Constitutive modeling of menisci tissue: a critical review of analytical and numerical approaches.

Menisci are fibrocartilaginous disks consisting of soft tissue with a complex biomechanical structure. They are critical determinants of the kinematics as well as the stability of the knee joint. Several studies have been carried out to formulate tissue mechanical behavior, leading to the development of a wide spectrum of constitutive laws. In addition to developing analytical tools, extensive numerical studies have been conducted on menisci modeling. This study reviews the developments of the most widely used continuum models of the meniscus mechanical properties in conjunction with emerging analytical and numerical models used to study the meniscus. The review presents relevant approaches and assumptions used to develop the models and includes discussions regarding strengths, weaknesses, and discrepancies involved in the presented models. The study presents a comprehensive coverage of relevant publications included in Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, Springer, and Scopus databases. This review aims at opening novel avenues for improving menisci modeling within the framework of constitutive modeling through highlighting the needs for further research directed toward determining key factors in gaining insight into the biomechanics of menisci which is crucial for the elaborate design of meniscal replacements.

Mechanical modeling and characterization of meniscus tissue using flat punch indentation and inverse finite element method.

In this paper, to characterize the mechanical properties of meniscus by considering its local microstructure, a novel nonlinear poroviscoelastic Finite Element (FE) model has been developed. To obtain the mechanical response of meniscus, indentation experiments were performed on bovine meniscus samples. The ramp-relaxation test scenario with different depths and preloads was designed to capture the mechanical characteristics of the tissue in different regions of the medial and lateral menisci. Thereafter, a FE simulation was performed considering experimental conditions. Constitutive parameters were optimized by solving a FE-based inverse problem using the heuristic Simulated Annealing (SA) optimization algorithm. These parameters were ranged according to previously reported data to improve the optimization procedure. Based on the results, the mechanical properties of meniscus were highly influenced by both superficial and main layers. At low indentation depths, a high percentage relaxation (p < 0.01) with a high relaxation rate (p < 0.05) was obtained, due to the poroelastic and viscoelastic nature of the superficial layer. Increasing both penetration depth and preload level involved the main layer response and caused alterations in hyperelastic and viscoelastic parameters of the tissue, such that for both layers, the shear modulus was increased (p < 0.01) while the rate and percentage of relaxation were decreased (p < 0.01). Results reflect that, shear modulus of the main layer in anterior region is higher than central and posterior sites in medial meniscus. In contrast, in lateral meniscus, posterior side is stiffer than central and anterior sides.