An arterial stenosis with 75% cross-sectional area reduction corresponds to what percentage of diameter reduction?

When considering arterial stenosis, the relationship between the reduction in cross-sectional area and the reduction in diameter is critical. Arterial lumen area is proportional to the square of the diameter (A = πr²). Therefore, when assessing how a reduction in area translates to a reduction in diameter, we must remember that a 75% reduction in cross-sectional area significantly affects the diameter.

If the cross-sectional area is reduced by 75%, this means that only 25% of the original area remains. Since the area is related to the square of the diameter, we draw the connection that a reduction in area does not correspond linearly to a reduction in diameter.

To find the percentage of diameter reduction that corresponds to a 75% reduction in area, we can use the formula for area reduction:

• Let the original diameter be D.

• The area corresponding to this diameter is A₀ = π(D/2)².

• A 75% area reduction means the new area A₁ = A₀ * 0.25.

• The new diameter D' is derived from the equation of the remaining area: A₁ = π(D'/2)².

By setting the equations for original and new areas equal:

0