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Abstract
We present here an extension of our finite element model of the Drosophila embryo to consider the interdependence of successive morphogenetic movements. A novel approach is used, which couples the Arbitrary Lagrangian Eulerian formulation with the harmonicparametrization. The combination of the two techniques allows to constantly update the deforming embryo geometry and simultaneously build an associated system of curvilinear coordinates. Thus, we are able to exactly describe the elementary cell deformations responsible for each biological event that are then defined with respect to the dynamic middle surface of the embryonic tissue and to their relative reference configuration. Both the active and the passive deformations occurring to the cells are considered through the deformation gradient decomposition. We develop a concurrent simulation of three morphogenetic movements: the ventral furrow invagination, the cephalic furrow formation and the germ band extension. The results show a consistent similarity with respect to the physical phenomena. More generally, the numerical approach that we propose could constitute a powerful tool to rigorously describe and simulate complex shape changes in biological systems.
Highlights
Biological tissues are heterogeneous materials whose constituents, and structure, are continually changing due to growth and response of the tissue to its physical and chemical environment.Multicellular organisms are fascinating in a double way
We develop a concurrent simulation of three morphogenetic movements: the ventral furrow invagination, the cephalic furrow formation and the germ band extension
In our previous paper (Allena et al, 2010a), we introduced a finite element model of it, which allowed us to simulate three individual movements occurring during the gastrulation www.ccsenet.org/mer phase of the development: the ventral furrow invagination (VFI), the cephalic furrow (CF) formation and the germ band extension (GBE)
Summary
Biological tissues are heterogeneous materials whose constituents, and structure, are continually changing due to growth and response of the tissue to its physical and chemical environment.Multicellular organisms are fascinating in a double way. During the whole process of embryogenesis, cells play a major role at both the individual and the collective levels to guarantee the perfect synchronization necessary for a successful development. An error in this process may cause serious consequences for the adult animal. A multiscale approach is very appropriate in order to better understand the series of morphogenetic movements that determine the final shape of the embryo. Each one of these biological events stands up for specific elementary deformations involving groups of cells located at different regions of the system. Cell strains that trigger later morphogenetic movements occur over a highly deformed shape created by previous movements, which causes a strong interdependence between all the events
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