Development and experimental validation of a dynamic numerical model for human articular cartilage

Abstract

The purpose of this study was to create a preliminary set of experimentally validated Finite Element Analysis (FEA) models, in order to predict the dynamic mechanical behaviour of human articular cartilage (AC). Current models consider static loading with limited independent experimental validation, while the models for this study assess dynamic loading of AC, with direct comparison and validation to physical testing. Three different FEA models of AC were constructed, which considered both linear elastic and hyperelastic models; Neo-Hookean and Ogden. Models were validated using the data collected from compression testing of human femoral heads across 0-1.7 MPa (quasi-static tests and dynamic mechanical analysis). The linear elastic model was inadequate, with a 10-fold over prediction of the displacement dynamic amplitude. The Neo-Hookean model accurately predicted the dynamic amplitude but failed to predict the initial compression of the cartilage, with a 10 times overprediction. The Ogden model provided the best results, with both the initial compression lying within one standard deviation of that observed in the validation data set, and the dynamic amplitude of the same order of magnitude. In conclusion, this study has found that the fast dynamic response of human AC is best represented by a third order Ogden model.

Keywords: Articular cartilage; dynamic mechanical analysis; finite element analysis; hyperelastic; transient.

Figure 1.

(a) Example of cartilage-bone core prior to dynamic mechanical analysis, (b) example of cartilage disc separated from the core using a medical scalpel ensuring no bone is left on sample and (c) sample in situ prior to DMA.

Figure 2.

Model building flow diagram. (a) Initial set up of 2D models. (b) Geometry from physical samples used to optimise and mesh the models. (c) Linear approximation used to determine Young’s Modulus for linear models alongside ABAQUS model parameter determination for the Ogden models. Neo-Hookean parameters were taken from literature. (d) Final model under compression.

Figure 3.

Applied pressures during experimentation and FEA models. A combination of the ramp compression physical test (a) and the 1 Hz DMA cycle (b) was applied to each model via the top surface, as a two-step process, each 1 s in duration (c).

Figure 4.

FEA comparative results panel. Each of the models generated was compared to an independent data set. Results are displayed for ramp compression on linear (a), Neo-Hookean (b), and Ogden (c) models and for dynamic amplitude compression on the same models respectively (d, e, and f). Dynamic Amplitude is shorted to DynAmp for convenience (mean ± SD).

Figure 5.

The overall compression of both the Neo-Hookean and Ogden models. This figure illustrates that although the dynamic amplitudes for both models are similar to the physical testing, the initial compression is distinctly non-linear for the Ogden model only, offering a physiological comparison.

Figure 6.

Hyperelastic model and experimental data comparisons: (a) pressure-displacement comparison, illustrating the non-linearity of the Ogden model, compared to the Neo-Hookean model and (b) hysteresis loops for the same models, demonstration the lack of time-dependency within the hyperelastic models.