Editing Fick principle (section)

==Underlying principles==
The Fick principle relies on the observation that the total uptake of (or release of) a substance by the peripheral tissues is equal to the product of the blood flow to the peripheral tissues and the arterial-venous concentration difference (gradient) of the substance. In the determination of cardiac output, the substance most commonly measured is the [[oxygen]] content of [[blood]] thus giving the arteriovenous oxygen difference, and the flow calculated is the flow across the pulmonary system.  This gives a simple way to calculate the cardiac output:{{cn|date=March 2021}}

:<math> \text{Cardiac Output} = \frac {\text{oxygen consumption}} {\text{arteriovenous oxygen difference}} </math>

Assuming there is no intracardiac shunt, the pulmonary blood flow equals the systemic blood flow.  Measurement of the arterial and venous oxygen content of blood involves the sampling of blood from the pulmonary artery (low oxygen content) and from the pulmonary vein (high oxygen content).  In practice, sampling of peripheral arterial blood is a surrogate for pulmonary venous blood. Determination of the oxygen consumption of the peripheral tissues is more complex.

The calculation of the arterial and venous oxygen concentration of the blood is a straightforward process.  Almost all oxygen in the blood is bound to [[hemoglobin]] [[molecule]]s in the [[red blood cell]]s.  Measuring the content of hemoglobin in the blood and the percentage of [[Oxygen saturation (medicine)|saturation of hemoglobin]] (the oxygen saturation of the blood) is a simple process and is readily available to physicians.  Using the fact that each gram of hemoglobin can carry {{val|1.34|ul=}} mL of O<sub>2</sub>, the oxygen content of the blood (either arterial or venous) can be estimated by the following formula:

:<math chem> \text{Oxygen Content of blood} = \left [\text{Hb} \right] \left ( \text{g/dl} \right ) \ \times\ 1.34 \left ( \text{mL}\ \ce{O2} /\text{g of Hb} \right ) \times\ O_2^{\text{saturation fraction}}  +\ 0.0032\ \times\ P_\ce{O2} (\text{torr}) </math>

Assuming a hemoglobin concentration of {{val|15|ul=g/dL}} and an oxygen saturation of 99%, the oxygen concentration of arterial blood is approximately {{val|200|ul=mL}} of O<sub>2</sub> per L.

The saturation of mixed venous blood is approximately 75% in health. Using this value in the above equation, the oxygen concentration of mixed venous blood is approximately {{val|150|ul=mL}} of O<sub>2</sub> per L.

Therefore, using the assumed Fick determination, the approximated cardiac output for an average man (1.9 m3) is:

:Cardiac Output = ({{val|125|ul=mL}} O<sub>2</sub>/minute × 1.9) / ({{val|200|ul=mL}} O<sub>2</sub>/L − {{val|150|ul=mL}} O<sub>2</sub>/L) = {{val|4.75|ul=L/minute}}

Cardiac output may also be estimated with the Fick principle using production of [[carbon dioxide]] as a marker substance.<ref>{{cite journal|last=Cuschieri|first=J|author2=Rivers, EP |author3=Donnino, MW |author4=Katilius, M |author5=Jacobsen, G |author6=Nguyen, HB |author7=Pamukov, N |author8= Horst, HM |title=Central venous-arterial carbon dioxide difference as an indicator of cardiac index.|journal=Intensive Care Medicine|date=June 2005|volume=31|issue=6|pages=818–22|pmid=15803301|doi=10.1007/s00134-005-2602-8|s2cid=8311073}}</ref>