Ultrasound Physics & Instrumentation
High School Physics Day
April 3rd, 2013
“SPI in a Nutshell”
Disclaimer:
This is an overview of some important concepts in ultrasound medical
imaging intended for high school physics students. It is intended to
spark student interest in physics and the myriad of applications of
physics, including medical ultrasound. This is not a complete
introduction to medical ultrasound – there are many important topics
not mentioned due to time constraints. Some slides are based on
Pegasus Lectures, copyrighted material.
Pegasus Lectures, Inc.
COPYRIGHT 2006
“SPI in a Nutshell” Outline
 Basic Physics Overview
 Wave physics
 Transducers
 Piezoelectric crystals
 Instrumentation Overview
 From pulses to images
 Attenuation and Some Example of Imaging Artifacts
 Signal-to-noise ratio
 Doppler and Hemodynamics
 Bioeffects
 Mechanical and thermal indexes
Metric Abbreviations
Think about how much easier the metric system is than the English system; all
you have to do is move the decimal point by the number of places specified by
the exponent.
G
M
k
h
da
d
c
m
m
n
= 109
= 106
= 103
= 102
= 101
= 10-1
= 10-2
= 10-3
= 10-6
= 10-9
1,000,000,000
1,000,000
1,000
100
10
0.1
0.01
0.001
0.000001
0.000000001
Pegasus Lectures, Inc.
COPYRIGHT 2006
Distance Equation
Distance  rate  time
We will begin by calculating the time it takes for sound to travel 1 cm in the body
(assuming a propagation velocity of 1540 m/sec). Since we want to solve for
time, we must rewrite the equation in the form time = distance/rate.
distance

 time
rate
1 cm
1  10 2 m
so
time =

 6.5  10 6sec  6.5 m sec
m
m
1540
1540
sec
sec
So it takes 6.5 msec to travel 1 cm or:
13 msec to image a structure at 1 cm because of the roundtrip effect.
Pegasus Lectures, Inc.
COPYRIGHT 2006
Distance Equation
6.5 m sec
1 cm
6.5 m sec
0 cm
Time
Distance
Imaging Depth
6.5 msec
1 cm
0.5 cm
13 m sec
2 cm
1 cm
26 m sec
4 cm
2 cm
39 m sec
6 cm
3 cm
52 m sec
8 cm
4 cm
65 m sec
10 cm
5 cm
78 m sec
12 cm
6 cm
91 m sec
14 cm
7 cm
104 m sec
16 cm
8 cm
117 m sec
18 cm
9 cm
130 m sec
20 cm
10 cm
Pegasus Lectures, Inc.
COPYRIGHT 2006
Time of Flight in the Body
Fig. 3: Imaging 1 cm Requires 13 msec (Pg 39)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Addition of Waves
2
1
1
0.75
-0.5
0.5
0
0
0.25
0.5
Constructive Interference
-1
-1.5
-2
Time (sec)
1
0.75
0.5
Sum = 0
1
0.75
-0.25
0.5
0
0
0.25
0.25
Destructive Interference
-0.5
-0.75
-1
Time (sec)
2
1.5
1
1
0.75
-0.5
0.5
0
0.25
0.5
0
Amplitude
Amplitude
Amplitude
1.5
-1
-1.5
-2
Time (sec)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Partial Constructive
Interference
Wave Propagation Classification
Mechanical waves are further classified according to how they propagate.
Fig. 2: (Pg 84)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Transverse Wave Propagation
Transverse waves propagate by particle motion that is perpendicular or
“transverse” to the wave propagation direction.
Fig. 3: Transverse Waves (Pg 85)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Longitudinal Wave Propagation
Longitudinal waves propagate by particle compression and rarefaction
that results in particle motion that is “along” or in the same direction as
the wave propagation direction.
Fig. 4: (Pg 85)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Wave Characteristics
As sound propagates, it causes mechanical changes in the medium
Frequency :
1 

f  Hz =
 and Period ( T : sec )
sec 

Propagation Speed : c ( m/sec )
Wavelength :
 ( meters )
Amplitude :
A ( Volts, or any units for acoustic variables )
Pegasus Lectures, Inc.
COPYRIGHT 2006
Graphical Depiction of a 2 Hz wave
Fig. 10: (Pg 93)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Wavelength Equation
The wavelength of a sound wave depends on both the frequency and the
propagation speed.
A higher propagation speed “stretches” out the wave.
A lower frequency “stretches” out the wave.
Pegasus Lectures, Inc.
COPYRIGHT 2006
Propagation Velocity (c)
In Level 1, we discussed the fact that sound was determined strictly by the
properties of the medium. It is now important to discuss which properties of the
medium affect the propagation velocity and how.
 The propagation velocity is related to the square root of the bulk
modulus of the medium.
 The propagation velocity is inversely related to the density of the
medium.
 modulus
c

Pegasus Lectures, Inc.
COPYRIGHT 2006
Propagation Velocities in the Body
Medium
Propagation Velocity
Air (25 degrees C)
347 m/sec
Lung
500 m/sec
Fat
1440 m/sec
Water (25 degrees C)
1495 m/sec
Brain
1510 m/sec
“Soft Tissue”
Average 1540 m/sec
Liver
1560 m/sec
Kidney
1560 m/sec
Blood
1560 m/sec
Muscle
1570 m/sec
Bone
4080 m/sec
Table 5: (Pg 121)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Speed Error Artifact Example
This speed error case results from a needle entering into a cystic structure. The
needle appears bent giving rise to the name “broken needle” or “bayonet” sign.
Fig. 17: (Pg 606)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Relationship of intensity with Amplitude
Power  Amplitude 
Intensity 

area
area
2
So if the amplitude is doubled, the power increases by a factor
of four, resulting in an increase in intensity by a factor of four.
Recall that voltage is a measure of amplitude.
Pegasus Lectures, Inc.
COPYRIGHT 2006
Same Frequency – Different Amplitude
Fig. 33:
(Pg 135)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Attenuation
Attenuation is a measure of how the medium affects the wave.
Attenuation will be divided into three subtopics:
 Absorption
 Reflection
 Refraction
Pegasus Lectures, Inc.
COPYRIGHT 2006
Reflection – Acoustic Impedance
The amount of reflection from a boundary is determined by the acoustic
impedance mismatch.
What this equation says is: the greater the acoustic impedance
mismatch between mediums, the greater the amount of reflection.
How much reflection would there be if z2 = z1?
Pegasus Lectures, Inc.
COPYRIGHT 2006
Transmission
All of the energy at an interface between media must be conserved.
Excluding absorption, this means that whatever energy does not reflect
must transmit (continue on through the patient).
Can you imagine why it is so important to not have too much reflection
from any one interface?
Pegasus Lectures, Inc.
COPYRIGHT 2006
Refraction and Snell’s Law
θtransmitted
ctransmitted
cincident
Medium 2
Medium 1
θincident
θreflected
Pegasus Lectures, Inc.
COPYRIGHT 2006
Range Specificity and a Very Short
Pulse
Fig. 2: (Pg 194)
Notice that the echoes from each of the three mountains return at distinct
times such that each mountain is resolved (range resolution).
Pegasus Lectures, Inc.
COPYRIGHT 2006
Foundational PW Drawing Revisited
Fig. 25: (Pg 220)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Scanned Modalities (Animation)
(Pg 207 A)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Creating a Frame & Acoustic Lines
Each transmit burst or “pulse” represents the beginning of one acoustic
line. Multiple acoustic lines constitute one frame (or an image).
Transmit 1
Transmit 2
Transmit 3
Time
Pegasus Lectures, Inc.
COPYRIGHT 2006
Piezoelectric Effect
Ultrasound transducers use the piezoelectric effect to convert electrical
energy into mechanical energy and mechanical energy back into
electrical energy.
Electrical to acoustic
transformation
Acoustic to electrical
transformation
Pegasus Lectures, Inc.
COPYRIGHT 2006
Piezoelectric Effect
Fig. 2a Expansion
Fig. 2b Contraction
(Pg 235)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Fig. 2c At Rest
Lateral Resolution and Beamwidth
The lateral resolution equals the lateral
beamwidth dimension. If the beam is
wider than the distance between two
structures, the echo from both structures
will overlap, making it impossible to
distinguish between the two structures
laterally.
Lateral Resolution  Beamwidth
Fig. 14: (Pg 248)
Pegasus Lectures, Inc.
COPYRIGHT 2006
SNR (can ask SBI students about it)
307 A: Poor SNR
307 D: Poor Apparent SNR
307 B: Good SNR
307 E: Good SNR
(Pg 307)
Pegasus Lectures, Inc.
COPYRIGHT 2006
307 C: Poor Apparent SNR
307 F: Poor Apparent SNR
Relative Motion and Angle
Notice that Observer A
sees the opposite
effect of Observer B.
Observer B sees a
compression in the
wavelength (a higher
frequency) whereas
Observer A sees an
elongated wavelength,
(a lower frequency).
The higher frequency is
referred to as a positive
shift, whereas the lower
frequency is referred to
as a negative shift.
Fig. 6: (Pg 532)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Fast Moving Plane (Animation)
(Pg 522)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Doppler Equation
In Level 1, we expressed the Doppler equation in a simplified form, ignoring the
angular correction of the cosine term. We can now add the angular correction
of the cosine term as follows:
f Dop
2 f o v cos  

c
Where:
f Dop  Doppler shifted frequency (relative to transmit frequency )
v  velocity of the sound source (target)
cos    angle correction
 = insonification angle (or angle to flow)
c  speed of sound
Pegasus Lectures, Inc.
COPYRIGHT 2006
Determining Flow Direction
Notice in this example that the flow is not changing in direction or speed (constant
velocity) yet the flow looks very different traversing the vessel. This appearance
is the result of the changing angle to flow formed between the constant flow
direction and the varying steering angle.
Fig. 54: (Pg 576)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Flow Direction: Case 3 (Animation)
(Pg 580 C)
Pegasus Lectures, Inc.
COPYRIGHT 2006
Flow Conversion between Potential and
Kinetic Energy
Assuming no loss of energy to heat, as the flow accelerates, there is a decrease
in potential energy and a compensatory increase in kinetic energy (transitioning
from region 1 to region 2) As the velocity decreases (region 2 to region 3) the
kinetic energy decreases and the potential energy increases back to the same
level as in region 1.
PE
PE
KE
PE
KE
KE
Fig. 1: (Pg 742)
Region 1
Lower Velocity
Region 2
Higher Velocity
Region 3
Lower Velocity
Pegasus Lectures, Inc.
Bioeffects Intensity Restrictions
“Greatest Risk of Mechanical”
B-Mode
“Lowest Risk of Thermal”
PW
PW
(larger
gate)
“Lowest Risk of Mechanical”
CW
“Highest Risk of Thermal”
Pegasus Lectures, Inc.
Basic System Functions
Fig. 6: (Pg 308)
Pegasus Lectures, Inc.
COPYRIGHT 2006
American Registry of Diagnostic
Medical Sonographers (ARDMS)
• Must be registered sonographer (ARDMS or CCI) to practice in Florida
• CCI exams easier than ARDMS
• Two principal prerequisites to take ARDMS board exams:
• Passing grade in ultrasound physics course
http://www.ardms.org/credentials_examinations/
• Clinical experience (several months, duration depends on specific
exam) http://www.ardms.org/files/downloads/Prerequisite_Chart.pdf
Thank you!
•
•
•
Questions?
If not, take your worksheet and follow SBI students to ultrasound lab
You can find this presentation at my website:
http://www.nhn.ou.edu/~blandon/
click on “SBI High School Physics Day”