What corresponds to an arterial stenosis that has 80% diameter reduction in terms of cross-sectional area reduction?

An arterial stenosis with an 80% reduction in diameter corresponds to a significant reduction in cross-sectional area due to the mathematical relationship between diameter and area. The cross-sectional area is proportional to the square of the diameter of the vessel.

When the diameter is reduced by 80%, it means that the remaining diameter is 20% of the original. To find the corresponding reduction in area, we calculate the area based on the remaining diameter:

If the original diameter is represented as 'D', the new diameter after an 80% reduction would be:

New Diameter = 0.2D (since 20% of D is left).

The area of a circle (cross-sectional area of the artery) is calculated as:

Area = π * (Diameter/2)^2.

So, for the original diameter:

Original Area = π * (D/2)^2.

For the new diameter:

New Area = π * (0.2D/2)^2 = π * (0.1D)^2 = π * (0.01D^2).

Now, calculating the reduction in area:

Original Area = π * (D/2)^2 = π * (D^2/4).

New Area = π *