Wound healing is governed by a complex cascade of related processes, involving cells, extracellular matrix and cytokines. In adults this always results in a scar whilst embryonic wound healing is scarless and extensive research worldwide is aimed at reducing scarring in adults. A mathematical framework for problems in dermal wound healing is developed that incorporates models of the individual processes involved. Cells are modelled as discrete individuals. Cytokines and other biologically active factors are modelled as continua. A novel tensorial approach is taken to modelling the extracellular matrix. The numeric and computational challenges associated with combining models for the individual processes are identified and investigated. These include the development of data structures and numeric methods for the continuous and discrete species. Effective visualisation methods for the large amounts of data generated by the model are also discussed. The possibilities offered by high performance computing in mathematical biology are highlighted in this work. The final part of this thesis gives an example of a combined model of the inflammatory and proliferative phases of dermal wound healing using the new computational framework. Both quantitative and qualitative methods are used to analyse the information-rich data sets generated by the model, offering insight into the dynamic systems that can be modelled using the new approach.
| Identifer | oai:union.ndltd.org:ADTP/265292 |
| Date | January 2006 |
| Creators | Cumming, Benjamin Donald |
| Publisher | Queensland University of Technology |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
| Rights | Copyright Benjamin Donald Cumming |
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