Illuminations: Cardiac Output, Rates of Change, and Accumulation

Cardiac Output, Rates of Change, and Accumulation

Make a Conjecture

Doctors and veterinarians are interested in a quantity called the "cardiac output" which is a measure of the rate of blood flow being pumped by the heart. To measure the cardiac output, a catheter (tube) is inserted through the heart. The catheter measures the temperature of the surrounding blood near the tip of the probe. The catheter has a small balloon at the tip which is inflated to help the probe move through the heart and then deflated. Once the catheter is inserted, ice water is injected through the catheter and emerges from a small hole approximately 12 inches before the end of the catheter.

Learning Objectives
 

Students will

  • explore rates of change and accumulation in context

Materials
 
  • Computer and Internet connection

Instructional Plan

How can the blood flow be measured by injecting ice water
and measuring the temperature?

X-ray of a catheter inserted in a dog

[Click here for a larger image]

Fluoroscope movie of a catheter
being inserted into a dog*

[Small size 116k] [Large size 1.6 MB]

Click here for more background information about the procedure or the catheter.

Think About This Situation

Based on the discussion above, the picture and the movie above, answer the following questions about measuring cardiac output.

  1. How will the temperature change as ice water is injected? Sketch a possible graph of the (time, temperature) relationship that you described.
  2. What does the change in temperature tell you about the amount of ice water in the blood stream?
  3. How would your temperature graph differ for a fast blood flow rate compared to a slow blood flow rate?
  4. How do you think that the (time, temperature) data might be used to determine the rate of flow?

References

NCTM Standards and Expectations
 
Data Analysis & Probability 9-12
  1. Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each.
  2. Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable.
  3. Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments.

References
 
  • R.A. Rhoades and G. A. Tanner, Medical Physiology, Little, Brown and Company, 1995, passage pp. 271-2, diagram pages 231 and 373.
  • Cornette, J., Ackerman, R., Keller, B. and G. Johnston (2000), Calculus for the Life Sciences, draft manuscript, to be published by Prentice Hall.
  • Ware, Wendy (1999). Fluoroscope of Cardiac Output being measured in a canine, Iowa State University, College of Veterinary Medicine, Ames, Iowa.
  
1 period   

NCTM Resources

Navigating through Data Analysis in Grades 9‑12

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