Bohr equation

The Bohr equation describes the amount of Physiological Dead Space in a person's lungs. This is given as a ratio of dead space to tidal volume. It differs from Anatomical Dead Space as measured by Fowler's method as it includes alveolar dead space.

Description

The bohr equation is used to quantify the ratio of physiological dead space to the total tidal volume, and gives an indication of the extent of wasted ventilation.

:$Vd/Vt\; =\; (PaCO2\; -\; PeCO2)\; /\; PaCO2$ [Respiratory Physiology: The Essentials, J. West, 2005, 7th ed, Page 169]

Derivation

Its derivation is based on the fact that only the ventilated gases involved in gas exchange (Va) will produce CO2. Because the Total tidal volume (Vt) is made up of $Va+Vd$, we can substitute Va for $Vt-Vd$.

:$Vt.Fe\; =\; Va.Fa$ Where Fe = Fraction expired CO2, and Fa = Alveolar fraction of CO2.

:$Vt.Fe\; =\; (Vt-Vd).Fa$ Substituted as above.

:$Vt.Fe\; =\; Vt.Fa\; -\; Vd.Fa$ Multiply out of the brackets.

:$Vd.Fa\; =\; Vt.Fa\; -\; Vt.Fe$ Rearrange.

:$Vd.Fa\; =\; Vt.(Fa\; -\; Fe)$

:$Vd/Vt\; =\; (Fa\; -\; Fe)\; /\; Fa$ Divide by Vt and by Fa.

Fa is analogous to PaCO2, and Fe is analogous to partial pressure of expired CO2, therefore:

:$Vd/Vt\; =\; frac\{PaCO2\; -\; PeCO2\}\{PaCO2\}$

References