Adv Physiol Educ 37: 427–435, 2013;
doi:10.1152/advan.00065.2012.
Sourcebook of Laboratory Activities in Physiology
An educational device for a hands-on activity to visualize the effect of
atherosclerosis on blood flow
J. P. P. G. L. de Almeida and J. L. M. P. de Lima
Marine and Environmental Research Centre, Institute of Marine Research, Department of Civil Engineering, Faculty
of Science and Technology, University of Coimbra, Rua Luís Reis Santos, Coimbra, Portugal Coimbra, Portugal
Submitted 25 April 2012; accepted in final form 13 August 2013
didactic cardiovascular apparatus; thickening and hardening of the
artery wall
THE MAIN OBJECTIVE of this activity is to promote the understanding
of how atherosclerosis alters cardiovascular physiology by simple
and direct experiments. The two blood flow reduction mechanisms that can be demonstrated are 1) thickening of the artery wall
and 2) hardening of the artery wall. To visualize the impact of
thickening of the artery wall, users are asked to activate a piston
pump that feeds water into two similar acrylic tubes, one of which
is partially obstructed. To demonstrate the impact of hardening of
the artery wall, users activate a piston pump that feeds water into
two similar latex tubes, one of which with an exterior acrylic tube
that stiffens its wall. At the distal ends of these four tubes, there
are openings that create vertical jets of water. Flow rate differences are expressed by unequal jet heights.
More advanced students can explain these phenomena using a
theoretical fluid mechanics model based on Poiseuille’s equation,
which was also used to predict the response of the educational
device (available in the APPENDIX). This theoretical model helps
students to understand blood flow changes in atherosclerosis.
Address for reprint requests and other correspondence: J. P. P. G. L. de
Almeida, DEC-FCTUC Rua Luís Reis Santos, Coimbra 3030-788, Portugal
(e-mail: [email protected]).
Background
Atherosclerosis is the most common form of arteriosclerosis.
The term “arteriosclerosis” encompasses three patterns of vascular diseases (atherosclerosis, Monckeberg’s medial sclerosis,
and hyaline and hyperplastic arteriosclerosis) that can thicken
and harden the arterial wall (8).
According to Wang (13), in the first stage, the atherosclerotic lesions, named fatty streaks, are simple deposits of lowdensity lipoproteins, but in the second stage, the lesions contain
not only more smooth muscle cells but also more collagens and
elastic tissues. In this second stage, they are called fibrous
plaques. At the final stage, the lesions are deposits of fibrins
and platelets, leading to thrombus formation.
Atherosclerosis is characterized by two major inconvenient
effects on arterial blood vessels:
1. Thickening of the wall
2. Hardening of the wall
Blood circulation can consequently be drastically impaired,
leading to several cardiovascular diseases associated with unusual hemodynamic conditions that sometimes culminate in
premature death. According to Ref. 13, atherosclerosis is
responsible for about half of all deaths in developed countries
such as the United States, Europe, and Japan.
One of the major problems of atherosclerosis is the absence
of early symptoms, which enables this silent disease to spread
and develop for decades (6). An important factor to overcoming atherosclerosis is the avoidance of foods high in animal fats
and in sugar, which are nowadays readily available, especially
to young people. This emphasizes the need to tell younger
generations about atherosclerosis and promote the understanding of cardiovascular physiology. Alternative teaching strategies, such as hands-on activities in science fairs or museums,
have already proved to be effective (12), suggesting that
similar approaches should be further developed in consciousness campaigns targetting atherosclerosis.
Human blood is a two-phase fluid comprising a liquid
(plasma), which accounts for just over 54% of total human
blood volume, in which elastic particulate cells are suspended.
The plasma that constitutes this continuous liquid phase of
blood is mostly composed of water. which is ⬃91% of the total
weight. Proteins are ⬃7%, and inorganic solutes and other
organic substances make up the remaining 2% of the total
plasma composition (9). The possible non-Newtonian properties of plasma were considered in the past, but a recent study
(10) has shown that plasma is a Newtonian fluid.
The second phase of blood is composed almost entirely of
erythrocytes, which can account for ⬃99% of the cell volume
fraction, and also by leukocytes and platelets (e.g., Ref. 11).
Erythrocytes constitute the hematocrit, which represents ⬃45% of
1043-4046/13 Copyright © 2013 The American Physiological Society
427
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de Almeida JPPGL, de Lima JLMP. An educational device for a
hands-on activity to visualize the effect of atherosclerosis on blood flow. Adv
Physiol Educ 37: 427–435, 2013; doi:10.1152/advan.00065.2012.—An educational device was created to develop a hands-on activity to illustrate how atherosclerosis can dramatically reduce blood flow in
human vessels. The device was conceived, designed, and built at the
University of Coimbra, in response to a request from the Exploratório
Infante D. Henrique Science Centre Museum, where it is presently
installed. The device was designed to allow lay audience to operate it,
including school-age youngsters. The two blood flow reduction mechanisms that can be visualized are 1) thickening of the artery wall and
2) hardening of the artery wall. The main objective is to promote
the understanding of atherosclerotic cardiovascular physiology by simple
and direct experiments. This original educational interactive device was
constructed using, in the conceptual and design stages of the project, a
Newtonian theoretical flow model based on Poiseuille’s equation. This
device is driven by human force and provides a visualization of the effect
of atherosclerosis on flow. The main aspects relating to its design and
construction are described here to explain and disseminate this approach.
Throughout more than 4 yr of real operation, this educational device
proved to be a simple and attractive way of understanding atherosclerosis,
especially among young people.
Sourcebook of Laboratory Activities in Physiology
428
EDUCATIONAL DEVICE TO VISUALIZE ATHEROSCLEROSIS
Q⫽␲
⌬P r4
(1)
L 8␩
where Q is the volumetric flow rate, ␲ is the trigonometric
constant, ⌬P is the pressure drop in the tube over the distance
L, r is the inner radius of tube, and ␩ is the coefficient of
dynamic viscosity.
Equation 1 can be simplified by removing the mathematical
constants, to read as follows:
Q⬀
⌬P r4
(2)
L ␩
In words, Eq. 2 shows that flow is directly proportional to the
pressure gradient and to the radius of the tube to the fourth
power and that flow is inversely proportional to the length of
the tube and to the viscosity of the fluid flowing through the
tube. More simply, as driving pressure and the tube diameter
increase, flow increases. If length or viscosity increase, flow
decreases.
C
L N ,1
LR ,1
rR ,1
X
rN ,1
LR , 2
rR , 2
In the human circulatory system, length and viscosity normally are constant, so we can simplify the equation further by
removing those variables, leaving the following:
Q ⬀ ⌬P r4
Equation 3 then shows the two primary factors influencing
blood flow in the body: the pressure gradient driving blood
through the blood vessels and the radius of the blood vessels.
Thickened artery walls. From Eq. 3, we can easily understand that if the blood vessel radius is reduced because of
atheromatous plaque formation, then blood flow will drop
dramatically unless the driving pressure is increased. To simulate the effect of a reduced blood vessel radius, we constructed the hydraulic circuit schematically shown in Fig. 1.
Two identical horizontal tubes, tubes AB and CD, begin at inlet
section X and end at the geometrically identical orifices,
orifices B and D. One of the tubes (tube CD) is partially
obstructed in several sections to simulate atheromatous
plaques. The two identical horizontal orifices at the end of the
two tubes allow water to exit, creating two vertical jets into the
air. If one jet is lower, this indicates the tube with the smaller
water flow.
Hardened artery walls. Blood vessels are complex ducts
whose walls have muscular and viscoelastic properties. The
elastic properties of the blood vessels play a decisive role in
smoothing the pulsatile flow generated by the cardiac cycle.
According to Ref. 1, the rubbery protein called elastin allows
the blood vessel walls to expand when subjected to the high
pressures during cardiac contraction (systole). The systolic
high pressure energy is temporarily stored as elastic wall
deformation. During cardiac relaxation (diastole), the elastin
recoils, and the energy is returned to the blood, acting like a
second pumping stage. By this mechanism, the upstream pulsatile flow generated by cardiac systole and diastole is considerably smoothed downstream.
The ability of a structure to deform under pressure is called
compliance. Mathematically, compliance (C) is defined as
follows:
C⫽
dV
(4)
dPTM
where V is volume and PTM is transmural pressure. Equation 4
expresses the ratio between a change in pressure and a change
in the volume of the structure. For blood vessels, this is the
blood pressure increase (dPTM) pressing on the wall of the
blood vessel and the corresponding blood vessel volume in-
LN ,2
rN , 2
LR , 3
rR ,3
hD
L N ,3
rN ,3
D
ZD
ZX
hB
rN
A
(3)
B
ZB
Fig. 1. Perspective view of the horizontal hydraulic circuit scheme, showing a left partially obstructed tube (tube CD) and a right normal tube (tube AB), both
originating in inlet section X. LR, total length of stretches with a reduced inner radius (rR); LN, total length of stretches with a normal inner radius (rN); hD and
hB, jet height of vertical jets D and B, respectively; ZX, ZD and ZB, elevation in inlet flow section X and in vertical jets D and B, respectively.
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the total human blood volume. Leukocytes and platelets represent
⬍1% of the total human blood volume.
Since human blood is not solely composed of plasma, it is
not possible to predict a priori Newtonian behavior for this
fluid. It has been demonstrated experimentally that blood can
exhibit non-Newtonian behavior, such as shear thinning, thixotropy, viscoelasticity, and yield stress, and that its rheology
can be influenced by many factors (14).
However, it has been observed that blood behaves like a
Newtonian fluid in large arterial blood vessels (14).
So, in vitro simulation of the process of atherosclerosis can
use water instead of human blood without compromising the
expected physical response because water is a Newtonian fluid.
The replacement of human blood by water has several
advantages:
1. The precious organic fluid cannot be misused
2. No protective sanitary measures are needed
3. There should be no negative psychological impact on
more sensitive people
4. No modification of fluid properties with time
5. Easy cleaning
6. Easy and cheap periodic replacement of operational fluid
A theoretical model to explain how thickened and hardened
artery walls affect blood flow. Poiseuille’s equation can be
used to compute blood flow rate for steady laminar flow
through a straight cylindrical horizontal tube, as follows (e.g.,
Refs. 3 and 5):
Sourcebook of Laboratory Activities in Physiology
EDUCATIONAL DEVICE TO VISUALIZE ATHEROSCLEROSIS
Learning Objectives
After completing this activity, students will be able to
understand the blood flow rate decrease due to both thickening
of the artery wall and hardening of the artery wall, based on a
hydrodynamic analogy.
Cross Section1
along (GH):
G
X
ZX
Activity Level
This activity is suitable for secondary education students and
adults in general. It can be made more complex for higher-level
students through the use of the quantitative material included in
the APPENDIX that accompanies this article.
Prerequisite Student Knowledge or Skills
Before doing this activity, students should have a basic
understanding of:
1. The structure of the heart
2. The structure of blood vessels
3. Blood composition
Time Required
This activity takes 20 min.
METHODS
Equipment and Supplies
The following equipment and supplies are needed for this activity:
1. Thirteen acrylic plates (10 mm thickness) of the following
dimensions: 1,240 ⫻ 360 mm (one plate), 1,240 ⫻ 280 mm (two
plates), 1,040 ⫻ 360 mm (one plate), 880 ⫻ 380 mm (one plate),
740 ⫻ 520 mm (one plate), 720 ⫻ 680 mm (two plates), 680 ⫻
520 mm (two plates), 520 ⫻ 180 mm (two plates), and 280
mm ⫻ 380 mm (one plate).
2. Two manual piston pumps (e.g., http://www.survivalunlimited.
com/handwaterpumpshallow.htm).
3. Two latex tubes (e.g., made from party balloons previously cut
at the end).
4. Four acrylic bars (100 ⫻ 30 ⫻ 30 mm).
5. Four PVC clamps (7.5 mm diameter).
6. Four cork or plastic stoppers (19 mm diameter).
7. Ten acrylic tubes (2 mm thickness) with the following characteristics: inner diameter of 15- and 700-mm length (three tubes),
inner diameter of 15- and 20-mm length (two tubes), inner
diameter of 3.5- and 10-mm length (four tubes), and inner
diameter of 3.5- and 700-mm length (one tube).
8. Polyurethane foam spray.
9. Water (100 liters).
If the device will have intensive use, for instance, in a science
museum, a robust stainless steel feedin hydraulic circuit should be
constructed, using the following material:
10. Two ball valves for stainless steel tubing (outer diameter of 18
mm; e.g., http://www.thevalveshop.com/menu/manual/apollo/
apollom.html).
r rGH
H
(r = rGH )
hH
ZH
hF
(r ≤ rEF )
E
Cross Section 2
along (EF):
F
r
ZF
rEF
Fig. 2. Perspective view of the horizontal hydraulic circuit scheme, showing a rigidified latex tube (tube GH) on the left and an expandable normal latex tube
(tube EF) on the right, both beginning at inlet flow section X. r, inner radius; rGH and rEF, inner radius of tubes GH and EF, respectively; hH and hF, jet heights
of vertical jets H and F, respectively; ZX, ZH, and ZF, elevations in inlet flow section X and vertical jets H and F, respectively.
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crease (dV), characteristic of elastic blood vessels as opposed
to rigid ones (5).
Blood vessel compliance diminishes as humans become
older. Besides the aging process, other factors can reduce
compliance, such as blood vessel wall thickening.
Blood vessels of normal wall thickness have no difficulty
expanding when blood pressure temporarily increases. But a
blood vessel with a thickened wall eventually becomes rigid
and unable to expand under a temporary pressure increase, thus
disabling the smoothing effect of the pulsatile blood flow
generated during the cardiac cycle. The progressive loss of the
blood vessel’s capacity to expand under a temporary pressure
increase is usually called hardening of the wall.
To simulate the impact of hardening of the artery wall on
blood flow, we can use the hydraulic circuit schematically
shown in Fig. 2. Like the previous circuit, it has two similar
parallel horizontal tubes, tubes EF and GH, both connected to
the inlet of the bifurcation, inlet X. Both tubes have the same
initial radius r and are made of latex, a material that provides
high compliance.
The left interior latex tube, tube GH, with radius r (dotted
line in cross-section 1 in Fig. 2) is inserted into a tightly fitting
transparent acrylic tube. The acrylic tube surrounds the latex
tube, preventing it from expanding when submitted to a pressure increase. This eliminates the compliance of the left latex
tube and restricts the expansion of the tube.
The right interior latex tube, tube EF, with radius r (dotted
line in cross-section 2 in Fig. 2) has an exterior acrylic tube
into which it is inserted (solid line in cross-section 2 in Fig. 2).
There is a gap between the two tubes that allows the inner latex
tube to expand when submitted to a pressure increase. Therefore, the compliance of the latex tube is not affected, and the
tube can expand under pressure. From Eq. 3, we can easily
understand that if the blood vessel radius increases, then the
blood flow rate increases.
At the end of both tubes, there are two horizontal orifices
that allow water to exit and create vertical jets into the
atmosphere. As described above, a smaller jet indicates the
tube with the lowest flow rate.
429
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430
EDUCATIONAL DEVICE TO VISUALIZE ATHEROSCLEROSIS
11. Ten elbows for stainless steel tubing (outer diameter of 18 mm;
e.g., http://www.buyfittingsonline.com/90degreeelbows.aspx).
12. Eight stainless steel tubes (0.6 mm thickness, outer diameter of
18 mm) of the following lengths: 530 mm (two tubes), 310 mm
(two tubes), 120 mm (two tubes), and 110 mm (two tubes).
If the device will have normal use, for instance, in a classroom, a
low-cost plastic hose feedin hydraulic circuit should be constructed
using the following material:
13. Two high-pressure hoses with an internal diameter similar to
the pump outlet diameter (1,000 mm long).
14. Four metallic clamps with a diameter superior to the pump
outlet diameter.
Instructions
4
The atherosclerosis educational interactive device (Fig. 3) has a
maximum height of 192 cm and a maximum base width of 74 cm,
which is compatible with the usual size of indoor passages, making it
very portable.
The device comprises a water reservoir (Fig. 4, 1), which feeds two
independent pump suction tubes (Fig. 4, 2) that convey water to two
independent manual piston pumps (Fig. 4, 3). In the piston pump
outlets, there are ball vales (Fig. 4, 4) that are adequately regulated to
prevent exaggerated flow rate in case pumps are operated with
excessive force (after an initial regulation, the ball valve pump levers
will be removed to prevent accidental detuning of the device). From
the piston pumps, water is driven to a stainless steel circuit (Fig. 4, 5)
that feeds the bifurcations (Fig. 4, X). Tubes AB and CD, transparent
acrylic tubes, are 700 mm long and have an inner diameter of 15 mm.
The ball valves and stainless steel tubing can be substituted by the
low-cost plastic hose feedin hydraulic circuit shown in Fig. 8, in case
of nonintensive use of the device.
To create partial inner obstructions to reduce the available cross
section, expandable polyurethane foam was spread inside tube CD.
Tubes EF and GH are 700 mm long.
Latex tube GH is surrounded by a transparent acrylic tube that
prevents it from expanding. Its inner diameter is 3.5 mm.
Latex tube EF is free to expand its inner diameter from 3.5 to 15
mm.
There is a transparent chamber (Fig. 4, 6) at the end of the
hydraulic circuits that prevents the jets from wetting the users. Water
from these jets falls into the reservoir (Fig. 4, 1) and can be reused.
The device is mainly made of acrylic, which was considered to be
safer than glass in the event of an accident. Other materials used
4
6
5
3
2
EF
5
GH
3
CD
2
AB
X
1
(1) - Reservoir that feeds the pumps and collects water from the jets
(2) - Suction feed in pipes
(3) - Manual piston pumps
(4) - Ball valve
(5) - Positive pressure feed in circuit
(6) - Transparent chamber that protects spillage from water jets
(X) - Bifurcations (see also Figs. 1 and 2)
(AB) - Unobstructed transparent acrylic tube (see also Fig. 1)
(CD) - Partially obstructed transparent acrylic tube (see also Fig. 1)
(EF) - Free expandable latex tube (see also Fig. 2)
(GH) - Confined latex tube (see also Fig. 2)
Fig. 4. Components of the atherosclerosis educational interactive device.
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Fig. 3. Three-dimensional representation and overall dimensions of the atherosclerosis educational interactive device.
include steel, silicone, and acrylic glue. Acrylic gluing techniques are
readily available on the internet (http://www.youtube.com/watch?v⫽
hT6Ow_cBTps).
The tare of the device is ⬃40 kg, and its gross weight, with a full
water reservoir, can reach 140 kg, which makes it very stable.
The device does not rely in any way on electrical, water supply, or
water drainage systems, so it can be easily taken to itinerant expositions and outdoor activities.
Figure 5 shows a photograph of the device.
The following are instuctions to construct the educational device:
Step 1. Drill a circular hole of 40 mm on top of a 680 ⫻ 520-mm
acrylic plate, as shown in Fig. 6 (this hole will serve to pass a hose to
add or withdraw water from the reservoir).
Step 2. Build two boxes by joining the acrylic plates, as shown in
Fig. 6, using standard acrylic gluing techniques.
Step 3. Build two bifurcations using the following procedure. First,
take an acrylic bar of 100 ⫻ 30 ⫻ 30 mm. Second, drill four
cylindrical holes with 19-mm diameter in one bifurcation and drill
two cylindrical parallel holes with 7.5-mm diameter and the remaining
cylindrical holes with 19-mm diameter in the other bifurcation, as
shown by the dashed lines in Fig. 7. Third, cover the extremity of the
longitudinal cylindrical holes with a cork or rubber stopper, as shown
by the gray small cylinder in Fig. 7. Finally, insert and glue a 19-mm
acrylic tube with a length of 20 mm in the single cylindrical transversal hole of each bifurcation to serve as the inlet connection.
Step 4. Build two jet outlet bases using the following procedures.
First, take an acrylic bar of 100 ⫻ 30 ⫻ 30 mm. Second, drill three
cylindrical horizontal holes with a diameter of 19 mm in one jet outlet
base and drill one cylindrical longitudinal horizontal hole with a
diameter of 19 mm and two parallel cylindrical horizontal holes with
a diameter of 7.5 mm in the other jet outlet base, as shown by the
dashed lines in Fig. 7. Third, drill two vertical cylindrical holes with
a diameter of 3 mm in each jet outlet base, as shown by the dashed
Sourcebook of Laboratory Activities in Physiology
EDUCATIONAL DEVICE TO VISUALIZE ATHEROSCLEROSIS
lines in Fig. 7. Finally, cover the extremity of the longitudinal
cylindrical holes with a cork or rubber stopper, as shown by the gray
small cylinder in Fig. 7.
Step 5. Connect the two pumps to the two reservoir lids using the
following procedure for each one, as shown in Fig. 8. First, take an
acrylic plate of 520 ⫻ 180 mm, which will serve as a reservoir lid;
pierce it with a cylindrical hole with a diameter slightly larger than the
exterior threaded base diameter of the pump. Second, insert the base
of the pump in the hole and use a washer and a nut to tighten it against
the acrylic plate. Finally, install the pump suction pipe by screwing it
around the internally threaded pump base.
Step 6. Build a tray to support the hydraulic circuits shown in Figs.
1 and 2 using the following procedure. First, take the acrylic plate of
880 ⫻ 380 mm, which will serve as a tray as well as a water reservoir
lid, and pierce half of it with some small holes that will allow water
drainage (see Fig. 9). Second, put a wire of 3-mm diameter inside the
19-mm diameter acrylic tube of 700 mm long and spray some
polyurethane foam inside it. Third, pull the wire, leaving a hole in the
middle of the dry foam. Fourth, connect a bifurcation and a jet outlet
base with two 19-mm diameter, 700-mm-long acrylic tubes, one of
them partially obstructed and the other completely clean. Fifth, glue
this set to the tray, as shown by tubes AB and CD in Fig. 9. Sixth,
insert and glue the four small acrylic tubes of 7.5 mm diameter and 10
mm long in the transversal horizontal parallel holes of a bifurcation
and of a jet outlet base, leaving half of each tube outside. Sixth, tie the
extremities of the latex tubes to wires and introduce them in
the acrylic tubes of 700 mm long, one tube of 19 mm diameter and the
other tube of 7.5-mm diameter (you should previously wet the interior
of the tube with water and you should stretch the latex tubes gently).
Seventh, connect the bifurcation and the jet outlet base with the latex
tubes using PVC clamps to join them to the previously glued four
small acrylic tubes. Finally, glue this set to the tray, as shown by tubes
EF and GH in Fig. 9.
Step 7. Cover the water reservoir with the central tray and with the
two lids, as shown in Fig. 10 (you can use some mechanical fixing
system or simply glue them with silicone that you can easily remove
in case of need for repair).
Step 8. In the version for intensive use, for instance, in a science
museum, connect each pump to a bifurcation with a stainless steel
feedin hydraulic circuit using conventional plumbing techniques according to the following sequence, as shown in Fig. 4: pump outlet ⫹
ball valve ⫹ elbow ⫹ 310-mm tube ⫹ elbow ⫹ 110-mm tube ⫹
elbow ⫹ 530-mm tube ⫹ elbow ⫹ 120-mm tube ⫹ elbow ⫹ bifurcation.
Step 9. In the low-cost alternative version for normal use, connect
each pump to a bifurcation with a high-pressure hose, as shown in Fig.
8. First, use adhesive tape to fill the gap between the inlet bifurcation
tube and the hose and then tighten with a metallic clamp, as shown in
Fig. 8. Next, connect the high-pressure hose to the pump outlet using
a threaded hose connector or simply clamping (use a metallic clamp)
the hose to the pump outlet, as shown in Fig. 8.
Step 10. Cover the jet base with the jet chamber, as shown in Fig.
10 (you can use some mechanical fixing system or simply glue it with
silicone that you can easily remove in case of need for repair).
The following are instuctions to operate the educational device:
Step 1. Put your hand on the lever of the right manual piston pump
(Fig. 4, 3).
Step 2. Push down the lever gradually until you observe the
formation of vertical jets.
Step 3. Check that there is a difference in the heights of the jets (use
a ruler to estimate the heights).
Step 4. Find out what is causing this difference.
Step 5. Specify which aspect of the atherosclerotic cardiovascular
disease is illustrated by this hydraulic circuit.
Step 6. Consider the left manual piston pump (Fig. 4, 3) and repeat
from step 2.
Troubleshooting
The manual pumps should not be operated with excessive strength,
because the water jets will be too high colliding with the roof of the
water chamber. This will make it impossible to identify water jet
height differences.
The latex tube should be replaced periodically; otherwise, it may
blow up during the activity.
Safety Considerations
This educational device does not rely in any way on electrical,
water supply, and water drainage systems, so it is safe to use.
Fig. 6. Assembling the water reservoir (left) and jet chamber (right).
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Fig. 5. Photograph of the device installed in the Exploratório Infante D.
Henrique Science Centre Museum.
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EDUCATIONAL DEVICE TO VISUALIZE ATHEROSCLEROSIS
Fig. 7. Building acrylic bifurcations (left) and jet outlet bases (right).
However, it may contain up to 100 liters of water in its base tank.
Therefore, it should not be overtopped or transported without previous
drainage.
RESULTS
In the case of tubes AB and CD, the heights of the jets during
typical operation are expected to be quite different. Students
are supposed to observe that the dramatic jet height reduction
in point D is due to the partial obstruction of tube CD with the
polyurethane foam. By transposing this observation to the
cardiovascular system, they will clearly perceive the negative
impact of atheromatous plaque formation. From these experimental observations, they will understand that impact of partial
obstruction can be explained by Poiseuille’s equation. The
application of this equation clearly shows that a reduction in
the radius of a tube or blood vessel dramatically decreases the
flow rate. Using this hydraulic analogy, they will be able to
explain the negative impact of atheromatous plaque formation
in blood flow rate.
Let us now consider tubes EF and GH. The heights of the
jets produced during typical operation are expected to be
considerably different. Students are supposed to observe that
the reduction of the jet located at point H is due to the rigid
wall that prevents the latex tube from expanding when water is
injected by the pumping action. By transposing this observation to the cardiovascular system, they will clearly perceive the
negative impact of hardening of the artery wall. Once more,
students can verify the agreement between Poiseuille’s equation and the experimental observations. Poiseuille’s equation
shows that an increase in the radius or diameter, as occurs in
the case of the elastic vessel, allows a significant increase in
flow rate. Students are expected to use this hydraulic analogy
Fig. 8. Connecting the pump to the water reservoir lid and to the bifurcation
(low-cost version).
Misconceptions
The device is ideal for a discovery activity in which the
teacher asks students to predict which tube will have the higher
jet: the one tube with the stiff wall or the tube with the elastic
wall, the one tube with the clean wall or the tube in which some
of the wall has been filled with foam. Students are likely to say
that the tube with the stiff wall will have a higher jet because
it has a stronger wall. It may be necessary to call their attention
to the fact that during pumping action, pressure increases and
the elastic tube will deform, increasing its radius, thus creating
more space available for the flow. So, flow will be easier inside
the elastic tube and the water jet should be higher. For more
advanced students, have them use Poiseuille’s equation to
show that with equal pressure but greater radius, the flow in the
tube with the elastic wall will be greater.
Inquiry Applications
As described above, the teacher decides the question to be
explored and plans the procedures to be used. Students carry
out the experiment.
Fig. 9. Tray with the hydraulic circuits shown in Figs. 1 and 2.
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Expected Results
to explain the negative impact of hardening of the artery wall
in the blood flow rate.
In real operation conditions, it has been observed that some
students tend to use unnecessary force on the manual pump
lever, resulting in considerably higher vertical jets. Under these
conditions, flow becomes turbulent, so Poiseuille’s equation
cannot be used to correctly predict the behavior of the educational device. However, given that the flow rate in turbulent
conditions is still proportional to the vessel radius, the vertical
jet height differences will remain qualitatively unchanged, and
the device can still be used to illustrate the effect of atherosclerosis on blood flow.
Sourcebook of Laboratory Activities in Physiology
EDUCATIONAL DEVICE TO VISUALIZE ATHEROSCLEROSIS
433
If we neglect the head losses in the jet orifice and the flow velocity
inside the tube (relative to the base jet flow velocity), PB becomes
solely a function of the jet height, as follows:
PB ⫽ ␥hB
(A2)
where ␥ is the specific weight of the water and hB is jet height.
The height of the water jet results from the total conversion of the
kinetic energy at the base of the jets into the gravitational potential
positional energy at the top of them, if energy losses are neglected.
Water jet heights can thus be related to the base jet velocity, using the
energy conservation principle, resulting in the following equation:
hB ⫽
2
Ujet,B
2g
(A3)
Ujet,B ⫽
Fig. 10. Joining the main components of the device.
The mathematical basis for the construction of the apparatus
can be used for more advanced students to ask them to predict
the size differential of the water jets. This information is
included in the APPENDIX available with this article.
aQB2 ⫹ bQB ⫹ c ⫽ 0
A device analogous to the one described in this article was
installed in the Exploratório Infante D. Henrique Science Centre
Museum (Coimbra, Portugal) in March 2009. Since then, it has
been included in the global exhibition on the relations between
basic sciences and human health. By the time of writing this article,
more than 65,000 visitors have attended the exhibition. The main
users of the device have been secondary school students.
The staff at the Exploratório Infante D. Henrique Science
Centre Museum reported that the device has been well received
by the students. They found it particularly interesting because
they can use their own force to activate the educational device
and visualize the vertical jets.
APPENDIX
4
␥rN
4
16g␲␩rorif
LXB
b⫽1
c⫽⫺
Background
Theoretical basis for water jet height prediction in sections B and
D. In the analysis that follows, we will neglect the effect of the very short
symmetrical bifurcation, which is equivalent to stating the following:
LXA ⫽ LXC ⫽ 0 and PX ⫽ PA ⫽ PC
where LXA is the length between X and A, LXC is the length between
X and C, PX is the inner pressure in X, PA is the inner pressure in A,
and PC is the inner pressure in C, respectively.
In the righthand tube (tube XB), the volumetric flow rate is driven
solely by the differential internal pressure between its ends, because
the elevation in X (ZX) equals the elevation in B (ZB), as follows:
LAB
8␩
(A1)
where QB is the volumetric flow rate in B, PB is the inner pressure in
B, rN is the inner radius under normal conditions, and LAB is the length
between A and B.
(A5)
4
␲PXrN
8␩LXB
(A6)
(A7)
(A8)
In the partially obstructed lefthand tube (tube XD), the volumetric
flow rate is also only driven by the differential internal pressure
between the extremities, because ZX ⫽ ZD, where ZD is the elevation
in D. Given that obstructed and unobstructed stretches are associated
in series, the volumetric flow rate at D (QD) can be computed in two
different ways, volumetric flow rates in stretches with a normal inner
N
R
radius (QD
) and with a reduced inner radius (QD
), as follows:
N
QD
⫽␲
QB ⫽ ␲
(A4)
where
a⫽
Additional Information
共 P X ⫺ P B兲
2
␲rorif
where rorif is the orifice radius.
By combining Eqs. A1–A4, we are able to compute QB using the
following equation:
Wider Educational Applications
4
rN
QB
R
QD
⫽␲
4
⌬PN rN
LN 8␩
⌬PR rR4
LR 8␩
(A9)
(A10)
where ⌬PN and ⌬PR are the total pressure drops in stretches with a
normal inner radius and a reduced inner radius, respectively; rR is the
reduced inner radius in the partially obstructed stretches of the
lefthand tube; and LN ⫽ LN,1 ⫹ LN,2 ⫹ LN,3, LR ⫽ LR,1 ⫹ LR,2 ⫹ LR,3,
LN, and LR are the total lengths of stretches with a normal inner radius
and with a reduced inner radius, respectively.
Considering that
N
R
QD ⫽ QD
⫽ QD
(A11)
共PX ⫺ PD兲 ⫽ ⌬PN ⫹ ⌬PR
(A12)
LXD ⫽ LN ⫹ LR
(A13)
N
and by combining Eqs. A9 –A13, we are able to compute QD
using the
following resulting equation:
Advances in Physiology Education • doi:10.1152/advan.00065.2012 • http://advan.physiology.org
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where Ujet,B is the average base jet velocity in the orifice.
QB can be related to the base jet velocity using the mass conservation principle, resulting in the following equation:
Sourcebook of Laboratory Activities in Physiology
434
EDUCATIONAL DEVICE TO VISUALIZE ATHEROSCLEROSIS
N
QD
⫽␲
冋冉
共 P X ⫺ P D兲
LXD
LN
⫺1
冊冉 冊 册
4
rN
⫹ 1 LN
rR
4
rN
8␩
(A14)
QB ⬵ 11.80 ⫻ 10⫺3 l ⁄ s, QD ⬵ 5.94 ⫻ 10⫺3 l ⁄ s
Assuming the same principles and considerations previously taken
in Eqs. A2–A5, we are able to obtain the following corresponding
equations:
pD ⫽ ␥hD
hD ⫽
(A15)
2
Ujet,D
(A16)
2g
Ujet,D ⫽
QD
(A17)
2
␲rorif
⫹ bQD ⫹ c ⫽ 0
(A18)
where
a⫽
4
16g␲␩rorif
冋冉
4
␥rN
LXD
LN
⫺1
冊冉 冊 册
rN
rR
4
b⫽1
c⫽⫺
8␩
冋冉
(A20)
4
␲PArN
LXD
LN
⫺1
(A19)
⫹ 1 LN
冊冉 冊 册
rN
rR
4
(The physical constants are taken as follows: g ⫽ 9.8 m/s2, ␥ ⫽ 9,800
N/m3, and ␩ ⫽ 10⫺3 N·s·m⫺2.)
Afterward, students are expected to select Eqs. A3, A4, A16, and
A17 and convert these flow rates into water jet heights, obtaining the
following values:
hB ⬵ 14.22 ⫻ 10⫺2 m, hD ⬵ 3.61 ⫻ 10⫺2 m,
hD
hB
⬵ 25%
Select the appropriate equations to explain and compute the
difference in the heights of the jets in sections F and H. Students will be given the geometric characteristics of the device and will
be informed about the average pressure to be considered at point X
during a typical operation, as follows:
LXF ⫽ LXH ⫽ 700 mm, rEF ⫽ 7.5 mm, rGH ⫽ 1.75 mm, rorif
⫽ 1.5 mm, PA ⫽ 1,800 Pa
They will observe that tube EF expands from r ⫽ 1.75 mm to r ⫽ 7.5
mm along ⬃90% of its total length. Based on these data, and
considering the same physical constants taken above, they should
compute the theoretical water jet heights.
The students should select and adapt Eq. A5 to the computation of
flow rate in the rigid latex tube (tube GH). They should obtain the
following value:
QH ⬵ 6.93 ⫻ 10⫺3 l ⁄ s
(A21)
⫹ 1 LN
Assuming the flow can be reasonably described by Poiseuille’s
equation, Eqs. A5 and A18 can be adopted to get some insight on the
variation of the volumetric flow rates. Using Eqs. A3, A4, A16, and
A17, the corresponding water jet heights can be computed.
Theoretical basis for water jet height prediction in sections
F and H. Assuming that flow in tube GH can be reasonably
described by Poiseuille’s equation, Eq. A5 can be adapted to compute
the volumetric flow rate. Using Eqs. A3 and A4, the corresponding
water jet height can be computed.
In tube EF, the cross-section will expand along a certain percentage
of its total length. So, assuming that Poiseuille’s equation is applicable, Eq. A18 can be adapted to compute the volumetric flow rate. Two
branches should be considered: the expanded branch with inner radius
rN ⫽ rEF and the nonexpanded branch with inner radius rR ⫽ rGH.
Once more, we will neglect the effect of the very short symmetrical
bifurcation, which is equivalent to stating the following:
LXG ⫽ LXE ⫽ 0 and PX ⫽ PG ⫽ PE
where LXG is the length between X and G, LXE is the length between X
and E, PG is the inner pressure in G, and PE is the inner pressure in E.
Activities for Advanced Students
Select the appropriate equations to explain and compute the
difference in the heights of the jets in sections B and D. At this
stage, students will be given the geometric characteristics of the
device. They will be informed about the average pressure to be
considered at point X during a typical operation and about the average
radius and length of the partially obstructed zone:
LXB ⫽ LXD ⫽ 700 mm, rN ⫽ 7.5 mm, rR ⫽ 1.5 mm, rorif
⫽ 1.5 mm, PX ⫽ 1,400 Pa
To compute the flow rate in the expandable latex tube (tube EF),
students should select and adapt Eq. A18. From Eq. A18, students will
understand that the expansion of tube EF allows a considerable flow
rate increase. From Eq. A18, they should obtain the following value:
QF ⬵ 12.47 ⫻ 10⫺3 l ⁄ s
By selecting Eqs. A3, A4, A16, and A17, students can convert these
flow rates into water jet heights, obtaining the following values:
hH ⬵ 4.91 ⫻ 10⫺2 m, hF ⬵ 15.88 ⫻ 10⫺2 m,
hH
hF
⬵ 31%
Outline the analogy between the cardiovascular system and
the hydraulic physical and theoretical models used in this
activity. Students will be asked to describe the analogy between the
cardiovascular system and the physical model. The water simulates
the blood, the manual piston pump simulates the heart, the tubes
simulate the vessels in several conditions (normal or suffering from
some atherosclerosis), and the jet height symbolizes the irrigation
capacity of the tissues served by the cardiovascular system.
Students will be asked to describe the analogy between the cardiovascular system and the theoretical model. In Poiseuille’s equation,
⌬P represents the heart effort, L represents the extent of the vessel, ␩
represents the resistance that blood offers to movement, and r represents the inner radius of the blood vessel.
ACKNOWLEDGMENTS
The authors express gratitude to the scientific and technical staff of the
Exploratorio Infante D. Henrique science centre museum (Coimbra, Portugal),
and particularly to its governing board, for providing the conditions needed to
develop this work.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the author(s).
Advances in Physiology Education • doi:10.1152/advan.00065.2012 • http://advan.physiology.org
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where hD is jet height and Ujet,D is average base jet velocity in the
orifice.
By combining Eqs. A11–A14, we are able to compute QD using the
resulting equation:
2
aQD
With these data, they are expected to select Eqs. A5 and A18 and solve
them to obtain the resulting theoretical flow rates:
Sourcebook of Laboratory Activities in Physiology
EDUCATIONAL DEVICE TO VISUALIZE ATHEROSCLEROSIS
AUTHOR CONTRIBUTIONS
Author contributions: J.P.P.d.G.L.d.A. conception and design of research;
J.P.P.d.G.L.d.A. performed experiments; J.P.P.d.G.L.d.A. analyzed data; J.P.
P.d.G.L.d.A. and J.L.M.P.d.L. interpreted results of experiments; J.P.P.d.G.L.d.A. prepared figures; J.P.P.d.G.L.d.A. drafted manuscript; J.L.M.P.d.L.
edited and revised manuscript; J.L.M.P.d.L. approved final version of manuscript.
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