Al-Badri, Georgina;
(2022)
A mathematical model of vascular network formation in a hydrogel.
Doctoral thesis (Ph.D), UCL (University College London).
Preview |
Text
GAB_thesis_final_copy.pdf - Accepted Version Download (21MB) | Preview |
Abstract
In this thesis, a multiphase model framework is adopted to simulate chemotaxis-driven formation of vascular-like structures within a hydrogel. Mathematical modelling is a powerful tool to probe the underlying mechanisms of such pattern formation, and inform optimisation of experimental variables for problems in tissue engineering, reducing experimental time and cost. Based on a balance of chemical and mechanical cues, vascular structures are formed by endothelial cells in vitro under favourable experimental conditions within a few days of culture. Options for mechanisms for inclusion in the model are based on a range of experimental assays described in literature, and the successes and limitations of previous mathematical models of vasculogenesis. A model selection process is first carried out on a 1D version of the multiphase model to inform the minimum number of model components required for chemotaxis-driven pattern formation. Subsequently, biologically relevant outcome metrics relating to pattern spacing and stability are considered for in vitro validation of the resulting 2D model simulations. The model equations are solved numerically by discretising each partial different equation (PDE) using the finite difference method. Each model variable is then solved for as a matrix problem in an algorithmic approach implemented in Python. Model analysis is conducted on a mixture of 1D Cartesian and 2D axisymmetric geometries using computational techniques including sensitivity analysis and parameter optimisation. Based on an experimental geometry of a hydrogel in a well-plate, oxygen concentration is introduced by expanding the model geometry to a two-layer domain of hydrogel and culture media. Oxygen-dependent mechanisms are informed based on a mixture of qualitative and quantitative data, including from a tailored in vitro experimental set designed to measure local oxygen concentration and VEGF mRNA levels of the endothelial cells for the purpose of this work. Overall, a parameterised multiphase model of vascular network formation is presented to inform experimental variables during fabrication of vascularised engineered tissues, including initial cell density, and ambient oxygen concentration.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | A mathematical model of vascular network formation in a hydrogel |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| Keywords: | Multiphase, PDE, vasculogenesis, computational, Python, modelling |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10160126 |
Archive Staff Only
 |
View Item |
