Pattern Formation by Lateral Inhibition in Physiological and Tumour Angiogenesis

Smith, Holly (2020) Pattern Formation by Lateral Inhibition in Physiological and Tumour Angiogenesis. PhD thesis, University of Nottingham.

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The sprouting of new blood vessels from existing blood vessels, called angiogenesis, plays a vital role in many biological processes, including tumour growth. Angiogenesis is initiated by angiogenic signals sent to the endothelial cells of an existing blood vessel. However, to prevent migration of all the cells along the blood vessel wall, a type of cell signalling called Notch signalling causes so-called lateral inhibition between neighbouring cells, where cells activated for migration inhibit their neighbour cells from adopting the same fate. Lateral inhibition has been represented in previous models of angiogenesis using discrete agents, which have limitations such as presuming a fixed cell size for all endothelial cells and forcing selected cells to migrate immediately.

This thesis aims to develop a continuous model of lateral inhibition that is not limited with respect to cell sizes and locations, and to couple this new continuous model to a model of angiogenesis. This is achieved by developing continuous models of lateral inhibition from existing discrete models, where the lateral inhibition is represented with a nonlocal term. The continuous model can be thought of as an average representation of variables from an irregular distribution of cells. The results of the model were comparable to those of the previous discrete models. The model is then extended to a surface to allow the model to be able to simulate the cell signalling along a capillary surface.

The surface continuous model of lateral inhibition is then combined with a model of angiogenesis to obtain an almost fully continuous coupled lateral inhibition-angiogenesis model. Numerical simulations show results which closely resemble blood vessel formation in angiogenesis, where cell migration is not forced. Results are presented that are relevant to both physiological and tumour angiogenesis. The coupled model could be used in the future to investigate further implications of angiogenesis, such as the effect it has on tumour growth and tumour drug delivery, and even the effect of antiangiogenic therapies on the growth of a tumour.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Matthews, P
Van der Zee, K
Owen, M
Keywords: biomathematics, angiogenesis, cancer cells
Subjects: Q Science > QA Mathematics > QA299 Analysis
Q Science > QH Natural history. Biology > QH301 Biology (General)
R Medicine > RC Internal medicine > RC 254 Neoplasms. Tumors. Oncology (including Cancer)
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 60269
Depositing User: Smith, Holly
Date Deposited: 24 Oct 2023 13:27
Last Modified: 24 Oct 2023 13:27

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