Biomechanical properties of single chondrocytes and chondrons determined by micromanipulation and finite-element modelling

Abstract

A chondrocyte and its surrounding pericellular matrix (PCM) are defined as a chondron. Single chondrocytes and chondrons isolated from bovine articular cartilage were compressed by micromanipulation between two parallel surfaces in order to investigate their biomechanical properties and to discover the mechanical significance of the PCM. The force imposed on the cells was measured directly during compression to various deformations and then holding. When the nominal strain at the end of compression was 50 per cent, force relaxation showed that the cells were viscoelastic, but this viscoelasticity was generally insignificant when the nominal strain was 30 per cent or lower. The viscoelastic behaviour might be due to the mechanical response of the cell cytoskeleton and/or nucleus at higher deformations. A finite-element analysis was applied to simulate the experimental force-displacement/time data and to obtain mechanical property parameters of the chondrocytes and chondrons. Because of the large strains in the cells, a nonlinear elastic model was used for simulations of compression to 30 per cent nominal strain and a nonlinear viscoelastic model for 50 per cent. The elastic model yielded a Young's modulus of 14 ± 1 kPa (mean ± s.e.) for chondrocytes and 19 ± 2 kPa for chondrons, respectively. The viscoelastic model generated an instantaneous elastic modulus of 21 ± 3 and 27 ± 4 kPa, a long-term modulus of 9.3 ± 0.8 and 12 ± 1 kPa and an apparent viscosity of 2.8 ± 0.5 and 3.4 ± 0.6 kPa s for chondrocytes and chondrons, respectively. It was concluded that chondrons were generally stiffer and showed less viscoelastic behaviour than chondrocytes, and that the PCM significantly influenced the mechanical properties of the cells.

Figure 1.

A three-dimensional schematic of the compression experiment and its finite-element mesh and boundary conditions.

Figure 2.

The generalized Maxwell model with three parameters.

Figure 3.

Experimental force relaxation data fitted by the load relaxation equation (3.4b) and the finite-element (FE) viscoelastic three-parameter model (regression coefficient for the fit, r² = 0.99). Filled circles, experiment; filled diamonds, fitting equation (3.4b); filled triangles, FE analysis.

Figure 4.

Typical (a) force–displacement curves and (b) force–time curves of a single chondrocyte compressed to 30 and 50% nominal strain, successively, and held. Compression speed of 6 µm s⁻¹. The diameter of the chondrocyte was 9.0 µm (regression coefficient for the fits of 30% nominal strain, r² = 0.51 in compression; regression coefficient for the fits of 50% nominal strain, r² = 0.89 in compression and r² = 0.99 in relaxation). FE, finite element. Open diamonds, experiment 30%; inverted triangles, FE analysis 30%; filled circles, experiment 50%; upright triangles, FE analysis 50%.

Figure 5.

Typical (a) force–displacement curves and (b) force–time curves of a single chondron compressed to 30 and 50% nominal strain, successively, and held. Compression speed of 6 µm s⁻¹. The diameter of the chondron was 9.4 µm (regression coefficient for the fits of 30% nominal strain, r² = 0.72 in compression; regression coefficient for the fits of 50% nominal strain, r² = 0.95 in compression and r² = 0.99 in relaxation). Open diamonds, experiment 30%; inverted triangles, FE analysis 30%; filled circles, experiment 50%; upright triangles, FE analysis 50%.

Figure 6.

Typical force–time curves of (a) a single chondrocyte and (b) chondron compressed to 50% nominal strain, held and then released. Compression speed of 6 µm s⁻¹. The diameters of the chondrocyte and chondron were 9.0 and 9.4 µm, respectively. The regression coefficient for the unloading phase is r² = 0.80 and 0.93 for the chondrocyte and chondron, respectively. Filled circles, experiment 50%; filled triangles, FE analysis 50%.