URGO MEDICAL

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:

• influence of limb circumference: independently of other factors, the more this increases, the more the pressure decreases. It is therefore essential to take into account this parameter and hence individual and inter-individual variations; (read more...)
  

The limb circumference at the measurement point is a very important parameter when determining the pressure level that is being delivered and has a major impact on how effective compression therapy is.

The greater the limb circumference, the lower the bandage interface pressure, for a given bandage, with an unchanged tension and application method (i.e. 50% stretch, 50% overlap).

Measurements are mainly taken at the ankle (at point B1 at the base of the calf muscle, i.e. 10-15 cm above the base of the heel)

Theoretical example :

i.e. a standard 10 cm bandage applied to a patient with an ankle circumference of 18 cm using a figure of 8 application method with a constant tension will provide a high compression pressure level in the region of 40 mmHg on average.

 

 

If the same clinician applies the same bandage with the same tension and application method to a person with an ankle circumference of 25 cm, the pressure delivered will be much lower (on average, in the region of 28 mmHg), i.e. a moderate pressure inadequate in the treatment of a venous leg ulcer, for example.

 

Conversely, if the same bandage with the same tension and the same application method is applied to a person with an ankle circumference of 14 cm, the pressure exerted by the bandage on the ankle will be higher (theoretically more than 50 mmHg) with a potential risk of causing irreversible damage to the limb (necrosis).

Once a diagnosis has been made and the most appropriate compression therapy and system has been chosen (mild, moderate or strong compression), it is essential to follow the instructions given by the manufacturer for applying it (method and bandage tension). It is also important to measure the patient’s ankle size carefully. The consequences may be serious in the event of significantly under or over-applying the amount of compression (risks are generally encountered more frequently with elastic systems, particularly in the case of very high compression, due to the resting therapeutic pressure being similar to the working pressure).

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• influence of bandage tension: the more a bandage is stretched, the more the pressure applied to the leg will increase; (read more...)
  

The bandage tension does not just depend on the bandage and its extensibility; it is also determined by the application and the amount of stretch applied which is operator-dependent.

For a given bandage, the higher the stretch percentage, the higher the interface pressure.

This parameter is particularly important for application of a long-stretch bandage. It is generally recommended that this type of bandage be applied with a 50% stretch. (Without any visual markers, the real stretch obtained on application by qualified personnel can vary from 35% to 70%, leading to a risk of under or over-application of pressure).

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• variation in number of layers: a bandage applied using the figure of 8 method with a 50% overlap will apply the equivalent of 4 layers whereas a bandage applied using the spiral method with a 50% overlap will apply the equivalent of 2 layers, i.e. a pressure that is twice as high in the former case, all other parameters being equal; (read more...)
  

The number of layers is also very important, since, theoretically, doubling the number of layers doubles the level of pressure applied.
The number of layers is linked to 2 factors: the number of bandages superimposed but also the application method.

The two most widely used bandage application methods are "spiral" and "figure of 8" with the overlap ranging from 50% to 75%.

For a spiral bandage :

• an overlap of 50% means that the leg is covered with 2 layers,
• an overlap of 2/3 means that the leg is covered with 3 layers,
• an overlap of 75% means that the leg is covered with 4 layers.

For a figure of 8 bandage, with an overlap of 50%, the leg is covered with 4 layers. This method, which is more complex than the spiral method, requires training and practice.

In conclusion, it is extremely important to comply exactly with the application method indicated by the manufacturer and with the recommended technique and overlap, to ensure the correct pressure is applied.

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• influence of bandage width: In theory, a bandage with a width of 8 cm will apply a slightly higher pressure than a bandage with a width of 12 cm, all other parameters being equal. (read more...)
  

The last parameter that plays a role in the theory of Laplace’s law is the bandage width.
This factor can have a moderate influence on pressure.

A variation in this factor can be used to increase or restore the decreasing pressure gradient from the ankle to the knee (or thigh): in this case, 8 cm wide bandages can be used on the foot and ankle, 10 cm for the calf and knee and, if necessary, 12 cm bandages for the thigh.

The use of bandages with several different widths is mainly recommended for column-shaped legs or lymphoedema, when there is little difference between the circumference of the ankle, calf and even the thigh. This ensures the maintainance of the decreasing pressure gradient from the distal to the proximal part of the limb.

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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.