Makindo Medical Notes

Related Subjects: Asthma |Acute Severe Asthma |Exacerbation COPD |Pulmonary Embolism |Cardiogenic Pulmonary Oedema |Pneumothorax |Tension Pneumothorax |Respiratory (Chest) infections Pneumonia |Fat embolism |Hyperventilation Syndrome |ARDS |Respiratory Failure |Diabetic Ketoacidosis

🫁 Introduction

• The alveolar gas equation estimates alveolar oxygen partial pressure (PAO₂) since direct sampling of alveoli is not practical.
• It allows comparison between expected alveolar oxygen and measured arterial oxygen (PaO₂), helping identify causes of hypoxaemia.
• The respiratory quotient (RQ) reflects metabolic fuel use:
  • Carbohydrates → RQ ≈ 1.0
  • Fats → RQ ≈ 0.7
  • Proteins → RQ ≈ 0.8–0.9
  • Mixed diet (Western) → RQ ≈ 0.8–0.82
• Indirect calorimetry can measure RQ by assessing O₂ consumption (VO₂) and CO₂ production (VCO₂).

📐 Alveolar Gas Equation

PAO₂ = (Patm − PH₂O) × FiO₂ − (PaCO₂ ÷ RQ)

🌍 At Sea Level (Patm = 760 mmHg)

PAO₂ = (760 − 47) × 0.21 − (40 ÷ 0.8) ≈ (713 × 0.21) − 50 ≈ 150 − 50 = 100 mmHg

🧮 A–a Gradient

A–a gradient = PAO₂ − PaO₂

• Normal: <15 mmHg in young adults (increases with age: roughly age/4 + 4).
• Raised: Indicates V/Q mismatch, diffusion impairment, or shunt physiology.

📖 Definitions

• PAO₂: Alveolar partial pressure of oxygen (calculated).
• PaO₂: Arterial partial pressure of oxygen (measured via ABG).
• PH₂O: Water vapour pressure (~47 mmHg at 37°C).
• FiO₂: Inspired oxygen fraction (0.21 on room air).
• PaCO₂: Arterial/alveolar CO₂ partial pressure (~40 mmHg).
• RQ: Respiratory quotient (VCO₂/VO₂), typically 0.8.

🧪 Clinical Relevance

• Normal A–a gradient, low PaO₂: Hypoventilation or low inspired O₂ (altitude, CNS depression, neuromuscular disease).
• High A–a gradient:
  • V/Q mismatch → pneumonia, COPD, pulmonary embolism.
  • Diffusion impairment → pulmonary fibrosis, ARDS.
  • Right-to-left shunt → congenital heart disease, severe pneumonia.

🧑‍⚕️ Worked Examples

1. Case 1: Hypoventilation ABG: PaO₂ = 60 mmHg, PaCO₂ = 60 mmHg (FiO₂ 0.21) PAO₂ = (713 × 0.21) − (60 ÷ 0.8) = 150 − 75 = 75 mmHg A–a gradient = 75 − 60 = 15 mmHg (normal) → hypoventilation as cause.
2. Case 2: V/Q mismatch (e.g., pneumonia) ABG: PaO₂ = 60 mmHg, PaCO₂ = 40 mmHg PAO₂ = (713 × 0.21) − (40 ÷ 0.8) = 150 − 50 = 100 mmHg A–a gradient = 100 − 60 = 40 mmHg (raised) → suggests gas exchange abnormality.
3. Case 3: High altitude (Patm ~500 mmHg) PAO₂ = (500 − 47) × 0.21 − (40 ÷ 0.8) = 95 − 50 = 45 mmHg → explains hypoxaemia despite healthy lungs.

📚 Summary

The alveolar gas equation is a cornerstone of respiratory physiology and clinical medicine. It allows clinicians to distinguish hypoxaemia due to:

• 🫁 Hypoventilation (normal gradient)
• ⚠️ V/Q mismatch / diffusion defect / shunt (raised gradient)