By Yves Lherry In On February 23, 2015
Level set models of interface evolution in animal morphogenesis
Abstract: We aim in this context at exploring level set methods for modelling and simulate tissue interface shape changes and apply our strategies to the early embryogenesis of chosen animal model organisms.
While finite elements methods have been largely used in numerical simulations of animal morphogenesis, these methods do not perform well in the case of large deformations and topology changes. Level set methods allow to represent interface evolution of a mathematical theory and with an accurate and stable numerical implementation.
This project is organized along the 3 years of the PhD thesis work:
1) Definition of a level set equation for the evolution of interfaces with locally defined mechanical properties: viscoelastic forces, plastic deformation, incompressibility constraint, filopodia, surface propagation of cell signalling (mechanical, electric…).
2) Definition of an accurate and stable numerical approximation of the main equation with finite differences or finite volume schemes.
3) Simulation based on the main level set equation of Sea urchin gastrulation including invagination, convergence extension, filopodia mediated traction, topology change. The same strategy might be applied to Tunicate and Amphioxus with the aim of defining similarities-differences.
4) Model validation will be achieved with the qualitative and quantitative comparison of simulated events with the specimens reconstructed from 3D+time in vivo data. Computation of the Haussdorf distance between data-model.
Keywords: level set methods, embryogenetical process, morphogenesis, gastrulation, sea urchin