Noshad Jamil, RajaAziz ur Rehman, Muhammad2012-05-292012-05-292012-05Archives Des Sciences 65 (5), 49-58 , 20121661-464Xhttps://escholar.umt.edu.pk/handle/123456789/506In this paper, we study a methodology for numerical simulation of sea urchin shapes in biological organism’s development particularly at the blastula phase, consisting of a hollow, two-layered sac of ectoderm and endoderm surrounding an archenteron that communicates with the exterior through the blastopore with the help of newly developed “PDE Methods”. The geometric modeling of the sea urchin shapes are under taken by means of surfaces generated as Partial Differential Equations (PDEs). We merge PDE based geometric modeling technique with numerical optimization in order to study the stable shapes adopted by the sea urchin during its blastula phase. Thus, by using the PDE method we produce a generic model which is then capably parameterized. Using this parameterization to set up a numerical optimization process which enables us to predict a series of sea urchin shapes at the early stage subject to given surface area and volume at that time.enTissuesSea urchinsMorphogeneticOptimizationPartial Differential EquationsSurface ModelingArticle