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      Stable finite element algorithms for analysing the vertebral artery

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      ColeyPhDThesis.pdf (2.124Mb)
      Date
      2009-09
      Author
      Coley, Lisa M.
      Type
      Thesis
      Degree Level
      Doctoral
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      Abstract
      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. 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. 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.
      Degree
      Doctor of Philosophy (Ph.D.)
      Department
      Mechanical Engineering
      Program
      Mechanical Engineering
      Supervisor
      Dolovich, A.
      Committee
      Sumner, D.; Sharma, J.; Bugg, J.; Zhang, C.; Schwab, A.
      Copyright Date
      September 2009
      URI
      http://hdl.handle.net/10388/etd-09182009-142812
      Subject
      finite element
      incompressibility
      mixed formulations
      soft tissue
      vertebral artery
      numerical instability
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