Bohr Equation Calculator

Bohr equation

The Bohr equation (first described by Christian Bohr in 1891) quantifies the ratio of physiological dead space to the total tidal volume, and thus provides an indication of the extent of wasted ventilation.

Physiologic dead space includes the anatomic dead space (all the non-respiratory parts of the bronchial tree) but also the proportion of alveoli that are well-ventilated but poorly perfused and are therefore less efficient at exchanging gas with the blood.

The equation is based on two main facts: that the total tidal volume is made out of alveolar volume and dead space volume and that the ventilated gases involved in gas exchange at alveolar level produce CO₂.

By assuming that CO₂ concentration in air is negligible, then the only source of CO₂ is the alveolar space. We then presume that the partial pressure of carbon dioxide in the end-tidal exhaled air is in equilibrium with CO₂ pressure in the blood that leaves the alveolar capillaries of the lung.

Bohr equation for the volume of pulmonary physiological dead space:

Vd = Vt x (PACO2 – PETCO2) / PACO2

Where:

• V_t is the tidal volume;
• P_ACO₂ is the partial pressure of carbon dioxide in the arterial blood;
• P_ETCO₂ is the partial pressure of carbon dioxide in the average expired (exhaled) air.

In healthy individuals, the anatomic and physiologic pulmonary dead spaces are roughly of similar volumes but in conditions where portions of the lung are poorly perfused, the physiologic dead space may be considerably larger than the anatomic dead space, hence the need to determine it.

An elevated physiological dead space, has proven to be a useful clinical marker of prognosis in patients with acute respiratory distress syndrome and for patients with severe heart failure.

References

Original reference

Bohr C. Ueber die Lungenathmung. Skand Arch Physiol 1891; 2: 236 – 268.

Other references

Robertson HT. Dead space: the physiology of wasted ventilation. European Respiratory Journal 2015 45: 1704-1716;

Enghoff H. Volumen inefficax. Bemerkungen zur Frage des schädlichen Raumes. Upsala Läk.-Fören Förh, 1938;44:191-218.