William Hunter-NM Lectures-Fall 2011

Main points from last week's lecture: “Decay of Radioactivity” Mathematics description nly yields probabilities and averages -λ t -0.693 t /T Interactions of Radiation Decay equation: N(t) = N(0) × e = N(0) × e 1/2 Activity: A(t) = -dN(t)/dt = λ N(t) with Matter Decay constant λ = A(t)/N(t) Half-life: T1/2 = ln(2) / λ = 0.693 / λ Average lifetime:  = 1 / λ -λ t -0.693 t / T William Hunter, PhD Decay factor (DF): e = e 1/2 Image frame decay correction - effective decay factors

[email protected] Approximation for short frame times relative to isotope half-life: e.g., DFeff ≈ ½ [DF(t)+DF(t+Dt)] Nuclear Medicine Basic Science Lectures Specific Activity 18 http://www.rad.washington.edu/research/our-research/groups/irl/education/ CFSA [Bq/g] = max SA ≈ 4.8 x 10 /(A x T1/2) for T1/2 given in days, A: atomic weight basic-science-resident-lectures Mixed radionuclide samples

September 20, 2011 Atotal(t) always eventually follows the slope of the longest half-life nuclide. Parent-daughter decay rates

1. Secular equilibrium: T½,parent >> T½,daughter  daughter activity quickly asymptotes to parent’s 2. Transient equilibrium: T½,parent ≥ T½,daughter  daughter activity slowly asymptotes to parent’s

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Passage of radiation through matter Types of Radiation depends on … Particles ejected from an unstable nucleus: • Alpha radiation = 2p+2n (same as a He nucleus). Usually from a heavy element 1. Type of radiation • Beta radiation = β- or β+ ( or ) • charged particle (e.g., electron, , etc.) For example: neutron conversion inside the nucleus: • electromagnetic (e.g., high (n → p + e- +  … or other permutations) such as x-ray or -ray) e • Heavy Ions and Neutrons! 2. Energy of radiation (e.g., in keV or MeV) Electromagnetic energy (): • Gamma radiation = 3. Nature of matter traversed (atomic number & density)  De-excitation of a nucleus following another nuclear decay • Other electromagnetic radiation All photons from sources other than nuclear decay (e.g., atomic electron-orbital transitions)!

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[email protected] William Hunter-NM Lectures-Fall 2011

I. Interactions of Interactions of Charged Particles with Matter Charged Particles with Matter Description of Passage

Types of charged particle radiation relevant to Nuclear Medicine Gradual loss of particleʼs energy Particle Symbol Charge Energy Imparted (amu) (relative) Energy transferred to nearby atoms and molecules Electron e-, - 0.000548 -1 kinetic

Positron e+, + 0.000548 +1 kinetic + 2 × 0.511MeV

Alpha  4.0028 +2 kinetic (can be large)

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Interactions of Charged Particles with Matter Interactions of Charged Particles with Matter Interaction mechanisms Excitation • Energy is transferred to an orbital electron, but not enough to free it.

• Electron is left in an excited state and energy is 1. Excitation dissipated in molecular vibrations or in atomic emission of infrared, visible or uv radiation, etc. 2. Ionization

3.

Fall 2011, Copyright UW Imaging Research Laboratory 7 From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 8

[email protected] William Hunter-NM Lectures-Fall 2011

Interactions of Charged Particles with Matter Interactions of Charged Particles with Matter Ionization Bremsstrahlung • Interaction between charged particle and orbital electron • Some particles will interact with the nucleus. • Energy transferred from passing particle to electron • The particle will be deflected by the strong electrical • When energy is greater than ionization potential, electron forces exerted on it by the nucleus. is freed (IONIZATION) • The particle is rapidly decelerated and loses energy • ionization potential for in the “collision”. The energy appears as a photon of carbon, nitrogen, and electromagnetic radiation. oxygen are in the range of 10-15 eV. Photon leaves

• Ejected  Photons produced energetic enough to by Bremsstrahlung cause secondary are called X-rays ionizations are called delta-rays

ion pair Charged particle continues on From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 9 From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 10

Interactions of Charged Particles with Matter Interactions of Charged Particles with Matter Collision versus radiation losses Paths of Charged Particles electron • Ionization and excitation are collisional losses. • Bremsstrahlung production is called a radiation loss. Radiation losses increase with increasing particle energy and increasing atomic number of + - alpha - the absorbing material. (x-ray tube anode) + - + - + - + - • High-energy electrons (-) in nuclear medicine - + - + - + - + - + dissipate most of their energy in collisional losses, + + + - which have short primary and secondary path - + + + - - - lengths. However, Bremsstrahlung production from betas results in longer-range secondaries - ++ - + + - (photons) that can be important when shielding - + - - + large quantities of energetic -emitters (e.g., tens 32 of mCi of P). path > range path = range Fall 2011, Copyright UW Imaging Research Laboratory 11 Fall 2011, Copyright UW Imaging Research Laboratory 12

[email protected] William Hunter-NM Lectures-Fall 2011

Interactions of Charged Particles with Matter Interactions of Charged Particles with Matter Energy deposition along track Energy deposition along track Specific ionization: Linear energy transfer (LET): Number of ion pairs produced per unit length Amount of energy deposited per unit path length (eV/cm) (total of both primary and secondary ionization events)

• Measure of energy deposition density, determines Bragg biological consequence of radiation exposure Ionization Peak Alpha particle • “high-LET” radiation (alpha particles, ) more in Air damaging than “low-LET” radiation (beta particles and ionizing electromagnetic radiation) ionization specific

distance traveled

Specific ionization increases as particle slows down. This gives rise to the Bragg ionization peak.

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Interactions of Charged Particles with Matter II. Interactions of -particles ranges photons with matter

Interaction Mechanisms!

1. Coherent (Rayleigh) scattering Increasing likelihood 2. with increasing 3. 4. Pair production

From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 15 Fall 2011, Copyright UW Imaging Research Laboratory 16

[email protected] William Hunter-NM Lectures-Fall 2011

Interactions of Photons with Matter Interactions of Photons with Matter Coherent (or Rayleigh) Scatter Photoelectric Effect (Absorption)

• Scattering interactions that occur between a photon and an atom as a whole. An atomic absorption process in which an atom absorbs all the energy of an incident photon. • Coherent scattering occurs mainly at <50 keV (uncommon in nuclear medicine and often ignored; Z is atomic number of the material, E is accounts for <5% of x-ray interactions above 70 keV) µ   Z3 PE energy of the incident photon, and r is E3 • Because of the great mass of an atom very little recoil energy is the density of the material. absorbed by the atom. The photon is therefore deflected with essentially no loss of energy. • It is the reason the sky is blue and sunsets are red.

 Before After  Fall 2011, Copyright UW Imaging Research Laboratory 17 From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 18

Interactions of Photons with Matter Interactions of Photons with Matter Photoelectric Effect (Absorption) Compton Scatter

Abrupt increase in likelihood of interaction at edges due to increased probability of photoelectric absorption when photon energy just exceeds Collision between a photon and a loosely bound outer binding energy shell orbital electron. Interaction looks like a collision between the photon and a “free” electron.

Bushberg Figure 3-10 Fall 2011, Copyright UW Imaging Research Laboratory 19 From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 20

[email protected] William Hunter-NM Lectures-Fall 2011

Interactions of Photons with Matter Interactions of Photons with Matter Compton Scatter Compton Scatter

The probability of Compton scatter is a slowly varying The scattering angle of the photon is determined by the function of energy. It is proportional to the density of the amount of energy transferred in the collision. material (r) but independent of Z.

µCS    is the density of the material.

As energy is increased scatter is forward peaked.

Fall 2011, Copyright UW Imaging Research Laboratory 21 From: Society of Nuclear Medicine: Basic Science of Nuclear Medicine CD Fall 2011, Copyright UW Imaging Research Laboratory 22

Interactions of Photons with Matter Interactions of Photons with Matter Angular distribution of Compton Scatter Angular distribution of Compton Scatter Polar plot of Klein-Nishina equation How likely is scattering to occur at different angles? (relative # per solid angle) • low energies: all angles () are equally probable • high energies: forward angle scatter is favored

The relative frequency of scatter angle for given incident energy is described by Klein-Nishina equation.

Fall 2011, Copyright UW Imaging Research Laboratory 23 From: Bruno, UC Berkeley masters thesis Fall 2011, Copyright UW Imaging Research Laboratory 24

[email protected] William Hunter-NM Lectures-Fall 2011

Interactions of Photons with Matter Interactions of Photons with Matter Pair Production Photoelectric vs Compton fractions

Pair production occurs when a photon interacts with the electric field of a charged particle. Usually the interaction is with an atomic nucleus but occasionally it is with an electron.

Photon energy is converted into an electron-positron pair and kinetic energy. Initial photon must have an energy of greater than 1.022 MeV (> 2 times rest mass of electron).

Positron will eventually interact with a free electron and produce a pair of 511 keV photons. e+

 Before After e-

Fall 2011, Copyright UW Imaging Research Laboratory 25 Bushberg Figure 3-11 Fall 2011, Copyright UW Imaging Research Laboratory 26

Interactions of Photons with Matter Interactions of Photons with Matter Attenuation Attenuation For a narrow beam of monoenergetic photons … the transmission of photons through an absorber is described by an exponential equation: When a photon passes through a thickness of absorber −µx material, the probability that it will experience an I,( x ) = I(0)e interaction (i.e., photoelectric, Compton scatter, or pair production) depends on the energy of the photon and on where the composition and thickness of the absorber. I(0)!= initial beam intensity, I(x) = beam intensity transmitted through absorber x != thickness of absorber, and µ = total linear attenuation coefficient of the absorber at the photon energy of interest (note units: cm-1).

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[email protected] William Hunter-NM Lectures-Fall 2011

Interactions of Photons with Matter Interactions of Photons with Matter Attenuation Coefficients Attenuation Coefficient

There are three basic components to the linear Linear attenuation coefficient µ attenuation coefficient: l • depends on photon energy µ due to the photoelectric effect;  • depends on material composition µ due to Compton scattering; and  • depends on material density µ due to pair production.  • dimensions are 1/length (e.g., 1/cm, cm-1) The exponential equation can then be written as: Mass attenuation coefficient µm I(x) = I(0) exp[ -(µ + µ + µ)x ] µm = µl /r (r = density of material yielding µl ) does not depend on material density or as dimensions are length2/mass (e.g., cm2/g) I(x) = I(0) exp[-µ x] exp[-µ x] exp[-µ x]

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Interactions of Photons with Matter Interactions of Photons with Matter Mass attenuation coefficients for soft tissue Examples of linear atten. coefficient! 10 NaI(Tl)! BGO! /g)

2 3

1

0.3

0.1

0.03

0.01

0.003 Mass attenuation coefficient (cm Massattenuation coefficient

0.001 10 100 1,000 10,000

Bushberg Figure 3-13 Fall 2011, Copyright UW Imaging Research Laboratory 31 From: Bicron (Harshaw) catalog Fall 2011, Copyright UW Imaging Research Laboratory 32

[email protected] William Hunter-NM Lectures-Fall 2011

Interactions of Photons with Matter Interactions of Photons with Matter Narrow beam vs broad beam attenuation Half and tenth value thicknesses

Half-value thickness is the amount of material needed to Without collimation, scattered photons cause artificially attenuate a photon flux by 1/2 (attenuation factor = 0.5). high counts to be measured, resulting in smaller measured values for the attenuation coefficients. -µHVT 0.5 = I/I0 = e µHVT = -ln(0.5) HVT = 0.693/µ

Tenth value thickness is given by

-µTVT 0.1 = I/I0 = e TVT = 2.30/µ

From: Society of Nuclear Medicine: Basic Science of Nuclear Medicine CD Fall 2011, Copyright UW Imaging Research Laboratory 33 Fall 2011, Copyright UW Imaging Research Laboratory 34

Interactions of Photons with Matter Interactions of Photons with Matter Half and tenth value thicknesses Beam Hardening • A polychromatic beam (multiple energies) (e.g., from Examples x-ray tube, Ga-67, In-111, I-131) has complex Material (energy) µ (cm-1) HVT (cm) TVT (cm) attenuation properties.

Lead (140 keV) 22.7 0.031 0.10 • Since lower energies are attenuated more than higher energies, the higher energy photons are Lead (511 keV) 1.7 0.41 1.35 increasingly more prevalent in the attenuated beam.

Water (140 keV) 0.15 4.6 15.4

Water (511 keV) 0.096 7.2 24.0

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[email protected] William Hunter-NM Lectures-Fall 2011

Interactions of Photons with Matter Interactions of Radiation with Matter Secondary Ionization Ionization more ionizing • The Photoelectric Effect & Compton Scattering ionize an atom.

• Pair production creates two charged e- e+ particles e- e+ e- e+ - + Big Particles • These energetic charged particles in turn - + e e e e e- e+ (alphas, protons) ionize more atoms producing many free e- e+ electrons • These secondary ionization are the basis for most photon detectors. Low-LET Radiation High-LET Radiation • Ionization also leads to breaking molecular bonds  basis of most radiation biological effects. EM Spectrum

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Example: Attenuation Calculation 1 Example: Attenuation Calculation 2

What fraction of 140 keV photons will escape unscattered What thickness of lead is required to attenuate 99% of from the middle of a 30 cm cylinder? 511 keV photons?

99% attenuated = 1% surviving Using the exponential attenuation formula -µd -(1.7/cm)d 0.01 = I/I0 = e = e ln(0.01) = -(0.17/cm)d d = -ln(0.01)/(1.7/cm) = 2.7 cm

Alternatively, if the TVT is known (1.35 cm), doubling the The photons must travel through 15 cm of water. TVT results in two consecutive layers which each transmit 1/10 of photons, or a total transmission of 1/100 -µd -(0.15/cm)(15cm) I/I0 = e = e = 0.105 = 10.5% or 1%. 2 * 1.35 cm = 2.7 cm.!

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[email protected] William Hunter-NM Lectures-Fall 2011

Example: Buildup Factors Example: Buildup Factors (broad beam versus narrow beam values) (broad beam versus narrow beam values)

The transmission factor for 511-keV photons in 1 cm of lead was found to be 18% for narrow-beam conditions. Estimate the actual transmission for broad-beam conditions.

From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 41 From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 42

Example: Buildup Factors Question: (broad beam versus narrow beam values)

The transmission factor for 511-keV photons in 1 cm of lead was found Why are radiation losses (I.e. Bremsstrahlung) more to be 18% for narrow-beam conditions. Estimate the actual important than collisional losses when shielding large transmission for broad-beam conditions. quantities of energetic b-emitters?

• HVT for lead is 0.4 cm. Therefore, µl = 0.693/0.4 cm = 1.73 cm-1. a) Radiation losses are more frequent than collisional losses.

• For 1 cm µlx = 1.73. b) Photon radiation travels further than beta radiation. • Using values from buildup factor table for lead and linear interpolation: c) Both (a) and (b) B = 1.243 + 0.73 * (1.396 - 1.243) d) Neither (a) and (b) B = 1.37

-µ x T = Be l

T = 1.37 * 18% = 25%

From: Physics in Nuclear Medicine (Cherry, Sorenson and Phelps) Fall 2011, Copyright UW Imaging Research Laboratory 43 Fall 2011, Copyright UW Imaging Research Laboratory 44

[email protected] William Hunter-NM Lectures-Fall 2011

Main points of this weekʼs lecture: Klein Nishina formula “Interaction with matter” Charged particles! Polar plot of Klein-Nishina equation • Short ranged in tissue (relative # per solid angle) ~ µm for alphas (straight path and continual slowing) ~ mm for betas (more sporadic path and rate of energy loss) • Interactions Types: Excitation, Ionization, Bremsstrahlung • Linear energy transfer (LET) - nearly continual energy transfer • Bragg ionization peak - specific ionization peaks as particle slows down Photons! • Relatively long ranged (range ~cm) • Local energy deposition - photon deposits much or all of their energy each interaction • Interactions Types: Rayleigh, Photoelectric, Compton, Pair Production • Compton - dominant process in tissue-equiv. materials for Nuc. Med. energies • Beam hardening – preferential absorption of lower E in polychromatic photon beam • Buildup factors - narrow vs. wide beam attenuation • Secondary ionization - useful for photon detection

NEXT WEEK: Dr. Lewellen- Radiation Detectors! Suggested reading: Chapter 7 of Cherry, Sorenson, and Phelps

Fall 2011, Copyright UW Imaging Research Laboratory 45 From: Bruno, UC Berkeley masters thesis Fall 2011, Copyright UW Imaging Research Laboratory 46

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