Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Ultrasound can be used to measure the velocity of blood flow in the ascending aorta by the application of the Doppler principle.
Reason (R) : If the area of cross-section of the aorta is known, the blood flow can be calculated as follows :-
Blood flow = $\frac{\text{velocity} \times \text{stroke} - \text{volume}}{\text{area}}$
In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Always check the units in formulas! Flow rate ($Q$) is measured in $cm^3/sec$ (or $mL/sec$). Velocity is $cm/sec$. Area is $cm^2$. Therefore, $cm/sec \times cm^2 = cm^3/sec$. Dividing by area as shown in (R) would yield $1/sec$, proving the formula is fake.

Answer 1

The Correct Option is C

Step 1: Concept:
This question evaluates the physics of biomedical ultrasound, specifically Doppler flowmetry, and the fundamental hemodynamic formulas used to calculate blood flow and stroke volume.

Step 2: Step-by-step Explanation:

• Analyzing Assertion (A): Doppler ultrasound is a standard, non-invasive clinical tool. By bouncing high-frequency sound waves off moving red blood cells, the change in frequency (Doppler shift) allows computers to accurately calculate the velocity of the blood flow in major vessels like the ascending aorta. Therefore, Assertion (A) is completely correct.

• Analyzing Reason (R): The reason provides a mathematical formula for calculating blood flow. However, the formula provided is physically and mathematically nonsensical.

• The correct physiological principle of fluid dynamics (Continuity Equation) states that Blood Flow (Volume Flow Rate, Q) is simply the product of the flow velocity and the cross-sectional area of the vessel: \[ Q \ (\text{Flow}) = V \ (\text{Velocity}) \times A \ (\text{Cross-sectional Area}) \]
• Alternatively, to calculate Stroke Volume (SV) using echocardiography, the formula used is: \[ SV = VTI \ (\text{Velocity Time Integral}) \times CSA \ (\text{Cross-sectional Area}) \]
• The formula presented in Reason (R) places Area in the denominator and subtracts volume, which breaks dimensional analysis and is entirely incorrect. Thus, Reason (R) is false.

Step 3: Final Answer:
(A) is correct but (R) is not correct.