Transcript Resident Physics Lectures

Resident Physics Lectures
• Christensen, Chapter 4
Basic Interactions
Between X-Rays
and Matter, Grid
Attenuation and
Filtration
George David
Associate Professor
Medical College of Georgia
Department of Radiology
Photons atoms
interations
• What happen when photons
interact with human tissue?
Photon Phate
*
• absorbed
 completely removed from beam
 ceases to exist
• scattered
 change in direction
 no useful information carried
 source of noise
• Nothing
 Photon passes unmolested
X
Image Noise Example
Caution!
Image
Noise
Basic Interactions
• Coherent Scattering
• Compton Scattering
• Photoelectric Effect
• Pair Production
• Photodisintegration
What is important in
this lecture
• How the interaction happen?
• When happen?
• The interaction affect on the
image quality?
Interaction depends on
• Photon energy e.v
• Atom atomic number Z
-
~ +
~ +
+ ~
-
Photon Interaction Probabilities
100
Pair Production
Photoelectric
Z protons
COMPTON
10
0.01
0.1
1.0
E energy (MeV)
10
100
Basic Interactions
• Coherent Scattering D
• Compton Scattering D
• Photoelectric Effect D
• Pair Production T
• Photodisintegration T
• D=Diagnostic radiology
• T=Treatment radiology
Photoelec
tric effect
Compton
scattering
Pair
productio
n
Coherent
scattering
Source
Photon
interacts
With inner
electrons
Photon
interacts
With outer
electrons
Photon
interacts
With
nucleus
photon
interacts
with all
electrons
of an atom
Photon
energy
low
medium
high
D OR T
D
D
T
Coherent Scattering
• Also called
unmodified scattering
classical scattering
• Types
Thomson
» photon interacts with single electron
Rayleigh
» photon interacts with all electrons of an atom
Coherent Scattering
• Change in direction
• No change in
 energy
 frequency
 wavelength
• No ionization
• Contributes to scatter as film fog
• Less than 5% of interactions
 insignificant effect on image quality compared to other
interactions
***
•
•
•
•
Pair Production Process
high energy photon interacts with nucleus
photon disappears
electron & positron (positive electron) created
energy in excess of 1.02 MeV given to
electron/positron pair as
kinetic energy.
-
+
-
~ +
~ +
+ ~
-
Positron Phate
• Positron undergoes ANNIHILATION REACTION
• Two 0.511 MeV photons created
• Photons emerge in exactly opposite directions
Pair Production
• Threshold energy for occurrence:
1.02 MeV
» energy equivalent of rest mass of 2 electrons
• Threshold is above diagnostic
energies
 does not occur in diagnostic radiology
-
+
~ +
~ +
+ ~
-
-
*
Photodisintegration
• photon causes ejection of part of
atomic nucleus
• ejected particle may be
neutron
proton
alpha
particle cluster
-
~ +
~ +
+ ~
?
-
Photodisintegration
• Threshold photon energy for
occurrence
nuclear binding energy
» typically 7-15 MeV
• Threshold is above diagnostic
energies
does not occur in diagnostic radiology
**
Photoelectric Effect
• photon interacts with bound
(inner-shell) electron
• electron liberated from atom
(ionization)
• photon disappears
Photon in
-
Electron out
PHOTOELECTRIC EFFECT
****
Photoelectric Effect
• Exiting electron kinetic energy
incident energy - electron’s binding energy
• electrons in higher energy shells
cascade down to fill energy void
of inner shell
» characteristic radiation
M to L
Photon in
-
Electron out
L to K
Photoelectric
Interaction Probability
• inversely proportional to cube of photon
energy
low energy event
• proportional to cube of atomic number
• more likely with inner (higher) shells
tightly bound electrons
1
P.E. ~ ----------energy3
P.E. ~ Z3
Photoelectric Effect
• Interaction much more likely for
low energy photons
high atomic number elements
1
P.E. ~ ----------energy3
P.E. ~ Z3
Photoelectric Effect
• Photon Energy Threshold
 > binding energy of orbital electron
• binding energy depends on
 atomic number
» higher for increasing atomic number
 shell
» lower for higher (outer) shells
• most likely to occur when photon
energy & electron binding energy are
nearly the same
Photoelectric Threshold
• Binding Energies
K: 100
L: 50
M: 20
Photon energy: 25
A
Photon in
B
Photon energy: 22
1
P.E. ~ ----------energy3
Which photon
has a greater
probability for
photoelectric
interactions with
the m shell?
Photoelectric Threshold
1
P.E. ~ ----------energy3
• Photoelectric interactions decrease
with increasing photon energy
BUT …
**
Photoelectric Threshold
• When photon energies just reaches binding
energy of next (inner) shell, photoelectric
interaction now possible with that shell
 shell offers new candidate target electrons
Interaction
Probability
L-shell
interactions
possible
L-shell
binding
energy
K-shell
binding
energy
Photon Energy
K-shell
interactions
possible
Photoelectric Threshold
• causes step increases in interaction
probability as photon energy exceeds
shell binding energies
Interaction
Probability
L-edge
K-edge
Photon Energy
**
Characteristic Radiation
• Occurs any time inner shell
electron removed
• energy states
orbital electrons seek lowest possible energy
state
» innermost shells
M to L
L to K
**
Characteristic Radiation
• electrons from higher states fall
(cascade) until lowest shells are
full
characteristic x-rays released whenever
electron falls to lower energy state
M to L
characteristic
x-rays
L to K
Characteristic Radiation
• only iodine & barium
in diagnostic
radiology have
characteristic
radiation which can
reach film-screen
Photoelectric Effect
Why is this important?
• photoelectric interactions provide
subject contrast
 variation in x-ray absorption for various substances
• photoelectric effect does not
contribute to scatter
• photoelectric interactions deposit
most beam energy that ends up in
tissue
 always use highest kVp technique consistent with
imaging contrast requirements
***
Compton Scattering
• Source of virtually all scattered
radiation
• Process
incident photon (relatively high energy)
interacts with free (loosely bound) electron
some energy transferred to recoil electron
» electron liberated from atom (ionization)
emerging photon has
» less energy than incident
» new direction
Electron out
(recoil electron)
Photon out
Photon in
Compton Scattering
• What is a “free” electron?
low binding energy
» outer shells for high Z materials
» all shells for low Z materials
Electron out
(recoil electron)
Photon in
Photon out
Compton Scattering
• Incident photon energy split between
electron & emerging photon
• Fraction of energy carried by
emerging photon depends on
incident photon energy
angle of deflection
» similar principle to
billiard ball collision
Photon in
Electron out
(recoil electron)
Photon out
Compton Scattering
Probability of Occurrence
• independent of atomic number (except for
hydrogen)
• Proportional to electron density
(electrons/gram)
 fairly equal for all elements except hydrogen (~ double)
Compton Scattering
Probability of Occurrence
• decreases with increasing photon energy
decrease much less pronounced than for photoelectric
effect
Interaction
Probability
Compton
Photoelectric
Photon Energy
Photon Interaction Probabilities
100
Pair Production
Photoelectric
Z protons
COMPTON
10
0.01
0.1
1.0
E energy (MeV)
10
100
Resident Physics Lectures
• Christensen, Chapter 5
Attenuation
George David
Associate Professor
Medical College of Georgia
Department of Radiology
Beam Characteristics
• Quantity
number of photons in beam
1, 2, 3, ...
~
~
~
~
~
Beam Characteristics
• Quality
energy distribution of photons in beam
1 @ 27 keV, 2 @ 32
keV, 2 at 39 keV, ...
~
~
~
~
10
20
30
40
50
Energy
~
~
Energy Spectrum
~
~
60
70
80
Beam Characteristics
• Intensity
weighted product of number and energy of
photons
depends on
324 mR
» quantity
» quality
~
~
~
~
~
~
~
~
Beam Intensity
• Can be measured in terms of #
of ions created in air by beam
• Valid for monochromatic or
for polychromatic beam
324 mR
~
+
Attenuation Coefficient
• Parameter indicating fraction of
radiation attenuated by a given
absorber thickness
• Attenuation Coefficient is function of
 absorber
 photon energy
Linear Attenuation Coef.
• Why called linear?
 distance expressed in linear dimension “x”
• Formula
N = No e -mx
where
N = number of incident photons
o
N = number of transmitted photons
e = base of natural logarithm (2.718…)
m = linear attenuation coefficient (1/cm); property of
N
N
o
energy
material
x = absorber thickness (cm)
x
Linear Attenuation Coef.
Larger Coefficient = More Attenuation
• Units:
1 / cm ( or 1 / distance)
• Properties
N = No e - m x
 reciprocal of absorber thickness that reduces beam
intensity by e (~2.718…)
» ~63% reduction
» 37% of original intensity remaining
 as photon beam energy increases
» penetration increases / attenuation decreases
» attenuating distance increases
» linear attenuation coefficient decreases
• Note: Same equation as used for
radioactive decay
Polychromatic Radiation
• X-Ray beam contains spectrum of
photon energies
highest energy = peak kilovoltage applied to tube
mean energy 1/3 - 1/2 of peak
» depends on filtration
X-Ray Beam Attenuation
• reduction in beam
intensity by
absorption (photoelectric)
deflection (scattering)
• Attenuation alters beam
quantity
quality
» higher fraction of low energy
photons removed
» Beam Hardening
Lower
Energy
Higher
Energy
Half Value Layer (HVL)
N = No e -mx
• absorber thickness that reduces
beam intensity by exactly half
• Units of thickness
• value of “x” which makes N
equal to No / 2
HVL = .693 / m
Half Value Layer (HVL)
• Indication of beam quality
• Valid concept for all beam
types
 Mono-energetic
 Poly-energetic
• Higher HVL means
 more penetrating beam
 lower attenuation coefficient
Factors Affecting Attenuation
• Energy of radiation / beam quality
higher energy
» more penetration
» less attenuation
• Matter
density
atomic number
electrons per gram
higher density, atomic number, or electrons per
gram increases attenuation
Polychromatic Attenuation
• Yields curved line on semi-log
graph
line straightens with increasing attenuation
slope approaches that of monochromatic
beam at the peak energy
• mean energy increases with
1
attenuation
beam hardening
Fraction .1
Transmitted
Polychromatic
.01
.001
Monochromatic
Attenuator Thickness
Photoelectric vs. Compton
• Fractional contribution of each
determined by
photon energy
atomic number of absorber
• Equation
m = mcoherent + mPE + mCompton
Small
Photoelectric vs. Compton
• As photon
energy
increases
m = mcoherent + mPE + mCompton
 Both PE & Compton
Interaction
decrease
Probability
 PE decreases faster
» Fraction of m that is
Compton
increases
» Fraction of m that is
PE decreases
Compton
Photoelectric
Photon Energy
Photoelectric vs. Compton
m = mcoherent + mPE + mCompton
• As atomic # increases
Fraction of m that is PE increases
Fraction of m that is Compton decreases
Interaction Probability
Photoelectric
Atomic
Number of
Absorber
Pair
Production
Compton
Photon Energy
• PE dominates for very low
energies
Interaction Probability
Photoelectric
Atomic
Number of
Absorber
Pair
Production
Compton
Photon Energy
• For lower atomic numbers
– Compton dominates for high energies
Interaction Probability
Photoelectric
Atomic
Number of
Absorber
Pair
Production
Compton
Photon Energy
• For high atomic # absorbers
– PE dominates throughout diagnostic energy range
Attenuation & Density
• Attenuation proportional to
density
difference in tissue densities accounts for
much of optical density difference seen
radiographs
• # of Compton interactions
depends on electrons / unit path
which depends on
» electrons per gram
» density
Relationships
• Density generally increases with
atomic #
different states = different density
» ice, water, steam
• no relationship between density
and electrons per gram
• atomic # vs. electrons / gram
hydrogen ~ 2X electrons / gram as most other
substances
as atomic # increases, electrons / gram
decreases slightly
Applications
• As photon energy increases
subject (and image) contrast decreases
differential absorption decreases
» at 20 keV bone’s linear attenuation coefficient 6 X water’s
» at 100 keV bone’s linear attenuation coefficient 1.4 X water’s
100
90
80
70
60
50
40
30
20
10
0
Bone
Water
20 keV
100 ke
Applications
Photoelectric
Pair
Production
Compton
• At low x-ray energies
attenuation differences between bone & soft tissue primarily
caused by photoelectric effect
» related to atomic number & density
Applications
Photoelectric
Pair
Production
Compton
• At high x-ray energies
attenuation differences between bone & soft tissue
primarily because of Compton scatter
» related entirely to density
Applications
• Difference between water & fat
only visible at low energies
effective atomic # of water slightly higher
» yields photoelectric difference
electrons / cm almost equal
» No Compton difference
Photoelectric dominates at low energy
Scatter Radiation
• NO Socially Redeeming Qualities
no useful information on image
detracts from film quality
exposes personnel, public
• represents 50-90% of photons
exiting patient
Abdominal Photons
• ~1% of incident photons on adult
abdomen reach film
• fate of the other 99%
mostly scatter
» most do not reach film
absorption
Scatter Factors
• Factors affecting scatter
field size
thickness of body part
kVp
An increase in any of above increases
scatter.
Scatter & Field Size
• Reducing field size causes significant
reduction in scatter radiation
II
Tube
II
Tube
X-Ray
Tube
X-Ray
Tube
Field Size & Scatter
• Field Size & thickness determine
volume of irradiated tissue
• Scatter increase with increasing
field size
initially large increase in scatter with
increasing field size
saturation reached (at ~ 12 X 12 inch field)
» further field size increase does not increase scatter
reaching film
» scatter shielded within patient
Thickness & Scatter
• Increasing patient thickness
leads to increased scatter
but
• saturation point reached
scatter photons produced far from film
shielded within body
kVp & Scatter
• kVp has less effect on scatter than
than
 field size
 thickness
• Increasing kVp
 increases scatter
 more photons scatter in forward direction
Scatter Management
• Reduce scatter by minimizing
field size
» within limits of exam
thickness
» mammography compression
kVp
» but low kVp increases patient dose
» in practice we maximize kVp
Scatter Control Techniques:
Grid
• directional filter for photons
• Increases patient dose
Scatter Control Techniques:
Air Gap
• Gap intentionally
left between
patient & image
receptor
• Natural result of
magnification
radiography
• Grid not used
• (covered in detail in
chapter 8)
Patient
Air
Gap
Patient
Grid
Film
Cassette
Resident Physics Lectures
• Christensen, Chapter 8
Grids
George David
Associate Professor
Department of Radiology
Medical College of Georgia
Purpose
• Directional filter for
photons
• Ideal grid
Focal
Spot
“Good”
photon
passes all primary photons
» photons coming from focal
spot
blocks all secondary
photons
» photons not coming from
focal spot
Patient
“Bad”
photon
XGrid
Film
Grid Construction
• Lead
~ .05“ thick upright strips (foil)
• Interspace
 material between lead strips
 maintains lead orientation
 materials
» fiber
» aluminum
» wood
Lead
Interspace
Grid Ratio
• Ratio of interspace height to
width
Lead
Interspace
h
w
Grid ratio = h / w
Grid Ratio
• Expressed as X:1
• Typical values
8:1 to 12:1 for general work
3:1 to 5:1 for mammography
• Grid function generally improves
with higher ratios
h
w
Grid ratio = h / w
Lines per Inch
• # lead strips per inch grid width
• Typical: 103
W
25.4
Lines per inch = -----------W+w
w = thickness of interspace (mm)
W = thickness of lead strips (mm)
w
Grid Structure
Grid Patterns
• Orientation of lead strips as seen
from above
• Types
Linear
Cross hatched
»
»
»
»
2 stacked linear grids
ratio is sum of ratios of two linear grids
very sensitive to positioning & tilting
Rare; only found in specials
Grid Styles
• Parallel
• Focused
Parallel Grid
• lead strips
parallel
• useful only
for
small field sizes
large source to
image distances
Focused Grid
• Slightly angled lead strips
• Strip lines converge to a point in
space called convergence line
• Focal distance
 distance from convergence line to grid plane
• Focal range
 working distance range
» width depends on grid ratio
» smaller ratio has greater range
Focal
range
Focal
distance
Grid Cassette
• Grid built into cassette front
• Sometimes used for portables
formerly used in mammography
• low grid ratios
• focused
Ideal Grid
• passes all primary radiation
Reality: lead strips block some primary
Lead
Interspace
Ideal Grid
• block all scattered radiation
Reality: lead strips permit some scatter to get
through to film
Lead
Interspace
Grid Performance
Measurements
• Primary Transmission (Tp)
• Bucky Factor (B)
• contrast improvement factor (K)
Resident Physics Lectures
• Christensen, Chapter 6
Filters
George David
Associate Professor
Department of Radiology
Medical College of Georgia
Energy Spectrum
• X-ray beams from tubes
 Polychromatic
» Brehmstrahlung
» Characteristic
 spectrum of energies from 0 – kVp set on generator
• average beam energy
1/3 to 1/2 of peak (kVp)
kVp
(as set on
generator)
Unfiltered Beams
• most energy deposited
in first few centimeters
of tissue
lowest energy photons
selectively removed
• energy of low energy
photons
contributes to dose
does not contribute to image
Patient
» photons don’t reach film
film
Ideal Filtration
• absorption characteristics
absorbs all low energy radiation
absorbs no high energy radiation
• high atomic number
desirable
increases photoelectric absorption
of low energy photons
Filter’s Function
• shape beam’s energy
Filter
spectrum
• selectively attenuate
low energy photons
less low energy radiation
incident on patient
energy deposited in filter, not
in patient
Film
Filtration Locations
• x-ray tube and housing
 inherent filtration
• metal sheets placed in beam path
 placed between tube and collimator or in collimator
 Usually aluminum
 added filtration
Filter
• collimator mirror*
• table (for under-table tube fluoro)
Lamp
* not mentioned in book
X-Rays
Light
Tabletop
Tabletop