Modelling oedemous limbs and venous ulcers using partial differential equations

Description

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.

Links & Downloads

1. Ugail H and Wilson MJ (2005) Modelling oedemous limbs and venous ulcers using partial differential equations. Theoretical Biology and Medical Modelling. 2(28).
2. http://hdl.handle.net/10454/541
3. https://doi.org/10.1186/1742-4682-2-28

Tags

Oedemus limbs

Venous ulcers

Partial differential equations

Modelling

Additional Fields

Identifer	oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/541
Date	January 2005
Creators	Ugail, Hassan, Wilson, M.J.
Source Sets	Bradford Scholars
Language	English
Detected Language	English
Type	Article
Rights	© 2005 Ugail and Wilson. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://www.creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.