Lesson Scenario - One Chamber Heart (Vensim)

Basic Model:

Description

This is a model of the ventricular volume in the heart over the course of a series of heartbeats. The diagram within the model shows the movement of blood through the heart ventricle, aorta, and body tissues as a result of several variables including venous pressure, viscosity, and systolic and diastolic pressure.

Background Information

Every heartbeat, blood moves into the right atrium, through the right ventricle, through the pulmonary artery into the lungs. In the lungs, the Carbon Dioxide is removed and replaced by oxygen. Then the oxygenated blood moves from the left atrium, through the left ventricle, and through the aorta into the rest of the body. This process is how nutrients, oxygen, and water are distributed throughout the body.

Science/Math

The fundamental principle behind this model is HAVE = HAD + CHANGE. The ventricular volume and cardiac output depend on the constantly changing volume of blood in the venous flow, arterial flow, and cardiac output.

Each time tick, the following things happen:

• Blood moves from the Heart Ventricle to the Aorta according to the user-set variables Heartrate and Stroke Volume. Cardiac Output = (PULSE TRAIN(Heartrate, TIME STEP, Heartrate, 1000)*Stroke Volume)/(TIME STEP) *Translation: Every time the heart beats (determined by Heartrate), a certain amount of blood (determined by Stroke Volume) moves from the Heart Ventricle to the Aorta.
• Blood moves from the Aorta to the Body Tissues according to the user-set variables Systolic Pressure, Diastolic Pressure, and Viscosity. Arterial Flow = (Mean Arterial Pressure * π * Venus Radius)/(8*Arterial Length * Viscosity) Mean Arterial Pressure = Diastolic Pressure + (Systolic Pressure - Diastolic Pressure)/3
• Blood moves from the Body Tissues to the Heart Ventricle according to the user-set variables Venus Radius, Venus Pressures, Venous Length, and Viscosity. Venus Flow = (Venus Pressure * π * Venus Radius)/(8 * Venous Length * Viscosity)

Teaching Strategies

An effective way of introducing this model is to ask students to brainstorm the process blood takes in passing through the heart. As students discuss this, draw the flow chart within the Vensim model on the board as a visual. Ask the following questions:

1. What factors determine the strength of arterial flow? Explain.
2. What factors determine the strength of venous flow? Are they the same or different from arterial flow? Why?
3. What role does the heart rate play in the amount of blood that flows into the aorta? Explain.
4. What is stroke volume? How does it influence cardiac output?

Implementation:

How to use the Model

This in depth model has many parameters that can be manipulated to produce different results:

1. The "heart rate" parameter determines how often the heart beats.
2. The "stroke volume" parameter determines how much blood is moved through the aorta when the heart beats.
3. The "time step" parameter determines how often the model calculates the amount of blood in each location.
4. The "arterial radius" parameter determines the radius of the coronary artery.
5. The "arterial length" parameter determines the length of the coronary artery.
6. The "viscosity" parameter determines the thickness of the blood and, therefore, the speed at which it moves through the veins and arteries.
7. The "diastolic pressure" parameter determines the pressure on the walls of the arteries in between heartbeats.
8. The "systolic pressure" parameter determines the pressure on the walls of arteries and vessels during a heartbeat.
9. The "venous radius" parameter determines the radius of the coronary vein.
10. The "venous pressure" parameter determines the pressure exerted on the walls of the coronary vein by the blood.
11. The "venous length" parameter determines the length of the coronary vein.

The aforementioned parameters are manipulated by clicking and dragging their respective sliders. The maximum, minimum, and step values for each parameter are pre-set. Any changes made to the sliders take effect immediately

Simulate on Change" button: Download File. The ventricular volume and cardiac output over time is displayed immediately in graphical form to the right of the model. For a complete tutorial on how to use Vensim, please go to the following link here.

Learning Objectives:

1. Understand the effect of the parameters on the ventricular volume.
2. Understand the effect of the parameters on the venous flow.
3. Consider the effect of systolic and diastolic pressure on mean arterial pressure.

Objective 1

Have students run the model with the default parameters. Then allow them to manipulate the parameters, focusing on the effect of the parameters on the ventricular volume. Ask the following questions:

• What affect does the heart rate have on the cardiac output? Does it increase or decrease the amplitude of the waves? Does it increase or decrease the frequency of the waves? Why or why not? Explain.
• What affect does the heart rate have on ventricular volume? Why? Explain.
• What affect does the stroke volume have on the cardiac output and ventricular volume? How does it affect the amplitude and frequency of the waves? Explain.
• What happens to the cardiac output and ventricular volume when the heart ventricle increases and decreases? Explain.

Objective 2

Have students run the model, focusing on the parameters that affect the venous flow. As they changed the parameters, ask them to watch the graph (a straight horizontal line that rises and falls) in the box surrounding the word "Venous Flow". Ask the following questions.

1. What happens to the venous flow when the venous length increases? What about when it decreases? Why?
2. What happens to the venous flow when the viscosity increases or decreases? Why is this the case? Explain.
3. What effect does venous pressure have on venous flow? Why?
4. What effect does venous radius have on venous flow? Explain why in geometric terms. How much does increasing the venous radius affect the amount of blood that can flow through the vein?
5. What values of these parameters allow for the highest venous flow? What causes the lowest venous flow? Explain.

Objective 3

Have students run the model with the default parameters. Then allow them to manipulate the parameters, focusing on the effect of systolic pressure and diastolic pressure on the mean arterial pressure. Ask the following questions:

1. What is systolic pressure? Explain.
2. What is diastolic pressure? Explain.
3. What affect does raising and lowering the systolic pressure have on the mean arterial pressure? Why is this the case?
4. What affect does raising and lowering the diastolic pressure have on the mean arterial pressure? Why?
5. Do these results make sense? Why or why not?

Extensions:

1. Think about the qualities this model still lacks when compared with the real world.
2. Explore the use of models for preventative medicine.

Extension 1

Have students discuss ways in which this model could be improved. Ask the following:

1. What does this model recognize as factors in ventricular volume and cardiac output? What parameters can the user change?
2. What factors is this model missing? What could be added to make the model less idealistic and more realistic?
3. Are there any other factors that affect venous flow? What about arterial flow? Explain.
4. What factors affect systolic and diastolic pressure? Could those be incorporated into the model? How?

Extension 2

Have students discuss ways in which this and other models could be used in preventative medicine. Ask the following:

1. In what situations would a model about the factors of ventricular volume and cardiac output be useful in preventative medicine? Explain.
2. Could a model be useful for explaining to a patient what causes blood pressure to rise and fall? Why or why not?
3. How could a model be used to determine the best treatment to improve heart health? What elements would the model need to include? Explain.
4. Would this particular model be useful in preventative medicine? Why or why not? If so, how would it be useful? If not, what would need to be changed about the model?
5. In what other ways could models be used in preventative medicine? In what ways are models and simulations being used in preventative medicine? This would be a good essay question.

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Pharmological Dosing Model

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Hares and Lynx Model

This is an agent model of the interaction between populations of lynx and hares. Students should discuss in what ways this model is a cyclical model like the Windkessel model.