Modelling of oedemous limbs and venous ulcers using partial differential equations

Area of Science:

• Biomedical Engineering
• Medical Imaging
• Computational Geometry

Background:

• Oedema, or tissue swelling, commonly affects limbs and can stem from venous diseases, trauma, infection, or surgery.
• Chronic venous insufficiency and lymphatic issues cause fluid pooling in extremities, leading to swelling, skin changes, and potential ulceration.

Purpose of the Study:

• To develop and present a novel method for modeling diverse limb geometries affected by oedema and venous ulcers.
• To utilize 3D scan data for creating accurate geometric representations of affected limbs and associated wounds.

Main Methods:

• A partial differential equation (PDE) based shape modeling approach is employed.
• Boundary curves extracted from 3D scan data serve as boundary conditions for solving PDEs.
• A combination of fourth and sixth-order PDEs is used to generate representative limb and ulcer shapes.

Main Results:

• The method successfully generates accurate geometric models of limbs with oedema and venous ulcers.
• Demonstrated capability in modeling both arm and leg shapes with associated ulcers using scan-derived curves.
• Examples showcase the method's effectiveness in producing representative shapes.

Conclusions:

• PDE-based shape modeling effectively generates diverse limb and ulcer geometries from scan data.
• The technique allows for manipulation of generic limb and wound shapes for patient-specific model tuning.
• This approach offers potential for personalized treatment planning in oedema and venous ulcer cases.