼15 nm; i.e., at macromolecular length scales. Using a spherical probe tip (R ∼ 12.5 μm), the magnitude of the dynamic complex indentation modulus, |E^∗|, and phase angle, φ, between the force and tip displacement sinusoids, were measured in the frequency range f ∼ 0.2–130 Hz at an offset indentation depth of δ₀ ∼ 3 μm. The experimentally measured |E^∗| and φ corresponded well with that predicted by a fibril-reinforced poroelastic model over a three-decade frequency range. The peak frequency of phase angle, f_peak, was observed to scale linearly with the inverse square of the contact distance between probe tip and cartilage, 1/d², as predicted by linear poroelasticity theory. The dynamic mechanical properties were observed to be independent of the deformation amplitude in the range δ = 7–50 nm. Hence, these results suggest that poroelasticity was the dominant mechanism underlying the frequency-dependent mechanical behavior observed at these nanoscale deformations. These findings enable ongoing investigations of the nanoscale progression of matrix pathology in tissue-level disease.     

Structure-Function Relations and Rigidity Percolation in the Shear Properties of Articular Cartilage

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G^∗| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G^∗| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction v_c lead to orders-of-magnitude changes in the modulus with |G^∗| scaling as (v_c – v₀)^ξ. Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue’s surface.     

Structure-Function Relations and Rigidity Percolation in the Shear Properties of Articular Cartilage

Among mammalian soft tissues, articular cartilage is particularly interesting because it can endure a lifetime of daily mechanical loading despite having minimal regenerative capacity. This remarkable resilience may be due to the depth-dependent mechanical properties, which have been shown to localize strain and energy dissipation. This paradigm proposes that these properties arise from the depth-dependent collagen fiber orientation. Nevertheless, this structure-function relationship has not yet been quantified. Here, we use confocal elastography, quantitative polarized light microscopy, and Fourier-transform infrared imaging to make same-sample measurements of the depth-dependent shear modulus, collagen fiber organization, and extracellular matrix concentration in neonatal bovine articular cartilage. We find weak correlations between the shear modulus |G^∗| and both the collagen fiber orientation and polarization. We find a much stronger correlation between |G^∗| and the concentration of collagen fibers. Interestingly, very small changes in collagen volume fraction v_c lead to orders-of-magnitude changes in the modulus with |G^∗| scaling as (v_c – v₀)^ξ. Such dependencies are observed in the rheology of other biopolymer networks whose structure exhibits rigidity percolation phase transitions. Along these lines, we propose that the collagen network in articular cartilage is near a percolation threshold that gives rise to these large mechanical variations and localization of strain at the tissue’s surface.     

Comparison of single-phase isotropic elastic and fibril-reinforced poroelastic models for indentation of rabbit articular cartilage

Classically, single-phase isotropic elastic (IE) model has been used for in situ or in vivo indentation analysis of articular cartilage. The model significantly simplifies cartilage structure and properties. In this study, we apply a fibril-reinforced poroelastic (FRPE) model for indentation to extract more detailed information on cartilage properties. Specifically, we compare the information from short-term (instantaneous) and long-term (equilibrium) indentations, as described here by IE and FRPE models. Femoral and tibial cartilage from rabbit (age 0–18 months) knees (n=14) were tested using a plane-ended indenter (diameter=0.544 mm). Stepwise creep tests were conducted to equilibrium. Single-phase IE solution for indentation was used to derive instantaneous modulus and equilibrium (Young's) modulus for the samples. The classical and modified Hayes’ solutions were used to derive values for the indentation moduli. In the FRPE model, the indentation behavior was sample-specifically described with three material parameters, i.e. fibril network modulus, non-fibrillar matrix modulus and permeability. The instantaneous and fibril network modulus, and the equilibrium Young's modulus and non-fibrillar matrix modulus showed significant (p<0.01) linear correlations of R²=0.516 and 0.940, respectively (Hayes’ solution) and R²=0.531 and 0.960, respectively (the modified Hayes’ solution). No significant correlations were found between the non-fibrillar matrix modulus and instantaneous moduli or between the fibril network modulus and the equilibrium moduli. These results indicate that the instantaneous indentation modulus (IE model) provides information on tensile stiffness of collagen fibrils in cartilage while the equilibrium modulus (IE model) is a significant measure for stiffness of PG matrix. Thereby, this study highlights the feasibility of a simple indentation analysis.     

A Fluorescence Detected Magnetic Resonance Investigation of the Carotenoid Triplet States Associated with Photosystem II of Isolated Spinach Thylakoid Membranes

The carotenoid triplet populations associated with the fluorescence emission chlorophyll forms of Photosystem II have been investigated in isolated spinach thylakoid membranes by means of fluorescence detected magnetic resonance in zero field (FDMR). The spectra collected in the 680–690 nm emission range, have been fitted by a global analysis procedure. At least five different carotenoid triplet states coupled to the terminal emitting chlorophyll forms of PS II, peaking at 682 nm, 687 nm and 692 nm, have been characterised. The triplets associated with the outer antenna emission forms, at 682 nm, have zero field splitting parameters |D| = 0.0385 cm⁻¹, |E| = 0.00367 cm⁻¹; |D| = 0.0404 cm⁻¹, |E| = 0.00379 cm⁻¹ and |D| = 0.0386 cm⁻¹, |E| = 0.00406 cm⁻¹ which are very similar to those previously reported for the xanthophylls of the isolated LHC II complex. Therefore the FDMR spectra recorded in this work provide insights into the organisation of the LHC II complex in the unperturbed environment represented by thylakoid membranes. The additional carotenoid triplet populations, detected by monitoring the chlorophyll emission at 687 and 692 nm, are assigned to carotenoids bound to inner antenna complexes and hence attributed to β-carotene molecules.     

Effects of gel thickness on microscopic indentation measurements of gel modulus

In vitro, animal cells are mostly cultured on a gel substrate. It was recently shown that substrate stiffness affects cellular behaviors in a significant way, including adhesion, differentiation, and migration. Therefore, an accurate method is needed to characterize the modulus of the substrate. In situ microscopic measurements of the gel substrate modulus are based on Hertz contact mechanics, where Young's modulus is derived from the indentation force and displacement measurements. In Hertz theory, the substrate is modeled as a linear elastic half-space with an infinite depth, whereas in practice, the thickness of the substrate, h, can be comparable to the contact radius and other relevant dimensions such as the radius of the indenter or steel ball, R. As a result, measurements based on Hertz theory overestimate the Young's modulus. In this work, we discuss the limitations of Hertz theory and then modify it, taking into consideration the nonlinearity of the material and large deformation using a finite-element method. We present our results in a simple correction factor, ψ, the ratio of the corrected Young's modulus and the Hertz modulus in the parameter regime of δ/h ≤ min (0.6, R/h) and 0.3 ≤ R/h ≤ 12.7. The ψ factor depends on two dimensionless parameters, R/h and δ/h (where δ is the indentation depth), both of which are easily accessible to experiments. This correction factor agrees with experimental observations obtained with the use of polyacrylamide gel and a microsphere indentation method in the parameter range of 0.1 ≤ δ/h ≤ 0.4 and 0.3 ≤ R/h ≤ 6.2. The effect of adhesion on the use of Hertz theory for small indentation depth is also discussed.     

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.     

Nanomechanical phenotype of chondroadherin-null murine articular cartilage

Chondroadherin (CHAD), a class IV small leucine rich proteoglycan/protein (SLRP), was hypothesized to play important roles in regulating chondrocyte signaling and cartilage homeostasis. However, its roles in cartilage development and function are not well understood, and no major osteoarthritis-like phenotype was found in the murine model with CHAD genetically deleted (CHAD^−/−). In this study, we used atomic force microscopy (AFM)-based nanoindentation to quantify the effects of CHAD deletion on changes in the biomechanical function of murine cartilage. In comparison to wild-type (WT) mice, CHAD-deletion resulted in a significant ≈ 70–80% reduction in the indentation modulus, E_ind, of the superficial zone knee cartilage of 11 weeks, 4 months and 1 year old animals. This mechanical phenotype correlates well with observed increases in the heterogeneity collagen fibril diameters in the surface zone. The results suggest that CHAD mainly plays a major role in regulating the formation of the collagen fibrillar network during the early skeletal development. In contrast, CHAD-deletion had no appreciable effects on the indentation mechanics of middle/deep zone cartilage, likely due to the dominating role of aggrecan in the middle/deep zone. The presence of significant rate dependence of the indentation stiffness in both WT and CHAD^−/− knee cartilage suggested the importance of both fluid flow induced poroelasticity and intrinsic viscoelasticity in murine cartilage biomechanical properties. Furthermore, the marked differences in the nanomechanical behavior of WT versus CHAD^−/− cartilage contrasted sharply with the relative absence of overt differences in histological appearance. These observations highlight the sensitivity of nanomechanical tools in evaluating structural and mechanical phenotypes in transgenic mice.     

Dynamic mechanical properties of the tissue-engineered matrix associated with individual chondrocytes

The success of cell-based tissue engineering approaches in restoring biological function will be facilitated by a comprehensive fundamental knowledge of the temporal evolution of the structure and properties of the newly synthesized matrix. Here, we quantify the dynamic oscillatory mechanical behavior of the engineered matrix associated with individual chondrocytes cultured in vitro for up to 28 days in alginate scaffolds. The magnitude of the complex modulus (|E*|) and phase shift (δ) were measured in culture medium using Atomic Force Microscopy (AFM)-based nanoindentation in response to an imposed oscillatory deformation (amplitude ～5 nm) as a function of frequency (f=1–316 Hz), probe tip geometry (2.5 μm radius sphere and 50 nm radius square pyramid), and in the absence and presence of growth factors (GF, insulin growth factor-1, IGF-1, and osteogenic protein-1, OP-1). |E*| for all conditions increased nonlinearly with frequency dependence approximately f^1/2 and ranged between ～1 and 25 kPa. This result, along with theoretical calculations of the characteristic poroelastic relaxation frequency, f_p, (～50–90 Hz) suggested that this time-dependent behavior was governed primarily by fluid flow-dependent poroelasticity, rather than flow-independent viscoelastic processes associated with the solid matrix. |E*(f)| increased, (f) decreased, and the hydraulic permeability, k, decreased with time in culture and with growth factor treatment. This trend of a more elastic-like response was thought to be associated with increased macromolecular biosynthesis, density, and a more mature matrix structure/organization.     

Structural and functional changes of the articular surface in a post-traumatic model of early osteoarthritis measured by atomic force microscopy

The functional integrity of the articulating cartilage surface is a critical determinant of joint health. Although a variety of techniques exist to characterize the structural changes in the tissue with osteoarthritis (OA), some with extremely high resolution, most lack the ability to detect and monitor the functional changes that accompany the structural deterioration of this essential bearing surface. Atomic force microscopy (AFM) enables the acquisition of both structural and mechanical properties of the articular cartilage surface, with up to nanoscale resolution, making it particularly useful for evaluating the functional behavior of the macromolecular network forming the cartilage surface, which disintegrates in OA.In the present study, AFM was applied to the articular cartilage surfaces from six pairs of canine knee joints with post-traumatic OA. Microstructure (RMS roughness) and micromechanics (dynamic indentation modulus, E^?) of medial femoral condyle cartilages were compared between contralateral controls and cruciate-transected knee joints, which develop early signs of OA by three months after surgery.Results reveal a significant increase in RMS roughness and a significant four-fold decrease in E^? in cartilages from cruciate-transected joints versus contralateral controls. Compared to previous reports of changes in bulk mechanics, AFM was considerably more sensitive at detecting early cartilage changes due to cruciate-deficiency. The use of AFM in this study provides important new information on early changes in the natural history of OA because of its ability to sensitively detect and measure local structural and functional changes of the articular cartilage surface, the presumptive site of osteoarthritic initiation.     

Quantitative investigation of calcimimetic R568 on beta cell adhesion and mechanics using AFM single-cell force spectroscopy

In this study we use a novel approach to quantitatively investigate mechanical and interfacial properties of clonal β-cells using AFM-Single Cell Force Spectroscopy (SCFS). MIN6 cells were incubated for 48 h with 0.5 mM Ca²⁺ ± the calcimimetic R568 (1 μM). AFM-SCFS adhesion and indentation experiments were performed by using modified tipless cantilevers. Hertz contact model was applied to analyse force–displacement (F–d) curves for determining elastic or Young’s modulus (E). Our results show CaSR-evoked increases in cell-to-cell adhesion parameters and E modulus of single cells, demonstrating that cytomechanics have profound effects on cell adhesion characterization.     

Spider silk softening by water uptake: an AFM study

We have investigated the mechanical properties of spider dragline fibers of three Nephila species under varied relative humidity. Force maps have been collected by atomic force microscopy. The Young’s modulus E was derived from the indentation curves of each pixel by the modified Hertz model. An average decrease in E by an order of magnitude was observed upon immersion of the fiber in water. Single fiber stretching experiments were carried out for comparison, and also showed a strong dependence on relative humidity. However, the absolute values of E are significantly higher than those obtained by indentation. The results of this work thus show that the elastic properties of spider silk are highly anisotropic, and that the silk softens significantly for both tensile and compressional strain (indentation) upon water uptake. In addition, the force maps indicate a surface structure on the sub-micron scale.     

An Annular Plasmonic Lens Under Illumination of Circularly Polarized Light

In this paper, we consider a circular central aperture surrounded with annular depth-tuned grooves and investigate the beaming effect of the structure under illumination of a circularly polarized (CP) plane wave. As a CP plane wave is equivalent to the superposition of two linearly polarized plane waves (TM and TE) with a phase difference of π/2, the superposition of the electric field intensity, ( | E_x |² + | E_y |² ) \left( {{{\left| {E_x} \right|}^2} + {{\left| {E_y} \right|}^2}} \right) , is observed in the transmission field. In addition, two plasmonic modes are found at the resonant wavelengths λ ₁ and λ ₂ with each consisting of multiple wavelengths. At the wavelength λ ₁ = 420 nm, the significant near-field collimation is formed along the direction z, having a long propagation distance up to 1.75 μm (≈4λ) away from the exit plane of the new plasmonic lens.     

Single-molecule force spectroscopy of cartilage aggrecan self-adhesion

We investigated self-adhesion between highly negatively charged aggrecan macromolecules extracted from bovine cartilage extracellular matrix by performing atomic force microscopy (AFM) imaging and single-molecule force spectroscopy (SMFS) in saline solutions. By controlling the density of aggrecan molecules on both the gold substrate and the gold-coated tip surface at submonolayer densities, we were able to detect and quantify the Ca²⁺-dependent homodimeric interaction between individual aggrecan molecules at the single-molecule level. We found a typical nonlinear sawtooth profile in the AFM force-versus-distance curves with a molecular persistence length of l_p = 0.31 ± 0.04 nm. This is attributed to the stepwise dissociation of individual glycosaminoglycan (GAG) side chains in aggrecans, which is very similar to the known force fingerprints of other cell adhesion proteoglycan systems. After studying the GAG-GAG dissociation in a dynamic, loading-rate-dependent manner (dynamic SMFS) and analyzing the data according to the stochastic Bell-Evans model for a thermally activated decay of a metastable state under an external force, we estimated for the single glycan interaction a mean lifetime of τ = 7.9 ± 4.9 s and a reaction bond length of x_β = 0.31 ± 0.08 nm. Whereas the x_β-value compares well with values from other cell adhesion carbohydrate recognition motifs in evolutionary distant marine sponge proteoglycans, the rather short GAG interaction lifetime reflects high intermolecular dynamics within aggrecan complexes, which may be relevant for the viscoelastic properties of cartilage tissue.     

Optimization of the Bowtie Gap Geometry for a Maximum Electric Field Enhancement

Optimization of the geometry of a metallic bowtie gap at radio frequency is presented. We investigate the geometry of the bowtie gap including gap size, tip width, metal thickness and tip angle at macroscale to find the maximum electric field enhancement across the gap. The results indicate that 90^° bowtie with 0.06 λ gap size has the most |E _t |² enhancement. Effects of changing the permittivity and conductivity of the material across the gap are also investigated. NEC-2 simulations show that the numerical calculations agree with the experimental results. Since the design and fabrication of a plasmonic device (nanogap) at nanoscale is challenging, the results of this study can be used to estimate the best design parameters for nanogap structure. Different amounts of enhancement at different frequency ranges are explained by mode volume. The product of the mode volume and |E _t |² enhancement is constant for different gap structures and different frequencies.     

Mechanical properties of elytra from Tribolium castaneum wild-type and body color mutant strains

Cuticle tanning in insects involves simultaneous cuticular pigmentation and hardening or sclerotization. The dynamic mechanical properties of the highly modified and cuticle-rich forewings (elytra) from Tribolium castaneum (red flour beetle) wild-type and body color mutant strains were investigated to relate body coloration and elytral mechanical properties. There was no statistically significant variation in the storage modulus E′ among the elytra from jet, cola, sooty and black mutants or between the mutants and the wild-type GA-1 strain: E′ averaged 5.1 ± 0.6 GPa regardless of body color. E′ is a power law function of oscillation frequency for all types. The power law exponent, n, averaged 0.032 ± 0.001 for elytra from all genotypes except black; this small value indicated that the elytra are cross-linked. Black elytra, however, displayed a significantly larger n of 0.047 ± 0.004 and an increased loss tangent (tan δ), suggesting that metabolic differences in the black mutant strain result in elytra that are less cross-linked and more pigmented than the other types. These results are consistent with the hypothesis that black elytra have a β-alanine-deficient and dopamine-abundant metabolism, leading to greater melanin (black pigment) production, probably at the expense of cross-linking of cuticular proteins mediated by N-β-alanyldopamine quinone.     

Determination of a molecular torsional angle in the metarhodopsin-I photointermediate of rhodopsin by double-quantum solid-state NMR

We present a solid-state NMR study of metarhodopsin-I, the pre-discharge intermediate of the photochemical signal transduction cascade of rhodopsin, which is the 41 kDa integral membrane protein that triggers phototransduction in vertebrate rod cells. The H-C10-C11-H torsional angles of the retinylidene chromophore in bovine rhodopsin and metarhodopsin-I were determined simultaneously in the photo-activated membrane-bound state, using double-quantum heteronuclear local field spectroscopy. The torsional angles were estimated to be || = 160 ± 10° for rhodopsin and = 180 ± 25° for metarhodopsin-I. The result is consistent with current models of the photo-induced conformational transitions in the chromophore, in which the 11-Z retinal ground state is twisted, while the later photointermediates have a planar all-E conformation.     

Nanomechanical Mapping of Hydrated Rat Tail Tendon Collagen I Fibrils

Collagen fibrils play an important role in the human body, providing tensile strength to connective tissues. These fibrils are characterized by a banding pattern with a D-period of 67 nm. The proposed origin of the D-period is the internal staggering of tropocollagen molecules within the fibril, leading to gap and overlap regions and a corresponding periodic density fluctuation. Using an atomic force microscope high-resolution modulus maps of collagen fibril segments, up to 80 μm in length, were acquired at indentation speeds around 10⁵ nm/s. The maps revealed a periodic modulation corresponding to the D-period as well as previously undocumented micrometer scale fluctuations. Further analysis revealed a 4/5, gap/overlap, ratio in the measured modulus providing further support for the quarter-staggered model of collagen fibril axial structure. The modulus values obtained at indentation speeds around 10⁵ nm/s are significantly larger than those previously reported. Probing the effect of indentation speed over four decades reveals two distinct logarithmic regimes of the measured modulus and point to the existence of a characteristic molecular relaxation time around 0.1 ms. Furthermore, collagen fibrils exposed to temperatures between 50 and 62°C and cooled back to room temperature show a sharp decrease in modulus and a sharp increase in fibril diameter. This is also associated with a disappearance of the D-period and the appearance of twisted subfibrils with a pitch in the micrometer range. Based on all these data and a similar behavior observed for cross-linked polymer networks below the glass transition temperature, we propose that collagen I fibrils may be in a glassy state while hydrated.     

Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy

Cartilage stiffness was measured ex vivo at the micrometer and nanometer scales to explore structure-mechanical property relationships at smaller scales than has been done previously. A method was developed to measure the dynamic elastic modulus, |E(*)|, in compression by indentation-type atomic force microscopy (IT AFM). Spherical indenter tips (radius = approximately 2.5 microm) and sharp pyramidal tips (radius = approximately 20 nm) were employed to probe micrometer-scale and nanometer-scale response, respectively. |E(*)| values were obtained at 3 Hz from 1024 unloading response curves recorded at a given location on subsurface cartilage from porcine femoral condyles. With the microsphere tips, the average modulus was approximately 2.6 MPa, in agreement with available millimeter-scale data, whereas with the sharp pyramidal tips, it was typically 100-fold lower. In contrast to cartilage, measurements made on agarose gels, a much more molecularly amorphous biomaterial, resulted in the same average modulus for both indentation tips. From results of AFM imaging of cartilage, the micrometer-scale spherical tips resolved no fine structure except some chondrocytes, whereas the nanometer-scale pyramidal tips resolved individual collagen fibers and their 67-nm axial repeat distance. These results suggest that the spherical AFM tip is large enough to measure the aggregate dynamic elastic modulus of cartilage, whereas the sharp AFM tip depicts the elastic properties of its fine structure. Additional measurements of cartilage stiffness following enzyme action revealed that elastase digestion of the collagen moiety lowered the modulus at the micrometer scale. In contrast, digestion of the proteoglycans moiety by cathepsin D had little effect on |E(*)| at the micrometer scale, but yielded a clear stiffening at the nanometer scale. Thus, cartilage compressive stiffness is different at the nanometer scale compared to the overall structural stiffness measured at the micrometer and larger scales because of the fine nanometer-scale structure, and enzyme-induced structural changes can affect this scale-dependent stiffness differently.     

Mechanobiology of soft skeletal tissue differentiation—a computational approach of a fiber-reinforced poroelastic model based on homogeneous and isotropic simplifications

The material properties of multipotent mesenchymal tissue change dramatically during the differentiation process associated with skeletal regeneration. Using a mechanobiological tissue differentiation concept, and homogeneous and isotropic simplifications of a fiber-reinforced poroelastic model of soft skeletal tissues, we have developed a mathematical approach for describing time-dependent material property changes during the formation of cartilage, fibrocartilage, and fibrous tissue under various loading histories. In this approach, intermittently imposed fluid pressure and tensile strain regulate proteoglycan synthesis and collagen fibrillogenesis, assembly, cross-linking, and alignment to cause changes in tissue permeability (k), compressive aggregate modulus (H_A), and tensile elastic modulus (E). In our isotropic model, k represents the permeability in the least permeable direction (perpendicular to the fibers) and E represents the tensile elastic modulus in the stiffest direction (parallel to the fibers). Cyclic fluid pressure causes an increase in proteoglycan synthesis, resulting in a decrease in k and increase in H_A caused by the hydrophilic nature and large size of the aggregating proteoglycans. It further causes a slight increase in E owing to the stiffness added by newly synthesized type II collagen. Tensile strain increases the density, size, alignment, and cross-linking of collagen fibers thereby increasing E while also decreasing k as a result of an increased flow path length. The Poisson's ratio of the solid matrix, _s, is assumed to remain constant (near zero) for all soft tissues. Implementing a computer algorithm based on these concepts, we simulate progressive changes in material properties for differentiating tissues. Beginning with initial values of E=0.05 MPa, H_A=0 MPa, and k=1×10^–13 m⁴/Ns for multipotent mesenchymal tissue, we predict final values of E=11 MPa, H_A=1 MPa, and k=4.8×10^–15 m⁴/Ns for articular cartilage, E=339 MPa, H_A=1 MPa, and k=9.5×10^–16 m⁴/Ns for fibrocartilage, and E=1,000 MPa, H_A=0 MPa, and k=7.5×10^–16 m⁴/Ns for fibrous tissue. These final values are consistent with the values reported by other investigators and the time-dependent acquisition of these values is consistent with current knowledge of the differentiation process.