A cartilage growth mixture model for infinitesimal strains: solutions of boundary-value problems related to in vitro growth experiments

Klisch, Stephen M.; Sah, Robert L.; Hoger, Anne

doi:10.1007/s10237-004-0060-9

Cited by 26 publications

(26 citation statements)

References 57 publications

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“…This assumption is supported by our solution to the dynamic growth problem presented in Klisch et al (2005b). We first proposed the incremental growth boundary-value problem in Klisch et al (2001) and later modified it in Klisch (2006b) to be compatible with the finite element method.…”

Section: Introductionmentioning

confidence: 82%

“…Future work will extend the bimodular stressstrain equation for the collagen constituent to include anisotropic behavior (Klisch 2006a). Also, it has been suggested that to accurately model specific growth experiments a collagen remodeling parameter (related to collagen-specific crosslink or fibril binding molecules) should be included that changes the mechanical properties of the collagen constituent (Klisch et al 2005a).…”

Section: Discussionmentioning

confidence: 99%

“…These two tools interactively solve the equilibrium growth boundary value problem (BVP) as proposed in (Klisch et al 2001;Klisch 2006b), subject to the growth theories presented in the CGMM . Since the time scale for each increment of in vitro growth is assumed to be 2-3 orders of magnitude greater than the time scale for in vitro loading, the dynamic effects of growth can be neglected (Klisch et al 2005b), Thus, the dynamic BVP that characterizes the mechanical response to loading and the growth equilibrium BVP that characterizes the growth of individual elements are solved independently.…”

Section: Methodsmentioning

confidence: 99%

“…Also note that both stimulated and unstimulated growth are assumed to occur uniformly in an element with respect to time during n, and represent only a small change in the specimen's mass. Likewise, during growth, only small changes in the tissue's composition occur over a relatively large timescale, so it is reasonable to assume that dynamic effects like the strain rate of the growing tissue are also negligible (Klisch et al 2005b). For these reasons, the growth BVP is treated as an equilibrium problem.…”

Section: Methodsmentioning

confidence: 99%

“…Various theories for the volumetric growth of elastic materials, as well as a cartilage growth mixture model (CGMM), have been proposed by Klisch and colleagues (Klisch et al , 2001(Klisch et al , 2005b. These theories allow for an elastic material to be composed of an arbitrary number of constituents that may grow and remodel independently.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A nonlinear finite element model of cartilage growth

Davol

Bingham

Sah

et al. 2007

Biomech Model Mechanobiol

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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 (MAT-LAB) 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.

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Section: Introductionmentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A nonlinear finite element model of cartilage growth

Davol

Bingham

Sah

et al. 2007

Biomech Model Mechanobiol

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Continuum Models of Growth with Emphasis on Articular Cartilage

Klisch

Mechanics of Biological Tissue

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Mathematical modeling of collagen turnover in biological tissue

et al. 2012

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We present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF-β and tissue inhibitors of metalloproteinases TIMP. While the upregulation of the former increases the collagen density, the upregulation of the latter increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.

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A cartilage growth mixture model for infinitesimal strains: solutions of boundary-value problems related to in vitro growth experiments

Abstract: PUBLISHED CITATIONKlisch SM, Sah RL, Hoger A. A cartilage growth mixture model for infinitesimal strains:solutions of boundary-value problems related to in vitro growth experiments.

Cited by 26 publications

References 57 publications

A nonlinear finite element model of cartilage growth

A nonlinear finite element model of cartilage growth

Continuum Models of Growth with Emphasis on Articular Cartilage

Mathematical modeling of collagen turnover in biological tissue

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