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The thesis is about an application of the shape optimization to themorphological evolution of Golgi stack. Golgi stack consists of multiple layersof cisternae. It is an organelle in the biological cells. Inspired by theHelfrich Model \cite{Helfrich}, which is a model for vesicles typically appliedto biological cells, a new model specially designed for Golgi stack isdeveloped and then implemented using FEM in this thesis.  In the Golgi model, each cisternae of the Golgi stack is viewed as a closedvesicle without topological changes, and our model is adaptable to bothsingle-vesicle case and multiple-vesicle case. The main idea of the math modelis to minimize the elastic energy(bending energy) of the vesicles, with someconstraints designed regarding the biological properties of Golgi stack. Withthese constraints attached to the math model, we could extend this model to anobstacle-type problem. Hence, in the thesis, not only the simulations of Golgistack are shown, but some interesting examples without biological meanings arealso demonstrated. Also, as multiple cisternaes are considered as a whole, thisis also a model handling multiple objects.  A set of numerical examples is shown to compare with the observed shape ofGolgi stack, so we can lay down some possible explanations to the morphologicalperformance of trans-Golgi cisternae.

Parametric FEM for Shape Optimization applied to Golgi Stack