Remodelling of collagen fibre transition stretch and angular distribution in soft biological tissues and cell-seeded hydrogels

The extracellular matrix in many biological tissues is adapted to its mechanical environment. In this study, a phenomenological model for collagen remodelling is introduced that incorporates angular remodelling (fibre reorientation) and the adaptation of the so-called transition stretch. This is achieved by introducing a local stress-free configuration for the collagen network by a multiplicative decomposition of the deformation gradient and the appropriate definition of the anisotropic free Helmholtz energy potentials and structure tensors. The collagen network is either treated using discrete fibre directions or a continuous angular distribution. The first part of the study illustrates the influence of force- and displacement-controlled loading on either stress- or deformation-driven remodelling processes in tissues with various degrees of fibre reinforcement. The model is then applied to recent experimental studies of collagen remodelling, specifically periosteum adaptation (Foolen et al. in J Biomech 43(16):3168-3176, 2010), collagen gel (Thomopoulos et al. in J Biomech Eng 127(5):742-750, 2005) and fibrin cruciform (Sander et al. in Ann Biomed Eng 1-16, 2010) compaction. The model is able to capture the basic effects of an adapting transition stretch over time in the periosteal simulations, as well as the compaction and the development of structural anisotropy in the collagen and fibrin gels. The model can potentially be applied to elucidate structure-function relationships, better interpret in vitro experiments involving collagen remodelling, and help investigate aspects of certain pathologies, such as connective tissue contracture.