Fick Equation For Cardiac Output Calculator

How does the Fick equation for cardiac output calculator work?

This health tool calculates the cardiac output based on the Fick principle of blood flow measurement with marker substance.

The Fick principle is based on the observation that the total uptake/release of substance by the peripheral tissues equals the product of the blood flow to the peripheral tissues and the arterial-venous concentration difference (gradient) of the substance.

The principle evolved by studying the oxygen blood flow in the body. The variables used in the Fick equation for cardiac output calculator are:

■ VO₂ - oxygen consumption in ml/min of pure gaseous oxygen, measured through a spirometer;

■ C_a - oxygen concentration of oxygenated blood taken from the pulmonary vein;

■ C_v - oxygen concentration of deoxygenated blood from an intravenous cannula.

At the same time, a note should be made that C_a - C_v is known as arteriovenous oxygen difference.

The Fick equation starts from:

VO₂ = (CO x C_a) - (CO x C_v)

Which means that the cardiac output equation is:

 CO = VO₂ / (C_a - C_v)

While in practice it can be hard to use the method by the books because of gas concentrations, the Fick determination is used with the help of an assumed value for VO₂ (oxygen consumption). One of the common assumed values is 125 mL/min per m² of BSA – body surface area.  

The Fick equation is applicable in a series of measurements in the clinical setting such as in renal physiology. It is important to know the amount of marker substance taken up by the organ per unit time, its concentration in the arterial blood supply to the organ and in the venous blood leaving the organ.

In order to measure the oxygen content of arterial and venous blood, there are two samples to be taken:

■ One from peripheral arterial blood to replace the need for a probe from the pulmonary vein, with high oxygen content;

■ One from the pulmonary artery, with low oxygen content.

Changes in stroke volume and heart beat are said to influence cardiac output, however, heart and lung condition do not affect the VO₂ component but influence the oxygen content concentrations in the Flick formula.

One of the criticisms received by the method refers to the fact that the VO₂ max cannot be accurately measured in either of the methods, with water-sealed spirometry or BSA based approximation.

Example of a calculation

Taking the case of a patient with an oxygen uptake of 900 mL/min, an arterial concentration of 0.18 mL O₂/mL blood and a venous concentration of 0.12 mL O₂/mL blood. How to calculate cardiac output by the Fick formula?

CO = VO₂ / (C_a - C_v) = 900 / (0.18 - 0.12) = 15,000 mL/min

References

1) Mahutte CK, Jaffe MB, Chen PA, Sasse SA, Wong DH, Sassoon CS. (1994) Oxygen Fick and modified carbon dioxide Fick cardiac outputs. Crit Care Med; 22(1):86-95.

2) Mahutte CK, Jaffe MB, Sassoon CS, Wong DH. (1991) Cardiac output from carbon dioxide production and arterial and venous oximetry. Crit Care Med; 19(10):1270-7.

3) Cuschieri J, Rivers EP, Donnino MW, Katilius M, Jacobsen G, Nguyen HB, Pamukov N, Horst HM. (2005) Central venous-arterial carbon dioxide difference as an indicator of cardiac index. Intensive Care Med; 31(6):818-22.

4) Stock MC, Ryan ME. (1996) Oxygen consumption calculated from the Fick equation has limited utility. Crit Care Med; 24(1):86-90.