8.12 - Cardiac output calculations

8.12 - Cardiac output calculations

Use heart rate and stroke volume to calculate cardiac output, rearrange the equation to find either factor, and compare results in consistent units.

Three quantities, one relationship

Each quantity describes a different aspect of the heart's pumping:

QuantityMeaningCommon unit
Heart rate (HR)number of heartbeats in one minutebeats per minute (bpm)
Stroke volume (SV)volume of blood pumped out of a ventricle in one heartbeatcm³ per beat, mL per beat or dm³ per beat
Cardiac output (CO)volume of blood pumped out of one ventricle in one minutecm³ per minute, mL per minute or dm³ per minute

During each beat, one ventricle pumps one stroke volume. In steady circulation, both ventricles pump the same volume; do not add their outputs together when calculating cardiac output. If there are 70 beats in a minute, it pumps that stroke volume 70 times. This is why cardiac output is found by multiplying a volume per beat by the number of beats per minute.

Cardiac output

cardiac output=stroke volume×heart rate\text{cardiac output} = \text{stroke volume} \times \text{heart rate} CO=SV×HRCO = SV \times HR

The units show what the equation means:

cm3beat×beatsmin=cm3min\frac{\text{cm}^3}{\text{beat}} \times \frac{\text{beats}}{\text{min}} = \frac{\text{cm}^3}{\text{min}}

The word beats cancels, leaving a volume per minute. If a table gives stroke volume simply as cm³, remember that stroke volume is already a per-beat quantity by definition.

Calculating cardiac output

Suppose a person's heart rate is 72 beats per minute and their stroke volume is 65 cm³ per beat. Find the cardiac output in dm³ per minute.

The requested quantity is cardiac output. The two given quantities are:

HR=72 beats min−1SV=65 cm3 beat−1HR = 72\ \text{beats min}^{-1} \qquad SV = 65\ \text{cm}^3\text{ beat}^{-1}

The requested output unit is dm³ per minute, so align the volume unit before substituting. The useful exact equivalences are 1 cm3=1 mL1\,\mathrm{cm}^{3} = 1\,\mathrm{mL} and 1000 cm3=1 dm3=1L1000\,\mathrm{cm}^{3} = 1\,\mathrm{dm}^{3} = 1 L. Therefore:

65 cm3=651000=0.065 dm365\ \text{cm}^3 = \frac{65}{1000} = 0.065\ \text{dm}^3

Now substitute into the equation:

CO=SV×HRCO = SV \times HR CO=0.065 dm3 beat−1×72 beats min−1CO = 0.065\ \text{dm}^3\text{ beat}^{-1} \times 72\ \text{beats min}^{-1} CO=4.68 dm3 min−1CO = 4.68\ \text{dm}^3\text{ min}^{-1}

The answer is sensible: about 0.065 dm³ is pumped in each of 72 beats, giving several cubic decimetres in one minute. The superscript 3 in cm³ or dm³ tells you that the unit measures volume; it is not an instruction to cube 65 or 0.065.

Finding heart rate or stroke volume

If cardiac output is given, division reverses the multiplication in the original equation:

HR=COSVandSV=COHRHR = \frac{CO}{SV} \qquad\text{and}\qquad SV = \frac{CO}{HR}

Choose the rearrangement by naming the quantity you need before touching the numbers.

Finding heart rate. A cardiac output is 5.40 dm³ per minute and stroke volume is 75 cm³ per beat. Find heart rate.

First use matching volume units:

5.40 dm3 min−1=5400 cm3 min−15.40\ \text{dm}^3\text{ min}^{-1} = 5400\ \text{cm}^3\text{ min}^{-1}

Then rearrange and substitute:

HR=COSV=5400 cm3 min−175 cm3 beat−1=72 beats min−1HR = \frac{CO}{SV} = \frac{5400\ \text{cm}^3\text{ min}^{-1}} {75\ \text{cm}^3\text{ beat}^{-1}} = 72\ \text{beats min}^{-1}

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