Mathematical modeling to predict the sub-bandage pressure on a conical limb for multi-layer bandaging

The effectiveness of the compression treatment by a medical compression bandage is dependent on the pressure generated at the interface between the bandage and the skin. This pressure is called interface pressure or sub-bandage pressure. The performance of a bandage depends upon the level of interface pressure applied by the bandage and the sustenance of this pressure over time. The interface pressure exerted by the bandage depends on several other factors like limb shape or size, application technique, physical and structural properties of the bandage, physical activities taken by the patient, etc. The current understanding of how bandages apply pressure to a limb is based on the Law of Laplace, which states that tension in the walls of a container is dependent on both the pressure of the container's content and its radius. This concept was translated mathematically into equation relating pressure to tension and radius by Thomas. In addition, a modified equation was generated by multiplying the model with a constant that represents the number of bandage layers in order to use the model to estimate the pressure applied by multi-layer bandages. This simple multiplication adjustment was questioned by researchers. They had doubts about the model validity and whether it can be used to predict the sub-bandage pressure applied by pressure garments. One of the questions that were raised regarding the bandage thickness affecting the sub-bandage pressure has been recently explored by Al Khaburi where he used the thin and thick cylinder shell theory to study the effect of Multi Component Bandage's (MCB) thickness on the sub-bandage pressure. The model by Al Khaburi and the earlier models developed for pressure prediction are all based on calculations considering the cylindrical limb shapes although the human limb normally is wider at the calf and reduces in circumference towards the ankle. So in our approach, the bandage is assumed to take a conical shape during application and membrane shell theory is used for developing pressure prediction model for multi-layers of bandage. Both analytical and experimental work showed that the effect of bandage thickness and the geometry of the limb on pressure produced by multi-layers of bandage are significant. The model developed when compared to the data obtained using experimental setup confirmed the validity of the mathematical model for multi-layers of bandage based on conical geometry of the limb.