**Question:** A 60-year-old patient, known case of hypertension for the past 25 years, underwent renal artery Doppler which showed narrowing and turbulence in right renal artery. If radius of artery is reduced by one-third, resistance increases by ________.

**Core Concept:** Resistance in an artery is directly proportional to the radius of the artery and inversely proportional to the blood flow velocity. When the radius of an artery is reduced, the resistance increases.

**Why the Correct Answer is Right:**
1. In a blood vessel, blood flow is mainly influenced by two factors: radius and blood flow velocity. According to Hagen-Poiseuille's Law, resistance (R) is calculated as:

R = 8 * μ * L * (π * (R1^2 - R2^2)) / L

Here, μ represents blood viscosity, L is the length of the artery, and R1 and R2 are the radii of the two segments of the vessel (in this case, the normal segment and the segment with a reduced radius).

2. If the radius of the artery is reduced by one-third (R2 = R1/3), the resistance (R2) will be:

R2 = (8 * μ * L * (π * (R1^2 - (R1/3)^2)) / L

Simplifying this equation gives us:

R2 = 8 * μ * π * (R1^2 - (R1/3)^2)

3. Since (R1/3)^2 is always less than R1^2, subtracting it from R1^2 will result in a positive number, which means the resistance increases.

**Why Each Wrong Option is Incorrect:**
1. **Option A:** The statement is incorrect because the radius of the artery remains the same, and the increased resistance is solely due to the reduced blood flow velocity (which is not mentioned in the question).
2. **Option B:** The statement is incorrect because it only considers blood viscosity (μ), but the actual increase in resistance is due to the reduced radius and increased resistance in each segment of the artery.
3. **Option C:** The statement is incorrect because it does not consider the actual reduction in radius and the resulting increase in resistance.
4. **Option D:** The statement is incorrect because it only considers the reduced radius but does not address the increased resistance due to reduced blood flow velocity.

**Clinical Pearl:**
It is essential to understand the interplay between radius, blood flow velocity, and blood pressure in determining arterial resistance. In this case, the reduced radius leads to increased resistance, which can lead to hypertension or other complications like atherosclerosis if left untreated.

**Correct Answer:** A: Option A is correct because the blood flow velocity decreases due to the reduced radius and increased resistance. The ratio of blood flow velocity to blood pressure is constant, so the increased resistance leads to an increase in blood pressure.