Biological remodelling: Stationary energy, configurational change, internal variables and dissipation

Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical setting. While some examples of remodelling are conveniently modelled as evolution of the reference configuration—Case I—others are more suited to an internal variable description—Case II. In this paper, we explore the applicability of stationary energy states to remodelled systems. A variational treatment is introduced by assuming that stationary energy states are attained by changes in microstructure via one of the two mechanisms—Cases I and II. The configurational change of a long-chain molecule is presented as an example of Case I, and collagen fibre reorientation in in vitro tissue constructs as an example of Case II. The second example is further studied for its thermodynamic dissipation characteristics. This leads to an important finding on the limitation of purely mechanical treatments of some types of remodelling phenomena.