dc.contributor.author Ugail, Hassan dc.date.accessioned 2022-03-20T06:29:58Z dc.date.accessioned 2022-04-29T06:56:01Z dc.date.available 2022-03-20T06:29:58Z dc.date.available 2022-04-29T06:56:01Z dc.date.issued 2009-01 dc.identifier.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. en_US dc.identifier.uri http://hdl.handle.net/10454/18948 dc.description No en_US dc.description.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. en_US dc.language.iso en en_US dc.subject Elliptic en_US dc.subject Partial differential equation en_US dc.subject Pressure ulcer en_US dc.subject Subdivision scheme en_US dc.subject Surface patch en_US dc.title Partial Differential Equations for Modelling Wound Geometry en_US dc.status.refereed Yes en_US dc.type Book chapter en_US dc.type.version No full-text in the repository en_US dc.identifier.doi https://doi.org/10.1007/978-3-642-00534-3_5 dc.rights.license Unspecified en_US dc.date.updated 2022-03-20T06:29:59Z dc.openaccess.status closedAccess en_US
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