On the Microstructural Modeling of Vascular Tissues

Abstract

Accurate determination of the biomechanical implications of vascular surgeries or pathologies on patients requires developing patient-specific models of the organ or vessel under consideration. In this regard, combining the development of advanced constitutive laws that mimic the behaviour of the vascular tissue with advanced computer analysis provides a powerful tool for modelling vascular tissues on a patient-specific basis. Collagen is the most abundant protein in mammals and provides soft biological tissue, like the vasculature, with mechanical strength, stiffness and toughness. In several tissues there is a strong alignment of the collagen fibres with little dispersion in their orientation, but in other cases, such as the artery wall, there is significant dispersion in the orientation, which has a significant influence on the mechanical response. Proposed structure-based models was used by taking into account the spatial dispersion or waviness of collagen fiber directions. Vascular tissues exhibits simultaneously elastic and viscous material response. The rate-dependent material behavior of this kind of materials has been well-documented and quantified in the literature. Furthermore, non-physiological loads drive soft tissue to damage that may induce a strong reduction of the stiffness. In this chapter, we have provided a critical review of the fundamental aspects in modeling this kind of the materials. The application of these constitutive relationships in the context of vascular system has been presented.