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For an animal cell, cytokinesis is the process by which a cell divides its cytoplasm to produce two daughter cells. We propose a new mathematical model for simulating cytokinesis. The proposed model is robust and realistic in deciding the position of the cleavage furrow and in defining the contractile force leading to cell division. We use an immersed boundary method to track the morphology of cell membrane during cytokinesis. For accurate calculation, we adaptively add and delete the immersed boundary points. We perform numerical simulations on the axisymmetric domain to have sufficient resolution and to incorporate three-dimensional effects such as anisotropic surface tension. Finally, we investigate the effects of each model parameter and compare a numerical result with the experimental data to demonstrate the efficiency and accuracy of our proposed method.

A scaffold is a three-dimensional matrix that provides a structural base to fill tissue lesion and provides cells with a suitable environment for proliferation and differentiation. Cell-seeded scaffolds can be implanted immediately or be cultured in vitro for a period of time before implantation. To obtain uniform cell growth throughout the entire volume of the scaffolds, an optimal strategy on cell seeding into scaffolds is important. We propose an efficient and accurate numerical scheme for a mathematical model to predict the growth and distribution of cells in scaffolds. The proposed numerical algorithm is a hybrid method which uses both finite difference approximations and analytic closed-form solutions. The effects of each parameter in the mathematical model are numerically investigated. Moreover, we propose an optimization algorithm which finds the best set of model parameters that minimize a discrete l(2) error between numerical and experimental data. Using the mathematical model and its efficient and accurate numerical simulations, we could interpret experimental results and identify dominating mechanisms.