### Theoretical pressures and in vivo pressures: practical consequences of Laplace's law

#### Laplace's law: theoretical pressures

The localised **static pressure** exerted on the leg by a compression system can be calculated overall using Laplace’s law:

The LaPlace equation was originally described in 1805 to define the relationship between the pressure of a closed elastic membrane and the tension within the membrane.

La Place's law states that sub-bandage pressure (P) is directly proportional to bandage tension (T) and inversely proportional to the circumference (C) of the limb to which it is applied. Ie: As the circumference of the limb increases, the pressure decreases. It is also important to consider the number of bandage layers applied (N) and the width of the bandage (W)

P is the interface pressure (in mmHg or hPa)

T/W is the tension (N) by width unit

R is the radius of the leg (m)

α is the proportionality coefficient

In practice, the radius of the leg cannot be easily measured, so the circumference is used instead. In addition, it is necessary to take into account the bandage application method. The pressure is expressed in mmHg; which gives the final equation:

P = the interface pressure under the bandage (in mmHg), also called the compression force

T = the tension of the bandage (Kgf), which depends on the material and its stretch %

N = the number of layers (defined by the level of overlap and the number of bandages)

C = the circumference at the measurement point (cm)

W = the bandage width (cm)

P is the localised static pressure exerted at a given point by the compression material. This localised static pressure depends on:

- the intrinsic technical characteristics of the bandage
- the bandage application method
- the patient (circumference at the measurement point i.e. ankle, at time t)

#### Relationship between Laplace's law and in vivo pressures

It is necessary to know the influence of these parameters and, above all, to understand the consequences in terms of pressure variation:

A variation in the different parameters of Laplace’s law therefore modifies the compression force applied to the patient’s leg and incorrect application of width, tension and overlap could cause a detrimental effect and potentially significant damage.

Laplace’s law therefore demonstrates the importance:

- for manufacturers, to provide a clear, accurate and precise application method for their bandages or compression systems
- for clinicians, to ensure they have received adequate training and thoroughly understood and fully mastered the application methods and techniques,

The objective being to reduce operator error as much as possible, thereby limiting the risks of insufficient or excessive pressure, which can sometimes have serious consequences.

** Important: Since Laplace’s law theoretically assesses a localised static pressure, it is important not to forget the influence of patient mobility on dynamic pressures (see chapter on compressive effects depending on bandage type). **

#### Anatomical realities of patients

**Decreasing ****pressure gradient from the foot to the thigh**

In the absence of any compression, there is a natural haemostatic gradient in the lower limb, which decreases from the foot to the thigh. It is extremely important to respect this gradient when applying compression.

In a lower limb with a normal morphology (in the shape of a truncated cone), the decreasing pressure gradient is obtained naturally due to the gradual increase in leg diameter from the ankle to the knee or thigh.

According to Laplace’s law, in the absence of variations in the other factors, if the circumference of the leg increases, there is an inversely proportional decrease in pressure. In other words, under compression, the decreasing pressure gradient is guaranteed by a normal leg morphology.

**Sensitive locations and atypical morphologies**

According to Laplace’s law, on bony prominences, such as the achilles tendon or pre-tibial (shin) bone, the pressures exerted will be greater than those on flat or hollow zones, such as the area behind the malleolus, since the radius of these prominent areas is much smaller than that of the limb.

To ensure safe and effective compression, it is necessary to restore an even conical shape to the leg, filling in hollows and rounding off prominent or bony areas using pads, wadding bandages or foam.

This action is essential to prevent areas of excessive pressure that could potentially cause local tissue ischaemia and necrosis.

Less commonly, some patients who need to wear a compression system may present atypical leg shapes: column-shaped legs, very wasted muscles in a particular area of the leg, etc. This mostly concerns elderly, malnourished patients presenting with an ulcer and/or severe trophic changes.

It is therefore necessary to restore a normal leg shape in these patients before applying the compression system in order to ensure an even pressure which respects the decreasing pressure gradient from foot to knee or thigh.