Measuring Heart Rate

Lawrence Davis

13 Measuring Heart Rate

Units

Working as a nurse, one of the most common measurements Jolene takes is heart rate. Heart rate is often measured by counting the number of pulses that occur in the wrist or the neck over a specified amount of time. In order to compare heart rates measured by different people we need to be sure that everyone is using the same measurement units. The medical field uses beats per minute (BPM) as the standard unit for heart rate measurements.

Unit Conversion

Rather than waiting and counting pulses over a full minute, you can make the measurement more quickly by counting pulses for six seconds and then multiplying the number by ten, to get the number of pulses that would have occurred in sixty seconds, or one minute. This process is known as unit conversion and the number ten was the conversion factor for this example.

Everyday Example: Heart Rate

Carlotta wants to determine her heart rate in BPM. She counts nine pulses in six seconds. She then uses a conversion factor of ten to convert from beats per six seconds to BPM and determines her heart rate to be 90 BPM:

$(9\, beats\, per\, six\, seconds) \times 10 = 90\, \bold{BPM}$

The chain-link method of unit conversion prevents mistakes by keeping track of all the values, units, and conversion factors.

To apply the chain-link method:

Write down the original value and units.
Set this equal to itself, only now with units written as a fraction.
Multiply by conversion factors to cancel undesired units and leave only desired final units.
Invert some conversion factors to get the undesired units to cancel, if needed.
Multiply the numbers across the top.
Multiply the numbers across the bottom.
Divide the top result by the bottom result.
Record the final value.
Add on the desired final units (top and bottom) that are left over after cancelling.

Applying the chain link method to the previous example gives us the same answer, only now we don’t need to just know ahead of time that we should multiply by ten, we only needed to know there are 60 seconds in one minute, which we use as our conversion factor.

Everyday Example: Heart rate

Carlotta wants to determine her heart rate in BPM. She counts nine pulses is in six seconds. She then uses a conversion factor of ten to convert from beats per six seconds to BPM and determines her heart rate to be 90 BPM:

$\begin{equation*} 9\, beats\, per\, six\, seconds = \frac{9\, beats}{6\, \cancel{seconds}}\left(\frac{60\, \cancel{seconds}}{1\, minute}\right) = \frac{9\, beats \times 10}{minute}=\frac{90\, beats}{minute} \end{equation*}$

$\begin{equation*} =90\, \bold{BPM} \end{equation*}$

Applying the chain link method to the previous example gives us the same answer, only now we don’t need to know ahead of time that we should multiply by ten, we only needed to know that were 60 seconds in one minute, which we used as our conversion factor.

The act of ensuring that your answer to a problem has the correct units is called unit analysis. The term chain-link method is often used interchangeably with the terms unit analysis or dimensional analysis, such as in this helpful video demonstrating unit analysis with the chain-link method. Let’s practice some more unit conversion using the chain-link method with multiple conversion factors:

Everyday Example

Ronnie wants to estimate how much money he will spend on gas driving back and forth from campus this term. A round-trip to campus is 14.2 miles, his car typically gets 27 miles per gallon (MPG) and gas is currently $2.86 per gallon. He needs to drive to campus and back four times per week. Let’s predict his cost for gas during the 11 week term.

$\begin{equation*} 11\, weeks\, per\, term = \left(\frac{11\, weeks}{1\, term} \right) \left(\frac{4\, trips}{1\, week} \right) \left(\frac{14.2\, miles}{1\, trip} \right) \left(\frac{1\, gallon}{27\, miles} \right) \left(\frac{2.86\, dollars}{1\, gallon} \right) \end{equation*}$

$\begin{equation*} =\left(\frac{66.18\, dollars}{1\, term} \right)= 66.18\, Dollars\, per\, term \end{equation*}$

Standard Units

Similar to medical professionals, scientists use standard scientific (SI) units when reporting measurements so we can all stay on the same page. For example, the fundamental SI unit of time is seconds. In this course we will primarily use seconds for time, meters for length, kilograms for mass, and Kelvin for temperature. All of the other units we use will be combinations of these few fundamental SI units. The table below shows all seven of the fundamental SI units and their abbreviations^[1]. All other standard scientific units are derived units, meaning they are combinations of those seven fundamental units. Throughout this book abbreviated units will be bold for clarity. The seven fundamental units and their abbreviations are summarized in the following table. Visit the National Institute for Standards and Technology (NIST) for more information on standard units.

Table of the fundamental International Standard (SI) units
Property	Unit	Abbreviation
Length	meter	m
Mass	kilogram	kg
Time	seconds	s
Number (Amount)	mole	mol
Temperature	Kelvin	K
Electrical Current	Ampere	A (amp)
Luminous Intensity	candella	cd

As with heart rate, the standard medical units and standard scientific units don’t always match up, which means that we will need to be skilled in unit analysis and unit conversion if we want to use physics to analyze the human body. Let’s practice again.

Everyday Example: Units for speed

Aasma ran as fast as she could while a friend drove alongside in a car with the speedometer reading 14 miles per hour (MPH). Can you determine how fast Aasma was running in units of meters per second (m/s)? There are 1.6 kilometers (km) in one mile (mi) and 1000 meters (m) in one kilometer. Remembering that there are 60 seconds (s) per minute (min) and 60 min per hour (hr).

$\begin{equation*}14\, \bold{MPH}= \left(\frac{14\, \bold{mi}}{1\, \bold{hr}} \right) \left(\frac{1.6\, \bold{km}}{1\, \bold{mi}} \right) \left(\frac{1000\, \bold{m}}{1\, \bold{km}} \right) \left(\frac{1\, \bold{hr}}{60\, \bold{min}} \right) \left(\frac{1\, \bold{min}}{60\, \bold{s}} \right) \end{equation*}$

$\begin{equation*} =\left(\frac{6.2\,\bold{m}}{\bold{s}} \right)= 6.2\,meters\, per \, second \end{equation*}$

Abozenadah, H., Bishop, A., Bittner, S., Lopez, O., Wiley, C., and Flatt, P.M. (2017) Consumer Chemistry: How Organic Chemistry Impacts Our Lives. CC BY-NC-SA. Available at: http://www.wou.edu/chemistry/courses/online-chemistry-textbooks/ch105-consumer-chemistry/ ↵

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