Fick principle
Developed by Adolf Eugen Fick (1829 - 1901), the Fick principle was first devised as a technique for measuring cardiac output. However, its underlying principles may be applied in a variety of clinical situations.
The essence of the Fick principle is that blood flow to an organ can be calculated using a marker substance if the following information is known:
- Amount of marker substance taken up by the organ per unit time
- Concentration of marker substance in arterial blood supplying the organ
- Concentration of marker substance in venous blood leaving the organ
In Fick's original method, the "organ" was the entire human body and the marker substance was oxygen.
The principle may be applied in different ways. For example, if the blood flow to an organ is known, together with the arterial and venous concentrations of the marker substance, then the uptake of marker substance by the organ may then be calculated.

# Variables
In Fick's original method, the following variables are measured:
- VO2, oxygen consumption in ml of pure gaseous oxygen per minute. This may be measured using a spirometer (with the subject re-breathing air) and a CO2 absorber
- Cv, the oxygen content of blood taken from the pulmonary artery (representing deoxygenated blood)
- Ca, the oxygen content of blood from a cannula in a peripheral artery (representing oxygenated blood)

# Equation
From these values, we know that:
where CO = Cardiac Output, Ca = Oxygen content of arterial blood and Cv = Oxygen content of mixed venous blood.
This allows us to say
and hence calculate cardiac output.

# Assumed Fick determination
In reality, this method is rarely used due to the difficulty of collecting and analysing the gas concentrations.  However, by using an assumed value for oxygen consumption, cardiac output can be closely approximated without the cumbersome and time-consuming oxygen consumption measurement.  This is sometimes called an assumed Fick determination.
A commonly-used value for O2 consumption at rest is 125ml O2 per minute per square meter of body surface area.

# 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, and the flow calculated is the flow across the pulmonary system.  This gives a simple way to calculate the cardiac output:
Assuming there are no shunts across the pulmonary system, 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 content of the blood is a straightforward process.  Almost all oxygen in the blood is bound to hemoglobin molecules in the red blood cells.  Measuring the content of hemoglobin in the blood and the percentage of 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 1.36 ml of O2, the oxygen content of the blood (either arterial or venous) can be estimated by the following formula:
Assuming a haemoglobin concentration of 15g/dl and an oxygen saturation of 99%, the oxygen content of arterial blood is approximately 200ml of O2 per litre.
The saturation of mixed venous blood is approximately 75% in health. Using this value in the above equation, the oxygen content of mixed venous blood is approximately 150ml of O2 per litre.
Cardiac output may also be estimated with the Fick principle using production of carbon dioxide as a marker substance.

# Use in renal physiology
The principle can also be used in renal physiology to calculate renal blood flow.
In this context, it is not oxygen which is measured, but a marker such as para-aminohippurate. However, the principles are essentially the same.