Dead Space Fraction (Bohr Equation)

VD/VT = (PaCO₂ − PeCO₂) ÷ PaCO₂

Normal: 0.25–0.35 at rest (25–35%); rises with age, COPD, ARDS, PE; > 0.60 predicts weaning failure

Variables

VD/VT

Dead space fraction(fraction (0–1))

Normal: 0.25–0.35 (25–35%)

PaCO₂

Arterial CO₂ tension(mmHg)

Normal: 35–45 mmHg

PeCO₂

Mixed expired CO₂ tension(mmHg)

Normal: 25–32 mmHg

What It Measures

The VD/VT ratio represents the fraction of each breath that is 'wasted' by ventilating areas that receive air but have no blood flow (physiological dead space). Dead space includes anatomic dead space (conducting airways, ~150 mL) and alveolar dead space (alveoli with ventilation but no perfusion, as in PE or ARDS).

When to Use

Calculate to assess weaning readiness, severity of V/Q mismatch, and response to therapy. VD/VT > 0.60 is a strong predictor of inability to wean from mechanical ventilation. Essential for understanding why a patient needs very high minute ventilation to maintain normal CO₂.

Interactive Calculator

PaCO₂ (arterial)(mmHg)

PeCO₂ (mixed expired)(mmHg)

Worked Examples

Normal young adult

→ 0.30 (30%)

Normal physiological dead space

Massive PE

→ 0.67 (67%)

Markedly elevated — two-thirds of each breath wasted; patient needs high V̇E to compensate

Clinical Significance

VD/VT rises in pulmonary embolism (dead alveoli with blood flow diverted), ARDS (alveolar consolidation), emphysema (destroyed alveolar capillary bed), and right heart failure. Capnography estimates VD/VT non-invasively using end-tidal CO₂ (PETCO₂) in place of PeCO₂.

Memory Tips

💡VD/VT: PaCO₂ is always higher than mixed expired CO₂ because dead space dilutes the exhaled CO₂
💡Dead space = ventilation without perfusion (opposite of shunt = perfusion without ventilation)
💡High VD/VT → need higher V̇E to maintain PaCO₂ → increased work of breathing → weaning failure

NBRC Pearls

VD/VT > 0.60 is a weaning predictor — patient will fail SBT due to inability to maintain minute ventilation
End-tidal CO₂ (PETCO₂) approximates PeCO₂ — capnography can non-invasively estimate VD/VT
In ARDS: VD/VT may be 0.60–0.70, explaining the very high minute ventilation requirements

← All Formulas

What It Measures

Memory Tips

💡VD/VT: PaCO₂ is always higher than mixed expired CO₂ because dead space dilutes the exhaled CO₂

💡Dead space = ventilation without perfusion (opposite of shunt = perfusion without ventilation)

💡High VD/VT → need higher V̇E to maintain PaCO₂ → increased work of breathing → weaning failure