Bohr Equation

\[\frac{V_D}{V_T}=\frac{P_{aCO_2}-P_{\bar E CO_2}}{P_{aCO_2}}\]

Variables

VDVT[VD/VT]physiological dead space fraction

PaCO2arterial carbon dioxide partial pressure (mmHg)

PECO2[PĒCO₂]mixed expired carbon dioxide partial pressure (mmHg)

Description

What is this formula?

The Bohr Equation estimates the physiological dead space fraction using carbon dioxide measurements. It compares arterial carbon dioxide partial pressure with mixed expired carbon dioxide partial pressure to determine the portion of ventilation that does not effectively participate in gas exchange.

When to use it

Use this formula when evaluating ventilation efficiency, interpreting pulmonary gas exchange, studying respiratory physiology, or monitoring patients receiving mechanical ventilation.

Example

Data:

PaCO2 = 40 mmHg

PECO2 = 28 mmHg

Formula:

VDVT = (PaCO2 − PECO2) / PaCO2

Substitution:

VDVT = (40 − 28) / 40

VDVT = 12 / 40

VDVT = 0.30

Result:

Physiological Dead Space Fraction = 0.30

Applications

- Pulmonary physiology

- Mechanical ventilation monitoring

- Critical care medicine

- Gas exchange assessment

- Evaluation of ventilation inefficiency

- Pulmonary embolism assessment

Note

The Bohr Equation is a physiological estimation model. It assumes that arterial CO2 represents ideal alveolar CO2 and that mixed expired CO2 reflects the dilution caused by dead space ventilation. Clinical variants, such as the Enghoff modification, may use arterial CO2 in a way that includes additional effects from gas exchange abnormalities.