11.3 Valve Area (Gorlin, Hakki) & Shunt Calculations
Key Takeaways
- Gorlin AVA = CO / (HR × SEP × 44.3 × √mean gradient); Gorlin MVA substitutes 37.7 and the diastolic filling period.
- Hakki shortcut: AVA ≈ CO (L/min) / √peak-to-peak (or mean) gradient — it tracks Gorlin near HR ~60–100.
- Severe AS teaching AVA is < 1.0 cm²; a normal aortic valve is about 3–4 cm².
- Qp/Qs = (Ao sat − MV sat) / (PV sat − PA sat); Flamm mixed venous is conceptually (3 SVC + 1 IVC) / 4; significant L→R is often taught at Qp/Qs ≥ 1.5.
- FFR and iFR are Procedures 1.C.5 coronary pressure ratios already taught in 10.3 — they do not replace Gorlin areas or oximetry-run shunt math.
Valve Area (Gorlin, Hakki) & Shunt Calculations
Once you can compute cardiac output, Procedures 1.C asks you to turn flow and a gradient into a valve area, and to turn an oximetry run into a shunt ratio. Fractional flow reserve (FFR) and instantaneous wave-free ratio (iFR) are outline item 1.C.5; they were taught in 10.3 — a short recap sits at the end of this section, not a second lecture. Severe-AS and Qp/Qs teaching thresholds below are cath-lab teaching values, not unpublished ARRT cutoffs.
Quick Answer: Gorlin AVA = CO / (HR × SEP × 44.3 × √mean gradient). Gorlin MVA uses 37.7 and the diastolic filling period. Hakki: AVA ≈ CO (L/min) / √peak-to-peak (or mean) gradient. Teaching severe aortic stenosis (AS) is AVA < 1.0 cm²; normal AVA ~3–4 cm². Qp/Qs = (Ao sat − MV sat) / (PV sat − PA sat). Flamm mixed venous ≈ (3 SVC + 1 IVC) / 4. Significant left-to-right teaching often Qp/Qs ≥ 1.5.
Gorlin valve area
The Gorlin equation says orifice area equals flow across the valve during the opening period divided by a constant times the square root of the mean pressure gradient.
Aortic valve area (AVA):
AVA = CO / (HR × SEP × 44.3 × √mean gradient)
- CO in mL/min when you want cm² with this writing
- HR in beats/min
- SEP = systolic ejection period in seconds per beat (the time the aortic valve is actually open)
- 44.3 is the aortic empiric constant in this teaching form
- Mean gradient in mmHg; Gorlin uses √mean, not the square root of a random peak-to-peak number unless a stem tells you to simplify
Mitral valve area (MVA) uses the same structure with two substitutions: constant 37.7 instead of 44.3, and diastolic filling period (DFP) instead of SEP — the mitral valve is open in diastole, not systole. Swapping 44.3/SEP onto the mitral valve, or 37.7/DFP onto the aortic valve, is a classic miss.
Flow in the numerator must match the valve: systemic CO for AVA (forward left-heart output). Severe regurgitation and shunts make which CO a physician-level problem; on the exam, do not plug a thermodilution number you already know is invalid from 11.2.
Worked Gorlin (teaching)
CO 4,800 mL/min, HR 80, SEP 0.30 s, mean gradient 36 mmHg (√36 = 6).
Denominator = 80 × 0.30 × 44.3 × 6 = 24 × 44.3 × 6 = 6,379.2
AVA = 4,800 / 6,379 ≈ 0.75 cm² — teaching severe (< 1.0 cm²), far below normal ~3–4 cm².
If heart rate doubles and SEP halves, Gorlin can stay similar because the opening-period term moved with HR. If you only change HR in Hakki and ignore SEP, the shortcut drifts.
Hakki simplified AVA
Hakki: AVA ≈ CO (L/min) / √peak-to-peak (or mean) gradient
It is a shortcut that tracks Gorlin near HR ~60–100, where SEP is not extreme. It is not a different physiology. At HR 40 or 140, systolic ejection period is no longer in the range Hakki absorbed into the simplification, and the two formulas separate. Teaching use: a quick area when you have output in L/min and a gradient, knowing it is Gorlin's cousin, not Gorlin's replacement at extreme heart rates.
Worked Hakki
CO 4.0 L/min, peak-to-peak gradient 64 mmHg.
√64 = 8
AVA = 4.0 / 8 = 0.5 cm²
That is severe AS on teaching cutoffs (< 1.0 cm²). A normal 3–4 cm² valve would need a tiny gradient at this output, not 64 mmHg. If someone divides 4.0 by 64 instead of by 8, they report 0.06 cm² — a number that should look impossible even for critical AS and should send you back to the square root.
Same output with a 16 mmHg gradient: √16 = 4, Hakki AVA = 4.0 / 4 = 1.0 cm², which sits on the severe-AS teaching border rather than deep in the 0.5 cm² range.
Oximetry run and shunts
A left-to-right (L→R) shunt dumps oxygenated blood into the right heart. The fingerprint is a step-up in oxygen saturation from the superior vena cava (SVC) toward right atrium (RA) / right ventricle / pulmonary artery (PA). Where the step-up appears suggests the level (atrial, ventricular, or great-vessel). That is anatomy. The ratio is arithmetic.
A right-to-left shunt desaturates the left heart; Qp/Qs then falls below 1.
Mixed-venous saturation (MV) for shunt math is not a random arm vein. Teaching Flamm formula:
MV ≈ (3 × SVC + 1 × IVC) / 4
SVC is weighted more because inferior vena cava saturation is jumpy (renal and hepatic streams). This is a conceptual 3:1 mix, not a claim that ARRT published the coefficients.
Qp/Qs = (Ao sat − MV sat) / (PV sat − PA sat)
Saturations may be percent or decimal as long as you are consistent on both sides. If pulmonary vein (PV) sat was not sampled and the lungs look normal, teaching labs often set PV ≈ arterial (Ao) sat.
Significant L→R is often taught at Qp/Qs ≥ 1.5. That is a teaching threshold — know the formula and the idea of a significant step-up.
Worked Qp/Qs
Ao sat 95%, PV sat 95%, PA sat 80%, Flamm mixed venous from SVC 64% and IVC 68%:
MV = (3 × 64 + 68) / 4 = (192 + 68) / 4 = 65%
Qp/Qs = (95 − 65) / (95 − 80) = 30 / 15 = 2.0
That is a significant L→R shunt at teaching level (≥ 1.5). If you accidentally invert the formula you get 0.5 and will call a left-to-right lesion a right-to-left lesion. If PA sat has not stepped up (PA sat still equals mixed venous), the denominator equals the numerator's arteriovenous gap and Qp/Qs ≈ 1 — no shunt by oximetry.
An oximetry run is a sequence, not a single PA sat: SVC, IVC, RA (high/mid/low as sampled), RV, PA, then left-heart or arterial sat, and PV when it is available. The step-up tells you where. Qp/Qs tells you how much.
FFR / iFR — recap of 1.C.5 (taught in 10.3)
Do not re-learn coronary physiology here. FFR is distal coronary pressure over aortic pressure during hyperemia (typically adenosine); teaching ischemia is often FFR ≤ 0.80. iFR is a resting, wave-free-period ratio; teaching ischemia is often iFR ≤ 0.89. These are pressure ratios in a coronary, not Gorlin areas and not Qp/Qs. If the item is a valve area or an oximetry run, FFR is the wrong toolbox. If the item is an intermediate coronary stenosis, Gorlin is the wrong toolbox.
Formula / constant / what it answers
| Tool | Teaching formula | What it answers |
|---|---|---|
| Gorlin AVA | CO / (HR × SEP × 44.3 × √mean gradient) | Aortic orifice area |
| Gorlin MVA | CO / (HR × DFP × 37.7 × √mean gradient) | Mitral orifice area |
| Hakki AVA | CO (L/min) / √gradient | Shortcut AVA near HR 60–100 |
| Flamm MV | (3 SVC + 1 IVC) / 4 | Mixed-venous sat for shunt math |
| Qp/Qs | (Ao − MV) / (PV − PA) | Pulmonary versus systemic flow ratio |
Exam traps
- Gorlin AVA uses 44.3 and SEP; MVA uses 37.7 and DFP. Swapping them is a classic miss.
- Hakki needs the square root. 4 / 64 is not 4 / 8.
- Severe AS teaching is AVA < 1.0 cm², not any gradient over 20 mmHg at unknown output.
- Qp/Qs inverted turns L→R into R→L.
- FFR/iFR do not replace Gorlin on a valve question or oximetry on a shunt question.
Using the Hakki shortcut, cardiac output 4.0 L/min and a peak-to-peak gradient of 64 mmHg give an aortic valve area of:
Which description of Gorlin teaching constants is CORRECT?
An oximetry run shows arterial (Ao) saturation 98%, pulmonary-vein saturation 98%, pulmonary-artery saturation 82%, and mixed-venous saturation 70%. Qp/Qs is: