Influence of articular cartilage sample geometry on mechanical response and properties using finite element simulation

Abstract

Mechanical testing of articular cartilage yields highly variable results, posing challenges for tissue characterization. Many factors cause variability, one is sample geometry. Using in-situ phase-contrast enhanced synchrotron micro-tomographs of cartilage samples while tested in unconfined compression (stress relaxation) our group found high variability in the mechanical response. Since all samples originated from a single bovine knee, they were assumed to share mechanical properties. Microscale tomography images showed geometric irregularities in samples that were not accounted for in the often assumed intended cylindrical shape. We aimed to determine the influence of sample shape on mechanical response in unconfined compression and how sample geometry affects identified mechanical properties. Using a parametric FE model incorporating geometric irregularities in a Design of Experiments approach, results were analysed with 2-way ANOVA. Furthermore, a material parameter fitting was done with multiple segmented sample-specific finite element models simultaneously to assess the influence of sample geometry on material parameters. Results revealed that the average inclined sample surface (4°) caused a 15 % decrease in reaction forces compared to the intended cylinder. Fitting multiple sample-specific geometries simultaneously altered material parameters between −70 to +159 % compared to the average model. Strikingly, initial fibril stiffness and permeability increased by 137 % and 159 %, while the root-mean-square error of the fit was reduced by ∼2/3 compared to using parameters from a cylindrical shape model. In conclusion, minor variability in sample geometry affects property characterization and can account for some of the inter-sample variability in the mechanical data for cartilage.