“Bohr equation”的意思、由来-开放百科全书

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Bohr equation

释义

Description
Derivation
References

{{hatnote|Not to be confused with the Bohr model or the Bohr effect.}}

The Bohr equation, named after Danish physician Christian Bohr (1855–1911), 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. The original formulation by Bohr, ^[1] required measurement of the alveolar partial pressure P_A.

The modification by Enghoff ^[2] replaced the mixed alveolar partial pressure of CO₂ with the arterial partial pressure of that gas. ^[3]

The Bohr equation, with Enghoff's modification, is commonly stated as follows:^[4]

Here is the physiological dead space volume and is the tidal volume;

is the partial pressure of carbon dioxide in the arterial blood, and

is the partial pressure of carbon dioxide in the average expired (exhaled) air.

Derivation

Its derivation is based on the fact that only the ventilated gases involved in gas exchange () will produce CO₂. Because the total tidal volume () is made up of (alveolar volume + dead space volume), we can substitute for .

Initially, Bohr tells us Vt = Vd + Va. The Bohr equation helps us find the amount of any expired gas, {{CO2}}, N₂, O₂, etc. In this case we will focus on {{CO2}}. Defining Fe as the fraction of expired {{CO2}} and Fa as the fraction of expired alveolar {{CO2}}, and Fd as fraction of expired dead space volume {{CO2}}, we can say

Vt x Fe = ( Vd x Fd ) + (Va x Fa ). This merely means all the {{CO2}} expired comes from two parts, the dead space volume and the alveolar volume.

If we suppose that Fd = 0 (since carbon dioxide concentration in air is normally negligible), then we can say that:^[5]

Where {{mvar|F_e}} = Fraction expired CO₂, and {{mvar|F{{sub|a}}}} = Alveolar fraction of CO₂.

Substituted as above.

Multiply out of the brackets.

Rearrange.

Divide by {{mvar|V_t}} and by {{mvar|F_a}}.

The above equation makes sense because it describes the total {{CO2}} being measured by the spirometer. The only source of the {{CO2}} we are assuming to measure is from the alveolar space where {{CO2}} and O₂ exchange takes place. Thus alveolar's fractional component, {{mvar|F_a}}, will always be higher than the total {{CO2}} content of the expired air, {{mvar|F_e}}, thus we will be always yielding a positive number.

Where Ptot is the total pressure, we obtain:

Therefore:

A common step is to then presume that the partial pressure of carbon dioxide in the end-tidal exhaled air is in equilibrium with that gas' tension in the pulmonary blood.

References

1. ^Bohr C. Ueber die Lungenathmung. Skand Arch Physiol1891; 2: 236 – 268.
2. ^Enghoff H. Volumen inefficax. Bemerkungen zur Frage des schädlichen Raumes. Upsala Läk.-Fören Förh, 1938;44:191-218. Article in German
3. ^Tipton, History of Exercise Physiology, p222
4. ^Respiratory Physiology: The Essentials, John B. West, 2005, 7th ed, Page 169
5. ^Davies, Andrew, and Carl Moores. The Respiratory System. Systems of the body. Edinburgh: Churchill Livingstone, 2003.

1 : Respiratory physiology

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