“Elastic Growth in Biology”

ABSTRACT
Growth plays an important function in many fundamental biological pro­cesses including morphogenesis, homeostasis, and pathological disorders. The growth of tissues such as arteries, bones, tumors, or plant stems is partly con­ditioned by their mechanical environment. As a tissue grows, it is not only affected by outside stresses but it also introduces stress itself. These stresses which develop through growth play an important role in the evolution and regulation of growth, both in physiological and pathological conditions.

Because soft tissues undergo large elastic deformations in response to physiological loading, their physical properties are best described within the theory of finite elasticity. We have developed a general formulation of growth for a three­dimensional nonlinear elastic body and applied it to specific ge­ometries relevant in many physiological and biological systems (such as the cylindrical growth of arteries and stems). This modelling approach helps us understand the fundamental interaction between mechanical stresses and growth processes and the time evolution it generates. In particular, in the case of homogeneous growth we can obtain a general form of the time evolu­tion leading to a dynamical systems coupling the growth and stresses. The solution to this system predicts the evolution of stresses, growth, and strains. Applying this formulation to simple examples can help us develop new in­sights into growth processes.