Anisotropic Growth in the presence of Noise and Mechanical Feedback in Elastic Tissues

Growth processes in biology are generally anisotropic and noisy. In elastic tissues, growth inhomogeneities induced by noise generate mechanical stresses. The mechanical stresses feed into the growth process and regulate it such that consequent growth relieves these stresses. How do closed curves, or clone boundaries, in the tissue evolve under such feedback controlled noisy growth? How does anisotropy in the background growth reflect in these shapes? We model a growing elastic tissue in two dimensions using continuum mechanics, and study the effects of noise and mechanical feedback on a background of exponential anisotropic growth. We examine some subtleties associated with setting up a perturbative treatment for noise that arise from anisotropy of the background growth, and discuss the implications of growth anisotropy on the evolution of clone boundaries.