Editing Diffusing capacity (section)

== Calculation ==

The diffusion capacity for oxygen <math>(D_{L_{O_2}})</math> is the proportionality factor relating the rate of oxygen uptake into the lung to the oxygen gradient between the capillary blood and the alveoli (per [[Fick's laws of diffusion]]). In [[respiratory physiology]], it is convenient to express the transport of gas molecules as changes in volume, since <math>{V_{O_2}}\propto {n_{O_2}}</math> (i.e., in a gas, a volume is proportional to the number of molecules in it).  Further, the oxygen concentration ([[partial pressure]]) in the pulmonary artery is taken to be representative of capillary blood.  Thus, <math>(D_{L_{O_2}})</math> can be calculated as the rate that oxygen is taken up by the lung <math>(\dot{V}_{O_{2}})</math> divided by the oxygen gradient between the alveoli ("A") and the pulmonary artery ("a").
{{NumBlk|::|<math>D_{L_{O_2}} =\frac {\dot{V}_{O_{2}}} {P_{A_{O_2}} - P_{a_{O_2}}} \simeq \frac {\dot{V}_{O_{2}}} {P_{A_{O_2}} - P_{v_{O_2}}}</math>   | {{EquationRef|1}} }}
::(For <math>\dot{V}</math>, say "V dot".  This is the notation of [[Isaac Newton]] for a first derivative (or rate) and is commonly used in respiratory physiology for this purpose.)

::::<math>\dot{V}_{O_{2}}</math> is the rate that oxygen is taken up by the lung (ml/min).
::::<math>P_{A_{O_2}}</math> is the partial pressure of oxygen in the alveoli.
::::<math>P_{a_{O_2}}</math> is the partial pressure of oxygen in the pulmonary artery.
::::<math>P_{v_{O_2}}</math> is the partial pressure of oxygen in the systemic veins (where it can actually be measured).

Thus, the higher the diffusing capacity <math>D_L</math>, the more gas will be transferred into the lung per unit time for a given gradient in partial pressure (or concentration) of the gas.  Since it can be possible to know the alveolar oxygen concentration and the rate of oxygen uptake - but not the oxygen concentration in the pulmonary artery - it is the venous oxygen concentration that is generally employed as a useful approximation in a clinical setting.

Sampling the oxygen concentration in the pulmonary artery is a highly invasive procedure, but fortunately another similar gas can be used instead that obviates this need ([[DLCO]]). [[Carbon monoxide]] (CO) is tightly and rapidly bound to hemoglobin in the blood, so the partial pressure of CO in the capillaries is negligible and the second term in the denominator can be ignored.  For this reason, CO is generally the test gas used to measure the diffusing capacity and the <math>D_L</math> equation simplifies to:
{{NumBlk|::|<math>D_{L_{CO}} = \frac {\dot{V}_{CO}} {P_{A_{CO}} }</math>. | {{EquationRef|2}} }}