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ABSTRACT: A continuum mixture model with distinct collagen (COL) and glycosaminoglycan elastic constituents was developed for the solid matrix of immature bovine articular cartilage. A continuous COL fiber volume fraction distribution function and a true COL fiber elastic modulus ([Formula: see text] were used. Quantitative polarized light microscopy (qPLM) methods were developed to account for the relatively high cell density of immature articular cartilage and used with a novel algorithm that constructs a 3D distribution function from 2D qPLM data. For specimens untreated and cultured in vitro, most model parameters were specified from qPLM analysis and biochemical assay results; consequently, [Formula: see text] was predicted using an optimization to measured mechanical properties in uniaxial tension and unconfined compression. Analysis of qPLM data revealed a highly anisotropic fiber distribution, with principal fiber orientation parallel to the surface layer. For untreated samples, predicted [Formula: see text] values were 175 and 422 MPa for superficial (S) and middle (M) zone layers, respectively. TGF-[Formula: see text]1 treatment was predicted to increase and decrease [Formula: see text] values for the S and M layers to 281 and 309 MPa, respectively. IGF-1 treatment was predicted to decrease [Formula: see text] values for the S and M layers to 22 and 26 MPa, respectively. A novel finding was that distinct native depth-dependent fiber modulus properties were modulated to nearly homogeneous values by TGF-[Formula: see text]1 and IGF-1 treatments, with modulated values strongly dependent on treatment.
Biomechanics and Modeling in Mechanobiology 12/2012; · 3.19 Impact Factor
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ABSTRACT: In vitro cultures with insulin-like growth factor-1 (IGF-1) and transforming growth factor-β1 (TGF-β1) have previously been shown to differentially modulate the growth of immature bovine articular cartilage. IGF-1 stimulates expansive growth yet decreases compressive moduli and increases compressive Poisson's ratios, whereas TGF-β1 maintains tissue size, increases compressive moduli, and decreases compressive Poisson's ratios. The current study's hypothesis was that sequential application of IGF-1 and TGF-β1 during in vitro culture produces geometric and compressive mechanical properties that lie between extreme values produced when using either growth factor alone. Immature bovine articular cartilage specimens were harvested and either untreated (D0, i.e., day zero) or cultured in vitro for either 6 days with IGF-1 (D6 IGF), 12 days with IGF-1 (D12 IGF), or 6 days with IGF-1 followed by 6 days with TGF-β1 (D12 SEQ, i.e., sequential). Following treatment, all specimens were tested for geometric, biochemical, and compressive mechanical properties. Relative to D0, D12 SEQ treatment enhanced volumetric growth, but to a lower value than that for D12 IGF. Furthermore, D12 SEQ treatment maintained compressive moduli and Poisson's ratios at values higher and lower, respectively, than those for D12 IGF. Considering the previously described effects of 12 days of treatment with TGF-β1 alone, D12 SEQ induced both growth and mechanical property changes between those produced with either IGF-1 or TGF-β1 alone. The results suggest that it may be possible to vary the durations of select growth factors, including IGF-1 and TGF-β1, to more precisely modulate the geometric, biochemical, and mechanical properties of immature cartilage graft tissue in clinical repair strategies.
Journal of Biomechanical Engineering 03/2012; 134(3):031001. · 1.90 Impact Factor
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ABSTRACT: Despite distinct mechanical functions, biological soft tissues have a common microstructure in which a ground matrix is reinforced by a collagen fibril network. The microstructural properties of the collagen network contribute to continuum mechanical tissue properties that are strongly anisotropic with tensile-compressive asymmetry. In this study, a novel approach based on a continuous distribution of collagen fibril volume fractions is developed to model fibril reinforced soft tissues as a nonlinearly elastic and anisotropic material. Compared with other approaches that use a normalized number of fibrils for the definition of the distribution function, this representation is based on a distribution parameter (i.e. volume fraction) that is commonly measured experimentally while also incorporating pre-stress of the collagen fibril network in a tissue natural configuration. After motivating the form of the collagen strain energy function, examples are provided for two volume fraction distribution functions. Consequently, collagen second-Piola Kirchhoff stress and elasticity tensors are derived, first in general form and then specifically for a model that may be used for immature bovine articular cartilage. It is shown that the proposed strain energy is a convex function of the deformation gradient tensor and, thus, is suitable for the formation of a polyconvex tissue strain energy function.
Mathematics and Mechanics of Solids 09/2011; 16(7):706-715. · 1.01 Impact Factor
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ABSTRACT: The negatively charged proteoglycans (PG) provide compressive resistance to articular cartilage by means of their fixed charge density (FCD) and high osmotic pressure (π(PG)), and the collagen network (CN) provides the restraining forces to counterbalance π(PG). Our objectives in this work were to: 1), account for collagen intrafibrillar water when transforming biochemical measurements into a FCD-π(PG) relationship; 2), compute π(PG) and CN contributions to the compressive behavior of full-thickness cartilage during bovine growth (fetal, calf, and adult) and human adult aging (young and old); and 3), predict the effect of depth from the articular surface on π(PG) in human aging. Extrafibrillar FCD (FCD(EF)) and π(PG) increased with bovine growth due to an increase in CN concentration, whereas PG concentration was steady. This maturation-related increase was amplified by compression. With normal human aging, FCD(EF) and π(PG) decreased. The π(PG)-values were close to equilibrium stress (σ(EQ)) in all bovine and young human cartilage, but were only approximately half of σ(EQ) in old human cartilage. Depth-related variations in the strain, FCD(EF), π(PG), and CN stress profiles in human cartilage suggested a functional deterioration of the superficial layer with aging. These results suggest the utility of the FCD-π(PG) relationship for elucidating the contribution of matrix macromolecules to the biomechanical properties of cartilage.
Biophysical Journal 08/2011; 101(4):916-24. · 3.65 Impact Factor
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Gregory M Williams,
Kristin J Dills,
Christian R Flores,
Michael E Stender,
Kevin M Stewart,
Lauren M Nelson,
Albert C Chen,
Koichi Masuda,
Scott J Hazelwood, Stephen M Klisch,
Robert L Sah
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ABSTRACT: Mechanisms of articular cartilage growth and maturation have been elucidated by studying composition-function dynamics during in vivo development and in vitro culture with stimuli such as insulin-like growth factor-1 (IGF-1) and transforming growth factor-beta 1 (TGF-beta1). This study tested the hypothesis that IGF-1 and TGF-beta1 regulate immature cartilage compressive moduli and Poisson's ratios in a manner consistent with known effects on tensile properties. Bovine calf articular cartilage from superficial-articular (S) and middle-growth (M) regions were analyzed fresh or following culture in medium with IGF-1 or TGF-beta1. Mechanical properties in confined (CC) and unconfined (UCC) compression, cartilage matrix composition, and explant size were assessed. Culture with IGF-1 resulted in softening in CC and UCC, increased Poisson's ratios, substantially increased tissue volume, and accumulation of glycosaminoglycan (GAG) and collagen (COL). Culture with TGF-beta1 promoted maturational changes in the S layer, including stiffening in CC and UCC and increased concentrations of GAG, COL, and pyridinoline crosslinks (PYR), but little growth. Culture of M layer explants with TGF-beta1 was nearly homeostatic. Across treatment groups, compressive moduli in CC and UCC were positively related to GAG, COL, and PYR concentrations, while Poisson's ratios were negatively related to concentrations of these matrix components. Thus, IGF-1 and TGF-beta1 differentially regulate the compressive mechanical properties and size of immature articular cartilage in vitro. Prescribing tissue growth, maturation, or homeostasis by controlling the in vitro biochemical environment with such growth factors may have applications in cartilage repair and tissue engineering.
Journal of biomechanics 09/2010; 43(13):2501-7. · 2.66 Impact Factor
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ABSTRACT: A constituent based nonlinear viscoelastic (VE) model was modified from a previous study (Vena, et al., 2006, "A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments," J. Biomech. Eng., 128, pp. 449-457) to incorporate a glycosaminoglycan (GAG)-collagen (COL) stress balance using compressible elastic stress constitutive equations specific to articular cartilage (AC). For uniaxial loading of a mixture of quasilinear VE constituents, time constant and relaxation ratio equations are derived to highlight how a mixture of constituents with distinct quasilinear VE properties is one mechanism that produces a nonlinear VE tissue. Uniaxial tension experiments were performed with newborn bovine AC specimens before and after approximately 55% and approximately 85% GAG depletion treatment with guanidine. Experimental tissue VE parameters were calculated directly from stress relaxation data, while intrinsic COL VE parameters were calculated by curve fitting the data with the nonlinear VE model with intrinsic GAG viscoelasticity neglected. Select tissue and intrinsic COL VE parameters were significantly different from control and experimental groups and correlated with GAG content, suggesting that GAG-COL interactions exist to modulate tissue and COL mechanical properties. Comparison of the results from this and other studies that subjected more mature AC tissue to GAG depletion treatment suggests that the GAGs interact with the COL network in a manner that may be beneficial for rapid volumetric expansion during developmental growth while protecting cells from excessive matrix strains. Furthermore, the underlying GAG-COL interactions appear to diminish as the tissue matures, indicating a distinctive remodeling response during developmental growth.
Journal of Biomechanical Engineering 10/2009; 131(10):101002. · 1.90 Impact Factor
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ABSTRACT: Recently a cartilage growth finite element model (CGFEM) was developed to solve nonhomogeneous and time-dependent growth boundary-value problems (Davol et al., 2008, "A Nonlinear Finite Element Model of Cartilage Growth," Biomech. Model. Mechanobiol., 7, pp. 295-307). The CGFEM allows distinct stress constitutive equations and growth laws for the major components of the solid matrix, collagens and proteoglycans. The objective of the current work was to simulate in vitro growth of articular cartilage explants in a steady-state permeation bioreactor in order to obtain results that aid experimental design. The steady-state permeation protocol induces different types of mechanical stimuli. When the specimen is initially homogeneous, it directly induces homogeneous permeation velocities and indirectly induces nonhomogeneous solid matrix shear stresses; consequently, the steady-state permeation protocol is a good candidate for exploring two competing hypotheses for the growth laws. The analysis protocols were implemented through the alternating interaction of the two CGFEM components: poroelastic finite element analysis (FEA) using ABAQUS and a finite element growth routine using MATLAB. The CGFEM simulated 12 days of growth for immature bovine articular cartilage explants subjected to two competing hypotheses for the growth laws: one that is triggered by permeation velocity and the other by maximum shear stress. The results provide predictions for geometric, biomechanical, and biochemical parameters of grown tissue specimens that may be experimentally measured and, consequently, suggest key biomechanical measures to analyze as pilot experiments are performed. The combined approach of CGFEM analysis and pilot experiments may lead to the refinement of actual experimental protocols and a better understanding of in vitro growth of articular cartilage.
Journal of Biomechanical Engineering 05/2009; 131(4):041008. · 1.90 Impact Factor
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ABSTRACT: The long range objective of this work is to develop a cartilage growth finite element model (CGFEM), based on the theories of growing mixtures that has the capability to depict the evolution of the anisotropic and inhomogeneous mechanical properties, residual stresses, and nonhomogeneities that are attained by native adult cartilage. The CGFEM developed here simulates isotropic in vitro growth of cartilage with and without mechanical stimulation. To accomplish this analysis a commercial finite element code (ABAQUS) is combined with an external program (MATLAB) to solve an incremental equilibrium boundary value problem representing one increment of growth. This procedure is repeated for as many increments as needed to simulate the desired growth protocol. A case study is presented utilizing a growth law dependent on the magnitude of the diffusive fluid velocity to simulate an in vitro dynamic confined compression loading protocol run for 2 weeks. The results include changes in tissue size and shape, nonhomogeneities that develop in the tissue, as well as the variation that occurs in the tissue constitutive behavior from growth.
Biomechanics and Modeling in Mechanobiology 09/2008; 7(4):295-307. · 3.19 Impact Factor
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ABSTRACT: Cartilage growth may involve alterations in the balance between the swelling tendency of proteoglycans and the restraining function of the collagen network. Growth factors, including IGF-I, TGF-beta1, BMP-7, and PDGF-AB, regulate chondrocyte metabolism and, consequently, may regulate cartilage growth. Immature bovine articular cartilage explants from the superficial and middle zones were incubated for 13 days in basal medium or medium supplemented with serum, IGF-I, TGF-beta1, BMP-7, or PDGF-AB. Variations in tissue size, accumulation of proteoglycan and collagen, and tensile properties were assessed. The inclusion of serum, IGF-I, or BMP-7 resulted in expansive tissue growth, stimulation of proteoglycan deposition but not of collagen, and a diminution of tensile integrity. The regulation of cartilage metabolism by TGF-beta1 resulted in tissue homeostasis, with maintenance of size, composition, and function. Incubation in basal medium or with PDGF-AB resulted in small volumetric and compositional changes, but a marked decrease in tensile integrity. These results demonstrate that the phenotype of cartilage growth, and the associated balance between proteoglycan content and integrity of the collagen network, is regulated differentially by certain growth factors.
Biomechanics and Modeling in Mechanobiology 09/2008; 7(4):263-76. · 3.19 Impact Factor
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ABSTRACT: Articular cartilage function depends on the molecular composition and structure of its extracellular matrix (ECM). The collagen network (CN) provides cartilage with tensile integrity, but must also remodel during growth. Such remodeling may depend on matrix molecules interacting with the CN to modulate the tensile behavior of cartilage. The objective of this study was to determine the effects of increasingly selective matrix depletion on tensile properties of immature and mature articular cartilage, and thereby establish a framework for identifying molecules involved in CN remodeling. Depletion of immature cartilage with guanidine, chondroitinase ABC, chondroitinase AC, and Streptomyces hyaluronidase markedly increased tensile integrity, while the integrity of mature cartilage remained unaltered after depletion with guanidine. The enhanced tensile integrity after matrix depletion suggests that certain ECM components of immature matrix serve to inhibit CN interactions and may act as modulators of physiological alterations of cartilage geometry and tensile properties during growth/maturation.
Archives of Biochemistry and Biophysics 07/2008; 474(1):175-82. · 2.93 Impact Factor
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ABSTRACT: A cartilage growth mixture (CGM) model is proposed to address limitations of a model used in a previous study. New stress constitutive equations for the solid matrix are derived and collagen (COL) remodeling is incorporated into the CGM model by allowing the intrinsic COL material constants to evolve during growth. An analytical validation protocol based on experimental data from a recent in vitro growth study is developed. Available data included measurements of tissue volume, biochemical composition, and tensile modulus for bovine calf articular cartilage (AC) explants harvested at three depths and incubated for 13 days in 20% fetal borine serum (FBS) and 20% FBS+beta-aminopropionitrile. The proposed CGM model can match tissue biochemical content and volume exactly while predicting theoretical values of tensile moduli that do not significantly differ from experimental values. Also, theoretical values of a scalar COL remodeling factor are positively correlated with COL cross-link content, and mass growth functions are positively correlated with cell density. The results suggest that the CGM model may help us to guide in vitro growth protocols for AC tissue via the a priori prediction of geometric and biomechanical properties.
Journal of Biomechanical Engineering 07/2008; 130(3):031006. · 1.90 Impact Factor
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ABSTRACT: Cartilage of articular joints grows and matures to achieve characteristic sizes, forms, and functional properties. Through these processes, the tissue not only serves as a template for bone growth but also yields mature articular cartilage providing joints with a low-friction, wear-resistant bearing material. The study of cartilage growth and maturation is a focus of both cartilage biologists and bioengineers with one goal of trying to create biologic tissue substitutes for the repair of damaged joints. Experimental approaches both in vivo and in vitro are being used to better understand the mechanisms and regulation of growth and maturation processes. This knowledge may facilitate the controlled manipulation of cartilage size, shape, and maturity to meet the criteria needed for successful clinical applications. Mathematical models are also useful tools for quantitatively describing the dynamically changing composition, structure and function of cartilage during growth and maturation and may aid the development of tissue engineering solutions. Recent advances in methods of cartilage formation and culture which control the size, shape, and maturity of these tissues are numerous and provide contrast to the physiologic development of cartilage.
Pediatric Research 06/2008; 63(5):527-34. · 2.70 Impact Factor
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Stephen M Klisch
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ABSTRACT: A strain energy function for finite deformations is developed that has the capability to describe the nonlinear, anisotropic, and asymmetric mechanical response that is typical of articular cartilage. In particular, the bimodular feature is employed by including strain energy terms that are only mechanically active when the corresponding fiber directions are in tension. Furthermore, the strain energy function is a polyconvex function of the deformation gradient tensor so that it meets material stability criteria. A novel feature of the model is the use of bimodular and polyconvex "strong interaction terms" for the strain invariants of orthotropic materials. Several regression analyses are performed using a hypothetical experimental dataset that captures the anisotropic and asymmetric behavior of articular cartilage. The results suggest that the main advantage of a model employing the strong interaction terms is to provide the capability for modeling anisotropic and asymmetric Poisson's ratios, as well as axial stress-axial strain responses, in tension and compression for finite deformations.
Journal of Biomechanical Engineering 05/2007; 129(2):250-8. · 1.90 Impact Factor
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ABSTRACT: The aim of this study was to design in vitro growth protocols that can comprehensively quantify articular cartilage structure-function relations via measurement of mechanical and biochemical properties. Newborn bovine patellofemoral groove articular cartilage explants were tested sequentially in confined compression (CC), unconfined compression (UCC), and torsional shear before (D0, i.e. day zero) and after (D14, i.e. day 14) unstimulated in vitro growth. The contents of collagen (COL), collagen-specific pyridinoline (PYR) crosslinks, glycosaminoglycan, and DNA significantly decreased during in vitro growth; consequently, a wide range of biochemical properties existed for investigating structure-function relations when pooling the D0 and D14 groups. All D0 mechanical properties were independent of compression strain while only Poisson's ratios were dependent on direction (i.e. anisotropic). Select D0 and D14 group mechanical properties were correlated with biochemical measures; including (but not limited to) results that CC/UCC moduli and UCC Poisson's ratios were correlated with COL and PYR. COL network weakening during in vitro growth due to reduced COL and PYR was accompanied by reduced CC/UCC moduli and increased UCC Poisson's ratios.
Journal of Biomechanics 02/2007; 40(16):3607-14. · 2.43 Impact Factor
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ABSTRACT: To examine the cartilage growth-associated effects of a disruption in the balance between the swelling pressure of glycosaminoglycans (GAGs) and the restraining function of the collagen network, by diminishing GAG content prior to culture using enzymatic treatment with chondroitinase ABC.
Immature bovine articular cartilage explants from the superficial and middle layers were analyzed immediately or after incubation in serum-supplemented medium for 13 days. Other explants were treated with chondroitinase ABC to deplete tissue GAG and also either analyzed immediately or after incubation in serum-supplemented medium for 13 days. Treatment- and incubation-associated variations in tissue volume, contents of proteoglycan and collagen network components, and tensile mechanical properties were assessed.
Incubation in serum-supplemented medium resulted in expansive growth with a marked increase in tissue volume that was associated with a diminution of tensile integrity. In contrast, chondroitinase ABC treatment on day 0 led to a marked reduction of GAG content and enhancement of tensile integrity, and subsequent incubation led to maturational growth with minimal changes in tissue volume and maintenance of tensile integrity at the enhanced levels.
The data demonstrate that a manipulation of GAG content in articular cartilage explants can distinctly alter the growth phenotype of cartilage. This may have practical utility for tissue engineering and cartilage repair. For example, the expansive growth phenotype may be useful to fill cartilage defects, while the maturational growth phenotype may be useful to induce matrix stabilization after filling defect spaces.
Arthritis & Rheumatism 02/2007; 56(1):188-98. · 7.87 Impact Factor
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Stephen M Klisch
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ABSTRACT: Cartilaginous tissues, such as articular cartilage and the annulus fibrosus, exhibit orthotropic behavior with highly asymmetric tensile-compressive responses. Due to this complex behavior, it is difficult to develop accurate stress constitutive equations that are valid for finite deformations. Therefore, we have developed a bimodular theory for finite deformations of elastic materials that allows the mechanical properties of the tissue to differ in tension and compression. In this paper, we derive an orthotropic stress constitutive equation that is second-order in terms of the Biot strain tensor as an alternative to traditional exponential type equations. Several reduced forms of the bimodular second-order equation, with six to nine parameters, and a bimodular exponential equation, with seven parameters, were fit to an experimental dataset that captures the highly asymmetric and orthotropic mechanical response of cartilage. The results suggest that the bimodular second-order models may be appealing for some applications with cartilaginous tissues.
Biomechanics and Modeling in Mechanobiology 07/2006; 5(2-3):90-101. · 3.19 Impact Factor
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ABSTRACT: A cartilage growth mixture (CGM) model is linearized for infinitesimal elastic and growth strains. Parametric studies for equilibrium and nonequilibrium boundary-value problems representing the in vitro growth of cylindrical cartilage constructs are solved. The results show that the CGM model is capable of describing the main biomechanical features of cartilage growth. The solutions to the equilibrium problems reveal that tissue composition, constituent pre-stresses, and geometry depend on collagen remodeling activity, growth symmetry, and differential growth. Also, nonhomogeneous growth leads to nonhomogeneous tissue composition and constituent pre-stresses. The solution to the nonequilibrium problem reveals that the tissue is nearly in equilibrium at all time points. The results suggest that the CGM model may be used in the design of tissue engineered cartilage constructs for the repair of cartilage defects; for example, to predict how dynamic mechanical loading affects the development of nonuniform properties during in vitro growth. Furthermore, the results lay the foundation for future analyses with nonlinear models that are needed to develop realistic models of cartilage growth.
Biomechanics and Modeling in Mechanobiology 07/2005; 3(4):209-23. · 3.19 Impact Factor
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ABSTRACT: Cartilage functions as a low-friction, wear-resistant, load-bearing tissue. During a normal gait cycle, one cartilage surface rolls and slides against another, all the while being loaded and unloaded. The durability of the tissue also makes for an impressive material to study. However, when cartilage is damaged or diseased, the tissue has little capacity to repair itself. The goal of cell-based repair strategies to replace damaged or diseased tissue requires that the functional biomechanical properties of normal (developing or mature), diseased, and repair cartilage be restored. This chapter addresses some of the major methods used to assess the biomechanical properties of native and tissue-engineered cartilage. First, the traditional methods of testing by compression, tension, shear, and indentation are reviewed. Next, additional methods to evaluate interfacial mechanics and lubrication are described. Thus, a variety of mechanical tests may be used to assess functional properties for normal, diseased, and tissue-engineered cartilage.
Methods in molecular medicine 02/2004; 101:157-90.
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ABSTRACT: In this paper, we present a growth mixture model for cartilage. The main features of this model are illustrated in a simple equilibrium boundary-value problem that is chosen to illustrate how a mechanical theory of cartilage growth may be applied to growth-related experiments on cartilage explants. The cartilage growth mixture model describes the independent growth of the proteoglycan and collagen constituents due to volumetric mass deposition, which leads to the remodeling of the composition and the mechanical properties of the solid matrix. The model developed here also describes how the material constants of the collagen constituent depend on a scalar parameter that may change over time (e.g., crosslink density); this leads to a remodeling of the structural and mechanical properties of the collagen constituent. The equilibrium boundary-value problem that describes the changes observed in cartilage explants harvested at different stages of a growth or a degenerative process is formulated. This boundary-value problem is solved using existing experimental data for developing bovine cartilage explants harvested at three developmental stages. The solution of the boundary-value problem in conjunction with existing experimental data suggest the types of experimental studies that need to be conducted in the future to determine model parameters and to further refine the model.
Journal of Biomechanical Engineering 05/2003; 125(2):169-79. · 1.90 Impact Factor
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ABSTRACT: US based early career researchers (Associate Professor and two graduate students) traveled to Politecnico di Milano for 3 months during the 2007 summer quarter. In Milan, they worked with Italian colleagues to accomplish two scientific aims that were designed to address limitations in the cartilage tissue growth models being developed under other NSF support. This report summarizes these scientific accomplishments, and also highlights the broader impacts associated with the international collaboration.
