The cardiovascular system consists of the heart and blood vessels such as arteries, veins, and capillaries. The blood delivers oxygen and nutrients to the tissues and carries waste products to the organs so that homeostasis is maintained. Cardiovascular tissues are fibrous composites assembled from a matrix material and embedded families of collagen fibers with orientations that are distributed spatially. The elementary building blocks of collagen are fibrils, which are assembled in a rather complex hierarchical structure. The mechanical properties of fibrils, and hence the load-bearing capacity of tissues, depend on the formation of covalent cross-links between the collagen molecules. As distinct from hard tissues, cardiovascular tissues experience large deformations, and from the biomechanics viewpoint, the modeling of these tissues fall within the realm of finite elasticity.
Imaging of cardiovascular diseases such as aneurysms and aortic dissections is a key contributor to related modeling and simulation, in particular when imaging is realized on the protein level. For example, the collagen structure (fiber direction/dispersion) changes remarkably with the state of disease. Improved microstructural modeling allows to better understand the relationship between the hierarchical tissue structure, the tissue function, and the biomechanical response of the tissue, which is typically characterized by strain energy, stress and strain. Imaging, patient-specific modeling and simulation may aid medical diagnosis, help to improve treatment plans for cardiovascular diseases and better identify the potential patient risk before treatment takes place. Most approaches to the modeling of cardiovascular tissues, however, are still in the development stage.
In this lecture we analyze the image-based collagen structure obtained from cardiovascular tissues in health and disease using high-resolution optical microscopy. Continuum mechanics is then used to describe the microstructure of collagen fibers, in particular the spatial variation of the fibers, and to derive material laws based upon imaging and mechanical data. Finite-element simulations are presented that highlight the need to incorporate the complex tissue microarchitecture. Finally, perspectives in imaging and trends in modeling and simulation are provided .
 G.A. Holzapfel and R.W. Ogden (Eds.), Biomechanics: Trends in Modeling and Simulation. Springer, 2017