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### Elastic Compression Bandage LaPlace's Law

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Pressure Applied to Leg by Elastic Compression Bandage LaPlace's Law

LaPlace's law states that within a tubular structure the change in pressure required to cause distension is proportional to the surface wall tension and inversely proportional to its radius. In other words, a structure with a larger radius and low surface tension requires minimal change in pressure to cause further dilatation however one with a smaller radius and high surface tension requires a significant amount of pressure.

According to Laplace's law medical sub-bandage pressure is directly proportional to bandage tension, but inversely proportional to the radius of curvature of the limb to which it is applied threfore. the theoretical relationship between the tension, T, of the bandage (force needed to stretch the bandage, which is given by the bandage mechanical properties and the applied stretch), the local curvature, r_{c}, of the limb and the locally applied pressure, P, is
given by the Laplace’s Law.

Eq. 1

Laplace's Law for a Cylinder

*P = T / r _{c}*

where

T = Tension of elastic ( lbf/in, N/mm )

r_{c} = local curvature

The Laplace equation used to predict sub-bandage pressure is derived from a formula described independently by Thomas Young (1773-1829) and by Pierre Simon de Laplace (1749-1827) in 1805. This defines the relationship between the pressure gradient across a closed elastic membrane or liquid film sphere and the tension in the membrane or film. a more rigourous formuls is:

Eq. 2

For spheres

*P _{α} - P_{β} = 2 γ / r *

Eq. 2a

For spheres

γ = ( P_{α} - P_{β} ) r / 2

where

*P _{α}* = pressure internal

*P*= Pressure external

_{β}*γ*= tension in elastic bandage or film

*r*= radius of curvature

Eq. 3

For cylinders

*P _{α} - P_{β} = γ / r*

*Eq. 3a
For cylinders
γ = ( P*

_{α}- P

_{β}) r

The equation indicates that the pressure inside a spherical surface is always greater than the pressure outside, but that the difference decreases to zero as the radius becomes infinite (when the surface is flat). In contrast, the pressure difference increases if the radius becomes smaller and tends to infinity as *r *tends to zero. However, the equation breaks down before *r *reaches zero, and so in practice this situation does not arise.

alternatively, the Bandage elastic modulus (K), can be determined experimentally ans by specification and is given in N/mm, determined by;

Eq. 2

Bandage elastic modulus

*K = F / [ W ( L _{f} - L_{i} ) / L_{i} ] *

*Eq. 3
*Force applied with known
Bandage elastic modulus

F = K [ W ( L

F = K [ W ( L

_{f}- L_{i}) / L_{i}]where

*K *= Bandage elastic modulus lbs/in (N/mm) - similar to spring constant*
F* = Force to stretch bandage, lbf (N)

*W*= Width of bandage, in. ( mm)

*L*= length of the stretched bandage, in (mm)

_{f}*L*= initial length, in. (mm)

_{i}Table 1, Mechanical properties of selected elastic bandages

Elastic Bandage | Longitudinal elastic modulus (N/mm) |
Force at stretch = 1.3 (N/mm) |

Biflex^{®} 16 (B16) |
0.23 |
0.070 |

Biflex^{®} 17 (B17) |
0.44 |
0.13 |

Table 2 Conversion Units

**Table 1: Conversion units**

Parameter | Coherent unit | Alternative unit | Conversion factor |

Pressure | Pascal | mmHg | 0.0075 |

Force | Newton | Kgf | 0.102 |

Length | Metre | Centimetre | 100 |

Radius | Circumference | 2 π r = (2 x 3.142 r ) |

The use of non-coherent units also means that a constant

Compression bandages are mainly classified as elastic and inelastic. Elastic compression bandages ( Table 3 ) are categorised according to the level of pressure generated on the angle of an average leg. Class 3a bandages provide light compression of 14–17 mmHg, moderate compression (18–24 mmHg) is imparted by class 3b bandages and 3c type bandages impart high compression between 25 and 35 mmHg . The 3d type extra high compression bandages (up to 60 mmHg) are not often used because the very high pressure generated will reduce the blood supply to the skin. It must be stated that approximately 30–40 mmHg at the ankle which reduces to 15–20 mmHg at the calf is generally adequate for healing most types of venous leg ulcers . Compression stockings provide support to treat DVT and varicose veins and to prevent venous leg ulcers. They are classified as light support (Class 1), medium support (Class 2) and strong support (Class 3) .

Table 3, Elastic bandage classification

Class | Bandage type | Bandage function |

1 | Lightweight conforming | Apply very low levels of sub-bandage pressure and are used to hold dressings in place. |

2 | Light support | Apply moderate sub-bandage pressure and are used to prevent oedema or for the treatment of mixed-aetiology ulcers. |

3a | Light compression | Exert a pressure range of 14–17 mm-Hg at the ankle. |

3b | Moderate compression | Exert a pressure range of 18–24 mm-Hg at the ankle. |

3c | High compression | Exert a pressure range of 25–35 mm-Hg at the ankle. |

3D | Extra high compression | Exert a pressure of up to 60 mm-Hg at the ankle. |

**Caution: If the pressure bandage is applied too tightly around an extremity, the pressure bandage becomes a tourniquet. A tourniquet cuts off the blood supply from the arteries. Once that blood supply has been cut off, the tissues separated from oxygen-rich blood flow such as the nerves, blood vessels, and muscles can be permanently damaged and result in loss of the limb. This document is not a substitutefor a medical professional and as such one should consultyour physician for the proper use and application of Elastic Compression Bandage.**

This document is not a medical guide call your doctor if:

- You have pain, numbness, or tingling
- Your toes or fingers turn a different color
- Your wrap gets wet
- The wrap is wrinkled or folded
- The wrap rubs against your skin or moves down
- Fluid leaks from the affected area to the outside of the wrap

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References

Experimental Investigation of Pressure
Applied on the Lower Leg by Elastic
Compression Bandage

Annals of Biomedical Engineering
The Journal of the Biomedical
Engineering Society

Fanette Chassagne, Frédéric Martin,
Pierre Badel, Reynald Convert, Pascal
Giraux & Jérôme Molimard

Advanced textiles for wound compression

S. Rajendran S.C. Anand Editor of the chapter S. Rajendran, in Advanced Textiles for Wound Care (Second Edition) ,

2019

Steve Thomas,
PhD

Director

Surgical Materials Testing Laboratory

Princess of Wales Hospital, Bridgend, Wales

May 2002