Alveolar gas equation

The partial pressure of oxygen (pO₂) in the pulmonary alveoli is required to calculate both the alveolar-arterial gradient of oxygen and the amount of right-to-left cardiac shunt, which are both clinically useful quantities. However, it is not practical to take a sample of gas from the alveoli in order to directly measure the partial pressure of oxygen. The alveolar gas equation allows the calculation of the alveolar partial pressure of oxygen from data that is practically measurable. It was first characterized in 1946.[1]

Assumptions

The equation relies on the following assumptions:

Inspired gas contains no carbon dioxide (CO₂)
Nitrogen (and any other gases except oxygen) in the inspired gas are in equilibrium with their dissolved states in the blood
Inspired and alveolar gases obey the ideal gas law
Carbon dioxide (CO₂) in the alveolar gas is in equilibrium with the arterial blood i.e. that the alveolar and arterial partial pressures are equal
The alveolar gas is saturated with water

Equation

p_{A}{\ce {O2}}=F_{I}{\ce {O2}}(P_{{\ce {ATM}}}-p{\ce {H2O}})-{\frac {p_{a}{\ce {CO2}}(1-F_{I}{\ce {O2}}(1-{\ce {RER}}))}{{\ce {RER}}}}

If $F_{I}{\ce {O2}}$ is small, or more specifically if $F_{I}{\ce {O2}}(1-{\ce {RER}})\ll 1$ then the equation can be simplified to:

p_{A}{\ce {O2}}\approx F_{I}{\ce {O2}}(P_{{\ce {ATM}}}-p{\ce {H2O}})-{\frac {p_{a}{\ce {CO2}}}{{\ce {RER}}}}

where:

Quantity	Description	Sample value
$p_{A}{\ce {O2}}$	The alveolar partial pressure of oxygen ( $p{\ce {O2}}$ )	107 mmHg (14.2 kPa)
$F_{I}{\ce {O2}}$	The fraction of inspired gas that is oxygen (expressed as a decimal).	0.21
P_ATM	The prevailing atmospheric pressure	760 mmHg (101 kPa)
$p{\ce {H2O}}$	The saturated vapour pressure of water at body temperature and the prevailing atmospheric pressure	47 mmHg (6.25 kPa)
$p_{a}{\ce {CO2}}$	The arterial partial pressure of carbon dioxide ( $p{\ce {CO2}}$ )	40 mmHg (5.33 kPa)
RER	The respiratory exchange ratio	0.8

Sample Values given for air at sea level at 37°C.

Doubling $F_{i}{\ce {O2}}$ will double $P_{i}{\ce {O2}}$ .

References

Curran-Everett D (June 2006). "A classic learning opportunity from Fenn, Rahn, and Otis (1946): the alveolar gas equation". Adv Physiol Educ. 30 (2): 58–62. doi:10.1152/advan.00076.2005. PMID 16709734.

External links

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[pmid16709734-1] Curran-Everett D (June 2006). "A classic learning opportunity from Fenn, Rahn, and Otis (1946): the alveolar gas equation". Adv Physiol Educ. 30 (2): 58–62. doi:10.1152/advan.00076.2005. PMID 16709734.

Respiratory physiology
Respiration	breath inhalation exhalation respiratory rate respirometer pulmonary surfactant compliance elastic recoil hysteresivity airway resistance bronchial hyperresponsiveness constriction dilatation mechanical ventilation
Control	pons pneumotaxic center apneustic center medulla dorsal respiratory group ventral respiratory group chemoreceptors central peripheral pulmonary stretch receptors Hering–Breuer reflex
Lung volumes	VC FRC Vt dead space CC PEF calculations respiratory minute volume FEV1/FVC ratio Lung function tests spirometry body plethysmography peak flow meter nitrogen washout
Circulation	pulmonary circulation hypoxic pulmonary vasoconstriction pulmonary shunt
Interactions	ventilation (V) Perfusion (Q) Ventilation/perfusion ratio V/Q scan zones of the lung gas exchange pulmonary gas pressures alveolar gas equation alveolar–arterial gradient hemoglobin oxygen–haemoglobin dissociation curve (Oxygen saturation 2,3-BPG Bohr effect Haldane effect) carbonic anhydrase (chloride shift) oxyhemoglobin respiratory quotient arterial blood gas diffusion capacity (DLCO)
Insufficiency	high altitude death zone oxygen toxicity hypoxia

Alveolar gas equation

Assumptions

Equation

See also

References

External links