Large-Scale Finite Element Modeling of Pre-stress in Articular Cartilage

Finite element (FE) methods and multiphasic equations are commonly used to model articular cartilage (AC). This tissue has a fixed negative charge that leads to osmotic pressure in its structure, causing pre-stress. A challenge in FE modeling of AC is to start the simulation with the correct in vivo pre-stressed state of the tissue, which is traditionally handled by custom optimizers, the so-called pre-stressing algorithm (PSA). These algorithms, which have been successfully implemented in small-scale models, detect either the geometrical stress-free state, constitutive stress-free state, or both. Therefore, this work aims to extend it to a larger-scale AC model in a human tibiofemoral joint, developed using depth-dependent and multiphasic equations of AC. We employed a unified optimizer, rather than sequential optimizers, to reduce the number of algorithmic iterations. Also, fibrillar orientations and other microstructural properties of the AC substructures are approximated by defining the approximate normalized depth. The pre-stressed state is calculated in around six hours, revealing the noted depth-dependent stresses. To facilitate future research, the PSA is open-sourced at https://github.com/shayansss/psa .