From cross-linked collagen molecules to arterial tissue: a nano-micro-macroscale elastic model

In this paper the influence of cross-links between collagen molecules on the elastic mechanical behaviour of biological collagen microstructures (namely fibrils and fibers) and soft tissues, such as arterial walls, is analyzed. A novel multiscale mechanical model is proposed, accounting for nanoscale mechanisms related to molecular and cross-link stretching, as well as for micro- and macroscale effects, by employing homogenization techniques. The model, based on few measurable histological parameters, is able to successfully reproduce well-established experimental evidences and atomistic modelling results, showing that stiffness of collagen fibrils is related to cross-link density and mechanical properties. In the case of aortic walls, dealt with multi-layered fiber-reinforced structures, the model allows to account for histological alterations occurring with age, fully reproducing available experimental results. Proposed evidences give also a clear mechanical interpretation of the influence of cross-link density and stiffness on arterial tissue elastic modulus and arterial compliance.