Cath-Lab Hemodynamic Calculations – Key Vocabulary

Why Calculations Matter

• Provide a concrete, trend-able number that reflects cardiovascular status at a given moment.
• Allow comparison with prior / future studies (e.g., EF improved from 35 % → 45 %).
• Drive treatment decisions (e.g., timing of valve replacement, medication titration).
• Accuracy & reproducibility depend on good data acquisition (waveforms, saturations, heights/weights, etc.).

Thermodilution vs Fick Cardiac Output

• Thermodilution: inject cold saline in RA, measure ΔT in PA (needs Swan–Ganz catheter).
• Fick (preferred / gold standard): uses O₂ uptake and O₂ content difference.
  • More accurate in presence of regurgitation, shunts, arrhythmias (AF), cardiomyopathy.

Six Items Required for a Fick Cardiac Output

1. Arterial O₂ saturation (AO-sat) – from femoral/aortic line.
2. Mixed-venous (PA) O₂ saturation (PA-sat) – from distal Swan or pulmonary artery sample.
3. Hemoglobin (Hb).
4. VO₂ – whole-body O₂ consumption (mL · min⁻¹) – supplied as a number on exams; cath-lab computers assign it from height/weight tables (≈ 250 mL·min⁻¹ average adult).
5. Constant 1.36 – theoretical O₂ binding per g Hb (built into software; provided on tests).
6. Patient height + weight → Body Surface Area (BSA) – needed because VO₂ tables are BSA-indexed.

Fick Cardiac Output Formula

Basic form
CO = \frac{VO2}{(CaO2 - CvO2)\times 10} Expanded form (using Hb, saturations & constant C = 1.36) \displaystyle CO = \frac{VO2}{[Hb\times C \times(SaO2)\; -\; Hb\times C \times(SvO2)]\times 10}

Where

• CaO2 = Hb \times 1.36 \times SaO2 (arterial O₂ content)
• CvO2 = Hb \times 1.36 \times SvO2 (venous O₂ content)
• Final unit: L · min⁻¹ (round to 1 decimal place; use standard rounding rules).

Worked Examples (Problems 1–4)

• Example 1 (VO₂ = 250, SaO₂ = 93 %, SvO₂ = 69 %, Hb = 13.4):
  • CaO2 = 13.4\times1.36\times0.93 = 16.9\;\text{vol %} • CvO2 = 13.4\times1.36\times0.69 = 12.6
  • CO = \frac{250}{(16.9-12.6)\times10}=\frac{250}{43}=5.8\;L\,min^{-1}
• Example 2 → 4.3 L·min⁻¹.
• Example 3 → 5.7 L·min⁻¹.
• Example 4 given CaO2 & CvO2 directly → 6.1 L·min⁻¹ (shows you can skip Hb, sats when contents supplied).

Arterial vs Venous O₂ Content (Key Definitions)

• CaO2 (arterial) and CvO2 (venous) are intermediate results you’ll need in other computations (e.g., shunt or valve sizing questions).
• Units: vol % (mL O₂ per 100 mL blood).

Angiographic Cardiac Output (Heart-Rate × Stroke-Volume)

Formula
CO = HR \times SV \div 1000

• HR in beats · min⁻¹.
• Stroke Volume (SV) in mL (convert to L by ÷1000).

Deriving SV from left-ventricular angiography

• Perform LV gram in 30° RAO.
• Trace LV at end-diastole → EDV.
• Trace LV at end-systole → ESV.
• SV = EDV - ESV

Ejection Fraction
EF = \frac{SV}{EDV}  (expressed as a %)

Cardiac Index (CI)
CI = \frac{CO}{BSA} Units: L · min⁻¹ · m⁻².

Worked Examples (5 & 6)

Problem 5

• EDV = 130 mL, ESV = 50 mL → SV = 80 mL.
• HR = 64 → CO = 64\times80/1000 = 5.1 L·min⁻¹.
• EF = 80/130 = 0.615 \approx 62\%.
• BSA = 1.6 → CI = 5.1/1.6 = 3.2 L·min⁻¹·m⁻².

Problem 6 gives SV = 60 mL, CO ≈ 4.6 L/min, EF ≈ 60 %, CI ≈ 3.3 L/min/m².

Manipulating the formula (Problem 7)

• SV = \frac{CO_{mL}}{HR}, so 4.7 L (= 4700 mL) ÷ 80 bpm → 59 mL.

Metric Conversions in the Cath Lab

• 1 inch = 2.54 cm (memorise).
• Height conversion examples
  • 29 in → $29\times2.54=73.7$ cm.
  • 80 cm → $80\div2.54=31.5$ in.
  • 5′9″ (69 in) → $69\times2.54=175.3$ cm.
• Accurate cm entry is essential (affects BSA-derived VO₂ and valve sizing).

Gorlin Valve-Area Calculations (Gold Standard)

Key ingredients

1. Mean trans-valvular pressure gradient (computed by overlapping LV & AO (or LA & LV) waveforms, NOT peak-to-peak).
2. Ejection (systolic) period for AV, or Diastolic filling period for MV.
3. Cardiac Output (L/min → convert to mL/min).
4. Gorlin constant • Aortic = 44.5 • Mitral = 37.7.

Four-Step Method (works for AV & MV)

1. Convert CO{L/min} \to CO{mL/min}.
2. Multiply opening time/beat (SEP or DFP) by HR → seconds valve open/min.
3. \text{Valve Flow} = CO_{mL/min} \div \text{seconds open/min} (unit: mL · s⁻¹).
4. Area = \frac{\text{Valve Flow}}{K \times \sqrt{\text{Mean Gradient}}}

Aortic Example (Problem 11)

• CO 4.9 L → 4900 mL/min.
• SEP 0.22 s, HR 72 → 0.22×72 = 15.8 s.
• Flow = 4900/15.8 = 310.1 mL·s⁻¹.
• Mean grad 45 mmHg; \sqrt{45}=6.7.
• Area = 310.1\,/\,(44.5\times6.7)=1.04\;cm^{2} (borderline severe; normal 3–4 cm²).

Mitral Example (Problem 13)

• CO 4.8 L → 4800 mL/min.
• DFP 0.44 s, HR 60 → 26.4 s.
• Flow = 4800/26.4 = 181.8 mL·s⁻¹.
• Mean grad 32 mmHg; \sqrt{32}=5.7.
• Constant 37.7 → Area = 181.8\,/\,(37.7\times5.7)=0.85\;cm^{2} (significant MS).

Hakki Valve-Area Shortcut

Formula
A_{valve}\;(cm^{2}) = \frac{CO\;(L/min)}{\sqrt{\text{Peak–Peak Gradient}}}

• Faster but less precise; uses peak-to-peak not mean.
• Example (Problem 15): CO 6.1 L/min, peak–peak 40 mmHg → $6.1/\sqrt{40}=0.97$ cm².

Regurgitant Fraction (RF)

Quantifies % of total LV output that regurgitates rather than enters systemic flow.
RF = \frac{CO{angio} - CO{Fick/TD}}{CO_{angio}}

• Example 73: Angio 5.4 L/min, Thermo 4.1 L/min →
  RF = \frac{5.4-4.1}{5.4}=0.24=24\% (Answer A).

Constants & Reference Values

• Normal CO ≈ 4–8 L/min.
• Normal CI ≈ 2.5–4.0 L/min/m².
• Normal EF ≈ 55–75 %.
• Normal AV area ≈ 3–4 cm²; severe AS < 1.0 cm².
• Normal MV area ≈ 4–6 cm²; severe MS < 1.0 cm².

Practical / Ethical Notes

• Waveform quality matters: The cath-lab monitor tech’s accurate zeroing, damping check & overlap tracing directly impact calculated valve areas – and thus whether a patient receives surgery.
• Unit vigilance: Keep track of L↔mL, inches↔cm; mis-entries propagate large calculation errors.
• Rounding discipline: Provide one decimal for CO; keep two for intermediate valve-flow steps to minimise error.
• Patient size equity: Indexing (CI) avoids unfairly labelling petite or large patients as abnormal.
• Historical insight: Dr. Adolph Fick (1870) & Drs. Gorlin (1951) developed these equations – still fundamental in modern interventional cardiology.