Finite element simulations of the active stress in the imaginal disc of the Drosophila Melanogaster

During the larval stages of development, the imaginal disc of Drosphila Melanogaster is composed by a monolayer of epithelial cells, which undergo a strain actively produced by the cells themselves. The well-organized collective contraction produces a stress field that seemingly has a double morphogenetic role: it orchestrates the cellular organization towards the macroscopic shape emergence while simultaneously providing a local information on the organ size. Here we perform numerical simulations of such a mechanical control on morphogenesis at a continuum level, using a three-dimensional finite model that accounts for the active cell contraction. The numerical model is able to reproduce the (few) known qualitative characteristics of the tensional patterns within the imaginal disc of the fruit fly. The computed stress components slightly deviate from planarity, thus confirming the previous theoretical assumptions of a nonlinear elastic analytical model, and enforcing the hypothesis that the spatial variation of the mechanical stress may act as a size regulating signal that locally scales with the global dimension of the domain.