Cardiac Reserve
This topic is discussed in Biol 241 and 242, Anatomy and Physiology. Thanks to Mary Bath-Balogh for
her help with this.
This is preparation for the final exam
Briefing: The purpose of the heart is to circulate blood around the body so that oxygen is delivered to
tissues and CO2 waste products are removed. The amount of blood that is circulated is a function of the
stroke volume (SV) which is the amount of blood that is pushed from the heart during a compression
and the heart rate (HR) which is the rate at which the heart beats. Cardiac Output (CO) is found from
the product of these two variables.
CO = SV × HR
Example. A person at rest may have a heart rate of 72 beats/min. If their stroke volume is 70 ml/beat
then their cardiac output is
CO = 70 × 72 = 5040
Since Cardiac output is typically shown in liters/min, then we can use dimensional analysis to convert
the value.
𝐶𝑂 = 70
𝑚𝑙
𝑏𝑒𝑎𝑡𝑠
1 𝑙𝑖𝑡𝑒𝑟
× 72
×
= 5.040 𝑙𝑖𝑡𝑒𝑟𝑠/𝑚𝑖𝑛
𝑏𝑒𝑎𝑡
𝑚𝑖𝑛
1000 𝑚𝑙
FYI: Since this is approximately the amount of blood in the human body, then at rest, the heart pumps
the entire blood volume every minute.
When a person exercises, their muscle tissues need more oxygen and so consequently, the heart
rate increases, thereby increasing the cardiac output. The maximum cardiac output is achieved when a
person’s heart rate reaches its maximum limit. In the case of well-trained athletes, this could be as high
as 200 beats per minute. Athletes have a second advantage compared to non-athletes as well. That is
that their heart muscle becomes stronger because of their training and therefore increases the stroke
volume. With both SV and HR increasing, there is a substantial increase in CO.
Cardiac output can be found using several methods. The first method is to use
echocardiography to find the stroke volume. The equation above can then be used to find the cardiac
output. The second method is to directly measure the cardiac output using a combination of measuring
devices while the subject runs on a treadmill.
Cardiac reserve is the difference between the maximum cardiac output and the basal or resting
cardiac output. The cardiac reserve is of particular interest because it corresponds to the capacity of an
individual to exercise. People with a higher cardiac reserve have greater aerobic exercise capacity. This
is relevant for people with heart disease and those who are athletes.
The problems in this paper focus on cardiac reserve.
1. In our investigation, we want to know if there is a correlation between resting heart rate and cardiac
reserve. If there is, we can use the heart rate to predict the cardiac reserve. Students from the campus
will be randomly selected for this research. Complete the research design table for the research we
could do to answer this question.
Research Design Table
Research Question:
Observational Study
Observational Experiment
Manipulative Experiment
Type of Research
What is the response variable?
What is the parameter that will be calculated?
Mean
List potential latent variables.
Grouping/explanatory Variables 1 (if present)
Levels:
Grouping/explanatory Variables 2 (if present)
Levels:
Proportion
Correlation
The (fictitious) data of 30 students is provided in the table below.
Resting Heart Rate
Cardiac Reserve
beats/min
Liters/min
58
25
58
30
63
24.6
63
17.6
68
25.9
74
12.2
63
21.9
75
17.3
67
20.7
72
8.4
77
11.1
74
15
72
15.3
78
17.8
76
18
60
28.1
56
25.5
57
16.4
62
22.1
61
24.5
75
19.3
66
15.8
68
15.4
63
18
70
11.4
73
15.9
74
18.4
72
8.7
80
11.4
79
12.3
One of the criteria for using a regression analysis is that the data are bivariate normally
distributed. While normality is often assumed, one way to determine it is by using Chi Square to see if
the data is consistent with the normal distribution. This can be done by creating intervals of deciles
(intervals of 10%). In this example, we will do this only for the cardiac reserve data. There is an extra
complication for testing if the data are consistent with a normal distribution that we haven’t
encountered in class yet, but the modification that will be made to the analysis is within your ability to
do. The modification that we will make is to lose 2 extra degrees of freedom since we will need to
estimate the population mean and standard deviation with the sample mean and standard deviation
when finding the boundaries of the deciles.
2a. Which Chi Square test is appropriate when you have different groups and know the percent that
should be in each group?
______Goodness of Fit
_____Independence
______Homogeneity
2b. What are the hypotheses?
H0:
H1:
I have determined the number of Cardiac Reserve observations that fell into each decile. They are
provided in the table below.
Decile
1st decile
2nd decile
3rd decile
4th decile
5th decile
6th decile
7th decile
8th decile
9th decile
10th decile
Observed
2
5
1
5
5
2
1
2
3
4
Expected
2c. If there are 30 subjects and we expect 10% of subjects to fall into each decile, then show the
expected values on the table above.
2d. Use the above table to determine the 2 value.
2e. Determine the number of degrees of Freedom. To do so, think about the particular Chi Square test
being used then follow the rules for determining the degrees of Freedom. Once you have done that,
subtract 2 more degrees of freedom. As mentioned above, the reason for removing these additional 2
degrees of freedom is that to determine the deciles for the normal distribution, we had to estimate µ
and σ with 𝑥̅ and s, respectively. That cost us two additional degrees of freedom that are not typically
lost in Chi Square test of this kind.
2f. What is the p-value?
2g. Can we conclude that the data are approximately normally distributed?
3a. Make a scatter plot of the heart rate and cardiac reserve data.
3b. What is the correlation of the heart rate and cardiac reserve data?
3c. What is the p-value for the correlation?
3d. Using α = 0.05, is the correlation significant?
3e. What is the equation of the line of best fit?
3f. Use the equation to determine the expected cardiac reserve of a person with a resting heart rate of
70 beats per minute.
For those with a low cardiac reserve, steps can be taken to improve it, but these involve becoming
active. Two possible strategies are aerobic training and interval training. Aerobic training involves
keeping the heart rate elevated for 30 or more minutes. This can be done through swimming, running,
biking, cross country skiing, rowing, etc. Interval training involves a mixture of activities that elevate the
heart rate and then allow recovery. Examples include weight lifting, calisthenics, parkour and mixing
faster speeds in swimming or running with short periods of rest.
The question is whether there is a difference in cardiac reserve improvement between those using
interval training and those using aerobic training? To find out, subjects were randomly assigned to one
of the two types of workouts. For a one-year period they participated in the assigned type of workout.
The change in cardiac reserve was found by subtracting their final cardiac reserve from their initial.
4a. Complete the design layout table below.
Research Design Table
Research Question:
Observational Study
Observational Experiment
Manipulative Experiment
Type of Research
What is the response variable?
What is the parameter that will be calculated?
Mean
List potential latent variables.
Grouping/explanatory Variables 1 (if present)
Levels:
Grouping/explanatory Variables 2 (if present)
Levels:
Proportion
Correlation
4b. A total of 30 subjects participated in the research. Of these, 14 were male and 16 were female. The
males were assigned a number between 1 and 14. The females were assigned a number between 1 and
16. The first seven males and eight females selected will be assigned to the aerobic group. Use row 8 in
the table of random digits in your book or seed your calculator with a 8 then list the numbers of the first
three males that will be selected.
______, ______, ______
4c. What are the hypotheses that should be used to test if there is a difference in the improvement in
cardiac output between those doing aerobic training and those doing interval training?
H0:
H1:
The Data:
5.2
2.3
Aerobic Training Change in Cardiac Output
6.2
5.4
5.7
4.2
1.3
3.6
4.1
5.0
6.4
5.7
3.1
2.0
3.5
6.4
8.6
5.6
Interval Training Change in Cardiac Output
4.1
3.4
3.8
3.3
8.5
5.5
3.4
8.1
4d. Create an appropriate graph for comparing these two data sets.
7.6
3.2
7.9
3.5
4e. Complete this table showing the statistics.
Aerobic
Interval
Mean
Standard Deviation
Median
Sample Size
4f. Use a 5% level of significance to test the hypotheses. Write a concluding sentence.
Sources
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1728626/pdf/v079p00289.pdf
https://gupea.ub.gu.se/bitstream/2077/4426/2/Ramen1.pdf
https://www.unm.edu/~lkravitz/Article%20folder/intervalCAD.html