Exam 3 Total, 30 possible

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Class average = 22.99

Papers-graded “soon”. Generally good, main problem isDescription not related to physics principles.

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 stuffthat decays in body producing particles come flying out.)

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.

High doses- enough deadcells for radiation sickness.Low dose damage DNA cancerBalance of risks

Special homework problems this week- construct your own!

Ultrasound: uses sound waves to see inside the body

Where am I?

HELLOHELLO

If I hear an echo what do I know? a. That something a head of me

reflects soundb. how far away it isc. what its made ofd. a and be. a, b, and c

If I hear an echo 1 second after I shout “Hello”, I can conclude that this surface is

a. about 331 m awayb. about 3x108 m awayc. about 115 m awayd. I don’t remember the speed of sound

in air.

Answer is d. But do know something of c.

Answer is c. Total Dist = velocity * time. Distance to surface = Total Dist/2

ULTRASOUND PROBE

Transmits: Short pulse of sound waveFrequency of sound(1 MHz – 5 MHz)MHz= megahertz (106 Hz)

Timing and Amplitude(Distance & something about Material)

Listens: Echos

~1% of time transmitting~99% of time listening

Sound waves reflect and refract at a surface interfaceAcoustic 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.

Which is true? a. Speed of sound in B is greater than Ab. Speed of sound in A is greater than Bc. I don’t know how to tell

Substance A Substance BTRAVELING SOUND WAVES

Ultrasound: Depth measurement

Substance Speed of Sound

Air 331 m/s

Fat 1450 m/s

Water 1450 m/s

Soft Tissue 1450 m/s

Brain 1451 m/s

Liver 1549 m/s

Kidney 1561 m/s

Blood 1570 m/s

Muscle 1585 m/s

Bone 4080 m/s

Reflecting layers

123

45

Why do they put the oil between you and the probe?

a. To protect the probeb. To protect your skin from ultraviolet rays

generated by the probec. To decrease the reflection of the sound

wave off your outer skind. To allow smooth movement of the probe.

Oil/Gel

Answer is c. If no gel, some air between probe and your skin. Reflects most of sound… Large difference in speed of sound between air and skin tissue!

Ultrasound: Depth measurement

Reflecting layers

123

45 Oil/Gel

Time

Am

plit

ude

Time

Am

plit

ude

Am

plit

ude

Am

plit

ude

(Assume incident soundwave strong enough to reach layer 5)

A

B

C

D

Ultrasound: Depth measurement

Reflecting layers

123

45 Oil/Gel

Am

plit

ude

(Assume incident soundwave strong enough to reach layer 5)

B

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

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5

Ultrasound: 2-D Image

Use Focused Sound Wave:

Measure Layer Depths at different angles --- 2D picture.

SpeakerProbe

Why Ultrasound? Human Hearing: Up to frequencies of 20 kHz

Frequency in Ultrasound Measurement: 1 MHz – 5 MHzMHz= megahertz (106 Hz)

speed of sound = wavelength x frequencyultrahigh 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. Differenttissue 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 µH- “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 pointperpendicular 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

H atom nucleus,internalmagnet

magnetic field, B

magnetic energy = µB

down

up

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.

Big magnet-- can point any direction. Magnetic of hydrogen nucleus. Only up or down! Like energy levels of electron- only certain energies.

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eUsing light to tell what kind of atoms you have.

method 1: whack atoms withelectrons, see what color lightcomes out. Yellow-sodium,red- neon, etc.

method 2?: sendin light of all colors.Detect amount ofeach color thatcomes 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

magneticenergy down

up

ans. DSend in different color light, only certain colors make electron jumpup. That light absorbed, does not come through.

E =h

Use same method to tellhow many H nucleus.How much radio waveis absorbed= # H atoms. 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?

particular yellow color absorbed-- sodium!certain red light absorbed-- neon

radio wave detector

magnet on bar demo- little pushes at right frequency.Push with magnet.

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 usesenergy, comes out of radio waves. Detector will see LESS.

Even simpler, send in only radio waves with exactly energyto flip H. See how much absorbed, tells how many H’s.

Analogy-- Barrel of different tuning forks, how many 440 Hz?

speaker putting out440 Hz.

22detector measureshow much of 440 Hzsound absorbed (byexciting 440 tuning forks)

Human body- big blob of H atoms (in molecules), more some placesthan others.

detector 1

detector 2

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).

Magnetic Resonance imagingmeasures amount of H atomsin different places.

radio waves.around 1 MHz.(really puny, not nearly enough energy to break apart molecules so no damage)

Which detector will detect MORE radio waves? a. det. 1, b. det. 2ans. b. detector 2. Less power absorbed in body = more in detector.

Make magnetic field different across body.Use magnetic field dependence of resonance.Do as slices, then slices of slices.

B

x

Compare energy needed to flipflip 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 leastc. LE most, nose second, RE leastd. nose least, RE and LE same andhigher.e. nose most energy, RE and LE less.

Good for detecting amount of H through whole body, but how tolook at details in particular location, like part of brain??

900 G 1000 G

BLE

BRE

ans. c, E = µB

Bx

E =µB

x

Power absorbed tells youhow many H atoms only in

slice of head where µB = hν.Always send in same exact frequency

Rf matches only at one B = one slice. Tells howmany H in that slice!

B

x

E =hν = m.m. x B

x

change B,now energymatch at different slice.

Power absorbed tells youhow many H atoms only in new slice of head.

Change B variation over time. Get number of H atomsat 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 Bvary in 3 D.

Absorbed energy all has to come fromH 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 whattype of molecule the H atom is in. Other atoms changethe B field a little.

HC

C

C

HC

C

C O

Hemoglobin withoutoxygen.

Hemoglobin with oxygen.Oxygen shifts magnetic field.H atom flips at slightly different frequency! Can tell difference.

demo with oscillating magnet in field.

energy/ atom = magnetic moment x B = hνChose different values of ν, find different types of atoms.Nuclear magnetic resonance chemical analysis.

magnetic moment of atomic nucleus. Dependson how protons and neutrons arranged.Each type of atom different.

hydrogen sodium hν1 hν2