The research described in this thesis began with a single long-term objective: modelling of the vertebral artery during chiropractic manipulation of the cervical spine. Although chiropractic treatment has become prevalent, the possible correlation between neck manipulation and subsequent stroke in patients has been the subject of debate without resolution. Past research has been qualitative or statistical, whereas resolution demands a fundamental understanding of the associated mechanics.<p>
Analysis in the thesis begins with a study of the anatomy and properties pertinent to the chiropractic problem. This indicates that the complexity of the problem will necessitate a long-term multidisciplinary effort including a nonlinear finite element formulation effective in analysing image data for soft tissue modelled as nearly incompressible. This leads to an assessment of existing finite element methods and the conclusion that new equation solving techniques are needed to ensure numerical stability.<p>
Three techniques for effectively eliminating the source of numerical instability are developed and demonstrated with the aid of original finite element codes. Two of the methods are derived as modifications of matrix decomposition algorithms, while the third method constitutes a new finite element formulation. In addition, the understanding gained in developing these methods is used to produce a theorem for assessing a different but related problem: deformation of a nearly incompressible material subjected to a single concentrated force. Throughout the thesis, an interdisciplinary path from chiropractic problem to numerical algorithms is outlined, and results are in the form of mathematical proofs and derivations of both existing and new methods.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:SSU.etd-09182009-142812 |
| Date | 21 September 2009 |
| Creators | Coley, Lisa M. |
| Contributors | Sumner, D., Sharma, J., Dolovich, A., Bugg, J., Zhang, C., Schwab, A. |
| Publisher | University of Saskatchewan |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://library.usask.ca/theses/available/etd-09182009-142812/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Saskatchewan or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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