Fick Calculator | Shunts, Cardiac Output & ECMO

The Fick Shunt Principle: The ratio of pulmonary blood flow to systemic blood flow (Q_p / Q_s) is determined by the oxygen content difference across each circulation. Under normal circumstances without shunting, Q_p / Q_s = 1.0. In intracardiac left-to-right shunts (e.g., ASD, VSD, PDA), Q_p / Q_s > 1.0 due to venous oxygen step-up. Conversely, right-to-left shunting produces systemic arterial desaturation with Q_p / Q_s < 1.0. In complex congenital heart disease, superadded intrapulmonary shunts (Q_s / Q_t) can be differentiated using the Berggren hyperoxia equation.

Calculate intracardiac and intrapulmonary shunt in the same patient Independent Panels

When checked, Systemic Arterial Saturation (SaO₂) and Venous Saturation (SvO₂) synchronize bidirectionally in real-time between both calculators.

Intracardiac Shunt Ratio (Qp / Qs)

Fick Oximetry

Systemic Arterial Saturation (SaO₂) Aorta / Radial

%

Mixed Venous Saturation (SvO₂) Caval / Right Atrium

%

Pulmonary Venous Saturation (SpvO₂) PV / Left Atrium (or 100%)

%

Pulmonary Arterial Saturation (SpaO₂) PA / Shunt branch

%

Pulmonary to Systemic Flow Ratio

0.71 : 1

Right-to-Left Shunt Net Shunt Fraction: 29%

Intracardiac Shunt Equations & Derivation Equations & Math ▼

Fick Principle of Shunts:

Qp / Qs = (CaO₂ − CvO₂) / (CpvO₂ − CpaO₂)

Assuming uniform hemoglobin across vascular beds and neglecting minor differences in physically dissolved oxygen, oxygen saturations substitute directly for contents:

Qp / Qs = (SaO₂ − SvO₂) / (SpvO₂ − SpaO₂)

Qp / Qs = (86 − 61) / (100 − 65) = 25.0 / 35.0 = 0.71 : 1

Shunt Fraction Formulas:

Left-to-Right Shunt (Qp/Qs > 1.0): Net L-to-R Shunt = (Qp − Qs) / Qp = ((Qp/Qs) − 1) / (Qp/Qs) × 100% Right-to-Left Shunt (Qp/Qs < 1.0): Net R-to-L Shunt = (Qs − Qp) / Qs = (1 − (Qp/Qs)) × 100%

Where SaO₂ = systemic arterial saturation, SvO₂ = mixed venous saturation (caval/RA), SpvO₂ = pulmonary venous saturation (PV/LA), and SpaO₂ = pulmonary arterial saturation.

Intrapulmonary Shunt Fraction (Qs / Qt)

Berggren Formula

FiO₂

Hemoglobin (Hb)

g/L

Arterial PaO₂

mmHg

Arterial SaO₂

%

Arterial PaCO₂

mmHg

Venous PvO₂

mmHg

Venous SvO₂

%

Derived Blood Oxygen Contents Berggren Formula Basis (mL/dL)

The Berggren intrapulmonary shunt equation strictly utilizes oxygen content (mL/dL), not saturation alone, to account for hyperoxia-dissolved oxygen in capillary blood:

End-Capillary (Cc'O₂)

20.8 mL/dL

(1.34 × 14.0 × 1.00) + (663 × 0.003)

Capillary blood: 100% Hb sat + dissolved P_AO₂

Systemic Arterial (CaO₂)

14.2 mL/dL

(1.34 × 14.0 × 0.75) + (41 × 0.003)

Arterial delivery: SaO₂ sat + dissolved PaO₂

Mixed Venous (CvO₂)

9.5 mL/dL

(1.34 × 14.0 × 0.50) + (28 × 0.003)

Venous return: SvO₂ sat + dissolved PvO₂

Capillary−Arterial Deficit (Cc'O₂ − CaO₂): 6.6 mL/dL

Capillary−Venous Span (Cc'O₂ − CvO₂): 11.3 mL/dL

Arteriovenous Extraction (CaO₂ − CvO₂): 4.7 mL/dL

Alveolar Gas Equation (P_AO₂ & A-a Gradient) Derives P_AO₂ for Cc'O₂ and automatically computes A-a Gradient

P_AO₂ = 663 mmHg A-a Grad = 622 mmHg Parameters ▼

The Alveolar Gas Equation calculates alveolar oxygen tension (P_AO₂). In the Berggren shunt calculation, P_AO₂ is required to derive physical dissolved oxygen in end-capillary blood: Cc'O₂ = (1.34 × Hb × 1.0) + (0.003 × P_AO₂).

P_AO₂ = FiO₂ × (P_atm − P_H₂O) − (PaCO₂ / R) = 1.00 × (760 − 47) − (40 / 0.80) = 713.0 − 50.0 = 663 mmHg

P_atm: 760 mmHg

P_H₂O (37°C): 47 mmHg

Resp. Quotient (R): 0.80

A-a Gradient: 622 mmHg

A-a Gradient: 622 mmHg (Markedly elevated on 100% FiO₂; normal is < 10–15 mmHg on room air; > 200 mmHg on 100% O₂ confirms substantial intrapulmonary shunting / V/Q mismatch).

Customize Barometric Pressure (P_atm) & Respiratory Quotient (R):

P_atm (mmHg)

Resp. Quotient (R)

Intrapulmonary Shunt (Qs / Qt)

58.1 %

PAO₂: 663 mmHg CcO₂: 20.8 mL/dL CaO₂: 14.2 mL/dL CvO₂: 9.5 mL/dL

Berggren Shunt Equations & Mass Balance Derivation Equations & Math ▼

Berggren Mass-Balance Principle:

Total O₂ delivery equals capillary blood plus shunted venous blood: Qt × CaO₂ = (Qt − Qs) × Cc'O₂ + (Qs × CvO₂) Expanding and solving for shunt fraction (Qs / Qt): Qt × CaO₂ = Qt × Cc'O₂ − Qs × Cc'O₂ + Qs × CvO₂ Qs × (Cc'O₂ − CvO₂) = Qt × (Cc'O₂ − CaO₂) Qs / Qt = (Cc'O₂ − CaO₂) / (Cc'O₂ − CvO₂) × 100%

Live Mass-Balance Calculation:

Qs/Qt = (Cc'O₂ − CaO₂) / (Cc'O₂ − CvO₂) × 100%

Individual Blood Oxygen Contents (mL/dL):

Cc'O₂ = (1.34 × Hb × 1.00) + (0.003 × PAO₂) CaO₂ = (1.34 × Hb × SaO₂/100) + (0.003 × PaO₂) CvO₂ = (1.34 × Hb × SvO₂/100) + (0.003 × PvO₂)

Normal intrapulmonary shunt is < 5%. Values > 20–30% indicate severe gas-exchange impairment, atelectasis, consolidation, or pulmonary arteriovenous malformations.

Illustrated Case: Hypoplastic Left Heart Syndrome (HLHS) with Cavopulmonary Shunt

A child with HLHS and a bidirectional cavopulmonary anastomosis (BCPA / Glenn shunt) presents with acute respiratory illness and cyanosis. Management requires distinguishing the baseline intracardiac right-to-left shunt from superadded intrapulmonary shunting (parenchymal lung disease or pulmonary arteriovenous malformations).

Phase 1: Baseline Intracardiac Shunt Qp:Qs = 0.71 : 1

At baseline catheterization: SaO₂ = 86%, SvO₂ = 61%, SpaO₂ = 65%, SpvO₂ = 100%.

Qp : Qs = (SaO₂ - SvO₂) / (SpvO₂ - SpaO₂) = (0.86 - 0.61) / (1.00 - 0.65) = 0.25 / 0.35 = 0.71 : 1

In a bidirectional Glenn shunt, upper body venous blood alone feeds the pulmonary circulation, so a baseline Q_p / Q_s < 1.0 (typically ~0.7:1, representing a ~30% right-to-left baseline shunt) is expected.

Phase 2: Hyperoxia Test (100% O₂) Qs/Qt = 59% (Severe)

On 100% FiO₂: PaO₂ = 41 mmHg, SaO₂ = 75%, PaCO₂ = 40 mmHg, Hb = 140 g/L; Central venous: PcvO₂ = 28 mmHg, SvO₂ = 50%.

PAO₂ = 1.0 × (760 - 47) - (40 / 0.8) = 663 mmHg CcO₂ = (1.34 × 1.0 × 14) + (663 × 0.003) = 20.75 mL/dL CaO₂ = (1.34 × 0.75 × 14) + (41 × 0.003) = 13.95 mL/dL CvO₂ = (1.34 × 0.50 × 14) + (28 × 0.003) = 9.30 mL/dL Qs/Qt = (20.75 - 13.95) / (20.75 - 9.30) = 59%

The intrapulmonary shunt fraction of 59% markedly exceeds the baseline cardiac shunt (~30%), proving the presence of severe extracardiac/pulmonary pathology (e.g., AVMs or consolidation).

Interactive Case Presets:

Equation Abbreviations & Variable Definitions

Qp / Qs: Pulmonary-to-systemic blood flow ratio: (SaO₂ − SvO₂) / (SpvO₂ − SpaO₂). Normal = 1.0; > 1.0 = left-to-right shunt (ASD, VSD, PDA); < 1.0 = right-to-left shunt (Cyanotic CHD, Glenn shunt)

Qp: Total pulmonary blood flow across the pulmonary circulation (L/min)

Qs: Total systemic blood flow across the systemic circulation (cardiac output, L/min)

Qs / Qt: Intrapulmonary (physiologic) shunt fraction via Berggren equation: (Cc'O₂ − CaO₂) / (Cc'O₂ − CvO₂) × 100% (normal < 5%; > 20% indicates significant intrapulmonary shunting)

Qt: Total cardiac output across the cardiopulmonary circulation (L/min)

SaO₂: Systemic arterial oxygen saturation (aorta or systemic arterial line, %)

SvO₂ (SmvO₂): Mixed venous oxygen saturation (upstream caval blood or right atrium prior to shunt mixing, %)

SpvO₂: Pulmonary venous oxygen saturation (blood returning from pulmonary veins or left atrium; typically 98–100%, %)

SpaO₂: Pulmonary arterial oxygen saturation (blood in the pulmonary artery trunk; elevated in left-to-right shunting by oxygenated venous step-up, %)

FiO₂: Fraction of inspired oxygen (e.g., 1.0 during 100% O₂ hyperoxia test)

P_AO₂: Alveolar oxygen partial pressure via Alveolar Gas Equation: FiO₂ × (P_atm − P_H₂O) − (PaCO₂ / R) (mmHg or kPa). Quantifies alveolar driving pressure for pulmonary gas exchange.

A-a Gradient: Alveolar-arterial oxygen partial pressure difference: P_AO₂ − PaO₂ (normal < 10–15 mmHg on room air; widening > 200 mmHg on 100% FiO₂ confirms severe intrapulmonary shunt / V/Q mismatch)

PaO₂: Systemic arterial partial pressure of dissolved oxygen (mmHg or kPa)

PaCO₂: Systemic arterial partial pressure of carbon dioxide (mmHg or kPa)

PvO₂: Mixed venous partial pressure of dissolved oxygen (mmHg or kPa)

Cc'O₂: End-capillary pulmonary oxygen content: (1.34 × Hb × 1.0) + (0.003 × P_AO₂) (mL/dL)

CaO₂: Systemic arterial oxygen content: (1.34 × Hb × SaO₂ / 100) + (0.003 × PaO₂) (mL/dL)

CvO₂: Mixed venous oxygen content: (1.34 × Hb × SvO₂ / 100) + (0.003 × PvO₂) (mL/dL)

Hb: Hemoglobin concentration (g/L or g/dL)

Classical Fick Principle (Adolf Fick, 1870): Cardiac output is derived from the total uptake of oxygen across the lungs divided by the arteriovenous oxygen content difference: CO = VO₂ / (C_aO₂ − C_vO₂). At low cardiac outputs, enhanced tissue oxygen extraction widens the AV-O₂ gap; in high-output states, diminished extraction narrows it. Because directly measuring VO₂ with a Douglas bag or metabolic cart is cumbersome, catheterization laboratories utilize assumed or predictive regression equations (Dehmer, LaFarge, Bergstra), which introduce systematic differences.

Oximetry & Demographics

Catheterization Lab

Systemic Arterial Saturation (SaO₂) Aorta / Femoral

%

Pulmonary Artery / Mixed Venous (SvO₂) Swan-Ganz catheter

%

Hemoglobin Concentration (Hb) Hüfner constant: 1.36 mL O₂/g

g/L

Age

yrs

Sex

Heart Rate

bpm

Height

cm

Weight

kg

Measured VO₂ (Optional) Metabolic cart / Douglas bag

mL/min

Fick Cardiac Output (Dehmer Method)

4.63 L/min

Cardiac Index: 2.43 L/min/m² AV-O₂ Diff: 51.4 mL/L Stroke Volume: 64 mL

Oxygen Uptake (VO₂)

238 mL/min

VO₂ Index: 125 mL/min/m²

Body Surface Area

1.90 m²

DuBois Formula

AV-O₂ Content Gap

5.14 mL/dL

Normal Extraction

Arterial O₂ Content (CaO₂)

17.6 mL/dL

CvO₂: 12.5 mL/dL

Comparison of Oxygen Consumption (VO₂) Predictive Equations

Select	Method	Formula Basis	Est. VO₂ (mL/min)	Cardiac Output	Cardiac Index

Note: Estimated cardiac output can vary by 15–25% depending entirely on the choice of assumed VO₂ formula, illustrating why assumed Fick can introduce notable errors in borderline low-output states.

Sweep Gas OFF Protocol (Shunt Fraction Model)

Bedside Weaning Protocol & Clinical Steps

Standardized step-by-step bedside trial for assessing native cardiac output prior to central VA ECMO decannulation.

1. Verify Cannulation

Confirm central right-atrial drainage to ascending-aorta return cannulation. Do not apply to femoral-femoral VA ECMO due to mixing zone dynamics.

2. Ensure Anticoagulation

Confirm Activated Clotting Time (ACT) > 200 s or therapeutic heparinization before reducing circuit flow to prevent cannula thrombus formation.

3. Maximize FiO₂

Increase ventilator FiO₂ to 1.0 (100%) to optimize pulmonary venous oxygenation and support the assumption of SpvO₂ ≈ 100%.

4. Reduce VA ECMO Flow

Decrease ECMO pump flow (Qe) to 10–20% of full support (typically 0.4–0.8 L/min idling flow) to allow the native ventricle to eject.

5. Turn Sweep Gas OFF

Turn sweep gas and oxygen flow to 0 L/min while keeping blood pump running. Wait ≥ 10 minutes to reach steady state (SpmO₂ = SvO₂).

6. Simultaneous Blood Gases

Simultaneously draw co-oximetry blood gases: systemic arterial (SaO₂, radial line) and mixed venous (SvO₂, PA catheter or circuit venous line).

7. Calculate Hemodynamics

Enter Qe, SaO₂, SvO₂ below. Keep SpvO₂ = 100% checked. If MAP and CVP are measured, enter them to calculate Cardiac Power Output Index (CPOi).

8. Weaning Criteria & Re-support

Recovery targets: Native CI ≥ 2.2 L/min/m², DO₂I > 300 mL/min/m², and optional CPOi ≥ 0.30 W/m². If sub-target, immediately restart sweep gas and restore full flow.

Clinical Hemodynamic Parameters

Unit: L/min

Extracorporeal Flow (Qe) Right atrial-to-aorta shunt flow

L/min

Systemic Arterial Saturation (SaO₂) Aortic / Radial arterial line

%

Mixed Venous / PA Saturation (SvO₂) Pulmonary artery catheter

%

Pulmonary Venous Saturation (SpvO₂)

Assume 100%

%

Body Surface Area (BSA)

m²

Hemoglobin (Hb)

g/L

Invasive Pressures (Optional for CPOi) Leave blank to omit

Mean Arterial Pres (MAP)

mmHg

Central Venous Pres (CVP)

mmHg

Calculated Native Cardiac Output (Qp)

3.20 L/min

Native SV Flow: 3200 mL/min Shunt Ratio (k): 0.800 Total Systemic (Qs): 4.00 L/min

Native Cardiac Index

1.93 L/min/m²

Systemic: 2.41 L/min/m²

Effective DO₂I

333 mL/min/m²

Convective O₂ delivery

Cardiac Power Output Index

0.26 W/m²

ΔP: 61 mmHg (Optional)

Central VA ECMO Shunt Fraction Formulation (Sweep Gas OFF)

Sweep Gas Discontinued (0 L/min) → SpmO₂ = SvO₂ (circuit blood unoxygenated)

Qp = Qe × (SaO₂ - SvO₂) / (SpvO₂ - SaO₂) = (k × Qe) / (1 - k)

Live Evaluation: k = (93 - 65) / (100 - 65) = 0.800 → Qp = (0.800 × 0.80) / (1 - 0.800) = 3.20 L/min.

Central VA ECMO Hemodynamic Model Sweep Gas OFF

Sensitivity Analysis: Impact of Pulmonary Venous Saturation (SpvO₂)

Impact of assuming 100%

Assuming SpvO₂ = 100% yields a conservative baseline estimate of native cardiac output. If the actual pulmonary venous saturation is lower (e.g. 96% due to atelectasis or intrapulmonary shunt), true native cardiac output is higher.

Assumed / Measured SpvO₂	Δ(PV - MV)	Shunt Ratio k (Qp / Qs)	Native CO (Qp)	Native CI (BSA = 1.66 m²)

Theoretical Derivation: Equivalence of Generalized Fick & Sweep Gas OFF Simplification +

1. Generalized Mass-Balance on VA ECMO:

Across the arterial mixing point in the aorta, systemic oxygen flow equals the sum of pulmonary flow and ECMO circuit flow:

Qs × CaO₂ = (Qp × CpvO₂) + (Qe × CpmO₂)

Since total systemic flow is the sum of native and ECMO flows (Q_s = Q_p + Q_e):

(Qp + Qe) × CaO₂ = (Qp × CpvO₂) + (Qe × CpmO₂) Qp × (CaO₂ - CpvO₂) = Qe × (CpmO₂ - CaO₂) Qp = Qe × (CpmO₂ - CaO₂) / (CaO₂ - CpvO₂)

Substituting oxygen saturation (as hemoglobin and binding capacity are uniform across central blood):

Qp = Qe × (SpmO₂ - SaO₂) / (SaO₂ - SpvO₂)

2. Simplification during Liberation (Sweep Gas OFF):

When sweep gas and oxygen flow are discontinued (0 L/min), no gas exchange occurs across the membrane lung. Consequently, blood exiting the circuit into the aorta has identical saturation to mixed venous blood entering the circuit (SpmO₂ = SvO₂):

SpmO₂ = SvO₂

Substituting into the generalized formulation gives:

Qp = Qe × (SaO₂ - SvO₂) / (SpvO₂ - SaO₂)

Which is identical to the classical shunt fraction formulation where k = Q_p / Q_s = (SaO₂ − SvO₂) / (SpvO₂ − SvO₂) and Q_p = (k · Q_e) / (1 − k) (Q.E.D.).

Equation Abbreviations & Variable Definitions

Qp: Native pulmonary blood flow (native cardiac output across aortic valve, L/min)

Qe: Extracorporeal ECMO pump circuit flow (L/min)

Qs: Total systemic blood flow (Qp + Qe, L/min)

SaO₂: Systemic arterial oxygen saturation (radial arterial line / ascending aorta, %)

SvO₂: Mixed venous oxygen saturation (pulmonary artery or caval venous drainage, %)

SpvO₂: Pulmonary venous oxygen saturation (blood returning from lungs to left atrium, %)

SpmO₂: Post-membrane oxygen saturation (blood exiting oxygenator; equals SvO₂ when sweep is OFF, %)

k: Shunt fraction ratio: k = Qp / Qs = (SaO₂ − SvO₂) / (SpvO₂ − SvO₂)

DO₂I: Effective convective oxygen delivery index (mL/min/m²)

CI: Cardiac index (flow normalized to body surface area, L/min/m²)

CPOi: Cardiac power output index: CI × (MAP − CVP) / 451 (W/m², native LV hydraulic workload)

MAP / CVP: Mean arterial pressure and central venous pressure (mmHg, optional)

Protocol Reference: Lim HS. A novel ‘shunt fraction’ method to derive native cardiac output during liberation from central VA ECMO. ESC Heart Fail (2024); 11(1): 570–573.

V-V Circuit & Oximetric Parameters

V-V ECMO Circuit Flow (Qecmo)

L/min

Oxygenator Return Saturation (SreturnO₂) Typically 100%

%

Drainage Limb Saturation (SdrainageO₂) Blood entering ECMO

%

True Central Venous Saturation (ScvO₂) Proximal systemic venous

%

Arterial Oxygen Saturation (SaO₂) Arterial line / Admixture

%

Hemoglobin (Hb)

g/L

Total Systemic Flow (Qs) & Native Bypass

4.00 L/min

ECMO Flow (Qecmo): 3.00 L/min Native Bypass: 1.00 L/min Qecmo / Qs: 0.75

Recirculation Fraction (Rf)

0%

Shunt Ratio: 1.00 : 1

Total DO₂

490 mL/min

Oxygen delivery

V-V ECMO Fick Equations (Mass Balance)

Recirculation Fraction (Rf) = (SdrainageO₂ - ScvO₂) / (SreturnO₂ - ScvO₂) × 100% Fick Shunt Ratio (Lim 2021, Eq 4) = (SreturnO₂ - ScvO₂) / (SreturnO₂ - SdrainageO₂) Qs (Total Systemic Flow) = Qecmo × (SreturnO₂ - ScvO₂) / (SaO₂ - ScvO₂) Native Bypass Flow = Qs - Qecmo [Physiologically non-negative: ≥ 0 L/min] DO₂ = Qs × 1.36 × (SaO₂ / 100) × Hb

V-V ECMO Recirculation Model

Physiological Derivation & Caveats: Mass Balance vs. Published Equation 7 +

1. Mass Balance at the Right Heart: In an in-series V-V ECMO circuit, blood entering the pulmonary artery and systemic circulation is the direct mixture of ECMO post-oxygenator return flow (Q_ecmo at S_returnO₂) and native systemic venous return that bypassed the circuit (Q_bypass at true upstream S_cvO₂):

              Qs × SaO₂ = (Qecmo × SreturnO₂) + (Qbypass × ScvO₂)

              Since Qbypass = Qs − Qecmo:

              Qs = Qecmo × (SreturnO₂ − ScvO₂) / (SaO₂ − ScvO₂)

Because systemic arterial saturation is bounded between central venous and ECMO return (S_cvO₂ ≤ S_aO₂ ≤ S_returnO₂), this mass balance guarantees that total systemic flow (Q_s) is always ≥ ECMO pump flow (Q_ecmo), ensuring that native bypass flow is always physiologically non-negative (≥ 0 L/min).

2. Caveat of Published Equation 7 (Lim HS, Perfusion 2021): In Equation 7 of the author's review, Q_s was derived by direct algebraic analogy to the classic congenital shunt formula (substituting S_pa → S_drainage):

              Qs = Qecmo × (SreturnO₂ − SdrainageO₂) / (SaO₂ − ScvO₂)   [Lim 2021, Eq 7]
            

When there is no recirculation (S_drainage = S_cv), both formulas yield identical results. However, when recirculation occurs (S_drainage > S_cv), the numerator (S_return − S_drainage) contracts. As noted in the paper's caveat, this causes Q_s to be underestimated and can mathematically produce a negative native bypass flow. This calculator therefore implements the Mass Balance formulation to preserve physiological consistency across all recirculation states.

3. Recirculation Metrics: We report both the Conventional Recirculation Fraction (R_f = 0% to 100%, representing the proportion of drainage flow drawn directly from the return cannula) and the Fick Shunt Ratio (Q_p/Q_s analogy from Equation 4, where baseline is 1.00 : 1 and values > 1.50 indicate significant recirculation).

Clinical Footnote: The Beta-Blocker & DO₂ Hemodynamic Paradox +

In high cardiac output patients on V-V ECMO, administering beta-blockers reduces native cardiac output. This increases the Q_ecmo / Q_s ratio and improves arterial saturation (SaO₂ may rise from 85% to 90%).

However, because total bulk flow (Q_s) is reduced, total convective oxygen delivery (DO₂) paradoxically drops (e.g., from 925 down to 734 mL/min). An improving SaO₂ must always be interpreted alongside convective DO₂.

Equation Abbreviations & Variable Definitions

Recirculation Fraction (Rf): Proportion of ECMO drainage flow drawn directly from the return cannula: (SdrainageO₂ − ScvO₂) / (SreturnO₂ − ScvO₂) × 100%

Fick Shunt Ratio (Qp/Qs): Intracardiac shunt analogy (Lim 2021, Eq 4): (SreturnO₂ − ScvO₂) / (SreturnO₂ − SdrainageO₂); baseline is 1.00 : 1, >1.50 indicates significant recirculation

Qecmo: Extracorporeal V-V ECMO circuit pump flow (L/min)

Qs: Total systemic blood flow (cardiac output, L/min) derived via mass balance: Qecmo × (SreturnO₂ − ScvO₂) / (SaO₂ − ScvO₂)

Native Bypass Flow: Deoxygenated systemic venous return that bypasses the ECMO circuit directly into the right heart (L/min): Qs − Qecmo (always ≥ 0 L/min)

SreturnO₂: Oxygen saturation of post-oxygenator blood returned into the right atrium via the return cannula (typically 100%, %)

SdrainageO₂: Oxygen saturation of blood drawn into the ECMO drainage cannula (elevated by recirculation, %)

ScvO₂: True central venous oxygen saturation prior to ECMO return admixture (upstream systemic venous return, %)

SaO₂: Systemic arterial oxygen saturation (radial arterial line / blood gas, %) reflecting the admixture of ECMO return and native bypass flow

DO₂: Total convective systemic oxygen delivery (mL/min): Qs × 1.36 × (SaO₂ / 100) × Hb

Hb: Hemoglobin concentration (g/L)

Reference: Lim HS. The physiology of extracorporeal membrane oxygenation: The Fick principle. Perfusion (2021); DOI: 10.1177/02676591211055971.

Admixture & Watershed Parameters

Peripheral VA ECMO Flow (Qecmo)

L/min

ECMO Return Saturation (SreturnO₂)

%

Native LV Ejection Saturation (SLVO₂) PCWP / LA / Transpulmonary

%

Arterial Admixture Saturation (SaO₂) Sampled from Right or Left Radial

%

Derived Native LV Output (QLV)

3.50 L/min

Total Systemic (Qs): 7.00 L/min Fractional ECMO Flow (FQecmo): 0.50 Fractional LV Flow (FQLV): 0.50

Aortic Admixture Equation

SaO₂ = (FQecmo × SreturnO₂) + (FQLV × SLVO₂) FQecmo = (SaO₂ - SLVO₂) / (SreturnO₂ - SLVO₂) Qs = Qecmo / FQecmo Native LV Output (QLV) = Qs - Qecmo

By sampling arterial blood at the right radial (brachiocephalic) and left radial (distal arch) arteries, the location of the watershed and native ejection fraction can be quantified at the bedside.

Equation Abbreviations & Variable Definitions

SaO₂: Arterial oxygen saturation at the sampling site within the mixing zone (right or left radial artery, %)

FQecmo: Fractional ECMO flow (Qecmo / Qs): proportion of total systemic flow delivered retrogradely by the VA ECMO circuit

FQLV: Fractional native LV flow (1 − FQecmo = QLV / Qs): proportion of systemic flow contributed by antegrade native LV ejection

SreturnO₂: Oxygen saturation of post-oxygenator blood returned retrogradely via the femoral arterial cannula (typically 100%, %)

SLVO₂: Oxygen saturation of native transpulmonary blood ejected by the LV (sampled from PCWP wedged position, LA, or LV, %)

Qecmo: Extracorporeal peripheral VA ECMO circuit pump flow (L/min)

Qs: Total systemic blood flow (antegrade LV flow + retrograde ECMO flow, L/min): Qecmo / FQecmo

Native LV Output (QLV): Transpulmonary blood flow ejected by the native left ventricle across the aortic valve (L/min): Qs − Qecmo

Reference: Lim HS. The physiology of extracorporeal membrane oxygenation: The Fick principle. Perfusion (2021); DOI: 10.1177/02676591211055971.