The methods explored in the measuring of cardiac output can be applied to other situations. Two of these situations are described here. The first examines the sediments flowing from the Des Moines River near Saylorville, Iowa. The second situation investigates the measurement of blood flow through the brain.
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Students will
- explore rates of change and accumulation in context
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- Computer and Internet connection
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 Sediments Flowing from a River:
Ecologists and scientists are interested in how much sediment is moved by a
river. Data on the water flow and suspended sediment in the Des Moines River
near Saylorville lake is given in the table.
Compute the total amount (kilograms) of suspended
sediment that passed that measurement point for the period December 1–5,
1993. |
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Des moines River Basin
Water Discharge Records
December
1993 |
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Day |
Discharge
Cubic Feet/Second |
Suspended Sediment
Mg per Liter |
|
1 |
1300 |
18 |
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2 |
1590 |
35 |
|
3 |
2000 |
58 |
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4 |
2200 |
64 |
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5 |
2350 |
66 |
Note: One cubic foot equals 28.3 liters. One kilogram
equals
1000 milligrams.
 Measuring
Cerebral Blood Flow:
Seymour Kety and Carl Schmidt describe a widely acknowledged and accurate
method for determination of cerebral blood flow cerebral physiological activity
such as metabolic rate of oxygen. It is commonly referred to as the Kety-Schmidt
technique.
An inert substance is introduced into the blood. For example a patient
breathes 15% nitrous oxide (N2O).
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N2O vol.%
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Minutes of Inhalation
Typical arterial (A) and internal jugular
(V) curves of N2O Conc. during a 10 min. period of inhalation
of 15 percent N2O. |
After the start of administration, the arterial concentration A is
measured in the radial artery. This is the concentration before the blood enters
the brain.
The venous concentration V is measured at the base of the skull in the
superior bulb of the internal jugular (at the point of exit of the jugular vein
from the brain). A sample table and graph of data is shown.
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Time (min) |
A * |
V * |
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0.00 |
0.000 |
0.000 |
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1.25 |
0.031 |
0.012 |
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3.25 |
0.039 |
0.027 |
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5.25 |
0.041 |
0.034 |
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10.00 |
0.044 |
0.042 |
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*Units for A and V: cc
N2O per cc blood |
Notice that after approximately 10 minutes the concentration flowing into the
brain and from the brain are approximately equal. The brain has become saturated
with N2O. Through other means the maximum amount of N2O in
the brain can be measured. Suppose that the maximum amount is determined to be
58.8 cc.
Assuming a constant cerebral blood flow rate,
F, compute an estimate of the total amount of N2O accumulated in
the brain during 10 minutes in terms of the flow F. Then compute an estimate for the flow rate.
For your information: For a normal adult, the blood flow rate is
between 600 and 900 gm / min or approximately 600 – 900 ml / min. Note that 1 cc
is approximately equal to 1 ml. The resting cardiac output is around 5 or 6
liters per minute.
Reflect on Your Work
How are these two problem situations similar to the cardiac output problem?
How are these two problem situations different from the cardiac
output problem?
How could you improve your estimates in either these problems or the cardiac
output problem?
What are two important mathematical concepts that arose in this
investigation?
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Data Analysis & Probability 9-12- Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each.
- Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable.
- Compute basic statistics and understand the distinction between a statistic and a parameter.
- Use simulations to construct empirical probability distributions.
- Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments.
- Understand histograms, parallel box plots, and scatterplots and use them to display data.
- For univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics.
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- Cornette, J., Ackerman, R., Keller, B. and G. Johnston (2000), Calculus for
the Life Sciences, draft manuscript, to be published by Prentice Hall.
- R.A. Rhoades and G. A. Tanner, Medical Physiology, Little, Brown and
Company, 1995, passage pp. 271-2, diagram pages 231 and 373.
- Ware, Wendy (1999). Fluoroscope of Cardiac Output being measured in a canine,
Iowa State University, College of Veterinary Medicine, Ames, Iowa.
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