Modelling of oedemous limbs and venous ulcers using partial differential equations
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Modelling of oedemous limbs and venous ulcers using partial differential equations Hassan Ugail*1 and Michael J Wilson2 Address: 1School of Informatics, University of Bradford, Bradford BD7 1DP, UK and 2Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK Email: Hassan Ugail* - [email protected]; Michael J Wilson - [email protected] * Corresponding author
Published: 03 August 2005 Theoretical Biology and Medical Modelling 2005, 2:28 28
Received: 11 May 2005 Accepted: 03 August 2005 doi:10.1186/1742-4682-2-
This article is available from: http://www.tbiomed.com/content/2/1/28 © 2005 Ugail and Wilson; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract Background: Oedema, commonly known as tissue swelling, occurs mainly on the leg and the arm. The condition may be associated with a range of causes such as venous diseases, trauma, infection, joint disease and orthopaedic surgery. Oedema is caused by both lymphatic and chronic venous insufficiency, which leads to pooling of blood and fluid in the extremities. This results in swelling, mild redness and scaling of the skin, all of which can culminate in ulceration. Methods: We present a method to model a wide variety of geometries of limbs affected by oedema and venous ulcers. The shape modelling is based on the PDE method where a set of boundary curves are extracted from 3D scan data and are utilised as boundary conditions to solve a PDE, which provides the geometry of an affected limb. For this work we utilise a mixture of fourth order and sixth order PDEs, the solutions of which enable us to obtain a good representative shape of the limb and associated ulcers in question. Results: A series of examples are discussed demonstrating the capability of the method to produce good representative shapes of limbs by utilising a series of curves extracted from the scan data. In particular we show how the method could be used to model the shape of an arm and a leg with an associated ulcer. Conclusion: We show how PDE based shape modelling techniques can be utilised to generate a variety of limb shapes and associated ulcers by means of a series of curves extracted from scan data. We also discuss how the method could be used to manipulate a generic shape of a limb and an associated wound so that the model could be fine-tuned for a particular patient.
1 Introduction Oedema, commonly known as tissue swelling, is associated with a range of causes such as venous disease, trauma, infection, joint disease, orthopaedic surgery and removal of the lymph nodes. Oedema and associated venous ulcers occur on mainly on the leg and the arm. It can be a painful, embarrassing and costly disorder [1,2]. It
occurs widely in the general population, especially from late mid
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