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Title: Mathematical modelling of embryonic tissue development
Author: Abdullah, A. R.
ISNI:       0000 0004 7659 0422
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2018
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Computational mathematics plays a significant role in the analysis and understanding of the outcomes of biological observations. Modelling cells and tissues is a current topic in mathematical biology. In this work, various mathematical tools including the vertex dynamics model that is implemented, for simulations, by the open software, Chaste, were used to investigate cellular dynamics in epithelial tissues. The results can be split into three parts: 1. Using the vertex dynamics model, mechanical properties of epithelial cells were studied by exposing them to stretching and contraction. The outcomes of numerical simulations, as well as of analytical studies, indicate that the vertex dynamics model confirms the elastic properties of cells. 2. Using the vertex dynamics model as well as analytical tools, topological features of epithelial tissue in the case of cell divisions, namely the distribution of cells according to the number of their edges, were studied. It was found that the histograms obtained via this model reproduced the experimental observations fairly well. Moreover, an analytical model of growing tissue which explained and reproduced topological features of epithelial tissues was developed. Also, a cellular automata model was developed that also confirmed the universal nature of epithelial tissue topology. 3. The vertex dynamics model was modified in a way that it reproduced dynamical changes in the cell shapes observed in the epithelial tissues. The model provided an explanation of patterns of cell migration and cell shape changes observed in experiments. Using this modification to investigate the impact of cellular dynamics, namely the rearrangement of cells and particularly the T1-transition (i.e. switching process of connected edge with their neighbours) processes, on tissue topology, it was found that the histograms of cell-edge distribution (CED) are approximately identical to that formed by proliferating cells.
Supervisor: Vasiev, Bakhti Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral