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Alveolar Gas and Ventilation Equations

Jun 28, 2025

Overview

This lecture explains the derivations of the alveolar ventilation and alveolar gas equations, focusing on their physiological basis and mathematical forms.

Dalton's Law and Partial Pressures

  • Dalton's Law states total pressure of a gas mixture equals the sum of partial pressures of each gas.
  • In the lungs, barometric pressure (Pb) is the sum of partial pressures of nitrogen, oxygen, carbon dioxide, and water vapor.
  • The partial pressure of a gas = its fractional concentration × total pressure.

Alveolar Ventilation Equation

  • Based on conservation of carbon dioxide: CO2 production rate = CO2 elimination rate by lungs.
  • V̇CO₂ = alveolar ventilation × fractional concentration of CO₂ in alveolar gas.
  • PₐCO₂ ≈ PaCO₂ (arterial and alveolar CO₂ are approximately equal).
  • Formula: PaCO₂ = (V̇CO₂ × barometric pressure) / alveolar ventilation.

Alveolar Gas Equation

  • Based on conservation of oxygen: net O₂ entering lungs equals O₂ consumption by the body.
  • Net O₂ in = alveolar ventilation × (fraction of O₂ inspired − fraction in alveolar air).
  • FIO₂* (fraction of O₂ in inspired air at alveolar level) accounts for water vapor dilution.
  • Respiratory quotient (RQ) = V̇CO₂ / V̇O₂, typically assumed as 0.8.
  • Alveolar gas equation (simplified): PAO₂ = PIO₂ − (PaCO₂ / RQ), where PIO₂ is pressure of inspired O₂.*

Alternative Forms & Considerations

  • Alternate form: Alveolar O₂ = inspired O₂ − O₂ used for metabolism.
  • Additional correction term exists, but is clinically negligible.
  • Assumptions: Dalton’s law holds, alveolar gas is saturated with water vapor, alveolar and arterial CO₂ are equal, inspired gas contains negligible CO₂.

Key Terms & Definitions

  • Dalton's Law — The total pressure of a gas mixture equals the sum of each gas's partial pressure.
  • Partial Pressure (P) — The pressure a single gas contributes to a mixture.
  • Alveolar Ventilation — The volume of air reaching the alveoli per minute.
  • Respiratory Quotient (RQ) — Ratio of CO₂ produced to O₂ consumed (usually 0.8).
  • FIO₂* — Fraction of inspired oxygen at the alveolar level (corrected for water vapor).
  • PaCO₂/PAO₂ — Partial pressure of CO₂/O₂ in arterial/alveolar gas.

Action Items / Next Steps

  • Review the derivations of alveolar ventilation and gas equations.
  • Read about factors influencing the respiratory quotient.
  • Prepare for upcoming lectures on ABG interpretation at high altitude.

Full transcript