A deformation gradient decomposition method for the analysis of the mechanics of morphogenesis.

A new finite element model is proposed for the analysis of the mechanical aspects of morphogenesis and tested on the biologically well studied gastrulation phenomenon, in particular ventral furrow invagination of the Drosophila melanogaster embryo. A set of mechanisms are introduced in the numerical model, which lead to the observed deformed shapes. We split the total deformation into two parts: an imposed active deformation, and an elastic deformation superimposed onto the latter. The active deformation simulates the effects of apical constriction and apico-basal elongation. These mechanisms are associated with known gene expressions and so in this way we attempt to bridge the well explored signalling pathways, and their associated phenotypes in a mechanical model. While the former have been studied in depth, much less can be said about the forces they produce and the mechanisms involved. From the numerical results, we are able to test different plausible mechanical hypotheses that generate the necessary folding observed in the invagination process. In particular, we conclude that only certain ratios between both modes (apical constriction and apico-basal elongation) can successfully reproduce the invagination process. The model also supports the idea that this invagination requires the contribution of several mechanisms, and that their redundancy provides the necessary robustness.