The alveolar gas equation is the method for calculating

partial pressure In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal g ...

of alveolar oxygen (P_AO₂). The equation is used in assessing if the

lungs The lungs are the primary organs of the respiratory system in humans and most other animals, including some snails and a small number of fish. In mammals and most other vertebrates, two lungs are located near the backbone on either side of ...

are properly transferring

oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as we ...

into the

blood Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in th ...

. The alveolar air equation is not widely used in clinical medicine, probably because of the complicated appearance of its classic forms. The

of oxygen (pO₂) in the

pulmonary alveoli A pulmonary alveolus (plural: alveoli, from Latin ''alveolus'', "little cavity"), also known as an air sac or air space, is one of millions of hollow, distensible cup-shaped cavities in the lungs where oxygen is exchanged for carbon dioxide. Al ...

is required to calculate both the alveolar-arterial gradient of oxygen and the amount of right-to-left

cardiac shunt A cardiac shunt is a pattern of blood flow in the heart that deviates from the normal circuit of the circulatory system. It may be described as right-left, left-right or bidirectional, or as systemic-to-pulmonary or pulmonary-to-systemic. The dire ...

, 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.

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 The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first st ...

* 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=F_I\ce(P_\ce-p\ce)-\frac\ce

F_I\ce

is small, or more specifically if

F_I\ce(1-\ce) \ll 1

then the equation can be simplified to: :

p_A\ce \approx F_I\ce(P_\ce-p\ce)-\frac\ce

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

F_i\ce

will double

P_i\ce

. Other possible equations exist to calculate the alveolar air. :

\begin 
P_A \ce & =  F_I \ce \left(PB-P \ce\right) - P_A C\ce \left(F_I \ce + \frac\right)
\\
& = P_I \ce - P_A C\ce \left(F_I \ce + \frac\right)
\\
& = P_I \ce - \frac\left(P_I \ce - P_E \ce\right)
\\
& = \frac
\end

Abbreviated alveolar air equation

P_A \ce = \frac

P_AO₂, P_EO₂, and P_iO₂ are the partial pressures of oxygen in alveolar, expired, and inspired gas, respectively, and VD/VT is the ratio of physiologic dead space over tidal volume.Fenn WO, Rahn H, Otis AB: A theoretical study of the composition of alveolar air at altitude. Am J Physiol 146:637-653, 1946

Respiratory quotient (R)

R = \frac

Physiologic dead space over tidal volume (VD/VT)

\frac = \frac

References

External links

Free interactive model of the simplified and complete versions of the alveolar gas equation (AGE)

S. Cruickshank, N. Hirschauer: ''The alveolar gas equation'' in Continuing Education in Anaesthesia, Critical Care & Pain, Volume 4 Number 1 2004Online Alveolar Gas Equation and iPhone application
by Medfixation.
A computationally functional Alveolar Gas Equation by vCalc.
{{DEFAULTSORT:Alveolar Gas Equation Respiratory physiology