Blood velocity in the human vascular system

Mike Meyer (Michigan Tech.)Yen Lee Loh (University of North Dakota)Justin Fendos (University of Minnesota)Tristan Darland (University of North Dakota)Alan Kay (University of Iowa)Scott Pedersen (South Dakota State University)Greg Heiberger (South Dakota State University)

Two fabulous facilitatorswww.heart-valve-surgery.com/heart-surgery-blog/2009/04/15/heart-beat-lifetime

Context

This unit is prepared for use within: •Introductory Biology•Introductory Physics •Animal Physiology•Across two 50 minute class periods•Prior reading regarding continuity equation & cardiovascular anatomy

Why study fluid in tubes?

O2

CO2

Brooker, et al. Biology, 2nd Ed. McGraw Hill. Figure 47.15

Why study fluid in tubes?

Normal Coronary Artery Atherosclerotic Coronary Artery

Library.med.utah.edu/webpath/cvhtml/cv004.html

730,000 deaths/year in US

300,000 bypass surgeries/year ($150,000 each)

Costs $45 billion/year

Why study fluid in tubes?

www.newswise.com/images/uploads/2011/05/9/underwoodnigeria.jpg

Why study fluid in tubes?

Why study fluid in tubes?

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Learning Activity 1

• Learning Goal 1: Students will use a model to understand how total cross sectional area affects fluid velocity.

• Learning Outcome 1: Students will be able to describe fluid velocity change due to total cross sectional area. (Bloom’s 1-2)

Learning Goals and Outcomes

Opening Clicker Question

What do think will happen as blood is flowing from a wider vessel into a more narrow vessel?

A. It will go faster through the narrow vessel.B. It will go slower through the narrow vessel.C. It will flow at the same velocity through both vessels.

A demo/active learning exercise: How velocity is affected by vessel size using a finite state cellular automaton model

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Repeat Clicker Question

What do think will happen as blood is flowing from a wider vessel into a more narrow vessel?

A. It will go faster through the narrow vessel.B. It will go slower through the narrow vessel.C. It will flow at the same velocity through both vessels.

The fork in the road…

• What if the tube splits into 2 and each is half as wide?

Learning Goals and Outcomes

• Learning Goal 2: Students will learn how to apply a mathematical model to understand a biological phenomenon.

• Learning Outcome 2: Students will be able to predict how blood velocity will change with changing cross sectional area. (Bloom’s 3-4)

Learning Activity 2

Let’s get Quantitative!

• Fluids in a Tube: Continuity Equation

Graphic courtesy of and more information at:http://www.aplusphysics.com/courses/honors/fluids/continuity.html

A1v1 = A2v2

Clicker question:

At some point in an artery, plaques have narrowed the artery such that Awide is twice Anarrow. Based on the continuity equation, you would expect:

A) vnarrow= 2 vwide

B) vnarrow= 4 vwide

C) vnarrow= ½ vwide

D) vnarrow = ¼ vwide

Radius vs. Area?1) Open the PhET simulation found at this link:http://phet.colorado.edu/en/simulation/fluid-pressure-and-flow

3) Click on the “handles” to create a 2” diameter tube flowing into a 1” diameter tube.

2) Switch to the “Flow” tab, and check the “Ruler” box.

4) Measure fluid speed in each tube - drag the speed tool into each region.

At some point in an artery, plaques have narrowed the artery such that rwide is three times rnarrow. Based on the continuity equation, you would expect:

A) vnarrow= 3 vwide

B) vnarrow= 9 vwide

C) vnarrow= 1/3 vwide

D) vnarrow = 1/9 vwide

Clicker question:

Rwide Rnarrow

Learning Goals and Outcomes

• Learning Goal 3: Students will understand how the principles explored in Goal 1 and 2 apply to blood velocity through vascular systems.

• Learning Outcome 3: Students will graphically predict blood velocity based on the model cover under learning activity 2. (Bloom’s 3-4)

• Learning Outcome 4: Students will revise their hypotheses to account for new data. (Bloom’s 3-4)

Learning Activity 3

• Students are given an empty graph (see slide 13 and handout)• Students predict velocity curve and fill in the graph• Students share and discuss in groups• Groups share with class & instructor • Instructor leads class discussion describing their results• Instructor provides the correct velocity graph, but does not

explain the correct answer in order to create suspense• This graph includes velocity and blood vessel radius

Aortar=1.5cm

Capillary r=0.0005 cm

Velo

city

Vena Cavar=1.0 cm

Hill, R., Wyse, G. & Anerson, M. Animal Physiology, 3rd Ed. Fig. 24.12 (part 1)

Velo

city

But wait……Aortar=1.5cm

Capillary r=0.0005 cm Vena Cavar=1.0 cm

Hill, R., Wyse, G. & Anerson, M. Animal Physiology, 3rd Ed. Fig. 24.12 (part 1)

Vel

ocity

Based on the velocity, calculate the cross-sectional area of the capillaries (using A1v1=A2v2 and data above).

AortaA=7.1 cm2

CapillaryA=?

Vena CavaA=3.14 cm2

32 cm/sec

2 cm/sec

Faculty.pasedena.edu/dkwon/chapter%2015_files/textmostly/slide16.html

Learning Activity 3 (cont.)• Make a sketch of 2 cross-sectional areas:

• Capillaries• Aorta

• Does your drawing explain the velocity in the aorta vs. the capillaries? If not, can you improve your drawing?

Hill, R., Wyse, G. & Anerson, M. Animal Physiology, 3rd Ed. Fig. 24.12 (part 1)

Visual of cross-section

Aorta

Capillary bed

Goals

• Learning Goal 1: Students will learn a model to understand how total cross sectional area affects fluid velocity.

• Learning Goal 2: Students will learn how to apply a mathematical model to understand a biological phenomenon.

• Learning Goal 3: Students will understand how the principles explored in Goal 1 and 2 apply to blood velocity through vascular systems.

Clicker question:Suppose you had a single pipe (rlarge = 7.0 mm) that feeds a shower head with many holes (rsmall = 1.0 mm). What is the number of small holes such that vsmall = vlarge?A) 7B) 21C) 49D) 70E) 343

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Exit ticket/formative assessment

On the back of your graphing worksheet, use the “effective” capillary area and the average size of each capillary to estimate the total number of capillaries in the bed.SHOW YOUR WORK!

The estimated number of capillaries is one billion.

Summative Assessment

• Test questions using continuity equation, bifurcation and the human circulatory system

Why Does Blood Flow Have to Slow in the Capillaries?

O2

CO2

Brooker, et al. Biology, 2nd Ed. McGraw Hill. Figure 47.15

There is more to this story & additional variables

Heath, Young, and Burkitt. Wheater’s Functional Histology: A Text and Colour Atlas

www.theheartattachgerm.com/anihart3.gif