Physics Applied to Radiology RADI R250 Fall 2003

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Physics Applied to RadiologyRADI R250 -- Fall
2003

• Chapter 13

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Particle vs. Photon Interactions

• particles (a, b, etc.)
• interactions based on
• electric charge on particle
• mass of particle
• photons (g, c, etc)
• interactions based on
• energy of photon
• type of matter

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Probability

• chance of event happening
• can be mathematically expressed
• example
• The probability of a woman experiencing breast
  cancer in her lifetime is 19
• x-ray interactions are chance events
• relative predictions can be made
• energy of the photons
• type of matter the x rays are passing through
• cannot predict how one photon will interact

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X-ray Interaction Probability

• probability
• depends on energy (i.e. l ) of photon
• depends on type of matter

• energy keV l interacts with
• low lt10 long l whole atom
• inter. 10-1000 middle l electron cloud
• high gt1MeV short l nucleus
• l of Dx x rays 10-8 to 10-9m
• Higher energy (short l) photons more likely to
  make it into the atom before interacting.

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Types of Photon Interactions

• Transmitted through matter unchanged
• Change direction with no energy loss
• Classical Scattering
• Change direction and lose energy
• Compton Scattering
• Deposit all energy in the matter
• Photoelectric Effect
• Pair Production
• Photodisintegration

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Classical Scattering Also called coherent or
elastic

• low photon energy (lt 10 keV) enters atom
• atom excited by photon
• releases (radiates) photon of same keV l
• new photon travels in different direction from
  original photon but usually forward (small
  scatter angle)

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Classical Scattering (cont.)

• subclassifications of classical scattering
• Rayleigh Scattering
• if interaction occurs with whole atom
• Thompson Scattering
• if interaction occurs with shell e-
• Results
• 1. photon D direction with no E loss
• Ei E li l
• 2. does not ionize matter
• 3. may cause slight film fogging (forward
  direction)

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Classical Scattering (cont.)

• Probability of classical scattering
• increases with
• 1) low Z materials
• soft tissue more likely than bone
• 2) lower photon energies
• 5 keV more likely than 10 keV

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Photoelectric Effect (Total absorption)

• intermediate photon energy (Dx range)

• photon ejects an inner shell e-
• photoelectron emitted with some KE
• photon loses all energy
• Ei EBE EKE
• characteristic radiation emitted when hole filled
• cascade of photons until atom is neutral again

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PE Energy example

• An 85 keV photon interacts with a K-shell
  electron whose BE is 62 keV. What will the
  ejected electrons KE?
• Ei EBE EKE
• EKE Ei - EBE
• 85 keV - 62 keV 23 keV
• If an L-shell electron whose BE is 940 eV fills
  the K-shell hole, what would be the
  characteristic x-ray energy?
• Exray D E
• -.94 keV - (-62 keV) 61.06 keV

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Photoelectric Effect (cont.)

• Results
• 1. photon disappears
• 2. atom is ionized
• ion pair atom photoelectron
• 3. characteristic photon(s) emitted
• secondary radiation
• biologic tissue produces very low Exray
• contrast agents (Ba I) produce higher Exray
  that may result in film fog
• cascade effect

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Photoelectric Effect (cont.)

• Probability (r)
• sharply as photon E
• edge at BE with r
• r µ 1/E3
• with Z (table 8-2, pg 201)
• Z of inner shell e-
• Z BE
• r µ Z3

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Compton Scattering (partial absorption)

• intermediate photon energy (Dx range)

• photon ejects outer shell e-
• acts like particle colliding with e-
• e- (Compton or recoil e-) ejected from atom with
  some KE
• photon loses energy
• E Ei - EBE EKE

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Compton Scattering Energy Example

• A 48 keV photon interacts with an outer shell
  electron bound by 72 eV.
• If the electron is emitted with a KE of 4.2
  keV, what is the scattered photons energy?
• E Ei - EBE EKE
• 48keV - .072keV 4.2keV
• 43.728 44 keV

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Compton Scattering (cont.)

• angle of scatter (pg. 204)

0Ð
180Ð

• as Ð , energy loss
• scattered photon has E
• E90Ð lt E 30Ð
• lowest E come from 180Ð (backscatter)

scatter E L
30Ð
90Ð
scatter E H
scatter E M

• high E photons scatter with smaller Ð
• high E photons more likely to forward scatter
• low E photons more likely to backscatter

photon E H
photon E L
large Ð
small Ð
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Compton Scattering (cont.)

• Results
• 1. photon D direction with E
• in DX range direction is usually forward
• E gt E l lt l
• 2. atom is ionized
• ion pair atom recoil e-
• 3. source of
• personnel / patient exposure
• film fog (contrast)

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Compton Scattering (cont.)

• probability of Compton interactions
• with density of matter (NOT Z)
• of e- per unit volume
• in matter containing abundant hydrogen
• H contains 2x of e-/gm compared to other matter
• with photon E
• mathematical probability
• P µ e- density / photon energy

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Compton PE vs. kVp

• Beam consisting of 10,000 photons
• kVp transmitted PE Compton
• 50 3000 4000 3000
• 100 7000 1000 2000
• As energy increases both PE Compton decrease
• PE decreases more rapidly than Compton
• PE decreased to 25 while Compton only 67

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Pair Production (Total absorption)

• high photon energy
• Ei gt 1.022 MeV (e- mass .511 MeV)

e

• photon interacts with nuclear force field
• uses 1.022 MeV to produce pair of electron like
  particles
• e (positron) e- (negatron)
• photon ceases to exist
• E 1.022 MeV EeKE Ee-KE

e-
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Pair Production (cont.)

• annihilation radiation

e

• e cant exist without KE
• e e- combine are destroyed
• matter converted back to energy
• 2 photons of .511 MeV emitted

.511 MeV
.511 MeV
e-
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Pair Production (cont.)

• Results
• photon disappears
• electron positron created
• e- after loss of KE free e-
• e after loss of KE cannot exist
• annihilation radiation produced
• e e- 2 (.511 MeV) photons

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Pair Production (cont.)

• probability
• energy must be ³ 1.022 MeV
• with Z (larger nuclear force field)

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Photodisintegration (Total Absorption)

• high photon energy
• Ei gt 10 MeV
• photon absorbed by the nucleus
• nucleus excited
• ejects particles and photons to return to ground
  state

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Photodisintegration (cont.)

• results
• photon disappears
• nucleus changes form
• Becomes a different nuclide

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Attenuation Transmission

• Photon Attenuation (figure 13-15, page 175)
• removal of photons
• all interactions total or partial absorbtion
• Photon Transmission
• incident photons that do not interact
• total beam attenuated transmitted
• 10,000 x rays 4350 absorbed 5650 transmitted

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Differential Absorption (DA)

• attenuation transmission in tissue that
• results in the image formation
• attenuation that enables image production
• image due to relative PE vs. transmission
• Compton interactions have NO image value
• important when subject contrast is low
• tissues that are similar in
• 1) density
• 2) atomic (Z)

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Factors that Influence DA

• 1) Beam Energy DA é as E ê
• due to é probability of PE at low E
• but also é in pt dose
• (PE total absorption)
• 2) Atomic Number DA é as Z é
• probability of PE é with é Z
• Z has no effect on Compton
• see Bushong table 13-6, pg 174

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DA vs. Atomic Number

• Substance Z
• fat 6.3
• muscle 7.4
• lung 7.4
• air 7.6
• bone 13.8
• iodine 53
• barium 56
• aluminum 13
• concrete 17
• lead 82

• similar DA based on similar Z
• ????
• good DA compared to above
• contrast media with excellent DA even in low
  concentration
• non biological materials

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Factors that Influence DA (cont.)

• 3) Mass Density of matter DA é as density é
• quantity of matter per unit volume
• do not confuse with image density
• é matter / volume é interactions
• both PE Compton
• tissue densities vary more widely than Z
• see Bushong table 13-5, pg 173

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DA vs. Z Tissue Density

• Substance Z Density
• fat 6.3 0.91
• muscle 7.4 1.00
• lung 7.4 0.32
• air 7.6 0.0013
• bone 13.8 1.85
• iodine 53 4.92
• barium 56 3.5
• aluminum 13 2.7
• concrete 17 2.35
• lead 82 11.35