The Dynamic Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell-Matrix Interactions Under Cyclic Compressive Loading

Abstract

Cyclic mechanical loading of articular cartilage results in a complex biomechanical environment at the scale of the chondrocytes that strongly affects cellular metabolic activity. Under dynamic loading conditions, the quantitative relationships between macroscopic loading characteristics and solid and fluid mechanical variables in the local cellular environment are not well understood. In this study, an axisymmetric multiscale model of linear biphasic cell-matrix interactions in articular cartilage was developed to investigate the cellular microenvironment in an explant subjected to cyclic confined compressive loading. The model was based on the displacement-velocity-pressure (u-v-p) mixed penalty weighted residual formulation of linear biphasic theory that was implemented in the COMSOL Multiphysics software package. The microscale cartilage environment was represented as a three-zone biphasic region consisting of a spherical chondrocyte with encapsulating pericellular matrix (PCM) that was embedded in a cylindrical extracellular matrix (ECM) subjected to cyclic confined compressive loading boundary conditions. Biphasic material properties for the chondrocyte and the PCM were chosen based on previous in vitro micropipette studies of cells or chondrons isolated from normal or osteoarthritic cartilage. Simulations performed at four loading frequencies in the range 0.01-1.0 Hz supported the hypothesized dual role of the PCM as both a protective layer for the cell and a mechanical transducer of strain. Time varying biphasic variables at the cellular scale were strongly dependent on relative magnitudes of the loading period, and the characteristic gel diffusion times for the ECM, the PCM and the chondrocyte. The multiscale simulations also indicated that axial strain was significantly amplified in the range 0.01-1.0Hz, with a decrease in amplification factor and frequency insensitivity at the higher frequencies. Simulations of matrix degradation due to osteoarthritis indicated that strain amplification factors were more significantly altered when loss of matrix stiffness was exclusive to the PCM. The findings of this study demonstrate the complex dependence of dynamic mechanics in the local cellular environment of cartilage on macroscopic loading features and material properties of the ECM and the chondron.

In situ chondrocyte viscoelasticity

“…It has been shown theoretically that the strain rate-dependent viscoelastic response of cartilage reduces periodic alterations of tissue strains (Suh et al, 1995) and cell deformations (Kim et al, 2008) (Freeman et al, 1994;Knight et al, 1998;Wu and Herzog, 2006;Kim et al, 2008). Pilot results obtained in a recent study on in vivo chondrocyte deformations in the intact knee loaded by muscular contractions suggest that the intrinsic viscoelastic response of chondrocytes substantially differs from that observed in isolated chondrocytes embedded in gel constructs (Abusara et al, 2011;Knight et al, 1998).…”

The Influence of Cell-Matrix Attachment and Matrix Development on the Micromechanical Environment of the Chondrocyte in Tissue-Engineered Cartilage

“…1) (radius = 19 mM; height = 38 mM) similar to the dimensions used previously. 16 Chondrocyte diameter and PCM outer diameter were 10 and 15 mM, respectively. The influence of the cell size was studied by varying the cell diameter to 5 and 15 mM, while the thickness of PCM was remained constant.…”

“…Using a multiscale modeling approach, in which the boundary conditions of a microscale model are obtained from the solution of a macroscale (millimeter-scale) model, 16 we simulated chondrocyte-seeded cartilage TE constructs under unconfined compression loading. The macroscopic mechanical conditions within TE constructs were compared to those in mature cartilage explants under the same loading condition.…”

“…For all cases the calculated mechanical strain fields were compared, considering the potential role of strain as a sensitive mechanical variable that may be involved in cellular signal transduction. 16 Macroscale finite element mesh A macroscale axisymmetric finite element model was created in Abaqus v6.11 (Dassault Systemes, Providence, RI) to either represent a cylindrical 2% agarose TE construct (diameter = 4 mm; height = 2 mm) similar to the dimensions often used in tissue engineering studies, 18,19 or a cartilage explant with native ECM content and distribution (Fig. 1).…”

On the relevance of using homogeneous biphasic models to characterize the mechanical behavior of the growth plate

“…It has been shown by numerous authors that chondrocytes mechanical behavior is time dependent. Whether their behavior is viscoelastic (Jones et al 1999;Leipzig and Athanasiou 2005), poroelastic (Kim et al 2008), or poroviscoelastic (Trickey et al 2006) is still an open question. Moreover, Ateshian et al (2007) showed that articular chondrocytes, modeled as a protoplasm surrounded by a semipermeable membrane, would behave either as a compressible or an incompressible viscoelastic (vs. biphasic/flow-dependent viscoelastic) solid when loaded in situ in their extracellular matrix or under isolated conditions, respectively.…”