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    Partial Differential Equations for Modelling Wound Geometry

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    Publication date
    2009-01
    Author
    Ugail, Hassan
    Keyword
    Elliptic
    Partial differential equation
    Pressure ulcer
    Subdivision scheme
    Surface patch
    Peer-Reviewed
    Yes
    Open Access status
    closedAccess
    
    Metadata
    Show full item record
    Abstract
    Wounds arising from various conditions are painful, embarrassing and often requires treatment plans which are costly. A crucial task, during the treatment of wounds is the measurement of the size, area and volume of the wounds. This enables to provide appropriate objective means of measuring changes in the size or shape of wounds, in order to evaluate the efficiency of the available therapies in an appropriate fashion. Conventional techniques for measuring physical properties of a wound require making some form of physical contact with it. We present a method to model a wide variety of geometries of wound shapes. The shape modelling is based on formulating mathematical boundary-value problems relating to solutions of Partial Differential Equations (PDEs). In order to model a given geometric shape of the wound a series of boundary functions which correspond to the main features of the wound are selected. These boundary functions are then utilised to solve an elliptic PDE whose solution results in the geometry of the wound shape. Thus, here we show how low order elliptic PDEs, such as the Biharmonic equation subject to suitable boundary conditions can be used to model complex wound geometry. We also utilise the solution of the chosen PDE to automatically compute various physical properties of the wound such as the surface area, volume and mass. To demonstrate the methodology a series of examples are discussed demonstrating the capability of the method to produce good representative shapes of wounds.
    URI
    http://hdl.handle.net/10454/18948
    Version
    No full-text in the repository
    Citation
    Ugail H (2009) Partial Differential Equations for Modelling Wound Geometry. In: Bioengineering Research of Chronic Wounds. Studies in Mechanobiology, Tissue Engineering and Biomaterials. Vol 1: 101-125.
    Link to publisher’s version
    https://doi.org/10.1007/978-3-642-00534-3_5
    Type
    Book chapter
    Collections
    Engineering and Informatics Publications

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