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Dari, Sonia (2025) Modelling the role of tissue inhibitors of matrix metalloproteinases as regulators of wound healing. PhD thesis, University of Nottingham.

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Abstract

Understanding the biochemistry and pharmacodynamics of chronic wounds is of key importance, due to the millions of people in the UK affected and the significant cost to the NHS. Chronic wounds are characterised by elevated concentrations of matrix metalloproteinases (MMPs) that destroy the surrounding extracellular matrix (ECM). However, fibroblasts can produce tissue inhibitors of MMPs (TIMPs) in order to regulate wound healing. The role of MMPs and TIMPs in both acute and chronic wounds has been largely under explored in the mathematical modelling literature.

This thesis develops mathematical models to investigate the interplay between MMPs and TIMPs in wound healing. We demonstrate that the models support travelling wave solutions under parameter regimes representing both acute and chronic wounds. Through bifurcation analysis, the models replicate key qualitative behaviours observed in experimental studies and provide insights with potential clinical relevance. In particular, we show that increased TIMP production enhances regulation of chronic wounds, whereas lower levels of TIMPs hinder reversal to a healed state. One of our models is extended to a more realistic two-dimensional spatial domain to explore the application of an external TIMP source as a therapeutic strategy. Asymptotic analysis is used to elucidate how key parameters influence TIMP delivery, regulatory effectiveness, and wound healing progression. Finally, we turn to experimental data on TIMP-containing hydrogels currently being developed as a treatment for chronic wounds. We formulate a mathematical model and conduct parameter estimation, revealing significant parameter non-identifiability in the current experimental setup. To address this, we design a synthetic data study to determine the experimental design required for accurate parameter inference, thereby laying the groundwork for future studies assessing the efficacy of such hydrogels in wound treatment.

Item Type:	Thesis (University of Nottingham only) (PhD)
Supervisors:	Fadai, Nabil O'Dea, Reuben
Keywords:	Metalloproteinases--Inhibitors, mathematical models, matrix metalloproteinases, tissue inhibitors of MMPs
Subjects:	Q Science > QA Mathematics Q Science > QP Physiology
Faculties/Schools:	UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID:	82850
Depositing User:	Dari, Sonia
Date Deposited:	12 Dec 2025 04:40
Last Modified:	12 Dec 2025 04:40
URI:	https://eprints.nottingham.ac.uk/id/eprint/82850

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