Dead space: bohr vs enghoff

7 min read Last updated April 8, 2026

Clinical frame: why this matters in anaesthesia/ICU

  • Dead space quantifies wasted ventilation: ventilation that does not eliminate CO₂.
    • High dead space → higher required minute ventilation to maintain PaCO₂ (risk: hypercapnia, increased work of breathing, ventilator burden).
  • Enghoff dead space is commonly used clinically because it can be calculated from arterial CO₂ and mixed expired CO₂; it reflects both dead space and V/Q mismatch (shunt-like effect).
    • Useful in ARDS/sepsis/PE: rising Enghoff VD/VT often correlates with severity and prognosis, but it is not a pure measure of anatomical+alveolar dead space.
  • Bohr dead space is the physiological definition (based on alveolar CO₂), but true PACO₂ is hard to measure directly at the bedside.
    • End-tidal CO₂ approximates PACO₂ only when V/Q is relatively uniform; it becomes unreliable with significant V/Q mismatch.

At-a-glance: what each equation is really measuring

  • Bohr: measures physiological dead space (anatomical + alveolar dead space) using PACO₂.
  • Enghoff: measures “Bohr dead space + effect of shunt/V/Q mismatch” using PaCO₂ as a surrogate for PACO₂.
  • Therefore: Enghoff VD/VT ≥ Bohr VD/VT (equal only when PaCO₂ ≈ PACO₂, i.e. minimal V/Q mismatch).

Definitions

  • Dead space (VD): volume of inspired gas that does not participate in CO₂ elimination.
    • Anatomical dead space: conducting airways to terminal bronchioles (plus equipment dead space if present).
    • Alveolar dead space: ventilated alveoli with no/low perfusion (high V/Q, including V/Q → ∞).
    • Physiological dead space = anatomical + alveolar dead space.
  • VD/VT: fraction of each tidal breath that is dead space.
    • Typical awake healthy adult: ~0.2–0.35 (increases with age, supine posture, lung disease, low VT ventilation, pulmonary vascular disease).

Bohr equation (physiological dead space)

  • Principle: all CO₂ in mixed expired gas comes from perfused alveoli; dead space gas contains ~0 CO₂.
  • Bohr equation: VD/VT = (PACO₂ − PECO₂) / PACO₂
    • PACO₂: mean alveolar CO₂ tension.
    • PECO₂: mixed expired CO₂ tension (from mixed expired sample or volumetric capnography).
  • Interpretation: quantifies true physiological dead space (anatomical + alveolar).
  • Practical limitation: PACO₂ is difficult to measure directly; end-tidal CO₂ (PETCO₂) is an imperfect surrogate when V/Q mismatch is present.

Enghoff modification (clinically used dead space index)

  • Enghoff replaces PACO₂ with PaCO₂: VD/VT = (PaCO₂ − PECO₂) / PaCO₂
    • PaCO₂ is easy to obtain, but it reflects the CO₂ of blood leaving all ventilated units, influenced by V/Q mismatch and shunt.
  • What it measures: a composite of dead space + V/Q inequality (including shunt effect).
    • Shunt (or low V/Q) increases PaCO₂ relative to PACO₂ by mixing venous blood with end-capillary blood, raising arterial CO₂ for a given alveolar CO₂.
    • Thus Enghoff VD/VT can rise even if anatomical/alveolar dead space is unchanged.
  • Clinical use: often termed physiological dead space in ICU literature, but strictly it is the Enghoff index (important viva distinction).

Relationship to capnography (PETCO₂, PECO₂, PACO₂)

  • PECO₂ (mixed expired) is not the same as PETCO₂ (end-tidal).
    • PECO₂ is the average CO₂ over the whole exhalation (requires mixed expired collection or volumetric capnography).
    • PETCO₂ is the plateau value at end-expiration (time capnography).
  • In ideal lungs: PACO₂ ≈ PETCO₂ ≈ PaCO₂ (small A–a CO₂ gradient).
  • With V/Q mismatch: PaCO₂ > PACO₂ and typically PaCO₂ > PETCO₂ (increased arterial–end tidal CO₂ gradient).
    • Common causes: pulmonary embolism, low cardiac output, COPD/asthma with uneven emptying, ARDS, severe pneumonia, high PEEP with overdistension.

How to obtain PECO₂ (mixed expired CO₂)

  • Douglas bag / mixed expired gas collection with CO₂ analysis (historical/physiology lab).
  • Volumetric capnography: integrates CO₂ against exhaled volume to derive PECO₂ and estimate dead space (including Fowler anatomical dead space).

Worked interpretation (numbers you can talk through in viva)

  • Example: PaCO₂ 6.0 kPa, PECO₂ 4.0 kPa → Enghoff VD/VT = (6−4)/6 = 0.33.
  • If significant V/Q mismatch: PaCO₂ 6.0 kPa, true PACO₂ 5.2 kPa, PECO₂ 4.0 kPa → Bohr VD/VT = (5.2−4)/5.2 = 0.23 but Enghoff = 0.33.
    • Difference (Enghoff − Bohr) reflects impact of V/Q inequality/shunt on PaCO₂.

Determinants of dead space (useful lists for short-answer questions)

  • Anatomical dead space increases with: upright posture, larger lung volumes, bronchodilation; decreases with: supine position, intubation/tracheostomy (bypasses upper airway).
  • Alveolar dead space increases with reduced pulmonary perfusion or overventilation: pulmonary embolism, low cardiac output, hypovolaemia, excessive PEEP/overdistension, emphysema, pulmonary vascular disease.
  • Equipment dead space: HME filters, catheter mounts, connectors; proportionally more important with small VT (paediatrics, lung-protective ventilation).
Define anatomical, alveolar and physiological dead space. How do they relate to each other?

Give crisp definitions and the additive relationship.

  • Anatomical dead space: conducting airways where no gas exchange occurs.
  • Alveolar dead space: alveoli that are ventilated but not perfused (high V/Q).
  • Physiological dead space = anatomical + alveolar dead space.
State the Bohr equation for dead space and explain the physiology behind it.

Start with the concept that dead space gas contains no CO₂, so mixed expired CO₂ is diluted by dead space.

  • VD/VT = (PACO₂ − PECO₂) / PACO₂.
  • CO₂ in expired gas originates from perfused alveoli; dead space contributes volume but ~0 CO₂ → lowers PECO₂ relative to PACO₂.
  • Therefore the fractional dilution of alveolar CO₂ by mixed expired CO₂ gives VD/VT.
What is the Enghoff modification? Why is it used clinically?

Highlight that it substitutes PaCO₂ for PACO₂ for practicality, at the cost of specificity.

  • VD/VT = (PaCO₂ − PECO₂) / PaCO₂.
  • Used because PaCO₂ is readily measured from an ABG; true PACO₂ is difficult to obtain.
  • It reflects dead space plus the effect of V/Q mismatch and shunt on arterial CO₂.
In what circumstance are Bohr and Enghoff dead space equal?

Link equality to PaCO₂ approximating PACO₂.

  • When PaCO₂ ≈ PACO₂, i.e. minimal V/Q mismatch/shunt and relatively uniform alveolar emptying.
  • Then substituting PaCO₂ for PACO₂ makes little difference, so Enghoff ≈ Bohr.
Why does Enghoff VD/VT increase in ARDS even if anatomical dead space is unchanged?

Explain the PaCO₂–PACO₂ divergence due to V/Q inequality and shunt.

  • ARDS causes marked V/Q heterogeneity and often shunt (low V/Q units).
  • Shunt/low V/Q raises PaCO₂ relative to mean PACO₂ (arterial blood is influenced by poorly ventilated units).
  • Enghoff uses PaCO₂, so VD/VT rises even if true dead space (Bohr) has not increased proportionally.
Differentiate PECO₂ and PETCO₂. Which one is used in Bohr/Enghoff calculations?

This is a common viva trap: mixed expired vs end-tidal.

  • PECO₂ is mixed expired CO₂ (average over the whole exhalation).
  • PETCO₂ is end-tidal CO₂ (plateau at end expiration).
  • Bohr/Enghoff require PECO₂ (mixed expired), not PETCO₂.
A patient has PaCO₂ 8.0 kPa and PECO₂ 4.0 kPa. Calculate Enghoff VD/VT and interpret it.

Show the calculation and what it implies clinically.

  • Enghoff VD/VT = (8 − 4) / 8 = 0.5.
  • High value suggests substantial wasted ventilation and/or significant V/Q mismatch/shunt effect (Enghoff index).
  • Expect increased PaCO₂–PETCO₂ gradient and higher ventilatory requirement to clear CO₂.
List causes of increased alveolar dead space and relate them to anaesthetic practice.

Think reduced pulmonary perfusion or overdistension.

  • Reduced perfusion: pulmonary embolism, low cardiac output, hypovolaemia, pulmonary vascular disease.
  • Overdistension/high alveolar pressure: excessive PEEP, high VT, emphysema (capillary bed loss).
  • Anaesthetic relevance: sudden rise in PaCO₂–ETCO₂ gradient and difficulty clearing CO₂ may indicate PE or low CO.
How does adding an HME filter affect dead space and CO₂ clearance? Who is most affected?

Distinguish equipment dead space and its proportional effect at low VT.

  • Adds equipment dead space, increasing VD/VT and raising PaCO₂ unless minute ventilation increases.
  • Most significant when VT is small: paediatrics, lung-protective ventilation, severe COPD with dynamic hyperinflation limiting VT.
Explain why PaCO₂ can be higher than PETCO₂ and give common causes in theatre/ICU.

Link to V/Q mismatch and increased dead space.

  • PaCO₂ > PETCO₂ when there is increased dead space/VQ mismatch: PETCO₂ reflects well-ventilated units, while PaCO₂ reflects whole-lung gas exchange.
  • Causes: PE, low cardiac output, ARDS, severe COPD/asthma with uneven emptying, excessive PEEP/overdistension, cardiac arrest/low pulmonary blood flow.

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