Predicting Articular Cartilage Constituent Material Properties Following In Vitro Growth Using a Proteoglycan-Collagen Mixture Model

Stender, Michael E.

doi:10.15368/theses.2011.19

Cited by 3 publications

(23 citation statements)

References 59 publications

(100 reference statements)

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“…The model used in this study builds upon these, adding a continuous distribution of collagen fibers [43].…”

Section: Biphasic Articular Cartilage Modelsmentioning

confidence: 99%

“…Additionally, for finite strain simulations, Abaqus requires the exact consistent Jacobian matrix in order to guide the solver to the correct solution. The formulation for the exact consistent Jacobian matrix was developed in [43,57] and is presented below in indicial notation.…”

Section: Constitutive Stress Equationsmentioning

confidence: 99%

“…The formulation for GAG stress is based on the Poisson-Boltzmann model of a unit cell of molecule in an ionic solution and was developed in [43]. The GAG constituent Cauchy stress tensor σ GAG is described by…”

Section: Glycosaminoglycan Constituent Stressmentioning

confidence: 99%

“…A hyperelastic Neo-Hookean solid was chosen to model the ground substance matrix [43]. The second Piola-Kirchoff stress tensor of a Neo-Hookean solid is expressed as…”

Section: Ground Substance Matrix Constituent Stressmentioning

confidence: 99%

“…The user material definition subroutine (UMAT) used in this study is based on the one previously developed in [43] and [63]. The previous UMAT implemented an isotropic COL fiber distribution, a GAG constituitve stress equation based on the Poisson-Boltzman unit cell model, and an isotropic MAT material.…”

Section: User Materials Definition Subroutinementioning

confidence: 99%

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Prediction of Articular Cartilage Remodeling During Dynamic Compression with a Finite Element Model

Yamauchi¹

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Prediction of Articular Cartilage Remodeling During Dynamic Compression with a Finite Element Model Kevin YamauchiFirst, an in vitro growth experiment was performed to test the hypothesis that applying dynamic unconfined compression during culture produces heterogeneous remodeling in newborn bovine articular cartilage explants. Heterogeneous measures of cartilage microstructure were obtained by biochemical assays and quantified polarized light microscopy. Significant differences were measured between the GAG content in the inner and outer portions of the samples stimulated with dynamic unconfined compression. The COL fiber network was found to be more highly aligned in the inner portion of the sample than in the peripheral region.Next, a poroelastic finite element model with a remodeling subroutine was developed to test the hypothesis that the magnitude of relative interstitial fluid velocity and maximum principle strain stimulate GAG and COL fiber network remodeling, respectively, in articular cartilage during culture with dynamic unconfined compression. The GAG remodeling law was successful in predicting the heterogeneous changes in GAG content. The collagen remodeling law was not successful in predicting the changes in the COL network microstructural orientation, suggesting another mechanical cue is responsible for stimulating the remodeling of the COL fiber network.iv

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“…The model used in this study builds upon these, adding a continuous distribution of collagen fibers [43].…”

Section: Biphasic Articular Cartilage Modelsmentioning

confidence: 99%

Section: Constitutive Stress Equationsmentioning

confidence: 99%

Section: Glycosaminoglycan Constituent Stressmentioning

confidence: 99%

“…A hyperelastic Neo-Hookean solid was chosen to model the ground substance matrix [43]. The second Piola-Kirchoff stress tensor of a Neo-Hookean solid is expressed as…”

Section: Ground Substance Matrix Constituent Stressmentioning

confidence: 99%

Section: User Materials Definition Subroutinementioning

confidence: 99%

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Prediction of Articular Cartilage Remodeling During Dynamic Compression with a Finite Element Model

Yamauchi¹

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Poroelastic Finite Element Analysis of a Heterogeneous Articular Cartilage Explant Under Dynamic Compression in ABAQUS

Kam¹

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A poroelastic finite element model of a heterogeneous articular cartilage disc was created to examine the tissue response to low amplitude (± 2% strain), low frequency (0.1 Hz) dynamic unconfined compression (UCC). A strong correlation has been made between the relative fluid velocity and stimulation of glycosaminoglycan synthesis. A contour plot of the model shows the relative fluid velocity during compression exceeds a trigger value of 0.25 μm/s at the radial periphery. Dynamic UCC biochemical results have also reported a higher glycosaminoglycan content in this region versus that of day 0 specimens. Fluid velocity was also found not to be the dominant physical mechanism that stimulates collagen synthesis; the heterogeneity of the fluid velocity contour plot conflicts with the homogeneous collagen content from the biochemical results. It was also found that a Tresca (shear) stress trigger of 0.07 MPa could provide minor stimulation of glycosaminoglycan synthesis. A feasibility study on modeling a heterogeneous disc was conducted and found convergence issues with the jump in properties from the superficial to middle layers of the disc. It is believed that the superficial layer contains material properties that allow the tissue to absorb much of the compressive strain, which in turn increases pressure and causes convergence issues in ABAQUS. The findings in this thesis may help guide the development of a growth and remodeling routine for articular cartilage. v Acknowledgements This thesis would not have been completed without the help and guidance of many individuals who have provided valuable knowledge and support for this project. I'd like to first and foremost thank my thesis committee. My committee chair Dr. Stephen Klisch and committee member Dr. Scott Hazelwood have provided me with their indispensible knowledge about the mechanics of articular cartilage and modeling in ABAQUS. It has been an honor working with such great individuals who have encouraged me throughout my career at Cal Poly. I would also like to extend my appreciation to my committee member Dr. Peter Schuster, who has challenged me with learning finite element analysis as well as providing help with stubborn convergence issues in ABAQUS.

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Viscoelastic Anisotropic Finite Element Mixture Model of Articular Cartilage using Viscoelastic Collagen Fibers and Validation with Stress Relaxation Data

Griebel¹

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Experimental results show that collagen fibers exhibit stress relaxation under tension and a highly anisotropic distribution. To further develop the earlier model of Stender [1], the collagen constituent was updated to reflect its intrinsic viscoelasticity and anisotropic distribution, and integrated with an existing mixture model with glycosaminoglycans and ground substance matrix. A two-term Prony series expansion of the quasi-linear viscoelastic model was chosen to model the viscoelastic properties of the collagen fibers. Material parameters were determined by using the simplex method to minimize the sum of squared errors between model results and experimental stress relaxation data of tissue in tension. Collagen elastic fiber modulus was calculated by fitting to the equilibrium data and viscoelastic parameters were determined by fitting to the relaxation curve. Results of newborn (∼1-3 week old) untreated bovine articular cartilage explants from the patellar femoral groove as well as explants cultured in transforming growth factor-β1 (TGF-β1), from both the superficial (∼0-0.5 mm from the articular surface) and middle (∼0.5-1.0 mm from the articular surface) layers were compared to examine the effects of TGF-β1. TGF-β1 has been shown to maintain or even enhance mechanical properties of articular cartilage in compression and tension [2, 3] and this study continues with the hope that it may be used to improve tissue engineering of mature cartilage to better survive implantation in vivo for the successful repair of articular cartilage defects. Results show that TGF-β1 has a maturational effect on collagen, causing the tissue to become stiffer through an increase in elastic collagen fiber modulus and less viscous through shorter relaxation time and less stress relaxation (tissue retained a higher percentage of residual stress). The results of this study further advance the understanding of the effects of location and treatment with TGF-β1.

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Predicting Articular Cartilage Constituent Material Properties Following In Vitro Growth Using a Proteoglycan-Collagen Mixture Model

Cited by 3 publications

References 59 publications

Prediction of Articular Cartilage Remodeling During Dynamic Compression with a Finite Element Model

Prediction of Articular Cartilage Remodeling During Dynamic Compression with a Finite Element Model

Poroelastic Finite Element Analysis of a Heterogeneous Articular Cartilage Explant Under Dynamic Compression in ABAQUS

Viscoelastic Anisotropic Finite Element Mixture Model of Articular Cartilage using Viscoelastic Collagen Fibers and Validation with Stress Relaxation Data

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