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Jepson, Jacob (2023) Multiphase Modelling of Engineered Tissue and Tumour Growth. PhD thesis, University of Nottingham.

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Abstract

In this thesis, we develop and analyse two multiphase, moving boundary models representing the evolution of biological tissue. The first model considers a description of engineered tissue growth, whereas the second describes solid tumour growth. The objective of this work is to characterise the effects of tissue mechanics, cell growth and nutrient limitation on various tissue structures. Additionally, we aim to derive novel mathematical results that can be applied to a wider class of mathematical models.

In the first part of this thesis, we derive a multiphase model representing the development of tissue in vitro in a porous scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy’s law to relate the velocity of the cell and liquid phases with their respective pressures. We reduce the model to a nonlinear reaction—diffusion equation for the cell phase, coupled to a moving boundary condition for the tissue edge. Numerical simulations reveal that the reduced model admits various regimes for the evolution of the tissue. Employing travelling-wave and asymptotic analysis, we characterise these regimes in terms of parameters related to cellular growth and motion.

The second part of this thesis provides some novel numerical and asymptotic analyses of the multiphase tumour growth model developed in Byrne et al. (2002). We first employ the model of Byrne et al. (2002) to investigate the initial development of a suspension of nutrient-rich in vitro tumour cells. Numerical simulations indicate that both travelling-wave and patterned solutions can be obtained, the latter corresponding to multiple regions of high cell density separated by regions of low cell density. A stability analysis of these travelling-wave solutions provides us with criteria for the occurrence of patterned solutions. After this, the model of Byrne et al. (2002) is revisited, and is employed to investigate the effects of nutrient limitation and tissue mechanics on a solid tumour in the avascular stage of growth.

Item Type:	Thesis (University of Nottingham only) (PhD)
Supervisors:	O'Dea, Reuben Fadai, Nabil Billingham, John
Keywords:	tissue mechanics, multiphase modelling, tissue growth, tumour growth
Subjects:	Q Science > QA Mathematics > QA801 Analytic mechanics Q Science > QH Natural history. Biology > QH301 Biology (General)
Faculties/Schools:	UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID:	76626
Depositing User:	Jepson, Jacob
Date Deposited:	24 Nov 2025 08:48
Last Modified:	24 Nov 2025 08:48
URI:	https://eprints.nottingham.ac.uk/id/eprint/76626

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