Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Applied Mathematics


Dr. Mikko Karttunen


The development of multicellular organisms is accompanied by the formation of tis- sues of precise shapes, sizes and topologies. Remarkable similarities between tissue topologies, in particular proliferating epithelial topologies, in various species suggest that the mechanisms that govern the formation of tissues are conserved among species. To understand these mechanisms various models have been developed.

In this thesis, we present a novel mechanical model for cell divisions and tissue for- mation. The model accounts for cell mechanics and cell-cell adhesion. In our model, each cell is treated individually, thus the changes in cell’s shape and its local rearrange- ments occur naturally as a response to the evolving cellular environment and cell-cell interactions. We introduce the processes of cell growth and divisions and numerically simulate tissue proliferation. As tissue grows starting from few cells, we follow the dynamics of the tissue growth and cell packing topologies. The outcomes are com- pared with experimental observations in Drosophila wing growth. Our model accounts for the exponential decay of the mitotic index and reproduces commonly observed cell packing topologies in proliferating epithelia.

Next, we consider two biologically relevant division schemes, namely, division through asymmetric division plane and division by Hertwig’s rule. We study the im- pact of division planes on tissue growth and show that the division plane may affect cell packing topologies. Development of the tissue is accompanied by cellular rearrange- ments. We vary the extent of cellular rearrangements and analyse their effects on tissue topology. We find that when cells are allowed to move freely, more organized packing topologies emerge.