0
Research Papers

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

[+] Author and Article Information
Eunjung Kim

Department of Mathematics, North Carolina State University, Raleigh, NC 27695

Farshid Guilak

Department of Surgery, and Department of Biomedical Engineering, Duke University Medical Center, Durham, NC 27710

Mansoor A. Haider

Department of Mathematics, North Carolina State University, Raleigh, NC 27695m_haider@ncsu.edu

J Biomech Eng 130(6), 061009 (Oct 14, 2008) (10 pages) doi:10.1115/1.2978991 History: Received September 05, 2007; Revised March 07, 2008; Published October 14, 2008

## 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 aspiration 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 0.01–1.0 Hz, 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.

<>

## Figures

Figure 1

Geometry and FEM mesh for simulation of microscale mechanical interactions between the chondron and ECM

Figure 2

Validation of the biphasic FEM model (symbols) against a previous theoretical solution for cyclic radial deformation (0.1 Hz) in a spherical chondron (50). (a) Spatial strain profile at t=5 s, radial strain (b) and pore pressure (c) at the chondron boundary and cell-PCM interface. Cell and PCM parameters were chosen based on Table 1 (normal case).

Figure 6

Simulations of axial strain transmitted to the microscale domain via the ECM shown at the top and bottom of the microscale domain for loading frequencies: (a) f=0.01 Hz, (b) f=0.02 Hz, (c) f=0.05 Hz, and (d) f=0.1 Hz

Figure 7

Simulations of axial strain amplification within the chondron via representative points located at 90% of the cell radius (chondrocyte), and 90% of the PCM thickness. Amplification factors are normalized to the macroscopic engineering strain ε0=1% and shown for the loading frequencies: (a) f=0.01 Hz, (b) f=0.02 Hz, (c) f=0.05 Hz, and (d) f=0.1 Hz.

Figure 8

Spatial profiles of axial strain magnitude at times corresponding to peak strain amplification for f=0.01 Hz ((a) t=80 s), f=0.02 Hz ((b) t=50 s), and f=0.05 Hz ((c) t=70 s), and steady state amplification at local minima for f=0.01 Hz ((d) t=480 s), f=0.02 Hz ((e) t=450 s), and f=0.05 Hz ((f) t=490 s)

Figure 4

Illustration of force transmission at three points along the symmetry axis located at 90% of the cell radius (chondrocyte), 90% of the PCM thickness and at the top of the microscale domain (ECM). Axial solid stress is shown at four loading frequencies: (a) f=0.01 Hz, (b) f=0.02 Hz, (c) f=0.05 Hz, and (d) f=0.1 Hz.

Figure 3

Simulations of pore pressure (a) and solid stress (b) transmitted to the microscale domain via the ECM based on the theoretical solution in Eqs. 5,6. Responses are shown at z=0.519 mm for five different loading frequencies in the range f=0.01–1.0 Hz.

Figure 5

Spatial profiles of the solid phase “spherical stress” shown after 4.5 loading cycles for loading frequencies: (a) f=0.01 Hz, (b) f=0.02 Hz, and (c) f=0.1 Hz.

Figure 9

Simulations of axial strain amplification within the chondrocyte via a representative point located at 90% of the cell radius comparing cases of normal PCM and ECM and OA exclusive to the PCM (see Table 1). Amplification factors are normalized to the macroscopic engineering strain ε0=1% and shown for the loading frequencies: (a) f=0.01 Hz, (b) f=0.02 Hz, (c) f=0.05 Hz, and (d) f=0.1 Hz.

Figure 10

Simulations of axial strain amplification within the chondrocyte via a representative point located at 90% of the cell radius comparing cases of normal PCM and ECM and OA PCM and ECM (see Table 1). Amplification factors are normalized to the macroscopic engineering strain ε0=1% and shown for the loading frequencies: (a) f=0.01 Hz, (b) f=0.02 Hz, (c) f=0.05 Hz, and (d) f=0.1 Hz.

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections