Papers-graded “soon”. Generally good, main problem is
Description not related to physics principles.
Exam 3 Total, 30 possible
Class average = 22.99
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2
1
29
27
25
23
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5
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Medical Imaging II. (ultrasound and MRI)
“ionizing radiation”- EM wave or energetic particle with enough energy to kick
electron off atom or molecule (“ionize”). Molecular damage.
e
1. X-ray.
2. PET scan (inject radioactive stuff
that decays in body producing
particles come flying out.)
High doses- enough dead
cells for radiation sickness.
Low dose damage DNA cancer
Balance of risks
Harmless Methods (if low power, just slight warming)
1. Ultrasound- sound waves don’t effect atoms and molecules at
all except shake a bit. S. M.
2. MRI- uses radio waves, very low frequency/energy.
Special homework problems this week- construct your own!
Ultrasound: uses sound waves to see
inside the body
If I hear an echo what do I know?
a. That something a head of me reflects
sound
b. how far away it is
c. what its made of
d. a and b
HELLO
HELLO e. a, b, and c
Where
am I?
Answer is d. But do know something of c.
If I hear an echo 1 second after I shout “Hello”,
I can conclude that this surface is
a. about 331 m away
b. about 3x108 m away
c. about 115 m away
d. I don’t remember the speed of sound in air.
Answer is c. Total Dist = velocity * time.
Distance to surface = Total Dist/2
ULTRASOUND PROBE
Transmits:
Short pulse of
sound wave
Frequency of sound
(1 MHz – 5 MHz)
MHz= megahertz (106 Hz)
Listens:
Echos
Timing and Amplitude
(Distance & something about
Material)
~1% of time transmitting
~99% of time listening
Sound waves reflect and refract at a surface interface
Acoustic equivalent to “index of refraction of light”
depends on:
Speed of Sound in substance
(Also on density of substance)
The bigger the difference in the speed of sound at the interface,
the more sound is reflected and the greater the refraction.
TRAVELING SOUND WAVES
Substance A
Substance B
Which is true?
a. Speed of sound in B is greater than A
b. Speed of sound in A is greater than B
c. I don’t know how to tell
Ultrasound: Depth measurement
Substance
Air
Fat
Water
Soft Tissue
Brain
Liver
Kidney
Blood
Muscle
Bone
Speed of Sound
331 m/s
1450 m/s
32
4
1450 m/s
Oil/Gel
1
5
1450 m/s
Reflecting layers
1451 m/s
1549 m/s Why do they put the oil between you and the
1561 m/s
probe?
1570 m/s Answer
a. To protect
is c. Ifthe
no probe
gel, some air between
1585 m/s probe
b. Toand
protect
from ultraviolet
youryour
skin.skin
Reflects
most of rays
4080 m/s sound…
generated
the probein speed of sound
Largebydifference
c. To decrease
the reflection
between
air and skin
tissue! of the sound
wave off your outer skin
d. To allow smooth movement of the probe.
Ultrasound: Depth measurement
Oil/Gel
1
5
Reflecting layers
Amplitude
(Assume incident soundwave strong
enough to reach layer 5)
A
Time
Amplitude
32
4
C
Amplitude
Amplitude
B
D
Time
Ultrasound: Depth measurement
Amplitude
B
32
4
Oil/Gel
1
5
Reflecting layers
(Assume incident soundwave strong
enough to reach layer 5)
1
2
5
3
4
Features:
1) All reflection peaks ~ same
width… all echos of same sound
pulse
2) Timing determined by distance
from probe: Layer 3 is twice as far
as layer 2… takes 2 times as long
3) Peak 1 received almost
instantaneously (oil/skin)
4) Peak 5 is larger … skin/air surface
gives large reflection
Ultrasound: 2-D Image
Use Focused Sound Wave:
Speaker
Probe
Measure Layer Depths at different angles --2D picture.
Why Ultrasound?
Human Hearing: Up to frequencies of 20 kHz
Frequency in Ultrasound Measurement: 1 MHz – 5 MHz
MHz= megahertz (106 Hz)
speed of sound = wavelength x frequency
ultrahigh frequency means wavelength very short.
In tissue, speed = 1540 m/s.
 = speed/ .
Wavelength = (1540 m/s )/(5 x 106 Hz) = 0.3 mm!
Shorter wavelength = higher resolution. Bats use sonar to
“see”.
Cross section baby torso: Fetus small, need high resolution!
2. Magnetic resonance imaging. (MRI)
I. basic idea- detects where hydrogen atoms are. Different
tissue has different distribution of H atoms.
II. Detect hydrogen atoms by how they absorb radio waves.
Do at each little spot in body.
We cover basic idea. Lots of more complicated stuff to get better
signals, detect environment of H atom (what kind of molecule H
is in).
H atoms--tiny magnets
How detect H atoms with
spatial selectivity?
“Magnetic resonance.”
Wonder of modern physics,
but NOT simple.
Uses many ideas of quantum physics already have seen.
Nucleus of each atom is tiny magnet. Each type of
atom nucleus has different size. magnet moment µ
H- “1”,
N = 1/14,
Na ¼, etc.
What happens if put magnet in a magnetic field?
a. tries to line up with field, b. nothing, c. tries to point
perpendicular to mag. field, d. tries to line up opposite to field.
d. Less energy if pointing opposite to field “spin down”.
takes energy to force it to line up with field “spin up”
B
B
Big magnet-- can point any direction. Magnetic of
hydrogen nucleus. Only up or down!
Like energy levels of electron- only certain energies.
H atom nucleus,
internal
magnet
up
magnetic field, B
magnetic energy = µB
down
atom magnet-quantum physics says, only up or down.
Two possible energy levels. Like electrons in atom.
Differences:
1) gap between levels depends on magnetic field. E = µB.
2) Energy gap is billion times smaller.
Detect H atoms with physics similar to atoms and light.
Using light to tell what kind of atoms you have.
e
e
method 1: whack atoms with
electrons, see what color light
comes out. Yellow-sodium,
red- neon, etc.
method 2?: send
in light of all colors.
Detect amount of
each color that
comes through.
can we figure out what kind of atoms there are by what comes through?
a. no, all atoms absorb blue, so only red light will come through.
b. no, all atoms absorb all colors, so fraction of light absorbed only tells
number of atoms.
c. yes, but color not important, the fraction of total light absorbed depends on
atom type. d. yes, color(s) of light absorbed depends on type of atom
ans. D
Send in different color light, only certain colors make electron jump
up. That light absorbed, does not come through.
particular yellow color absorbed-- sodium!
certain red light absorbed-- neon
E =h
up
Use same method to tell
how many H nucleus.
How much radio wave
is absorbed= # H atoms.
magnetic
energy
down
E =h,
But E about billion times less than
light. Radio waves not visible light.
Difference in energy. Depends on size of magnet and size of magnetic field
E= 2µB = energy of photon = h.
If measure that nucleus flipped spin and know energy took to do it matched µ
of hydrogen, know if was H atom. Why better than method #1?
magnet on bar demo- little pushes at right frequency.
Push with magnet.
radio wave detector
Detector will see the least radio waves when?
a. radio wave is higher freq. than nucleus flip frequency.
b. radio wave matches nucleus flip frequency.
c. radio wave is lower freq. than spin flip.
d. will always be the same independent of radio wave frequency.
b. if frequency exactly matches, will flip nuclei, this uses
energy, comes out of radio waves. Detector will see LESS.
Even simpler, send in only radio waves with exactly energy
to flip H. See how much absorbed, tells how many H’s.
Analogy-- Barrel of different tuning forks, how many 440 Hz?
22
speaker putting out
440 Hz.
detector measures
how much of 440 Hz
sound absorbed (by
exciting 440 tuning forks)
Human body- big blob of H atoms (in molecules), more some places
Magnetic Resonance imaging
than others.
measures amount of H atoms
in different places.
detector 1
detector 2
radio waves.
around 1 MHz.
(really puny, not nearly
enough energy to break
apart molecules so no
damage)
how much power absorbed?
= number of atoms in path x B x mag. mom.
1) To make absorbed power large
enough to see easily make B BIG!
(adjust ν).
Which detector will detect MORE radio waves? a. det. 1, b. det. 2
ans. b. detector 2. Less power absorbed in body = more in detector.
Good for detecting amount of H through whole body, but how to
look at details in particular location, like part of brain??
Make magnetic field different across body.
Use magnetic field dependence of resonance.
Do as slices, then slices of slices.
900 G
1000 G
BLE
B
BRE
x
ans. c, E = µB
Compare energy needed to flip
flip H atom nucleus at left ear (LE)
right ear (RE), and nose (N).
a. same at all three places.
b. RE most, nose second, LE least
c. LE most, nose second, RE least
d. nose least, RE and LE same and
higher.
e. nose most energy, RE and LE less.
change B,
now energy
match at
different slice.
B
B
x
x
E =µB
Rf matches only at one
B = one slice. Tells how
many H in that slice!
x
Power absorbed tells you
how many H atoms only in
slice of head where µB = hν.
Always send in same exact frequency 
E =hν =
m.m. x B
x
Power absorbed tells you
how many H atoms only in
new slice of head.
Change B variation over time. Get number of H atoms
at each different slice. Change B by changing currents
through wires. Move a little, makes lots of noise!
To get measure of each spot (not just slope) make B
vary in 3 D.
Absorbed energy all has to come from
H atoms at the spot where µx B = hν
Have B varying in x,y, z.
Measure power absorbed.
Change B's and repeat over and over.
Map out H atom distribution in
entire head/body. Takes a while.
Getting even fancier!!
If measure frequency really really carefully, can tell what
type of molecule the H atom is in. Other atoms change
the B field a little.
C
C
C
C
H
C
Hemoglobin without
oxygen.
H
C
O
Hemoglobin with oxygen.
Oxygen shifts magnetic field.
H atom flips at slightly
different frequency! Can tell
difference.
demo with oscillating magnet in field.
magnetic moment of atomic nucleus. Depends
on how protons and neutrons arranged.
Each type of atom different.
energy/ atom = magnetic moment x B = hν
Chose different values of ν, find different types of atoms.
Nuclear magnetic resonance chemical analysis.
hydrogen
hν1
sodium
hν2