# Laplace Equation Calculator

Posted by Dinesh on

Use this simple health heart stress calculator tool solving Laplace’s equation using cylindrical and spherical vessel wall thickness coordinates.

## Laplace Law:

The larger the vessel radius, the larger the wall tension required to withstand a given internal fluid pressure.
For a given vessel radius and internal pressure, a spherical vessel will have half the wall tension of a cylindrical vessel.

The Law of Laplace can also be used to explain why the pressure-overloaded left ventricle (such as that associated with aortic stenosis) will incur a higher myocardial oxygen demand than the volume-overloaded ventricle (as in aortic regurgitation). Laplace stated that wall tension is proportional to PR /2, where P is chamber pressure, and R is chamber radius. The pressure-overloaded ventricle shows a large increase in the pressure variable, which will equate to much higher wall tension, and hence MVO2 . Conversely, in the volume-overloaded ventricle the radius will increase, but not as dramatically as the pressure in the pressure-overload model. Hence the rise in wall stress in the volume overload setting will be less substantial, and the corresponding MVO2 less dramatically elevated.

A simple Laplace equation measuring the tension in the walls of a cyllinder can be related to blood vessels. Properties of this relationship helps to understand the variable thickness of arteries, veins, and capillaries.

## Laplace Law Cylindrical, Spherical Vessel Wall Thickness Calculation

 Pressure [p] (in mmHg) : Radius [R] (in cm) : Cylindrical Vessel Thickness [T] (in mm) : Spherical Vessel Thickness [T] (in mm) :

### Formula:

i. T = P × R (for Cylindrical Vessel)
ii. T = (P × R / 2) (for Spherical Vessel)

where,
• T - Wall thickness
• P - Pressure in mmHg