Modeling of collagenous tissues using distributed fiber orientations

Collagen is the most abundant protein in mammals and is the major component of load-bearing tissues including tendons, ligaments, cartilage, and others. The mechanical behavior of collagenous tissues depends on the relative collagen content and its organization. Fiber orientation plays a crucial role in the mechanical behavior of these tissues. Several mechanical properties such as anisotropy and Poisson’s ratio are mostly determined by fiber organization. Additionally, mechanical models that include fiber orientation distributions better predict the mechanical behavior of collagenous tissues. Dr. Lanir proposed a pioneering formulation to model the mechanics of collagenous tissues that includes fiber nonlinearity, buckling, and distributed orientations. This formulation had been used to model a variety of tissues and is considered the gold standard for the analysis of distributed fibers. The objective of this chapter is to describe the methods to analyze the mechanical behavior of tissues with fiber orientation distributions. This chapter includes methods to measure fiber orientation, a detailed description of Lanir’s formulation, simplified versions of Lanir’s approach, and applications to several collagenous tissues.