Editing Cardiac output (section)

===Fick principle===
{{main|Fick principle}}
[[File:Spirometry NIH.jpg|alt=An illustration of how spirometry is done|thumb|An illustration of how spirometry is done]]

The Fick principle, first described by [[Adolf Eugen Fick]] in 1870, assumes the rate of oxygen consumption is a function of the rate of blood flow and the rate of oxygen picked up by the red blood cells. Application of the Fick principle involves calculating the oxygen consumed over time by measuring the oxygen concentration of venous blood and arterial blood. ''Q'' is calculated from these measurements as follows:
* ''V''<sub>O<sub>2</sub></sub> consumption per minute using a [[spirometer]] (with the subject re-breathing air) and a [[Carbon dioxide|CO<sub>2</sub>]] absorber
* the oxygen content of blood taken from the pulmonary artery (representing mixed venous blood)
* the oxygen content of blood from a cannula in a peripheral artery (representing arterial blood)

From these values, we know that:

:<math chem>V_\ce{O2} = (Q \times C_A) - (Q \times C_V)</math>

where
* ''C''<sub>A</sub> is the oxygen content of arterial blood, and,
* ''C''<sub>V</sub> is the oxygen content of venous blood.
This allows us to say

:<math chem> Q\ = \frac{{V}_\ce{O2}}{{C}_{A} - {C}_{V}} </math>

and therefore calculate ''Q''. (''C<sub>A</sub>'' – ''C<sub>V</sub>'') is also known as the [[arteriovenous oxygen difference]].{{cn|date=August 2022}}

While considered to be the most accurate method of measuring ''Q'', the Fick method is invasive and requires time for sample analysis, and accurate oxygen consumption samples are difficult to acquire. There have been modifications to the Fick method where respiratory oxygen content is measured as part of a closed system and the consumed oxygen is calculated using an assumed oxygen consumption index, which is then used to calculate ''Q''. Other variations use [[inert gas]]es as tracers and measure the change in inspired and expired gas concentrations to calculate ''Q'' (Innocor, Innovision A/S, Denmark).

The calculation of the arterial and venous oxygen content of the blood is a straightforward process. Almost all oxygen in the blood is bound to [[hemoglobin|hæmoglobin]] molecules in the red blood cells. Measuring the content of hæmoglobin in the blood and the percentage of saturation of hæmoglobin—the oxygen saturation of the blood—is a simple process and is readily available to physicians. Each [[gram]] of haemoglobin can carry 1.34 mL of [[oxygen|O<sub>2</sub>]]; the oxygen content of the blood—either arterial or venous—can be estimated using the following formula:

:<math chem>\begin{align}
\text{Oxygen content of blood} &= \left [\text{haemoglobin} \right] \left ( \text{g/dL} \right ) \ \times\ 1.34 \left ( \text{mL}\ \ce{O2} /\text{g of haemoglobin} \right ) \\
&\times\ \text{saturation of blood}\ \left ( \text{percent} \right )\ +\ 0.0032\ \times\ \text{partial pressure of oxygen} \left ( \text{torr} \right )
\end{align} </math>