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WORKBOOK 2
BLOOD GLUCOSE HOMEOSTASIS
(Form D)
INTRODUCTION
Today you will learn more about an important concept of physiology: homeostasis. Homeostasis refers to
physiological processes that maintain certain conditions in the body at a steady state. For instance, your
body temperature tends to stay at 98.6o F (37o C) because there is a process that keeps your body at that
temperature, despite variations in the outside temperature or in how hard you exercise. This process is
called a homeostatic process because its function is to keep the body temperature steady.
Maintaining homeostasis requires that the body continuously monitor its internal conditions. From body
temperature to blood pressure to levels of certain nutrients, each physiological condition has a particular
set point. A set point is the physiological value around which the normal range fluctuates. The normal
range is the restricted set of values that is optimally healthful and stable. For example, the set point for
normal human body temperature is approximately 37°C (98.6°F). Physiological quantities, such as body
temperature, tend to fluctuate within a normal range a few degrees above and below that point. Control
centers in the brain play roles in regulating physiological quantities and keeping them within the normal
range. As the body works to maintain homeostasis, any significant deviation from the normal range will be
resisted and homeostasis restored through a process called negative feedback. Negative feedback is a
mechanism that prevents a physiological response from going beyond the normal range by reversing the
action once the normal range is exceeded. The maintenance of homeostasis by negative feedback goes
on throughout the body at all times, and an understanding of negative feedback is thus fundamental to an
understanding of human physiology.
For many purposes in science and medicine, it suffices just to know whether the homeostatic process is
functioning properly. This requires knowing how a properly functioning homeostatic process behaves.
Then measurements of a person’s physiological quantity (e.g., body temperature) can be compared to the
values when the process is properly functioning. For example, we know that when the negative feedback
loop for body temperature is properly functioning, the body’s temperature should be close to 98.6 o F. If
the temperature is too high, then the person is sick with a fever. If the temperature is too low, the person
has something else wrong with them.
Sometimes it is important not only to know the steady state value of a quantity, but also how quickly the
body reacts to a stimulus that pushes that value out of its normal range. For instance, if a person is
immersed in frigid water, how fast does the body react? Measuring the dynamic response of the body as
it tries to restore homeostasis can be an important measure of fitness.
This is where system dynamics modeling becomes important. A system dynamics model can represent
how the body behaves when the negative feedback loop is working properly. If the graphs produced by
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the model do not match the measurements observed of a person, then the researcher or doctor can tell
that something is wrong with the person’s negative feedback loop.
THE SIMPLEST MODEL OF HOMEOSTASIS
Often, a very simple model suffices. In fact, the simplest model of negative feedback in Dragoon has just
three nodes. It’s simple because it assumes that the set point of the homeostatic process is zero.
Here’s how the model works. If the value of the physiological quantity becomes positive (i.e., greater than
zero), then the loop subtracts a little bit from it until the quantity falls to zero. On the other hand, if the
value becomes negative, then the loop adding a little bit to the value until it rises back to zero.
To be more concrete, suppose that if the value > 0, we subtract 10% of the value. On the other hand, if
value < 0, then we add 10% of its absolute value. Actually, adding 10% of the absolute value of a
negative number is the same thing as subtracting 10% of the value. Thus, we have this very simple rule:
If value≠0, then subtract 10% of the value.
Complete the problem “Zero set point homeostasis” in Dragoon. When you are finished, answer
the following questions.
QUESTION 1
1a. Open the graph window. The graph for controlled quantity looks blank because the red and green
lines are both horizontal lines at zero, and thus right on top of the horizontal axis. Given the
parameter values, does this make sense physiologically?
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1b. Suppose the controlled quantity starts out higher than the set point (zero). This should cause the
negative feedback loop to kick into action and try to restore the quantity to zero. In the graph window,
set the initial value of controlled value to a positive value. Now describe how the value of controlled
quantity changes over time.
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1c. Now set the initial controlled quantity to -3. You should see a red horizontal line at zero. That is the
behavior of the correct model when the parameter values are left alone. The green line shows the
behavior of your model when the parameter values have been changed, as has occurred here, where
the value of initial controlled quantity has been changed from 0 to -3. Now describe how your
model’s value for controlled quantity (the green line) changes over time.
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1d. Compare the graphs you have in 1b and 1c, that is, when the initial controlled quantity is positive and
when it’s negative by the same amount. How are the graphs similar? How are they different?
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HOMEOSTASIS WITH A NON-ZERO SET POINT
Now let’s develop a more general model, where the set point doesn’t have to be zero. In fact, let’s
assume the set point is 98.6, as if the controlled quantity were body temperature.
Please do Dragoon problem “Nonzero set point homeostasis” and then answer the questions
below.
QUESTION 2
2a. Open the graph window. Check only Show controlled quantity and make sure Show change in
quantity and Show difference are not checked. The graph for controlled quantity has the red and
green lines right on top of each other, perfectly horizontal, at 98.6 on the vertical axis. Given the
parameter values, does this make sense physiologically?
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2b. Using the slider, increase the value of initial controlled quantity. The red line is the model’s
response when it has the given values for the parameters, so it is a flat line at 98.6 because that’s
what the initial value of the controlled quantity is and the system tries to keep it at the level. The green
line shows the model’s response when you manipulate the sliders (or make a mistake entering the
value of a parameter). As you move the initial value considerably above the set point, how does the
graph change and what does this mean?
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2c. Using the same slider gain, explore what happens when the controlled quantity starts out with an
initial value that is lower than the set point. Describe the curve you see.
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2d. Does it matter whether the controlled quantity starts out above zero or below zero? (You can type
values into the box instead of moving the slider.)
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TWO-LOOP HOMEOSTASIS
When the regulation of body temperature was discussed in your textbook, the effector actions for lowering
body temperature (e.g., sweating) were different from the effector actions for raising body temperature
(e.g., shivering). Body temperature is typical of many homeostatic processes in that different effectors are
used for lowering the controlled quantity than for raising the controlled quantity.
Because different bodily mechanisms are used for lowering body temperature than raising it, there are
two negative feedback loops in operation. One lowers the body temperature (via sweating, etc.) and the
other raises body temperature (via shivering, etc.). Let’s develop a general model of such homeostatic
processes, where there are two negative feedback loops—one for raising the value of the controlled
quantity and another for lowering it.
As you know from your last model, the current value of the controlled quantity is compared to the set point
by subtracting the set point from it. Thus, if the controlled quantity is too high, the comparison is positive.
If the controlled quantity is too low, the comparison is negative. For the two-loop model, we need to send
the positive comparison to one negative feedback loop, and send the negative comparison to another
feedback loop. This can be done using a mathematical function, named “max” that Dragoon will let you
use inside the expression box. When you give function “max” 2 or more values as inputs, it will return the
maximum value (not absolute value; real value). Thus:

max(0,2) returns 2

max(-2, 0) returns 0

max(1,2,3,4,-2,5) returns 5

max(temperature1, temperature2) will return the value of temperature2 if temperature1 <
temperature2. On the other hand, if temperature1 = 5 and temperature2 = 3.5 what will it return?
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The function max can be used to split the comparison value. Suppose that C is our comparison value.
Then max(0,C) will return:


C if C is positive
0 if C is negative
Similarly, max(0,-C) will return:


-C if C is negative
0 if C is positive
Let’s try this out. Suppose C = 5.
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What does max(0,C) return? ________________________

What does max(0,-C) return? ________________________
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Now suppose that C = -5.

What does max(0,C) return? ________________________

What does max(0,-C) return? ________________________
Thus, we can use max(0,C) to send C to the negative feedback loop that lowers the value of the
controlled quantity, and we can use max(0,-C) to send -C to the negative feedback loop that raises the
value of the controlled quantity.
With this in mind, go to Dragoon, do the problem “Two loop homeostasis” and then answer the
following questions.
QUESTION 3
3a. Click on the table option. Set the initial value of controlled quantity to 118.6. Write the first three
values that are input to the accumulator from each of its inputs, and then answer the questions below:

Values for change to reduce deficits:
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Values for change to reduce surplus:
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
Which feedback loop is active: the one for reducing a surplus or for reducing a deficit?
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3b. In the same table window, set the initial value of controlled quantity to 78.6. Write the first three
values that are input to the accumulator from each of its inputs.

Values for change to reduce deficits:
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
Values for change to reduce surplus:
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
Which feedback loop is active: the one for reducing a surplus or for reducing a deficit?
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3c. Circle one option: The sentence below in italics is:
True
False
When a feedback loop is not active, then the value of the “change to reduce …” node is zero.
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3d. Compare the answers to question 3a and 3b. Please explain why the non-zero numbers are twice as
large in 3b as they are in 3a.
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BLOOD GLUCOSE HOMEOSTASIS
Blood glucose homeostasis is a specific example of a two-loop homeostatic process. Glucose is a simple
sugar. Glucose is required for cellular respiration and is the preferred fuel for all body cells. The body
derives glucose from the breakdown of the carbohydrate-containing foods and drinks we consume.
Glucose is transported from the digestive system to all the other cells in the body by the blood.
It is important that the level of glucose be kept relatively constant. If it falls too low, the cell respiration will
slow and the cells will not have enough energy to function properly—they will starve. If the glucose levels
in the blood are too high, tissue damage can occur.
However, the supply of glucose from digestion does change. When a person has just eaten, ample
glucose enters the blood. When the person has not eaten for many hours, little glucose enters the blood.
Similarly, the amount of glucose withdrawn from the blood by cell respiration changes. When the body is
exercising heavily, glucose is absorbed rapidly to feed the energy demands of the cells. When the body is
sleeping, little glucose is absorbed. When there is an oversupply of glucose, it can be stored by the liver
and muscles as glycogen. It can also be stored in the fatty tissue as triglycerides.
Hormones regulate both the storage and the utilization of glucose. Receptors located in the pancreas
sense blood glucose levels, and subsequently the pancreatic cells secrete glucagon or insulin to maintain
normal levels. Glucagon and insulin are hormones.
More specifically, blood glucose is regulated by two negative feedback loops. One reacts to an
oversupply of glucose in the blood and causes the body to remove glucose from the blood. The other
negative feedback loop reacts to an undersupply of glucose in the blood and causes the body to add
glucose to the blood. The loop that removes glucose is controlled by insulin, whereas glucagon controls
the loop that adds glucose to the blood. Although there is much more to learn about blood glucose
homeostasis, you now know enough to create a simple model of it. In fact, the model is just a
specialization of the generic, two-loop model you just constructed.
Please solve the Dragoon problem “Simple blood glucose homeostasis” and then answer these
questions.
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QUESTION 4
4a. Suppose the body just digested a candy bar, which was converted rapidly to glucose, and raised
initial blood glucose level to 112 mg/dL. That is 20 mg/dL higher than normal. Using either the table or
graph, set 112 as the value of initial blood glucose and note at what time the blood glucose level
falls to around 100 mg/dL.
Now suppose that the body only digested half the candy bar, so only half the glucose was added to
the blood. That’s only 10 mg/dL above normal. Thus, set 102 as the value of initial blood glucose
and note at what time the blood glucose level falls to around 100 mg/dL.
Circle one option to complete the sentence: When the amount of sugar eaten is doubled, the length of
time that the blood sugar is moderately above normal (i.e., at 100 mg/dL or more) is:
A. unaffected
B. doubled
C. tripled
D. quadrupled
4b. Using the initial blood glucose slider, compare an initial surplus to an initial deficit of the same size.
Circle one of the italicized words in each pair:
The surplus is removed [slower; faster] than the deficit because its rate of convergence is [larger; smaller]
than the convergence rate for removing deficits.
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A MORE REALISTIC MODEL OF THE GLUCOSE-INSULIN NEGATIVE
FEEDBACK LOOP
Many people have diabetes and it can be a serious, and even fatal, disease. When people have diabetes,
the negative feedback loop that reduces blood glucose is damaged. To detect diabetes better and to
understand what causes it, mathematical biologists have created many models of the glucose-insulin
negative feedback loop. One review of the medical literature1 found hundreds of models of this system.
Many of these models are refinements and improvements on a simple model constructed in 1980. It is
widely known as the “minimal model” of the glucose-insulin negative feedback loop.2 It is used to predict
how the body will react to an injection of a small amount of glucose into the blood. As you saw in your
previous Dragoon model, the pancreas should detect the oversupply of glucose and release insulin, and
the insulin should cause the body to gradually remove the glucose and restore the glucose level to its
normal value. The minimal model does an accurate job of predicting exactly how much insulin is released
and how fast the glucose returns to normal.
In the remainder of today’s lesson, you will construct the minimal model in Dragoon and study how it
behaves. Unlike the parameter values used in the preceding model of blood glucose homeostasis, these
parameter values are realistic and were derived from human data.3
Just like the model you completed earlier, glucose in the blood is represented by an accumulator.
However, instead of assuming that insulin concentrations are the same everywhere in the body, the
minimal model assumes that the insulin concentration could be different in the blood and in the so-called
“remote tissues” which are the muscles and other tissues that burn glucose to generate energy or store it
as glycogen or triglycerides. These tissues are called “remote” because the insulin must travel through
the blood to get to them from the pancreas. Thus, the minimal model has two more accumulators, which
represent the amount of insulin in the blood and the amount of insulin in the remote tissues.
Please do Dragoon problem “glucose min model” and then answer the following questions.
1
Ajmera, M. Swat, C. Laibe, N. Le Novere and V. Chelliah (2013). The impact of mathematical modeling
on the understanding of diabetes and related complications. CPT Pharmacometrics Syst. Pharmacol. 2,
e54; doi: 10.1038/psp.2013.30.
2 R.N. Bergman, C. Cobelli, Minimal modelling, partition analysis and the estimation of insulin sensitivity,
Federation Proc. 39 (1980) 110–115. R.N. Bergman, The minimal model: yesterday, today and tomorrow,
in: R.N. Bergman, J.C. Lovejoy (Eds.), The Minimal Model Approach and Determination of Glucose
Tolerance, LSU Press, 1997, pp. 3–50. R.N. Bergman, The minimal model of glucose regulation: a
biography, in: J. Novotny, M. Green, R. Boston (Eds.), Mathematical Modeling in Nutrition and Health,
Kluwer Academic/Plenum, 2001.
3 N. Van Riel, Minimal models for glucose and insulin kinetics—A Matlab implementation, Dept. of
Electrical Engineering, BIOMIM & Control Systems, Eindhoven University of Technology, Preprint,
February 2004.
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QUESTION 5
5a. Take a look at your Dragoon model. There are two negative feedback loops that control blood
glucose. One is long and involves insulin. Here is a list of nodes involved. Fill in the blanks.
1. Blood glucose
2. Glucose difference
3. Insulin from pancreas
4. Blood insulin
5.
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6. Blood insulin to remote
7. Remote insulin
8.
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9. And back to blood glucose, thus completing the negative feedback loop.
5b. There is a second negative feedback loop, with one missing. Please fill in the blank.
1. Blood glucose
2. Glucose difference
3.
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4. And blood glucose again, thus completing the negative feedback loop.
5c. When a person has Type 2 diabetes, their remote cells do not take up blood insulin as fast as a
normal person. Thus, a diabetic’s remote cells burn less glucose than a normal person when the
blood has the same amount of insulin as a normal person. Which parameter in the minimal model can
be varied to represent the effects of Type 2 diabetes? (circle one option):
A. glucose effectiveness
B. insulin sensitivity
C. blood insulin set point
5d. Look carefully at the graph of blood glucose level over time. Does the blood glucose level go a little
lower than its set point? Could this explain why you sometimes feel sleepy after a big lunch or dinner?
Approximately when does this occur?
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