Model selection and sensitivity analysis in the biomechanics of soft tissues: A case study on the human knee meniscus

Abstract

Soft tissues—such as ligaments and tendons—primarily consist of solid (collagen, predominantly) and liquid phases. Understanding the interaction between such components and how they change under physiological loading sets the basis for elucidating the essential link between their internal structure and mechanical behavior. In fact, the internal heterogeneous structure of this kind of tissues leads to a wide range of mechanical behaviors, which then determine their own function(s). Characterizing these behaviors implies an important experimental effort in terms of tissue harvesting, sample preparation, and implementation of testing protocols—which, often, are not standardized. These issues lead to several difficulties in both collecting and providing comparable and reliable information. In order to model the behaviors of heterogeneous tissues and identify material parameters, a large volume of reproducible experimental data is required; unfortunately, such an amount of information is often not available. In reality, most of the studies that are focused on the identification of material parameters are largely based on small sets of experimental data, which present a large variability. Such a large variability opens on to uncertainties in the estimation of material parameters, as reported in the literature. Hence, the use of a rigorous probabilistic framework, that is able to address uncertainties due to paucity of data, is of paramount importance in the field of biomechanics; in this perspective, Bayesian inference represents a promising approach. This study was focused on the analysis of the knee meniscus as a paradigmatic example of human soft tissue. Indeed, the heterogeneous internal architecture of this structure is linked to functionally graded material properties, which enable this fibrocartilaginous tissue to perform a wide range of functions within the knee joint. More in detail, within this work we specifically addressed: (i) the variability of parameters for the meniscal nonfibrous, fibrous solid phase, and for the liquid one, (ii) the material models currently used to interpret experimental data, (iii) a comparative finite element study on the knee joint in which the meniscus is modeled by using several material models, and (iv) an outlook on Bayesian inference for the identification of material parameters, and model selection and comparison. Our findings suggest that an accurate descriptions of the time-independent, time-dependent, and spatial variability of soft tissues, such as the human meniscus, are essential to correctly define and develop any modeling solution. This work is relevant to the description of the physiological biomechanics of human menisci, and paves the way to generalize this approach to different soft tissues.