Alveolar Gas Equation Calculator

The alveolar gas equation calculates partial pressure of oxygen in the alveoli (PAO₂). PAO₂ = (FiO₂/100) × (P_atm – PH₂O) – PaCO₂/RQ. It estimates how well oxygen moves from inspired air into the alveoli.

On room air (FiO₂ 21%), normal PAO₂ is approximately 100–110 mmHg. Values below 80 mmHg suggest impaired gas exchange.

The A-a gradient is the difference between alveolar oxygen (PAO₂) and arterial oxygen (PaO₂). It quantifies how efficiently oxygen transfers from alveoli into the blood.

Normal A-a gradient on room air is typically 10–20 mmHg. The gradient increases with age; a rough estimate is age/4 + 4. Gradients >20 mmHg suggest V/Q mismatch, diffusion impairment, or shunt.

A widened A-a gradient indicates impaired gas exchange due to V/Q mismatch, shunt (e.g., ARDS, pneumonia), or diffusion impairment (e.g., pulmonary fibrosis). Normal A-a gradient with hypoxemia suggests hypoventilation.

The PaO₂/FiO₂ ratio (P/F ratio) divides arterial oxygen by the fraction of inspired oxygen. It is used to assess the severity of hypoxemia and define ARDS.

ARDS severity by P/F ratio: Mild (P/F 200–300), Moderate (P/F 100–200), Severe (P/F <100). These criteria require specific ventilator settings and clinical context.

A normal P/F ratio is >300–500 mmHg. Values <300 indicate acute lung injury (ALI), and <200 indicate ARDS per the Berlin definition.

RQ is the ratio of CO₂ produced to O₂ consumed. The standard value is 0.8, reflecting a typical mixed diet. RQ ranges from 0.7 (fat metabolism) to 1.0 (carbohydrate metabolism).

Water vapor in the alveoli dilutes inspired gases. At body temperature (37°C), partial pressure of water vapor is 47 mmHg. This constant is subtracted to account for humidification.

At higher altitudes, barometric pressure decreases, reducing the driving pressure for oxygen. PAO₂ falls proportionally, leading to hypoxemia unless compensatory hyperventilation occurs.

Hypoventilation causes CO₂ retention (hypercapnia), which lowers PAO₂ and PaO₂ through the alveolar gas equation. The A-a gradient remains normal in pure hypoventilation.

Ventilation-perfusion (V/Q) mismatch occurs when some lung areas receive blood flow without ventilation (shunt-like) or ventilation without blood flow (dead space). It is the most common cause of hypoxemia.

A shunt is blood that passes through the lungs without participating in gas exchange. True shunt (e.g., from ARDS, pneumonia, atelectasis) causes hypoxemia that does not correct with supplemental oxygen.

The shunt equation (Q̇_S/Q̇_T) calculates the fraction of cardiac output that bypasses oxygenation. It uses PAO₂, PaO₂, and mixed venous oxygen content. Shunt &gt;20% indicates severe lung injury.

PAO₂ (alveolar oxygen) is calculated from the alveolar gas equation. PaO₂ (arterial oxygen) is measured from an arterial blood gas. The difference (A-a gradient) reflects lung efficiency.

Arterial oxygen content (CaO₂) = (Hb × 1.34 × SaO₂) + (0.003 × PaO₂). It represents the total oxygen delivered to tissues, combining hemoglobin-bound and dissolved oxygen.

Oxygen delivery (DO₂) = cardiac output × CaO₂. Normal DO₂ is approximately 1,000 mL/min. It reflects how much oxygen reaches the tissues per minute.

Increasing FiO₂ directly increases PAO₂. Each 10% increase in FiO₂ raises PAO₂ by approximately (P_atm – PH₂O) × 0.10 – (change in PaCO₂/RQ). High FiO₂ can cause absorption atelectasis.

Hyperoxemia is abnormally high arterial oxygen (PaO₂ &gt;120 mmHg). It can result from excessive supplemental oxygen and may cause oxygen toxicity, absorption atelectasis, and vasoconstriction.

This sigmoidal curve relates PaO₂ to SaO₂. A right shift (increased 2,3-DPG, acidosis, fever) decreases hemoglobin affinity for O₂, facilitating tissue unloading. A left shift has the opposite effect.

Type 1 respiratory failure is defined by PaO₂ <60 mmHg on room air. Causes include pneumonia, pulmonary edema, ARDS, and pulmonary embolism. It is characterized by a widened A-a gradient.

Type 2 respiratory failure is defined by PaCO₂ &gt;50 mmHg with hypoxemia. Causes include COPD, opioid overdose, neuromuscular disease, and chest wall deformities. The A-a gradient is typically normal.

ARDS requires acute onset, bilateral opacities on imaging, P/F ratio <300 with PEEP >5 cmH₂O, and exclusion of cardiogenic pulmonary edema. Severity is graded by P/F ratio.

Positive end-expiratory pressure (PEEP) recruits collapsed alveoli, improves V/Q matching, and increases PaO₂. Optimal PEEP balances recruitment with overdistension and hemodynamic compromise.

Driving pressure = plateau pressure – PEEP. Driving pressure <15 cmH₂O is associated with improved survival in ARDS. It reflects the strain applied to the lung during mechanical ventilation.

OI = (FiO₂ × MAP × 100) / PaO₂. It incorporates mean airway pressure to assess oxygenation severity. OI &gt;40 indicates severe respiratory failure requiring ECMO consideration.

The ROX index = (SpO₂/FiO₂) / respiratory rate. It predicts high-flow nasal cannula success in hypoxemic respiratory failure. ROX &gt;4.88 after 12 hours suggests success.

Prolonged exposure to FiO₂ &gt;0.6 (60%) can cause oxygen toxicity, leading to pulmonary inflammation, absorption atelectasis, and tracheobronchitis. Clinical signs include substernal chest pain and cough.

Deoxygenated hemoglobin has a higher affinity for CO₂ and H⁺ than oxygenated hemoglobin. This facilitates CO₂ transport in venous blood and CO₂ unloading in the lungs.

The Fick principle states that oxygen consumption (VO₂) = cardiac output × (arterial O₂ content – venous O₂ content). It is the gold standard for measuring cardiac output.

PAO₂ is used to calculate the A-a gradient, assess gas exchange efficiency, guide ventilator settings, and evaluate the severity of hypoxemic respiratory failure.

At 37°C, PH₂O is 47 mmHg. Hypothermia reduces PH₂O (e.g., 32°C → 36 mmHg), while hyperthermia increases it (e.g., 40°C → 55 mmHg). This affects PAO₂ calculations in extreme temperatures.

Dead space (V_D/V_T) is the fraction of each breath that does not participate in gas exchange. Normal is 0.2–0.3. Elevated dead space in ARDS is associated with increased mortality.

Capnography measures exhaled CO₂ over time. The waveform has four phases: dead space (A), mixed (B), alveolar plateau (C), and inspiration (D). End-tidal CO₂ approximates PaCO₂ in healthy lungs.