Biorheology of swelling tissue.
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Connective Tissue↗
Biomedical subjects
V C Mow
Publications and source records attributed to V C Mow.
Material properties and structure-function relationships in the menisci.
The menisci serve several important biomechanical functions in the knee. They distribute stresses over a broad area of articular cartilage, absorb shocks during dynamic loading, and probably assist in joint lubrication. These functions enhance the ability of articular cartilage to provide a smooth, near-frictionless articulation and to distribute loads evenly to the underlying bone of the femur and tibia. In addition, the menisci provide stability to the injured knee when the cruciate ligaments or other primary stabilizers are deficient. The ability to perform these mechanical functions is based on the intrinsic material properties of the menisci as well as their gross anatomic structure and attachments. The material properties of the menisci are determined by their biochemical composition and, perhaps more important, by the organization and interactions of the major tissue constituents: water, proteoglycan, and collagen. Interactions among the important constituents of the fibrocartilage matrix cause meniscal tissue to behave as a fiber-reinforced, porous, permeable composite material similar to articular cartilage, in which frictional drag caused by fluid flow governs its response to dynamic loading. The menisci are one-half as stiff in compression and dissipate more energy under dynamic loading than articular cartilage. Energy dissipation, or shock absorption, by the menisci is the result of high frictional drag caused by low permeability of the matrix, which is about one-sixth as permeable as articular cartilage. The dynamic shear modulus of meniscal tissue is only one-fourth to one-sixth as great as that of articular cartilage. The coarse, circumferential Type I collagen fiber bundles of the meniscus give the tissue great tensile stiffness (range, 100-300 megapascals) and strength. The highly oriented collagen ultrastructure of the menisci makes the tissue anisotropic in tension, compression, and shear and appears to dominate its behavior under all loading conditions.
Collagen↗
The influence of link protein stabilization on the viscometric properties of proteoglycan aggregate solutions.
The dynamic, steady-shear and transient shear flow properties of precisely prepared link-stable (s0 136, 66% aggregate) and link-free (s0 93, 59% aggregate) proteoglycan aggregate solutions at concentrations ranging from 10 to 50 mg/ml were determined using a cone-on-plate viscometer in a mechanical spectrometer. All proteoglycan solutions tested possessed: (1) linear viscoelastic properties - as measured by the dynamic complex modulus under small amplitude steady oscillatory conditions (1 less than or equal to omega less than or equal to 100 rad/s) - and (2) nonlinear shear-rate dependent apparent viscosities and primary normal stress difference under steady shearing conditions (0.25 less than or equal to gamma less than or equal to 250 s-1). Our transient flow data show that all proteoglycan aggregate solutions exhibited transient stress overshoot effects in shear stress and normal stress. From these steady and transient flow data, we conclude that link protein stabilized aggregates have significant effects on their dynamic and steady-shear properties as well as transient flow properties. The transient stress overshoot data provide a measure of the energy per unit volume of fluid required to overcome the proteoglycan networks in solution from a resting state. Thus we found that link-stable aggregates form much stronger networks than link-free aggregates. This is corroborated by the fact that link-stable aggregates form more elastic (lower than delta) and stiffer (higher [G*]) networks than link-free aggregates. The complete spectrum of viscometric flow data is entirely compatible with the proposed role of link protein in adding structural stability to the proteoglycan-hyaluronate bond. In cartilage, the enhanced strength of the networks formed by link-stable aggregates may play an important role in determining the material properties of the tissue and thereby contribute to the functional capacity of cartilage in diarthrodial joints.
Animals↗
Centrifugal characterization of proteoglycans from various depth layers and weight-bearing areas of normal and abnormal human articular cartilage.
Ultracentrifugal polydispersity differential [g(S)] distributions were determined for the proteoglycans of various postmortem human articular cartilage samples extracted from six lateral patellar grooves in nondissociative conditions after mild collagenase digestion of the tissue. The samples consisted of 53 slices (250 microns thick), from normal, mildly fibrillated, and extensively ulcerated knee joints. When statistically analyzed in various subgroupings, the obtained average sedimentation coefficients and polydispersity profiles supported the following conclusions: (a) loss of proteoglycan aggregation and sedimentability is confirmed to be a primary sign of cartilage matrix degradation; (b) higher S values for proteoglycans of the high weight (HW)-bearing areas and lower values for those of the low weight (LW)-bearing areas were a typical finding in normal cartilage samples; (c) inversion of this pattern was indicative of matrix degradation, suggesting that the HW regions are more affected than the LW-bearing areas; (d) the average S value distribution across cartilage thickness tended to resemble the corresponding proteoglycan content versus distance from articular surface; and (e) the deepest cartilage layer had, in most cases, the smallest amount of aggregates while the highest average sedimentability was observed at the middle zone of the normal samples. In the discussion, a role of proteoglycan aggregation for providing a means to "pack" more proteoglycans within the collagen meshwork and to control the generation of osmotic pressure gradients is suggested.
Adult↗
Material properties of the normal medial bovine meniscus.
The intrinsic compressive and tensile properties of normal bovine medial menisci were measured, and the variations in these properties with respect to the structural organization of the tissue and test specimen location were examined. Using a confined compression experiment, the compressive aggregate modulus and permeability of the meniscus were determined. The permeability of the tissue was also compared with the permeability as measured experimentally using a direct permeation experiment. Deep posterior specimens are significantly stiffer in compression than deep anterior and central-anterior specimens, while deep anterior specimens are significantly less stiff than deep posterior and central-posterior specimens. Posterior specimens have a significantly higher average water content. In addition, the permeability of the bovine meniscus was found to be about one-tenth that of bovine articular cartilage. The tensile stiffness of meniscal tissue was determined from constant strain rate uniaxial tension tests. To asses the directional variations in the tensile properties, specimens were obtained from the circumferential and radial orientations. The results indicate that the femoral surface of the meniscus is isotropic in tension, while specimens from within the meniscus are anisotropic--the circumferential specimens are much stiffer than the radial specimens. Furthermore, circumferential posterior specimens from the interior of the meniscus are significantly stiffer than similar anterior specimens. Layer inhomogeneities in the tensile properties with respect to distance from the femoral surface are also present.
Animals↗
Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study.
Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.
Algorithms↗
Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications.
The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A "pseudo-no-slip" kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.
Cartilage, Articular↗
The effect of cryopreservation on canine menisci: a biochemical, morphologic, and biomechanical evaluation.
This study evaluated the effect of cryopreservation on the structural organization, biosynthetic activity, and material properties of canine menisci. The menisci were cryopreserved by incubating them in a 4% solution of dimethyl sulfoxide (DMSO) in physiologic media and freezing them to -100 degrees C using a controlled rate freezing system. The menisci were then stored for varying periods of time from zero to 12 weeks in liquid nitrogen (-196 degrees C). Following rapid thawing, changes in the histological appearance and biosynthetic activity of the menisci were evaluated as functions of storage time. In addition, the effects of the cryopreservation process on the tensile strength and modulus of the meniscal tissue were assessed. Although cryopreservation and short-term storage did not appear to affect the morphological appearance or biomechanical character of the menisci, biosynthetic activity, as determined by Na2S35SO4 incorporation, was diminished to less than 50% of normal control values immediately following cryopreservation and thawing. Autoradiographic examination of these tissues revealed that only approximately 10% of the meniscal cells were metabolically active, however, indicating that a marked increase in the metabolic activity of individual cells occurs following the freeze-thaw cycle. Total metabolic activity continued to decline with storage time.
Animals↗
Viscoelastic properties of proteoglycan solutions with varying proportions present as aggregates.
Monomer and aggregated proteoglycans were prepared from pig laryngeal cartilage. Vascoelastic flow properties, comprising linear complex dynamic shear modulus, nonlinear steady-state shear-rate dependent viscosity, and primary normal stress difference, were measured in proteoglycan solutions containing varying proportions of aggregate (0-80%) and at different concentrations (10-50 mg/ml). Results were analyzed using the simple Oldroyd four-parameter nonlinear rate-type rheological equation. All solution properties were strongly dependent on proteoglycan concentration and on the proportion of aggregates present. Aggregation was found to have a great effect on the zero shear-rate viscosity at 50 mg/ml, which increased fivefold from 0-100% aggregate. The results showed that network formation in proteoglycan solutions increased with concentration from 10-50 mg/ml and also increased with aggregation. All proteoglycan solutions showed shear thinning, which was most marked with aggregated proteoglycan at high concentration (50 mg/ml), where the viscosity decreased tenfold from the zero shear-rate limit to the infinite shear-rate limit. The intermolecular interactions in the network were therefore increasingly disrupted by increasing shear rate, but repeated measurements showed that these were reversible changes and that testing did not induce disaggregation or degradation of proteoglycan. These rheological properties show that aggregation is likely to immobilize proteoglycan at high concentration within cartilage and to contribute to the material properties of the porous solid matrix of articular cartilage that are important for its load-bearing function.
Animals↗
Tensile properties of human knee joint cartilage. II. Correlations between weight bearing and tissue pathology and the kinetics of swelling.
The nonequilibrium or kinetic swelling behavior of normal, fibrillated, and osteoarthritic (OA) (removed from total knee joint replacements) human knee joint cartilage has been measured using our isometric tensile apparatus (ITA). We found that large local variations exist in the manner with which human knee joint cartilage swells, including anisotropic effects, inhomogeneities, and dependence on local biochemical composition and pathological condition. The ITA provides three convenient biomechanical parameters--peak stress (sigma p), stress relaxation (sigma R), and diffusion coefficient (D)--to quantify the kinetics of swelling. We used these parameters to quantify and differentiate the kinetic swelling behavior of normal, fibrillated, and osteoarthritic cartilage, as well as the swelling behavior of cartilage from high and low weight-bearing areas. Also, these kinetic swelling parameters correlated very well, though by varying degrees, with such biochemical measures as collagen/proteoglycan ratio, hexosamine content/wet weight, and hydroxyproline content/dry weight, providing important insight into the mechanisms and processes involved during the course of swelling. Hence, the kinetic swelling behavior of cartilage should be used to provide important information not obtainable from equilibrium swelling studies.
Body Water↗
Biphasic indentation of articular cartilage--I. Theoretical analysis.
A mathematical solution has been obtained for the indentation creep and stress-relaxation behavior of articular cartilage where the tissue is modeled as a layer of linear KLM biphasic material of thickness h bonded to an impervious, rigid bony substrate. The circular (radius = a), plane-ended indenter is assumed to be rigid, porous, free-draining, and frictionless. Double Laplace and Hankel transform techniques were used to solve the partial differential equations. The transformed equations and boundary conditions yielded an integral equation of the Fredholm type which was analyzed asymptotically and solved numerically. Our asymptotic analyses showed that the linear KLM biphasic material behaves like an incompressible (v = 0.5) single-phase elastic solid at t = 0+; the instantaneous response of the material is governed by the shear modulus (mu s) of the solid matrix. The linear KLM biphasic material behaves like a compressible elastic solid with material properties defined by those of the solid matrix, i.e. (lambda s, mu s) or (mu s, v s) as t----infinity. The transient viscoelastic creep and stress-relaxation behavior, 0 less than t less than infinity, of this material is controlled by the frictional drag (which is inversely proportional to the permeability k) associated with the flow of the interstitial fluid through the porous-permeable solid matrix. For given values of the Poisson's ratio of the solid matrix v s and the aspect ratio a/h, where a is the radius of the indenter and h is the thickness of the layer, the creep behavior with respect to the dimensionless time H Akt/a2 is completely controlled by the load parameter P/2 mu sa2 and the stress relaxation behavior is completely controlled by the rate of compression parameter R0 = kH A/V0h where H A = lambda s + 2 mu s and the equilibrium strain u0/h. This mathematical solution may now be used to describe an indentation experiment on articular cartilage to determine the intrinsic material properties of the tissue, i.e. permeability k, and the elastic coefficients of the solid phase (lambda s, mu s) or (mu s, v s).
Cartilage, Articular↗
Tensile properties of human knee joint cartilage: I. Influence of ionic conditions, weight bearing, and fibrillation on the tensile modulus.
The flow-independent (intrinsic) tensile modulus of the extracellular matrix of human knee joint cartilage has been measured for normal, fibrillated, and osteoarthritic (removed from total knee joint replacements) cartilage. The modulus was determined in our isometric tensile apparatus and measured at equilibrium. We found a linear equilibrium stress-strain behavior up to approximately 15% strain. The modulus was measured for tissues from the high and low weight-bearing areas of the joint surfaces, the medial femoral condyle and lateral patello femoral groove, and from different zones (surface, subsurface, middle, and middle-deep) within the tissue. For all specimens, the intrinsic tensile modulus was always less than 30 MPa. Tissues from low weight-bearing areas (LWA) are stiffer than those from high weight-bearing areas (HWA). The tensile modulus of the ECM correlates strongly with the collagen/proteoglycan ratio; it is higher for LWA than for HWA. Osteoarthritic cartilage from total knee replacement procedures has a tensile stiffness less than 2 MPa.
Adult↗
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.
Cartilage, Articular↗
Fundamentals of fluid transport through cartilage in compression.
This paper describes the flow patterns and related viscoelastic behaviors of articular cartilage under four different loading configurations: 1) confined compression, 2) unconfined compression, 3) translating parabolic surface traction of constant loading span over a cartilage layer, and 4) spreading parabolic surface traction of periodically varying span on a cartilage layer. Brief summaries of formulations and solutions of these problems are given and discussed. For the first two cases, emphasis is given to the differences in the flow mechanisms giving rise to the observed compressive viscoelastic behavior of the tissue. These two fundamental solutions can provide a basis for interpreting the results of the deformation and flow patterns obtained from more complicated loading configurations. The last two cases simulate two main geometric features of joint articulations. Fluid efflux patterns at the articulating surface depend on the kinematics of loading as well as the intrinsic material properties of the tissue: the moduli and permeability of the solid matrix. The predominant mechanism controlling the viscoelastic behavior of the tissue in compression is determined by the relative magnitude of the fluid drag and the intrinsic stiffness of the organic solid matrix.
Biomechanical Phenomena↗
Viscoelastic properties of proteoglycan subunits and aggregates in varying solution concentrations.
Using a cone-on-plate mechanical spectrometer, we have measured the linear and non-linear rheological properties of cartilage proteoglycan solutions at concentrations similar to those found in situ. Solutions of bovine nasal cartilage proteoglycan subunits (22S) and aggregates (79S) were studied at concentrations ranging from 10 to 50 mg ml-1. We determined: (1) the complex viscoelastic shear modulus G (omega) under small amplitude (0.02 radians) oscillatory excitation at frequencies (omega) ranging from 1.0 to 20.0 Hz, (2) the non-linear shear rate (gamma) dependent apparent viscosity napp (gamma) in continuous shear, and (3) the non-linear shear rate dependent primary normal stress difference sigma 1 (gamma) in continuous shear. Both the apparent viscosity and normal stress difference were measured over four decades of shear rates ranging from 0.25 to 250 s-1. Analysis of the experimental results were performed using a variety of materially objective non-linear viscoelastic constitutive laws. We found that the non-linear, four-coefficient Oldroyd rate-type model was most effective for describing the measured flow characteristics of proteoglycan subunit and aggregate solutions. Values of the relaxation time lambda 1, retardation time lambda 2, zero shear viscosity no, and nonlinear viscosity parameter muo were computed for the aggregate and subunit solutions at all of the solute concentrations used. The four independent material coefficients showed marked dependence on the two different molecular conformations, i.e. aggregate or subunit, of proteoglycans in solution.
Animals↗
Fluid transport and mechanical properties of articular cartilage: a review.
This review is aimed at unifying our understanding of cartilage viscoelastic properties in compression, in particular the role of compression-dependent permeability in controlling interstitial fluid flow and its contribution to the observed viscoelastic effects. During the previous decade, it was shown that compression causes the permeability of cartilage to drop in a functional manner described by k = ko exp (epsilon M) where ko and M were defined as intrinsic permeability parameters and epsilon is the dilatation of the solid matrix (epsilon = tr delta u). Since permeability is inversely related to the diffusive drag coefficient of relative fluid motion with respect to the porous solid matrix, the measured load-deformation response of the tissue must therefore also depend on the non-linearly permeable nature of the tissue. We have summarized in this review our understanding of this non-linear phenomenon. This understanding of these flow-dependent viscoelastic effects are put into the historical perspective of a comprehensive literature review of earlier attempts to model the compressive viscoelastic properties of articular cartilage.
Biological Transport↗
A continuum theory and an experiment for the ion-induced swelling behavior of articular cartilage.
Swelling of normal bovine articular cartilage equilibrated in NaCl solutions was dimensionally measured in thin strips of tissue. The ion-induced strains show that free swelling of articular cartilage is anisotropic and inhomogeneous. For the molar concentrations used, contraction increased linearly with concentration, defining a "coefficient of chemical contraction" (alpha c). Isometrically constrained specimens registered a rise in tensile force followed by stress relaxation. An extension of the biphasic theory incorporating this ion-induced strain is proposed. This theory can describe the equilibrium anisotropic swelling behavior of cartilage and explain the transient force history observed in the isometric experiment.
Animals↗
An analysis of the unconfined compression of articular cartilage.
Analytical solutions have been obtained for the internal deformation and fluid-flow fields and the externally observable creep, stress relaxation, and constant strain-rate behaviors which occur during the unconfined compression of a cylindrical specimen of a fluid-filled, porous, elastic solid, such as articular cartilage, between smooth, impermeable plates. Instantaneously, the "biphasic" continuum deforms without change in volume and behaves like an incompressible elastic solid of the same shear modulus. Radial fluid flow then allows the internal fluid pressure to equilibrate with the external environment. The equilibrium response is controlled by the Young's modulus and Poisson's ratio of the solid matrix.
Biomechanical Phenomena↗