Uncertainties in indentation testing of articular cartilage: a fibril-reinforced poroviscoelastic study

Indentation testing provides a quantitative technique to evaluate mechanical characteristics of articular cartilage in situ and in vivo. Traditionally, analytical solutions proposed by Hayes et al. [Hayes WC, Keer LM, Herrmann G, Mockros LF. A mathematical analysis for indentation tests of articular cartilage. J Biomech 1972;5(5):541-51] have been applied for the analysis of indentation measurements, and due to their practicality, they have been used for clinical diagnostics. Using this approach, the elastic modulus is derived based on scaling factors which depend on cartilage thickness, indenter radius and Poisson's ratio, and the cartilage model is assumed isotropic and homogeneous, thereby greatly simplifying the true tissue characteristics. The aim was to investigate the validity of previous model assumptions for indentation testing. Fibril-reinforced poroviscoelastic cartilage (FRPVE) model including realistic tissue characteristics was used to simulate indentation tests. The effects of cartilage inhomogeneity, anisotropy, and indentation velocity on the indentation response were evaluated, and scaling factors from the FRPVE analysis were derived. Subsequently, the validity of scaling factors obtained using the traditional and the FRPVE analyses was studied by calculating indentation moduli for bovine cartilage samples, and comparing these values to those obtained experimentally in unconfined compression testing. Collagen architecture and compression velocity had significant effects on the indentation response. Isotropic elastic analysis gave significantly higher (30-107%) Young's moduli for indentation compared to unconfined compression testing. Modification of Hayes' scaling factors by accounting for cartilage inhomogeneity and anisotropy improved the agreement of Young's moduli obtained for the two test configurations by 14-28%. These results emphasize the importance of realistic cartilage structure and mechanical properties in the indentation analysis. Although it is not possible to fully describe tissue inhomogeneity and anisotropy with just the Young's modulus and Poisson's ratio, accounting for inhomogeneity and anisotropy in these two parameters may help to improve the in vivo characterization of tissue using arthroscopic indentation testing.