Applied Mathematics and Mathematical Physics Seminar: Jean-Francois Ganghoffer

The surface growth of biological tissues is presently analyzed at the continuum scale of tissue elements, adopting the framework of the thermodynamics of surfaces and in line with Eshelbian mechanics. From a kinematic viewpoint, growth is assumed to occur in a moving referential configuration, considered as an open evolving domain exchanging mass, work, and energy with its environment. The growing surface is endowed with a superficial excess concentration of moles, which is ruled by an appropriate kinetic equation. The material surface forces for growth are evaluated versus a surface Eshelby stress, the curvature tensor of the growing surface, the gradient of the chemical energy of nutrients and the applied superficial force field. A system of coupled field equations is written for the superficial density of minerals, their concentration and the surface velocity of the growing surface. Application of the developed formalism to bone external remodeling highlights the interplay between transport phenomena and generation of surface mechanical forces. The model is able to describe both bone growth and resorption, according to the respective magnitude of the chemical and mechanical contributions to the material surface driving force for growth.