Bohr equation

frac{VD}{VT}  =  frac{PaCO2-PECO2}{PaCO2}

This describes the amount of physiological dead space in the lungs, it’s given as a ratio and a typical value is 0.2 – 0.35.

bohr.jpg

All expired carbon dioxide (FE) must, by definition, come from alveolar gas (VA x FA) not dead space gas (VD).

Therefore to derive the Bohr equation (explanatory notes in brackets):

VT  x  FE  =  VA  x  FA

VT  x  FE  =  (VT-VD)  x  FA   (As VA=VT-VD)

VT  x  FE  =  VT  x  FA  –  VD  x  FA  (Multiply out brackets)

VD  x  FA  =  VT  x  FA  –  VT  x  FE  (Rearrange)

VD  x  FA  =  VT  x  (FA-FE)  (Simplify)

frac{VD}{VT}  =  frac{(FA-FE)}{FA}  (Divide by VT and FA)

The fraction of CO2 in the alveoli (FA) can’t realistically be measured, so the partial pressure of CO2 in the blood is used as it is virtually identical. The fraction of expired CO2 can easily be measured as a partial pressure with a capnometer.

frac{VD}{VT}  =  frac{PaCO2-PECO2}{PaCO2}

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