Cardiac output, which is the rate at which blood is pumped by the heart, can be determined using the Fick principle. According to this principle, the amount of oxygen (O2) delivered to the lungs must equal the amount of oxygen carried away by the pulmonary veins. This can be expressed using equations:

Equation 16.1: O2 delivery to the lungs (q1) = O2 concentration in pulmonary arterial blood ([O2]pa) multiplied by pulmonary arterial blood flow (Q), which is equal to cardiac output.

Equation 16.2: Rate of O2 uptake by the pulmonary capillaries from the alveoli (q2) equals the O2 consumption of the body.

Equation 16.3: Rate of O2 carried away by the pulmonary veins (q3) = O2 concentration in pulmonary venous blood ([O2]pv) multiplied by total pulmonary venous flow, which is virtually equal to pulmonary arterial blood flow (Q).

Equation 16.4: Conservation of mass.

Equation 16.5: Cardiac output calculation.

To calculate cardiac output using the Fick principle, three values are required: (1) O2 consumption of the body, (2) O2 concentration in pulmonary venous blood ([O2]pv), and (3) O2 concentration in pulmonary arterial blood ([O2]pa).

O2 consumption is determined by measuring the volume and O2 content of expired air. [O2]pv is obtained from a sample of peripheral arterial blood, while samples for O2 analysis from pulmonary arterial blood are taken using a catheter. The compositions of pulmonary arterial blood and mixed systemic venous blood are similar.

Using the given values, cardiac output can be calculated as follows: If the O2 consumption is 250 mL/minute, the arterial (pulmonary venous) O2 content is 0.20 mL of O2 per milliliter of blood, and the mixed venous (pulmonary arterial) O2 content is 0.15 mL of O2 per milliliter of blood, cardiac output equals 250/ (0.20 − 0.15) = 5000 mL/minute.
Terminal bronchiole To pulmonary veins From pulmonary artery Pulmonary artery q1 q2 O2 consumption 250 mL O2 /min [O2 ] pv 0.20 mL O2 /mL blood [O2 ] pa 0.15 mL O2 /mL blood q1 + q2 = q3 Alveolus q3 Pulmonary vein Alveoli •Fig. 16.45 Schema Illustrating the Fick Principle for Measuring Cardiac Output. Thechangeincolorfrompulmonaryarterytopulmonaryveinrepresentsthechangeincolorofthebloodasvenousbloodbecomesfullyoxygenated.
the pulmonary artery, plus the quantity of O2 that enters the pulmonary capillaries from the alveoli, must equal the quantity of O2 that is carried away by the pulmonary veins. The Fick principle is depicted schematically in
Fig.
16.45.
The rate of O2 delivery to the lungs (q1) equals the O2 concentration in pulmonary arterial blood ([O2]pa), multiplied by pulmonary arterial blood flow (Q), which equals cardiac output; that is,
Equation 16.1
If q2 is the net rate of O2 uptake by the pulmonary capillaries from the alveoli, then at steady state, q2 equals the O2 consumption of the body. The rate at which O2 is carried away by the pulmonary veins (q3) equals the O2 concentration in pulmonary venous blood ([O2]pv), multiplied by total pulmonary venous flow, which is virtually equal to pulmonary arterial blood flow (Q); that is,
Equation 16.2
From the law of conservation of mass,
Equation 16.3
Therefore,
Equation 16.4
When this is solved for cardiac output,
Equation 16.5
Eq. 16.5 is the statement of the Fick principle.
To determine cardiac output by this method, three values must be known: (1) O2 consumption of the body, (2) the O2 concentration in pulmonary venous blood ([O2]pv), and (3) the O2 concentration in pulmonary arterial blood ([O2]pa). O2 consumption is computed from measurements of the volume and O2 content of expired air over a given interval. Because the O2 concentration of peripheral arterial blood is essentially identical to that in the pulmonary veins, [O2]pv is determined with a sample of peripheral arterial blood withdrawn by needle puncture. The compositions of pulmonary arterial blood and mixed systemic venous blood are virtually identical to one another. Samples for O2 analysis are obtained from the pulmonary artery or right ventricle through a catheter. A very flexible catheter with a small balloon near the tip can be inserted into a peripheral vein. As the flexible tube is advanced, the flowing blood carries it toward the heart. By monitoring the pressure changes, the physician can advance the catheter tip into the pulmonary artery.
With the values depicted in
Fig. 16.45 , cardiac output can be calculated as follows: If the O2 consumption is 250 mL/minute, the arterial (pulmonary venous) O2 content is 0.20 mL of O2 per milliliter of blood, and the mixed venous (pulmonary arterial) O2 content is 0.15 mL of O2 per milliliter of blood, cardiac output equals 250/ (0.20 − 0.15) = 5000 mL/minute.