6.3 Valve Area, Bernoulli & Shunt Calculations

6.3 Valve Area, Bernoulli & Shunt Calculations

Quick Answer: Valve stenosis severity and intracardiac shunts are quantified with three calculation families RCIS candidates must know: the modified Bernoulli equation (4v²) for instantaneous gradients, the Gorlin formula with constants 44.3 (aortic) and 37.7 (mitral) for valve area, and Qp:Qs shunt ratios derived from oximetry step-ups and Fick cardiac output at pulmonary and systemic circuits.

These calculations appear throughout CCI's Diagnostic Procedures domain — often as numeric items requiring one-step arithmetic. The RCIS role is to prepare hemodynamic data, ensure correct sample sequence, and verify that inputs (CO, gradients, saturations) come from valid measurements.

Modified Bernoulli Equation

When blood accelerates through a stenotic orifice, the pressure drop is related to velocity by the simplified Bernoulli equation:

ΔP (mmHg) = 4 × v²

Where v = peak velocity in m/s (not cm/s).

Worked Example

Peak aortic jet velocity = 4.5 m/s:

ΔP = 4 × (4.5)² = 4 × 20.25 = 81 mmHg

RCIS note: Bernoulli gives peak instantaneous gradient. Mean gradient (from Doppler trace integration or simultaneous cath pull-back) is used for Gorlin valve area. Echo and cath gradients may differ slightly due to technique.

Exam trap: Using velocity in cm/s instead of m/s produces a gradient 10,000× too large. Always confirm units.

Gorlin Valve Area Formula

The Gorlin equation estimates effective orifice area from flow and pressure drop across a valve:

Valve Area (cm²) = CO (mL/min) ÷ (C × SEP or DFP × HR × √(mean gradient))

Where C is the empiric constant:

• Aortic valve: C = 44.3 (uses systolic ejection period, SEP)
• Mitral valve: C = 37.7 (uses diastolic filling period, DFP)

Simplified Exam Form

RCIS items often use a reduced formula when SEP/DFP and HR are embedded or given as a combined factor:

Aortic valve area (AVA) ≈ CO ÷ (44.3 × √mean gradient)

Mitral valve area (MVA) ≈ CO ÷ (37.7 × √mean gradient)

(CO in mL/min or L/min depending on item setup — read carefully and convert: 5 L/min = 5000 mL/min.)

Worked Example: Aortic Stenosis

Given: CO = 5.0 L/min (5000 mL/min), mean aortic gradient = 40 mmHg

AVA = 5000 ÷ (44.3 × √40) = 5000 ÷ (44.3 × 6.32) = 5000 ÷ 280 ≈ 0.79 cm²

Worked Example: Mitral Stenosis

Given: CO = 4.5 L/min, mean mitral gradient = 10 mmHg

MVA = 4500 ÷ (37.7 × √10) = 4500 ÷ (37.7 × 3.16) = 4500 ÷ 119 ≈ 0.38 cm² → severe mitral stenosis (<1.5 cm²)

RCIS exam tip: Memorize constants 44.3 = aortic, 37.7 = mitral. Wrong constant selection is a common distractor.

Shunt Detection: Step-Up Oximetry

Intracardiac shunts mix oxygenated and deoxygenated blood, creating a step-up in O₂ saturation at the chamber where shunted blood enters.

Sampling Order (Mandatory)

Obtain blood samples sequentially:

SVC → RA → RV → PA → Aorta (or systemic artery)

Record saturation and O₂ content at each site. A ≥5–7% saturation step-up between adjacent sites localizes the shunt level.

Left-to-right shunt physiology: Oxygenated blood from the left side crosses to the right, raising O₂ saturation downstream of the defect. Right-to-left shunts (e.g., Eisenmenger) show decreased saturations and are detected by lower PA/Ao sat relative to expected — not a step-up pattern.

Worked Oximetry Example

Analysis: Step-up of 7% from SVC (75%) to RA (82%) localizes an atrial-level left-to-right shunt (ASD). Minimal RV rise suggests the shunt is complete at the atrial level. Confirm with bubble study or echocardiography.

Qp:Qs Shunt Ratio

Qp = pulmonary blood flow (total flow through lungs) Qs = systemic blood flow (flow to body excluding shunt recirculation)

Qp:Qs = Qp ÷ Qs

Calculated precisely using the Fick principle at both circuits:

Qp = VO₂ ÷ (pulmonary vein O₂ content − PA O₂ content)

Qs = VO₂ ÷ (Ao O₂ content − mixed venous O₂ content)

When pulmonary vein blood is unavailable, use the saturation method with assumed pulmonary vein saturation (often 99–100% on room air):

Qp:Qs = (Ao sat − MV sat) ÷ (PV sat − PA sat)

(Simplified forms vary by reference — follow the institutional formula on exam day.)

Worked Qp:Qs Estimate

Using simplified saturation ratio: Ao 98%, MV (mixed venous from SVC/RA blend) 70%, assumed PV 99%, PA 85%:

Qp:Qs = (98 − 70) ÷ (99 − 85) = 28 ÷ 14 = 2.0:1 → hemodynamically significant shunt.

Integrating Valve and Shunt Data

Shunts invalidate thermodilution CO and alter Fick calculations if sampling is incorrect. Always:

1. Complete full oximetry run before calculating Qp:Qs
2. Use true PA blood for mixed venous (not RA in shunt patients)
3. Report valve area only with simultaneously measured CO and mean gradient
4. Communicate when shunt physiology may overestimate Fick CO (left-to-right shunt lowers C(a-v)O₂ difference artifactually)

RCIS Support Checklist

• Label syringes in sampling order before the case starts
• Keep oximetry machine calibrated; record hemoglobin for content calculations
• Document step-up magnitude and location on the hemodynamic sheet
• Verify CO source (Fick vs thermodilution) before Gorlin calculation
• Never delay sample processing — O₂ content changes with delay

Common Exam Traps

1. Bernoulli with wrong units — always m/s
2. Gorlin constant swap — 44.3 aortic, 37.7 mitral
3. RA sample as mixed venous in ASD — RA sat is elevated by shunt blood
4. Ignoring step-up threshold — a 3% change is likely noise; ≥5–7% is significant
5. Confusing peak and mean gradient — Gorlin uses mean gradient