Cal Poly Cartilage Biomechanics Group

P.I. Stephen M. Klisch, Ph.D.

Modeling AC growth with a continuum mechanics cartilage growth mixutre model

Growth, resorption, and remodeling are fundamental processes that influence the size, shape, and structure-function relations of biological tissues. The articular cartilage (AC) extracellular matrix (ECM) is synthesized, maintained, and degraded by chondrocytes (i.e. cells). Tissue growth occurs when the normal balance between anabolic (i.e. deposition) and catabolic (i.e. resorption) processes are shifted toward matrix deposition or resorption. A key feature of AC growth is that metabolism can be regulated by mechanical stimuli. When a stimulus is applied to cartilage in vivo or in vitro, the properties of the tissue serve as a filter and determine how this stimulus translates into a change in the cellular and extracellular microenvironments. These microenvironments, along with biological factors, govern mRNA production and, consequently, can lead to changes in the properties of the tissue which then change how the external stimuli are filtered before signaling the cells, creating a feedback loop.

Continuum mechanics growth models attempt to close this feedback loop by modeling the temporal evolution of tissue composition and, consequently, the biomechanical properties of the ECM. We have developed growth theories to describe the growth of compressible elastic, thermoelastic, and multiphasic materials from which specific cartilage growth mixture (CGM) models have been proposed. First, a general continuum theory of growth was developed that modeled the tissue as a fluid and an arbitrary number of growing elastic materials, where all growing tissue constituents can experience distinct, yet interdependent, stresses, strains, diffusive velocities, mechanical properties, and mass deposition/removal rates. The motivation for developing such a complex theory was that many tissue constituents appear to play a role in growth and remodeling (e.g., various types of glycosaminoglycans (GAGs), collagens (COLs), cellular components including membrane receptors and intracellular structures, and enzymes, growth factors, etc.) and the relative importance of their functional roles are unknown.

The goal of our CGM models is to model and predict the evolution of tissue geometry, composition, and biomechanical properties for in vitro growth experiments under controlled conditions. The model is proposed to capture the following observations from in vitro growth experiments: the GAG and COL constituents serve distinct mechanical roles that are crucial to tissue function and they grow in a differential yet interdependent manner. The CGM model employs a mixture of a water constituent and a growing ECM. The ECM is modeled as a mixture of two growing elastic materials, GAG and COL. A basic assumption of the model is the stress balance hypothesis that states that the solid matrix stress is equal to the sum of the GAG and COL stresses.

We developed experimental and analytical validation protocols to test the predictive capability of the CGM model. Specimens from three successive layers were prepared: (S) superficial ~0.4 mm thick; (M1) first middle zone ~0.25 mm thick; and (M2) second middle zone ~0.25 mm thick. Some specimens were tested immediately (control). Other specimens were incubated for 13 days in medium or medium with 0.1mM BAPN. Since BAPN inhibits PYR crosslink formation, the stress balance hypothesis suggests that enhanced volumetric tissue growth should occur by blocking the metabolic pathway for the formation of COL crosslinks. Dynamic tension moduli were measured and scaled by factors based on more recent measurements of equilibrium and dynamic moduli. Biochemical measurements included GAG, COL, PYR, and DNA. Preliminary results suggested that the CGM model must include COL remodeling in order to match volumetric tissue growth; consequently, each COL material constant was multiplied by a remodeling factor (χ) so that grown tissue volume was matched. This analytical protocol allows for the theoretical prediction of mechanical properties relative to the grown configuration. There was not a significant difference between experimental and theoretical values of tensile modulus; that result serves as validation of the CGM model for the select growth protocols.

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© 2008 Stephen M. Klisch | Mechanical Engineering

College of Engineering | Cal Poly San Luis Obispo