# Cardiac output

Cardiac output is the volume of blood being pumped by the heart in a minute. It is equal to the heart rate multiplied by the stroke volume.

So if there are 70 beats per minute, and 70 ml blood is ejected with each beat of the heart, the cardiac output is 4900 ml/minute. This value is typical for an average adult at rest, although cardiac output may reach up to 30 liters/minute during extreme exercise.

When cardiac output increases in a healthy but untrained individual, most of the increase can be attributed to increase in heart rate. Change of posture, increased sympathetic nervous system activity, and decreased parasympathetic nervous system activity can also increase cardiac output. Heart rate can vary by a factor of approximately 3, between 60 and 180 beats per minute, whilst stroke volume can vary between 70 and 120 ml, a factor of only 1.5.

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## Measuring Cardiac Output

There are many invasive and several non-invasive methods for measuring cardiac output in mammals.

An extremely crude non-invasive method, often used in the teaching of physiology to under-graduates, reasons as follows:

• The pressure in the heart rises as blood is forced into the aorta
• The more stretched the aorta, the greater the pulse pressure
• In healthy young subjects, each additional 2ml of blood results in a 1mmHg rise in pressure (This is the crude assumption, which even if the subject did have a model aorta, the elastic properties of the aorta mean that it offers increased resistance to expansion at increased pressures)
• Therefore Stroke volume = 2ml x Pulse pressure
• Cardiac Output is therefore 2ml x Pulse Pressure x Heart Rate

### The Fick principle

Developed by Adolf Eugen Fick (1829 - 1921), this involves measuring:

• VO2 consumption per minute using a spirometer (with the subject re-breathing air) and a CO2 absorber
• the oxygen content of blood taken from the pulmonary artery (representing venous blood)
• the oxygen content of blood from a cannula in a peripehral artery (representing arterial blood)

From these values, we know that:

[itex]VO_2 = (CO \times\ C_A) - (CO \times\ C_V)[itex]

where CO = Cardiac Output, CA = Oxygen concentration of arterial blood and CV = Oxygen concentratio of venous blood.

This allows us to say

[itex]CO = \frac{VO_2}{C_A - C_V}[itex]

and hence calculate cardiac output. In reality, this method is rarely used these days due to the difficulty of collecting and analysing the gas concentrations.

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:

[itex]Cardiac\ Output = \frac{Oxygen\ consumption}{ArterioVenous\ Oxygen\ difference}[itex]

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 serrogate 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 simple process. Most 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:

[itex]Oxygen\ content\ of\ blood = \left [ Hemoglobin \right ] \left ( g/dl \right )\ \times\ 1.36 \left ( ml\ O_2 /g\ of\ hemoglobin \right ) \times\ 10\ \times\ percentage\ saturation\ of\ blood[itex]

### Dilution methods

This method measures how fast flowing blood can dilute a marker substance introduced to the circulatory system, ususally using a pulmonary artery catheter. Early methods used a dye, the cardiac output being inversely proportional to the concentration of dye sampled downstream. A more modern technique is to introduce cold or room temperature water, and then measure the change in temperature downstream. This method can however be affected by the phase of respiration, especially under mechanical ventilation, and should therefore be performed at the same phase of the respiratory cycle (typically end-expiratory).

### Doppler method

This technique uses ultrasound and the Doppler effect to measure cardiac output. The blood velocity through the aorta cause a 'Doppler shift' in the frequency of the returning ultrasound waves. Echocardiographic measurement of the aortic root cross-sectional area (or, alternatively, the descending aorta area) combined with the flow velocity allows calculation of the cardiac output.

### Impedance plethysmography

This advanced technique was developed by NASA, it measures changes resistance in the chest as the heart beats to calculate cardiac output.

## Equations

By simplifying D'arcy's Law, we get the equation that

[itex] Flow = \frac{Pressure} {Resistance}[itex]

When applied to the circulatory system, we get:

[itex] Cardiac\ Output = \frac{ABP - RAP}{TPR}[itex]

Where ABP = Aortic (or Arterial) Blood Pressure, RAP = Right Atrial Pressure and TPR = Total Peripheral Resistance.

However, as ABP>>RAP, and RAP is approximately 0, this can be simplified to:

[itex]Cardiac\ Output \approx \frac{Aortic\ Blood\ Pressure}{Total\ Peripheral\ Resistance}[itex]

Physiologists will often re-arrange this equation, making ABP the subject, to study the body's responses.

As has already been stated, Cardiac Output is also the product of the heart rate and the stroke volume, which allows us to say:

[itex]Heart\ Rate \times Stroke\ Volume \approx \frac{ABP}{TPR}[itex]

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