The thermodynamic driving force for bone growth and remodelling: a hypothesis

Abstract

The Eshelby stress (static energy momentum) tensor is derived for bone modelled as an inhomogeneous piezoelectric and piezomagnetic Cosserat (micropolar) medium. The divergence of this tensor is the configurational force felt by material gradients and defects in the medium. Just as in inhomogeneous elastic media, this force is identified with the thermodynamic force for phase transformations, in bone it is the thermodynamic cause of structural transformations, i.e. remodelling and growth. The thermodynamic approach shows that some terms of driving force are proportional to the stress, and some acting on material inhomogeneities are quadratic in the stress—the latter outweigh by far the former. Since inertial forces due to acceleration enter the energy–momentum tensor, it follows that the rate of loading matters and that both tension and compression stimulate growth, which is favoured at heterogeneities.