Multiple Choice Questions: Bernoulli's Principle in Cardiovascular Physiology
Question 1: Pressure-Velocity Relationship in Stenotic Lesions
A 65-year-old patient with aortic stenosis undergoes Doppler echocardiography showing a peak velocity of 4.5 m/s across the aortic valve. Using the simplified Bernoulli equation, what is the estimated peak pressure gradient?
A) 40 mmHg
B) 61 mmHg
C) 81 mmHg
D) 101 mmHg
Correct Answer: C) 81 mmHg
Explanation: The simplified Bernoulli equation (ΔP = 4V²) is the standard clinical tool for converting velocity to pressure gradient 1, 2. With V = 4.5 m/s, the calculation is 4 × (4.5)² = 4 × 20.25 = 81 mmHg 2. This simplified equation assumes the proximal velocity is negligible (<1.0 m/s), which is the default setting on echocardiography machines 1, 2. The Bernoulli principle demonstrates that as blood accelerates through a narrowed valve orifice, kinetic energy increases while pressure energy decreases, creating a measurable pressure gradient 1.
Question 2: Components of Pressure Loss Across Coronary Stenosis
In a patient with coronary artery stenosis, the total pressure drop across the lesion is derived from two distinct sources. Which statement correctly describes these components?
A) Both components increase linearly with flow velocity
B) Viscous friction losses increase linearly with flow, while convective acceleration losses increase with the square of flow velocity
C) Both components increase with the square of flow velocity
D) Viscous friction losses are negligible compared to convective acceleration losses
Correct Answer: B) Viscous friction losses increase linearly with flow, while convective acceleration losses increase with the square of flow velocity
Explanation: The total pressure gradient across a stenosis comprises frictional losses (following Poiseuille's Law) that increase linearly with flow, and exit losses from convective acceleration (following Bernoulli's Law) that increase with the square of flow velocity 1, 2. The mathematical relationship is expressed as ΔP = (f₁Q) + (f₂Q²), where the first term represents viscous friction and the second term represents Bernoulli-related convective acceleration 1. This quadratic relationship explains why pressure gradients increase disproportionately at higher flow rates, particularly during hyperemia 1.
Question 3: Pressure Recovery Phenomenon
A patient with aortic stenosis and a small ascending aorta (diameter 2.0 cm) shows a Doppler-measured peak gradient of 70 mmHg, but catheterization reveals a gradient of only 50 mmHg. What explains this discrepancy?
A) Technical error in Doppler alignment
B) Pressure recovery phenomenon
C) Overestimation due to high cardiac output
D) Catheter damping artifact
Correct Answer: B) Pressure recovery phenomenon
Explanation: Pressure recovery occurs when kinetic energy reconverts to potential energy distal to the stenosis, causing the Doppler-measured gradient to overestimate the true hemodynamic burden 1, 2. This phenomenon is particularly significant in patients with a small ascending aorta, where the Doppler gradient can be substantially higher than the invasively determined pressure gradient 1. The pressure recovery can be calculated as PR = 4V² × (1 − EOA/AoA), where EOA is the effective orifice area and AoA is the ascending aorta cross-sectional area 2. In this clinical scenario, the 20 mmHg difference represents energy that is recovered downstream as the high-velocity jet decelerates in the aorta 1, 2.
Question 4: Modified Bernoulli Equation Application
A patient with a bioprosthetic aortic valve shows a peak velocity of 2.2 m/s across the prosthesis and a proximal LVOT velocity of 1.6 m/s. Which approach provides the most accurate pressure gradient estimation?
A) Use simplified Bernoulli: ΔP = 4(2.2)² = 19 mmHg
B) Use modified Bernoulli: ΔP = 4[(2.2)² − (1.6)²] = 9 mmHg
C) Average the two calculations
D) Use only the proximal velocity
Correct Answer: B) Use modified Bernoulli: ΔP = 4[(2.2)² − (1.6)²] = 9 mmHg
Explanation: When the proximal velocity is elevated (>1.5 m/s), the modified Bernoulli equation ΔP = 4(V₂² − V₁²) must be used to avoid significant overestimation of pressure gradients 1, 2. In normally functioning bioprostheses with low V₂ values (often <2 m/s), using the simplified Bernoulli equation can cause clinically significant overestimation of 13-19% 1. In patients with high cardiac output or narrow LVOT, the proximal velocity may be elevated and therefore not negligible 1. The modified equation accounts for the energy already present in the blood before it reaches the stenosis 1, 2.
Question 5: Coronary Stenosis Hemodynamics
During cardiac catheterization with simultaneous pressure and flow measurements, a 63% coronary stenosis demonstrates a quadratic pressure drop-velocity relationship. What physiological principle explains this finding?
A) Linear viscous friction dominates at all flow rates
B) Convective acceleration losses become increasingly important at higher flow velocities
C) Autoregulation maintains constant pressure gradient
D) Microvascular resistance is the primary determinant
Correct Answer: B) Convective acceleration losses become increasingly important at higher flow velocities
Explanation: The quadratic nature of the stenosis pressure drop-velocity relationship (ΔP = Av + Bv²) reflects that convective acceleration losses (Bernoulli's Law) increase with the square of flow velocity and become dominant at higher flow rates 1. The constants A and B represent viscous and separation losses determined by stenosis geometry and blood fluid properties 1. During hyperemia induced by adenosine, flow velocity increases substantially, and the quadratic term (Bernoulli component) becomes the predominant source of pressure loss 1. This explains why stenoses that appear hemodynamically insignificant at rest can become flow-limiting during exercise or pharmacological stress 1.
Question 6: Clinical Pitfall in Gradient Assessment
Which scenario would cause the MOST significant overestimation of aortic valve gradient using Doppler echocardiography?
A) Mistaking mitral regurgitation jet for aortic flow
B) Doppler beam angle of 15° to flow direction
C) Mild elevation in cardiac output
D) Proximal velocity of 0.8 m/s
Correct Answer: A) Mistaking mitral regurgitation jet for aortic flow
Explanation: Mistaking the mitral regurgitation flow signal for transaortic flow signal causes substantial overestimation because MR starts earlier and lasts longer than aortic flow, and MR velocities are typically much higher 1. The MR jet can reach velocities of 4-6 m/s, which would translate to gradients of 64-144 mmHg using the Bernoulli equation—far exceeding true aortic gradients 1. Other sources of overestimation include high flow states and angle correction (which is not recommended), but these produce smaller errors 1. A Doppler beam angle <20° is considered acceptable and causes minimal error 1. Underestimation occurs with failure to align parallel to the highest velocity jet, low flow states, or elevated systemic blood pressure 1.