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11/19/2014

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2014-2015 Residents' Core Physics Lectures

Mondays 7:00-8:00 am in VA Radiology and UCSDMC Lasser Conference Rooms

Textbook: The Essential Physics of Medical Imaging, Bushberg, et al., Philadelphia: Lippincott

Williams & Wilkins, 2002, 2nd Edition

Course Web Site??: http://3dviz.ucsd.edu/~radiology_residents/Home.html

Topic Chapters Date Faculty

1 Introduction and Basic Physics 1, 2 M 11/17 Andre

2 Interaction of Radiation and Matter 3 M 11/24 Andre

RSNA Week No Lecture M 12/01

3 Computers 4 M 12/08 Hall

4 X-Ray Production 5 M 12/15 Andre

Christmas and New Year’s Holiday M 12/22,

12/29

5 Generators 5 M

01/05/2015

Andre

Nuclide Families

Family Nuclides with Same: Example

Isotopes Atomic number (Z) I131, I125: Z=53

Isobars Mass number (A) Mo99, Tc99: A=99

Isotones Neutron number (A-Z) 53I131: 131-53=78

Isomers A and Z same but different Tc99m and Tc99:

energy state Z=43, A=99, ΔE=142

keV

2

X = element symbol

Z = number of protons

A = number of protons + neutronsZXA

• Stable isotopes found

along line N/Z = 1 at

low Z

• Stable isotopes found

along line N/Z = 1.5 at

high Z

• Odd N and odd Z tend

to be unstable

• Odd Z elements offer

potential for NMR

(unpaired p+)

ZXA

X = element symbol

Z = number of protons

A = number of protons + neutrons

“Huge relevance

to a Resident”

Chapter 3: Interaction of Radiation with Matter

The Basis of X-Ray Imaging

or digital detector

Next time

we address

these

devices


in Radiology and Nuclear Medicine

• Particle Interactions

• X- and Gamma-Ray Interactions

• Attenuation of X- and Gamma-Rays

• Absorption of Energy from X- and Gamma-Rays

• Imparted Energy, Equivalent Dose and Effective Dose

Lots of new definitions here!

Important to us for radiographic and CT image contrast, patient dose, x-ray production, Rad Tx, and more…

Recall: Contrast, Sharpness, Noise, Distortion, Dose

This topic affects Contrast, Noise and Dose

AAPM/ABR Syllabus

Module 4: Interactions of Ionizing Radiation with Matter

After completing this module, the resident should be able to apply the “Fundamental Knowledge” and “Clinical

Applications” learned from the module to example tasks, such as those found in “Clinical Problem-Solving.”

Fundamental Knowledge:

1. Describe how charged particles interact with matter and the resulting effects these interactions can have on the

material.

2. Describe the processes by which x-ray and γ-ray photons interact with individual atoms in a material and the

characteristics that determine which processes are likely to occur.

3. Indentify how photons are attenuated (i.e., absorbed and scattered) within a material and the terms used to

characterize the attenuation.

Clinical Application:

1. Identify which photon interactions are dominant for each of the following imaging modalities: mammography,

projection radiography, fluoroscopy, CT, and nuclear medicine imaging procedures.

2. Understand how image quality and patient dose are affected by these interactions.

3. What are the appropriate x-ray beam energies to be used when iodine and barium contrast agents are used?

4. How does the type of photon interaction change with increasing energy, and what is the associated clinical

significance?

Clinical Problem-Solving:

1. Select an appropriate thyroid imaging agent based on its particulate emissions for pediatric imaging and for adult

imaging. Would these agents use the same isotopes or different isotopes? How does dose differ between these

imaging isotopes?

2. What is the purpose of adding Cu filters in vascular imaging?

3. What makes a contrast agent radiolucent instead of radio-opaque?

6

11/19/2014

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Recall: Chapter 2

• Energy: Definition?

– Ability to do Work

• Radiation: Definition?

– Propagation of energy through space

• Types in Medicine

– Heat (infrared) [EM]

– Visible light [EM]

– X-Rays [EM]

– γ-Rays [EM]

– Microwaves (MRI) [EM]

– Particulate [Mass, charge, kinetic energy]

– Sound [Mechanical]

1 eV 1Ve-

Which is/are true? The energy of a photon is:

– A. Proportional to its wavelength

– B. Proportional to its frequency

– C. Inversely proportional to the exposure time

– D. Inversely proportional to its wavelength

– E. Can be expressed in terms of potential

difference (volts)

Which is/are true? The energy of a photon is:

– A. Proportional to its wavelength

– B. Proportional to its frequency

– C. Inversely proportional to the exposure time

– D. Inversely proportional to its wavelength

– E. Can be expressed in terms of potential

difference (volts)

E = h f = h c / λ

E (keV) = 12.4 / λ (Å)


in Radiology and Nuclear Medicine

• Particle Interactions

• X- and Gamma-Ray Interactions

• Attenuation of X- and Gamma-Rays

• Absorption of Energy from X- and Gamma-Rays

• Imparted Energy, Equivalent Dose and Effective Dose

Lots of new definitions here!

Important to us for radiographic and CT image contrast, patient dose, x-ray production, Rad Tx, and more…

Recall: Contrast, Sharpness, Noise, Distortion, Dose

This topic affects Contrast, Noise and Dose

Particles in Medicine

Particle SymbolRelative

Charge

Mass

(amu)

Energy

Equivalent

(MeV)

Alpha α, 4He2+ +2 4.0028 3727

Proton p, 1H+ +1 1.007593 938

Electron e-, β- -1 0.000548 0.511

Positron e+, β+ +1 0.000548 0.511

Neutron n0 0 1.008982 940

Particles interact with matter through Scattering:

•Elastic (no net Kinetic Energy loss)

•Inelastic (KE imparted)

• Excitation

• Ionization

• Radiation loss

1 eV 1Ve-

Excitation

Excitation

• Imparted E < Binding Energy

• Results in e- at higher energy

state

• 70% of all particulate

interactions are non-ionizing

De-excitation with radiation

• Photon (low energy)

• Auger electron

11/19/2014

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• Imparted E > B.E.

• Ion pair results

• Secondary ionization

Ionization

Light vs. Heavy Charged Particles

• Linear Energy Transfer

• LET = Energy/unit path length (eV/cm)

• LET proportional to Q2/K.E.

• LET (eV/cm) = Spec. Ion.(IP/cm) • Avg. E per IP (eV/IP)

• LET largely determines “biological effectiveness”

• High LET: α , p+

• Low LET: β+, β-, electromagnetic

Light Heavy

• Decelerate e- ( velocity)

• Bremsstrahlung x-ray

E = h = K.E. loss of e-

• Probability of interaction is

proportional to Z2 of absorber

• Results in spectrum of x-ray

energies

Bremsstrahlung

[“Braking”]

Radiation

E Loss by Bremsstrahlung = K.E.(MeV) • Z

E Loss by Excitation + Ionization 820

Why is this important to you?

Bremsstrahlung is the principal

source of x-ray production in

radiology (Chapter 5, next time)

Excitation

Summary of Particle Interactions

• Scattering

• Excitation

• Ionization (Direct and Indirect)

• Radiation (Bremsstrahlung)

• Electron-Positron annihilation (Chapter 22, PET)

Two 180º opposed 0.511 MeV photons

• Neutron interactions (Chapter 19)

– Interact with nuclei, mainly Hydrogen in tissue

– Split nucleus (fission)

– Or captured by nucleus

X- and Gamma-Ray Interactions

• Attenuation Absorption + Scattering

• Methods of Interaction:

1. “Coherent or Rayleigh or Classical” Scattering

2. Compton Scattering

3. Photoelectric Absorption

4. Pair Production

5. Photo-disintegration

*

*

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Rayleigh Scattering

• No net loss of energy by

incident photon, no ionization

• Excites entire atom

• Results in change of direction

of photon

• Occurs in tissue only at low x-ray energies, E = h

therefore low frequencies, long wavelengths

• Less significant for diagnostic radiology

• <5% of interactions above 70 keV

• Maximum occurrence of 12% at 30 keV




1. “Coherent,” “Rayleigh” or “Classical” Scattering

2. Compton Scattering (incoherent)


4. Pair Production

5. Photodisintegration

• #2 and #3 are

dominant

in radiology

*

*

• 30 keV to 30 MeV:

Photon interactions

in soft tissue are

predominantly

Compton

• Main source of

undesirable

scattered radiation

which reduces

image contrast

Compton Scattering

(Incoherent) Involves only

Low B.E. e-

φ

• Occurs for loosely bound

electrons with negligible B.E.

• Input: photon

Output: photon + electron

• hinc = hscat + K.E. e-

• Scattered photon: 0° 180°

• Scattered electron: 0° φ 90°

Compton Scattering

φ

Involves only

Low B.E. e-

• hscat = Energy of scattered photon

• hinc = Energy of incident photon

• = scatter angle of photon

• As E of incident photon increases,

(and φ) decrease, so they hit receptor

• 2(scattered) = 1(incident) + [conserve E]

• (E loss) is maximum when = 180° (backscatter)

• Probability of Compton interaction

P (C) 1/hinc = 1/Einc

P (C) is not dependent on Z

P (C) electron density ~ (g/cm3)

Compton Scattering

φ

cos1511

1

keV

h

hh

inc

incscat

When low energy photon undergoes Compton interaction, majority of energy is retained by scattered photon and only slight amount is transferred to electron.

1. Example: 20 keV photon scattered at 180°

h 2 = 18.6 keV

Ek (electron) = 1.4 keV

2. Example: 2 MeV incident photon at 180° scatter

h 2 = 226 keV

Ek = 1774 keV

(Motivation for Megavoltage Rx)

Compton Scattering

φ

11/19/2014

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1. “Coherent,” “Rayleigh” or “Classical” Scattering

2. Compton Scattering (incoherent)


4. Pair Production

5. Photodisintegration

• #2 and #3 are

dominant

in radiology

*

*

Photoelectric Effect

• Products of interaction:

– 1. Photoelectron (ejected electron)

– 2. Positive ion (remaining atom)

– 3. Characteristic radiation (discrete x-rays emitted when electron cascades to fill vacant shells) or Auger electrons

– 4. Original photon disappears

• X-ray energy is unique to the element (characteristic)

53I

Photoelectric Effect in Iodine

Ee- = h inc – EB.E.

If h inc< EB.E. interaction does not occur

53I

Photoelectric Effect

• Probability of photoelectric interaction per unit mass

– P (P.E.) Z3

– P (P.E.) 1/(h )3 = 1/E3

– P (P.E.) (g/cm3)

– Higher probability when (h ) is close to EB.E.

– Higher probability with higher EB.E. such as K shell

53I

• Prob. of Absorption

(Photoelectric mass

attenuation

coefficients) for

– Tissue (Z=7),

– Iodine (Z=53),

– Barium (Z=56)

• Huge increase in

Prob. Absorption

above the K-shell

B.E.

Photoelectric Effect: K-Edge

K-edge < 1 keV

K-edge = 33.2 keV

Semi-log plot

Pro

bab

ilit

y o

f A

bso

rpti

on K-edge = 37.4 keV

K-shell electron binding energies

or “absorption edges”

7.4 Avg Tissue 0.5

20 Calcium 4.04

53 Iodine 33.2

56 Barium 37.4

74 Tungsten 69.5

Atomic Number, Z Material K-Edge, keV

82 Lead 88.0

11/19/2014

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Radiological Significance of Photoelectric Effect

• No scatter radiation (characteristic x-rays in tissue have very low E, < 1 keV), “pure” x-ray contrast

• P(P.E.) Z3 means that P.E. enhances subject contrast (differences in attenuation between tissues), inversely proportional to E3

• Higher doses to patient when it occurs in tissue: total absorption of photon, no energy escapes

• Iodine and barium image contrast are highest when kVp is set match the k-edge

Effect of Scatter on Radiographic Contrast

Scatter masks image contrast (noise)

Scatter included Scatter reduced

(grid)

Not collimated Collimated

Pair Production

• h > 1.02 MeV

• Excess is K.E. of

β’s

• Probability of pair

production

– P (PP) Z

– P (PP) h > 1.02

MeV

– P (PP) (g/cm3)

Photodisintegration

• High energy photon ejects a nuclear particle.

• Except for beryllium, this occurs for h > 7 MeV.

• Not significant for diagnostic radiology but

important for Rx.

Which of the following is false? A photon can undergo a

_____ interaction followed by a _____ interaction.

a. Compton, pair production

b. Compton, another Compton

c. Compton, photoelectric

d. Photoelectric, Compton

Which of the following is false? A photon can undergo a

_____ interaction followed by a _____ interaction.

a. Compton, pair production

b. Compton, another Compton

c. Compton, photoelectric

d. Photoelectric, Compton

11/19/2014

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Attenuation of X- and

Gamma-Rays

• Removal of photons from

beam, or sum of scatter and

absorption (from all interactions)

• For monochromatic (single

energy) radiation of intensity I0

– I = Io e-x or N = No e-x

– = linear attenuation coefficient (cm-1)

– = ln 2/HVL

– HVL (cm) = 0.693/ = thickness of absorber that attenuates beam by 1/2

– is function of: E (h), Z,

• = Rayleigh + Compton + Photoelectric + Pair Prod + Photodisint

• is function of: E (h), Z,

• / = mass attenuation coefficient (cm-2/g)

Pro

ba

bil

ity o

f A

bs

orp

tio

n

Which is/are False? The linear attenuation coefficient:

a. Is equal to the mass attenuation coefficient multiplied by

the density of the absorbing material.

b. Varies mainly due to changes in electron density.

c. Is equal to the fractional reduction in the intensity per

unit absorber thickness.

d. Becomes less dependent on Compton interactions than

on photo-electric interactions at higher energies.

e. Is a constant for monoenergetic photon beam in a given

absorbing material.

Which is/are False? The linear attenuation coefficient:

a. Is equal to the mass attenuation coefficient multiplied

by the density of the absorbing material.

b. Varies mainly due to changes in electron density.

c. Is equal to the fractional reduction in the intensity

per unit absorber thickness.

d. Becomes less dependent on Compton interactions than

on photo-electric interactions as energy increases.

e. Is a constant for monoenergetic photon beam in a

given absorbing material.

Ice cubes

Air bubbles

Measuring Attenuation of X- and Gamma-Rays

• For monochromatic (single energy) radiation of intensity I0

– I = Io e-x or N = No e-x

– = linear attenuation coefficient (cm-1)

– = ln 2/HVL

– HVL = 0.693/ = thickness of absorber that attenuates beam by 1/2

– is function of: h , Z,

11/19/2014

8

xeI

I 0

Monochromatic X-Rays

1st HVL = 2nd HVL

Avg Energy (quality) and HVL increases

Beam Hardening

Photon intensity (quantity) decreases

Polyenergetic X-Rayse.g., Diagnostic x-ray beam

2nd HVL > 1st HVL

An attenuation curve for a 120 kVp x-ray beam yields the following data:

Added filtration (mm Al) Relative Intensity

0 100%

0.5 50

1 40

2 27

3 20

4 15

5 12

The second half value layer Add 1 mm to the beam. What

is approximately: is the HVL now?

a. 1.0 mm a. 1.0 mm

b. 1.7 mm b. 1.5 mm

c. 2.0 mm c. 2.0 mm

d. 2.2 mm d. 2.5 mm

e. 3.0 mm e. 3.0 mm

0

25

50

75

100

0 1 2 3 4 5



0 100%

0.5 50

1 40

2 27

3 20

4 15

5 12



a. 1.0 mm a. 1.0 mm

b. 1.7 mm b. 1.5 mm

c. 2.0 mm c. 2.0 mm

d. 2.2 mm d. 2.5 mm

e. 3.0 mm e. 3.0 mm

0

25

50

75

100

0 1 2 3 4 5



0 100%

0.5 50

1 40

2 27

3 20

4 15

5 12



a. 1.0 mm a. 1.0 mm

b. 1.7 mm b. 1.5 mm

c. 2.0 mm c. 2.0 mm

d. 2.2 mm d. 2.5 mm

e. 3.0 mm e. 3.0 mm

0

25

50

75

100

0 1 2 3 4 5

Next Session

• Monday December 8, 7:00 a.m. @ VA

– Chapter 4: Computers, Dr. Hall


– Chapter 5: X-Ray Production

• No Lectures Monday December 22 or 29

11/19/2014

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Attenuation of X- and Gamma-Rays

A

NFluencePhoton

A

hNFluenceEnergyPhoton

RateFluencet

A

N

FluxPhoton

A narrow monoenergetic photon beam interacts with an

absorber. Which is/are True?

a. The photon fluence decreases exponentially with

increasing depth in the absorber.

b. The photon fluence becomes zero beyond a maximum

range determined by the photon energy.

c. The LET depends on the depth in the absorber.

d. The photon fluence is reduced by the same fraction, as

the beam passes through equal thickness of the absorber

at any depth.

A narrow monoenergetic photon beam interacts with an

absorber. Which is/are True?

a. The photon fluence decreases exponentially with

increasing depth in the absorber.

b. The photon fluence becomes zero beyond a maximum

range determined by the photon energy.

c. The LET depends on the depth in the absorber.

d. The photon fluence is reduced by the same fraction,

as the beam passes through equal thickness of the

absorber at any depth.

AAPM/ABR Syllabus

Module 5: Radiation Units

After completing this module, the resident should be able to apply the “Fundamental Knowledge”

and “Clinical Applications” learned from the module to example tasks, such as those found in

“Clinical Problem-Solving.”

Fundamental Knowledge:

1. Recognize that there are 2 different systems for units of measurement (i.e. SI and Classical)

used to describe physical quantities.

2. Describe the SI and Classical units for measuring the ionization resulting from radiation

interactions in air (e.g., exposure-related quantities).

3. Describe the concepts of dose‐related quantities and their SI and Classical units.

Clinical Application:

1. Discuss the appropriate use or applicability of radiation quantities in the health care

applications of imaging, therapy, and safety.

Clinical Problem-Solving:

1. Explain radiation exposure and dose quantities in lay language to a patient.

52

Units of Radiation

• Exposure (R) 1 R = 2.58 x 10-4 C/kg

• Absorbed Dose (Gy) 1 Gy = 100 rad = 1 J/kg = 1 erg/gm

• Kerma (Gy) K.E. transferred to charged particles

K = Ψ (tr/)E

• Equivalent Dose (Sv) H = wR D = 100 rem

• Effective Dose (Sv) E = ΣT wT HT

• Activity (Bq) 3.7x1010 Bq = 1 Ci

(Also known as Quality Factor, largely based on LET)

• Effective Dose (Sv) E = ΣT wT HT

11/19/2014

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Which of the following is not equal to one Gray?

a. 1.0 Joule/kg

b. 100 rads

c. 1.0 Sv/Quality Factor

d. (100 R)•(f-factor)

e. 100 ergs/gm

Which of the following is not equal to one Gray?

a. 1.0 Joule/kg

b. 100 rads

c. 1.0 Sv/Quality Factor

d. (100 R)•(f-factor)

e. 100 ergs/gm

Next Session


– Chapter 4: Computers, Dr. Hall


– Chapter 5: X-Ray Production

• No Lectures Monday December 23 or 30

Specific Ionization (Ion Pairs/mm)

•Specific Ionization increases with charge of particle

•Decreases with velocity of incident particle

•E.g., alpha may be as high as 7,000 IP/mm in air

compared to e- of 50-100 IP/cm

•As α slows, Bragg peak occurs

•Bragg peak may be useful for Rad Tx

7.69 MeV αlpha in air

Two materials are irradiated by monoenergetic photons.

Material A has an atomic number of 14 and B has an

atomic number of 7. The photoelectric component of the

mass attenuation coefficient of A is ______ times that of

B.

a. 16

b. 8

c. 4

d. 2

e. 0.5

11/19/2014

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Two materials are irradiated by monoenergetic photons.

Material A has an atomic number of 14 and B has an

atomic number of 7. The photoelectric component of the

mass attenuation coefficient of A is ______ times that of

B.

a. 16

b. 8

c. 4

d. 2

e. 0.5

P (P.E.) Z3

HVL

HVL

MFP

44.1

693.0

1

1

Mean Free Path

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