Just how fast is your blood traveling?

```HPP Activity 57v1
Just how fast is your blood traveling?
Exploration
We need to understand one more piece of physics before putting together how the Doppler effect
with sound can be used to gain noninvasively significant information about the body. The issue
involves looking at what happens when the source of sound is not coming straight at the
observer.
Look at the Doppler Effect simulation.
Set the ambulance speed at about 125 [m/s] and the siren frequency at 500 [Hz].
Play the simulation.
Stop the simulation before the ambulance passes the man.
GE 1.
For the time at which the simulation is stopped, suppose there is a second
observer in a helicopter, that remains directly above the ambulance at all
times.
1. Compare the wavelength observed by the man on the ground with the
wavelength observed by the person in the helicopter.
2. Compare the frequencies heard by the two observers to the frequency
produced by the ambulance (500 [Hz]). Rank the 3 frequencies from largest to
smallest. Explain how you arrived at your conclusion.
The observed Doppler effect depends not just on the observer and source speeds, but also on the
angle between the two. If the helicopter were to stay over the ambulance, the observers on the
helicopter would hear the same frequency as the ambulance driver! The medical application of
the Doppler effect, Doppler Ultrasound, involves a slightly different situation.
Take a look at the Doppler Ultrasound simulation. The basic set-up is shown below.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP Activity 57v1
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GE 2.
The artery carries blood flowing at some speed, either to the left or to the
right. The Doppler Ultra-sonograph device will send out a pulse of sound at a
known frequency. Play the simulation.
1. Compare the received frequency with the transmitted frequency for this case
(with the transducer at right angles to the blood flow)?
2. You can change the angle that the sonograph device makes with respect to
the blood velocity. Explore how this angle affects the received frequency.
3. Suppose your sonograph device can measure both the transmitted and
received frequency. Describe how you might get information on the blood
speed from this device. What information do you need to make your idea
practical?
Invention
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 57v1
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Using the Doppler effect to get information on blood flow requires that we know how the
frequency shift, between transmitted and received frequencies, depends on angle between sound
and the blood velocity, and how it depends on the blood speed.
GE 3.
The figure below shows the basic geometry of the Doppler ultrasound
instrument and the blood flow velocity. Let the average speed of sound in the
tissue be represented by the symbol c.

VB
1. What is the speed of the blood directly away from the Doppler US device?
Express in terms of . Remember that velocity is a vector and therefore has a
component perpendicular to the axis of the device and a component parallel to
the axis of the device.
2. Let the frequency produced by the device be fd . Treat the blood as a
receiver of sound. What would be the frequency the blood volume observes?
Call this frequency fB and express it in terms of fd, using the Doppler shift
formula.
3. The blood volume reflects the sound pulse. In this case the blood acts as a
source of sound at the frequency fB found above and in this case the blood is
moving away at the speed you calculated in 1. Also in this case, the device
becomes the observer. What frequency would the device observe? Call this
frequency ff, for final frequency, and express it in terms of fB.
4. Combine the results from question 2 and 3 and see if you can arrive at a
formula for the frequency shift, f  f f  f d , observed by the detector.
5. Compare your result with the equation below. How well did you do?
Activity Guide
 2010 The Humanized Physics Project
HPP Activity 57v1
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vB
cos( )
c
f  2 f d
v
1  B cos( )
c
f  2 f d
vB
cos( )
c
(1)
Application
GE 4.
determine the speed of blood flow. Assume the speed of sound in the tissue is
1500. [m/s].
1. What measurements can be obtained from the simulation?
2. Specify numerical values for as many quantities in equation (1) as you can.
3. Find the speed of the blood in the simulation. Show your work
Congratulations! You should now have a basic understanding of the physics of ultrasound
imaging. Along the way you learned about wave properties and what happens when waves
interact with abrupt changes in media through which they travel. The physics of sound and waves
allow many disciplines to design ultrasound imaging systems that all work in the same way while
all are uniquely suited to a particular application. Even among the medical imaging community,
there are many different ultrasound transducers with different frequencies that produce images of
organs deep inside the body and details of detached retinas or tumors within the human eye.
Activity Guide
 2010 The Humanized Physics Project
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