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A method of numerical simulation of cell division using phase fields is presented. The cell division plane is obtained as a result of the spindle position and orientation considered with the spatial distribution of the activated cortical force generators and the dividing cell shape. To exemplify the application of the proposed method, numerical simulations of the development of cysts and early embryos are performed. The numerical results demonstrate that the activated cortical force generators that are localized at the lateral cortices of the epithelial cells lead to the formation of a single central lumen. It is additionally shown that the linear distribution of the activated cortical force generators along the animal-vegetal axis of a spherical cell engenders a similar cell proliferation of the divided embryo generated by the 32 cell period in a sea cucumber.
Akiyama et al. (2018) studied this question.