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 facilitators
www.heart-valve-surgery.com/heart-surgeryblog/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?
CO2
O2
Brooker, et al. Biology, 2nd Ed. McGraw Hill. Figure 47.15
Why study fluid in tubes?
Normal Coronary Artery
Library.med.utah.edu/webpath/cvhtml/cv004.html
Atherosclerotic Coronary Artery
Why study fluid in tubes?
730,000 deaths/year in US
300,000 bypass surgeries/year
($150,000 each)
Costs $45 billion/year
www.newswise.com/images/uploads/2011/05/9/underwoodnigeria.jpg
Why study fluid in tubes?
Why study fluid in tubes?
http://www.hurriyetdailynews.com/gelana-upsets-kenyans-to-win-soggy-marathon.aspx?pageid=238&nid=27143
Learning Activity 1
Learning Goals and Outcomes
• 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)
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
Facebook.com/mms
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
A1v1 = A2v2
Graphic courtesy of and more information at:
http://www.aplusphysics.com/courses/honors/fluids/continuity.html
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
2) Switch to the “Flow” tab, and check the “Ruler” box.
3) Click on the
“handles” to create a 2”
diameter tube flowing
into a 1” diameter tube.
4) Measure fluid speed in each tube - drag the speed tool
into each region.
Clicker question:
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
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
Velocity
Aorta
r=1.5cm
Capillary r=0.0005 cm
Vena Cava
r=1.0 cm
Hill, R., Wyse, G. &
Anerson, M. Animal
Physiology, 3rd Ed. Fig.
24.12 (part 1)
Velocity
But wait……
Aorta
r=1.5cm
Capillary r=0.0005 cm
Vena Cava
r=1.0 cm
Hill, R., Wyse, G. &
Anerson, M. Animal
Physiology, 3rd Ed. Fig.
24.12 (part 1)
Velocity
32 cm/sec
2 cm/sec
Aorta
A=7.1 cm2
Capillary
A=?
Vena Cava
A=3.14 cm2
Faculty.pasedena.edu/dkwon/chapter%2015_files/textmostly/slide16.html
Based on the velocity, calculate the cross-sectional area
of the capillaries (using A1v1=A2v2 and data above).
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
Capillary
bed
Aorta
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) 7
B) 21
C) 49
D) 70
E) 343
www.archiexpo.com/prod/bossini/shower-heads-80-247322.html
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?
CO2
O2
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