It is the blood flow we are interested in: this is cardiac output. This method is the purest and most accurate means of estimating the cardiac output. It is not confused by low output states, valvular regurgitation, shunts or arrhythmias. The major source of error is the act of measuring the amount of exhaled oxygen, and the change in cardiac output over the period of measurement.
In practice, it is too fiddly to apply outside the laboratory. Also, ICU patients have inflamed lungs whose parenchyma consumes oxygen and confuses the issue further.
The principle in detail
VO2, the oxygen consumption, is simply the difference between the inspired and expired O2. You can measure it with an exhaled gas collection bag.
You can also estimate it. Conventionally, resting metabolic consumption of oxygen is
3.5 ml of O2 per kg per minute, or
125ml O2 per square meter of body surface area per minute.
Lets say the meaty pinkish lump below is the patient.
Fick teaches us that VO2 (oxygen extraction) is determined by the following equation:
We can rearrange that to form an equation which calculates cardiac output on the basis of oxygen extraction:
So, in a normal person, with a body surface area of 2m2 and thus with a VO2 of 250ml per minute,
CO = 250ml / (200ml – 150ml)
= 250 / 50
= 5 L/min
And there you have it. That is the "direct" Ficks method for measuring cardiac output.