Part A: The Situation

Terry, a twenty-five year-old taxi driver, is out with some friends at a bar. Terry and two others are not drinking any alcoholic beverages tonight. A fourth friend is drinking beer; the fifth is drinking shots of tequila; the sixth is drinking wine. As the six friends start their evening, Terry is wondering about the following questions:

Knowing that the legal blood alcohol limit is 0.1% in this state (for driving), how many drinks will it take for the three to exceed that limit?

Will the blood alcohol get broken down faster if a person drinks a lot at the beginning, or drinks smaller amounts over a longer period of time? (the total amount of alcohol is the same)

Once they've become "illegal", how many hours will it take before they are below the legal limit again?

Unfortunately, there was no easy way for Terry to answer these questions. The next day, still thinking about these issues, he called up a local government health agency and asked them. They didn't know the answers, but decided to hire some consultants to find out. They hired (at a very expensive hourly rate) some expert human physiologists to investigate-- you!

Your assignment is to use your knowledge of stocks and flows to build a STELLA computer model of the breakdown of alcohol in the body. You will use this model to help answer his questions. Your fee will be presented upon completion.

Part B: Alcohol Degradation: Model I

Building a model is like writing a paper: First you do a rough draft, then you do a final copy. With a model, you start with a quick approximate model, test it, and see what makes sense and what doesn't. Then you can change your assumptions behind the model to make it more complex (and more accurate).

Your first model will have four assumptions:

1. The blood alcohol will decrease at a constant rate.
2. It takes about six hours for a person to sober up.
3. This person is already intoxicated at the legal level.
4. There is no increase in alcohol (i.e., this person has stopped drinking).

Place a "stock" (or "reservoir") for the blood alcohol level by loading STELLA, and then going to the second "level" of the program by clicking once on the downward arrow button at the top left side of the screen. Click once on the "stock" icon at the top left which looks like a rectangle. Then click once in the screen field to place the stock on the screen. Label the stock "Blood Alcohol" by just typing it in.

Now you are going to place a "flow" going out of the blood alcohol stock.

Question 1

What should the outflow for blood alcohol be called? In other words, what process directly decreases the level of alcohol in your blood? (Hint: It has nothing to do with the kidneys)

Place the outflow on the screen.

Click the flow icon at the top of the screen.

Hold down the mouse button on top of the stock and drag it right several inches.

While the flow is highlighted, type the name of your outflow.

Now that you have created the structure of your model, you need to fill in the details.

Click the globe in the upper left corner of the screen; it should change to a large x2.

This lets STELLA know that you want to enter the mathematical relationships in the model.

Question 2

In many states you are legally intoxicated when 0.1% (1 ml of alcohol/1000 ml blood) of your blood is alcohol. If a person has 6000 milliliters of blood with 0.1% alcohol concentration, how many milliliters of alcohol are in his system?

Set the initial value of the Blood Alcohol.

Double-click the stock "Blood Alcohol".

Type the number of milliliters of alcohol that you gave for the previous question.

Click the OK button.

Note that the question mark has disappeared, meaning you have entered a value for

that element.

Question 3

Given the initial amount of alcohol, how many milliliters of alcohol will need to be removed each hour in order for all the alcohol to be gone after six hours?

Set the outflow to your answer for question 3.

Double-click your outflow.

Type in your answer to the previous question.

Click OK.

The blood alcohol will go down that many milliliters each hour.

Make a graph so you can see the simulation.
Click the graph icon at the top of the screen.
Click below your stock/flow assembly. (You should see a blank graph.)
Choose Define Graph...from the Model menu.

Tell STELLA what elements to graph.
Click "Blood Alcohol" in the left hand list
Click the >> button.
Click OK to go back to the graph.

Before you run the simulation, make a prediction. Draw a graph of the level of blood alcohol as it changes over the course of 12 hours.

Run the simulation.
Choose Run from the Run menu.

Draw the simulation result on the following graph.

Question 4

Is this graph what you expected? If not, explain.

Close the graph window and go back to the diagram.
Click the box in the upper left corner of the graph window.

You will now modify your model to make it more accurate, adding this assumption:

The rate at which alcohol is broken down depends upon the amount of alcohol in the blood.

The model which you constructed above assumes something different-- that the rate at which alcohol is broken down stays the same regardless of the amount that is in the body. We know intuitively that this isn't the case. To be really clear in your own mind, think about the next two questions.

Question 5

Suppose there is a very high concentration of alcohol in the blood.

Will the body remove more, less, or the same amount of alcohol per hour as it would when there is a low concentration of alcohol in the blood?

Why?

Question 6

How much alcohol will be removed per hour when the concentration of alcohol in the blood is zero?
 

Blood Alcohol Levels-Part 2

We can build this 30% breakdown rate into our model using the "converter" icon in the tool bar. It looks like a circle (in the upper-left of the screen).

* Click once on the converter icon.

* Then click on the screen near your flow to place the converter into the model.

* Give the converter the name MULTIPLIER.

* Double click on the converter and enter 0.30 which is the 30% breakdown rate that we want.

* Now connect the converter to the flow with a connector (the red arrow icon). To do this click once on the connector icon, then aim the pointer arrow right in the converter and click and hold the mouse, then drag while holding the mouse button down over to the big circle part of the flow icon until you see it turn gray; then let go of the mouse. If you have done this correctly, there should be an arrow connecting the converter to the flow; if not, try it again. This connector arrow shows that alcohol breakdown depends on the converter.

The breakdown of alcohol depends also on the amount of alcohol in the blood, as we have been saying. So use another connector to connect the blood alcohol reservoir to the flow. Do this like you did the other connection.

* Click once on the connector icon and then aim the pointer arrow right in the reservoir. Then click and hold the mouse, and drag the arrow while holding the mouse button down over to the big circle part of the flow icon until you see it turn gray; then let go of the mouse. If you have done this correctly, there should be an arrow connecting the converter to the flow; if not, try it again.

Now you are ready to write an equation in the flow which describes the breakdown of alcohol per unit of time. If 30% of the blood alcohol is broken down in any given unit of time, you can indicate this quantity mathematically as 0.30 times the amount of blood alcohol. Stella will then subtract for you this amount from the current amount of blood alcohol to give the new amount of blood alcohol at the next time step. So...

* Click twice on the big circle part of the flow icon and simply type 0.30*blood alcohol (notice the multiply sign on a computer is the asterisk).

* Then click O.K.

Before you simulate, make a prediction of how the alcohol changes over time. Draw your prediction of the level of blood alcohol on graph like the one below.

 

To make your graph (over time) look nicer, set a range for alcohol.
Choose Range in the Run menu.
Click "Blood Alcohol."
Type in a range of 0 to 10 (just type a 10 in the Max. box)
Click Set.
Click OK to go back to the diagram.

Run your model.
Double-click the graph to see your axes.
Choose Run from the Run menu.

Draw the resulting graph.
 

Question 11

Was the simulation run the same as you predicted?

If not, why not?

Keep trying until you get a good simulation run. If your model does not give the result you expect, take another look at your graphical relation. You might need to change the scale of your graphical relation. Keep simulating until the alcohol is gradually neutralized, with about 90% gone after six hours. Make sure you draw a prediction each time you simulate.

Get rid of the graph by clicking the small box at the top left once.

Question 12

Draw or print your final model. Explain what the model does.

Part D: Alcohol Degradation while Drinking

Now the you have a working model of alcohol degradation, you can see how quickly a drink is broken down.

Question 13

What should the inflow for blood alcohol be called? In other words, what directly increases the level of alcohol in your blood?

Place your inflow on the screen.
Click the flow icon at the top of the screen.
Hold down the mouse, starting about an inch to the left of the stock, and drag the flow on top of the stock.
Release the mouse button when the stock turns grey.
Type the name of your inflow.

To tell STELLA that a person has had a drink, you will create another graphical function, this one

over time.
Double-click your inflow and type "time."
Click Become Graph.
Set the scale of your graphical function to 0 through 5 on the vertical axis.
Click the picture of a graph on the lower left hand corner. It should turn into a series of horizontal steps. If you don't see the steps, click again on the graph picture until you do.

Tell STELLA that you will take a drink containing 4 milliliters of alcohol at 2 hours after the start of

the simulation.
Type "4" in the right hand "Output" column next to the "2" in the "Input" column.
Click OK to go back to the diagram.

Set the initial level of alcohol to 0.
Double-click the stock of blood alcohol.
Type "0"
Click OK.

Show a horizontal line at 0.1% blood alcohol, the legal limit.
In your STELLA model, create a "converter" by first clicking on the o icon at the top of the screen.
Then click near your model to place the converter on the screen. Name the icon "Legal Limit."
Double click on the converter. Place the appropriate # mils that would give a person a 0.1% blood alcohol level (see your answer for question 2 at the beginning of the lab). Click OK when done.
Tell STELLA to plot a horizontal line at this level by clicking the RUN menu and selecting Range. Click on Legal limit then type 10 in the Max. box and click Set Then click OK. Double click on your graph icon. The graph should appear. In the Diagram menu again select Define Graph Click once on Legal limit then click the >> button. Then click OK.

Before you run the simulation, make a prediction on the axes.

Run the simulation. Draw the simulation result on a graph.

Get rid of the graph by clicking once on the small box in the upper left.

Now you will attempt to answer terry's questions, listed in the beginning of this worksheet.

Set up a simulation where a person takes 3 drinks, with an alcohol content of four milliliters each, within one hour. Do this by going to the graphical relation in your inflow, and enter an output of 12 at input 1. (Make output 0 at input 2) This tells STELLA your person drinks 12 milliliters of alcohol in an hour. Set the range of the y axis from the graph from 0 to 15 (using the Range menu item in the Run menu). Set it for BOTH blood alcohol AND legal limit (type 15 in each "Max." box and click "Set" after typing each). Click OK when done setting BOTH ranges to 15.

Sketch your Prediction:
 
 

Double click the graph icon to see your graph. Then select Run in the Run menu.

Draw or print the Simulation Result:
 

Now, your person is going to spread the three drinks over several hours. Set the inflow with a four milliliter drink at 1 hour, another at hour 2, and another at hour 3.

Sketch your Prediction:
 
 

Draw or print the Simulation Result:

Question 14

After 6 hours, which simulation has the lowest amount of blood alcohol?

Using your model, determine the answers to Terry's other two questions.

Question 15

How many drinks (of four milliliters alcohol content each) will it take for Terry's friends to go above the legal limit?

Question 16

Once they've become "illegal," how many hours will it take before they are below the legal limit again? (Estimate this both for one drink of 12 ml at hour 1 AND three drinks of 4 ml each at hours 1, 2, and 3.)

Back to Part I

This paper has been edited from an original work by:
William Glass

Catalina Foothills High School