Radiation Interactions

Robert Metzger, Ph.D.

Interactions with MatterCharged particles lose energy as they interact with the orbital electrons in matter by excitation and ionization, and/or radiative losses.Excitation occurs when& the incident particle bumps an electron to a higher orbital in the absorbing medium.Ionization occurs when the transferred energy exceeds the binding energy of the electron and it is ejected. The ejected electron may then also produce further ionizations.

Specific Ionization

The number of ion pairs produced per unit path length is the specific ionization.Alpha particles can produce as many as 7,000 IP/mm. Electrons produce 50-100 IP/cm in air.LET is the product of the specific ionization and the average energy deposited per IP [IP/cm x eV/IP].About 70% of electron energy loss leads to non-ionizing excitation.

Charged Particle Tracks ee-- follow tortuous paths through matter as the result of multiple follow tortuous paths through matter as the result of multiple

Coulombic scattering processes Coulombic scattering processes An An αα2+2+, due to it’s higher mass follows a more linear trajectory, due to it’s higher mass follows a more linear trajectory Path length = actual distance the particle travels in matter Path length = actual distance the particle travels in matter Range = effective linear penetration depth of the particle in matter Range = effective linear penetration depth of the particle in matter Range Range ≤ path length≤ path length

c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2ndnd ed., p.34. ed., p.34.

Bremsstrahlung Deceleration of an eDeceleration of an e-- around a around a

nucleus causes it to emit nucleus causes it to emit Electromagnetic radiation or Electromagnetic radiation or bremsstrahlung (G.): ‘breaking bremsstrahlung (G.): ‘breaking radiation’ radiation’

Probability of bremsstrahlung Probability of bremsstrahlung emission emission Z Z2 2 Ratio of eRatio of e-- energy energy loss due to bremsstrahlung vs. loss due to bremsstrahlung vs. excitation and ionization = excitation and ionization = KE[MeV]∙Z/820 KE[MeV]∙Z/820

Thus, for an 100 keV eThus, for an 100 keV e-- and and tungsten (Z=74) tungsten (Z=74) ≈ 1%≈ 1%

c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2ndnd ed., p.35. ed., p.35.

Electromagnetic Radiation Interactions

Raleigh Scattering: Photon is scattered with no energy loss. Uncommon at diagnostic energies.

Compton Scattering:Photon strikes outer electron and ejects it, resulting in energy loss of photon and change of direction.

Photoelectric Effect: Photon is totally absorbed by K or L shell electron which is ejected.

Pair Production: High energy photon interaction.

Rayleigh Scattering Excitation of the total Excitation of the total

complement of atomic complement of atomic electrons occurs as a result of electrons occurs as a result of interaction with the incident interaction with the incident photon photon

No ionization takes place No ionization takes place No loss of E No loss of E <5% of interactions at <5% of interactions at

diagnostic energies.diagnostic energies.

c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2ndnd ed., p. 37. ed., p. 37.

Compton Scattering Dominant interaction of x-rays with Dominant interaction of x-rays with

soft tissue in the diagnostic range soft tissue in the diagnostic range and beyond (approx. 30 keV - and beyond (approx. 30 keV - 30MeV)30MeV)

Occurs between the photon and a Occurs between the photon and a “free” e“free” e-- (outer shell e (outer shell e- - considered considered free when Efree when E >> binding energy, >> binding energy,

EEbb of the e of the e-- ) )

Encounter results in ionization of Encounter results in ionization of the atom and probabilistic the atom and probabilistic distribution of the incident photon distribution of the incident photon E to that of the scattered photon E to that of the scattered photon and the ejected eand the ejected e- -

A probabilistic distribution A probabilistic distribution determines the angle of deflectiondetermines the angle of deflection

c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2ndnd ed., p. 38. ed., p. 38.

Compton Scattering Compton interaction probability is dependent on the total Compton interaction probability is dependent on the total

no. of eno. of e-- in the absorber vol. (e in the absorber vol. (e--/cm/cm33 = e = e--/gm · density) /gm · density) With the exception of With the exception of 11H, eH, e--/gm is fairly constant for /gm is fairly constant for

organic materials (Z/A organic materials (Z/A 0.5), thus 0.5), thus the probability of the probability of Compton interaction proportional to material density (Compton interaction proportional to material density () )

Conservation of energy and momentum yield the Conservation of energy and momentum yield the following equations: following equations: EEoo = E = Escsc + E + Eee--

, where m, where meecc22 = 511 keV = 511 keV

0

sc0

2e

EE =

E1+ 1- cosθ

m c

Compton Scattering As incident EAs incident E00 both photon both photon

and eand e- - scattered in more forward scattered in more forward direction direction

At a given At a given fraction of E fraction of E transferred to the scattered transferred to the scattered photon decreases with photon decreases with E E0 0

For high energy photons most For high energy photons most of the energy is transferred to of the energy is transferred to the electron the electron

At diagnostic energies most At diagnostic energies most energy to the scattered photon energy to the scattered photon

Max E to eMax E to e-- at at of 180 of 180oo; max E ; max E scattered photon is 511 keV at scattered photon is 511 keV at of 90 of 90oo

c.f. Bushberg, et al. The Essential Physics of Medical Imaging, c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 22ndnd ed., p. 39. ed., p. 39.

All E transferred to eAll E transferred to e- - (ejected photoelectron) as kinetic energy (E (ejected photoelectron) as kinetic energy (Eee) less the ) less the

binding energy: Ebinding energy: Eee = E = E00 – E – Ebb

Empty shell immediately filled with eEmpty shell immediately filled with e- - from outer orbitals resulting in the from outer orbitals resulting in the emission of characteristic x-rays (Eemission of characteristic x-rays (E = differences in E = differences in Ebb of orbitals), for of orbitals), for

example, Iodine: Eexample, Iodine: EKK = 34 keV, E = 34 keV, ELL = 5 keV, E = 5 keV, EMM = 0.6 keV = 0.6 keV

c.f. Bushberg, et al. c.f. Bushberg, et al. The Essential Physics The Essential Physics of Medical Imaging, of Medical Imaging, 22ndnd ed., p. 41. ed., p. 41.

Photoelectric Effect

Photoelectric Effect EEbb Z Z22

PhotoePhotoe-- and cation; characteristic x-rays and/or Auger e and cation; characteristic x-rays and/or Auger e-- Probability of photoeProbability of photoe-- absorption absorption Z Z33/E/E33 (Z = atomic no.) (Z = atomic no.)

Explains why contrast Explains why contrast as higher energy x-rays are used in the as higher energy x-rays are used in the imaging process imaging process

Due to the absorption of the incident x-ray without scatter, Due to the absorption of the incident x-ray without scatter, maximum subject contrast arises with a photoemaximum subject contrast arises with a photoe-- effect effect interaction interaction

Increased probability of photoeIncreased probability of photoe-- absorption just above the E absorption just above the Ebb of of

the inner shells cause discontinuities in the attenuation profiles the inner shells cause discontinuities in the attenuation profiles (e.g., K-edge)(e.g., K-edge)

Photoelectric Effect

c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 1c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 1 stst ed., p. 26. ed., p. 26.

Photoelectric Effect Edges become significant factors for higher Z materials Edges become significant factors for higher Z materials

as the Eas the Ebb are in the diagnostic energy range: are in the diagnostic energy range: Contrast agents – barium (Ba, Z=56) and iodine (I, Z=53) Contrast agents – barium (Ba, Z=56) and iodine (I, Z=53) Rare earth materials used for intensifying screens – lanthanum Rare earth materials used for intensifying screens – lanthanum

(La, Z=57) and gadolinium (Gd, Z=64) (La, Z=57) and gadolinium (Gd, Z=64) Computed radiography (CR) and digital radiography (DR) Computed radiography (CR) and digital radiography (DR)

acquisition – europium (Eu, Z=63) and cesium (Cs, Z=55) acquisition – europium (Eu, Z=63) and cesium (Cs, Z=55) Increased absorption probabilities improve subject contrast and Increased absorption probabilities improve subject contrast and

quantum detective efficiency quantum detective efficiency At photon E << 50 keV, the photoelectric effect plays an At photon E << 50 keV, the photoelectric effect plays an

important role in imaging soft tissue, amplifying small important role in imaging soft tissue, amplifying small differences in tissues of slightly different Z, thus differences in tissues of slightly different Z, thus improving subject contrast (e.g., in mammography)improving subject contrast (e.g., in mammography)

Pair Production Conversion of mass to E occurs upon the interaction of a high E photon Conversion of mass to E occurs upon the interaction of a high E photon

(> 1.02 MeV; rest mass of e(> 1.02 MeV; rest mass of e-- = 511 keV) in the vicinity of a heavy = 511 keV) in the vicinity of a heavy nucleusnucleus

Creates a negatron (Creates a negatron (ββ--) - positron () - positron (ββ++) pair ) pair The The ββ++ annihilates with an e annihilates with an e- - to create two 511 keV photons separated at to create two 511 keV photons separated at

an an of 180 of 180oo

c.f. Bushberg, et al. The c.f. Bushberg, et al. The Essential Physics of Essential Physics of Medical Imaging, 2Medical Imaging, 2ndnd ed., ed., p. 44.p. 44.

Radiation Interactions

WHICH ISHIGH kVp CHEST RADIOGRAPH AND WHICH IS LOW kVp CHEST RADIOGRAPH ?

A

B

Compton vs Photoelectric

WHICH ISLOW kVp BONE RADIOGRAPHAND WHICH ISHIGH kVp BONE RADIOGRAPH ?

A

B

Linear Attenuation Coef Cross section is a measure of the probability (‘apparent Cross section is a measure of the probability (‘apparent

area’) of interaction: area’) of interaction: (E) measured in barns (10(E) measured in barns (10-24-24 cm cm22) ) Interaction probability can also be expressed in terms of Interaction probability can also be expressed in terms of

the thickness of the material – linear attenuation the thickness of the material – linear attenuation coefficient: coefficient: (E) [cm(E) [cm-1-1] = Z [e] = Z [e-- /atom] · N /atom] · Navgavg [atoms/mole] · [atoms/mole] ·

1/A [moles/gm] · 1/A [moles/gm] · [gm/cm [gm/cm33] · ] · (E) [cm(E) [cm22/e/e--] ] (E) (E) as E as E , e.g., for soft tissue , e.g., for soft tissue

(30 keV) = 0.35 cm(30 keV) = 0.35 cm-1-1 and and (100 keV) = 0.16 cm(100 keV) = 0.16 cm-1 -1

(E) = fractional number of photons removed (E) = fractional number of photons removed (attenuated) from the beam by absorption or scattering (attenuated) from the beam by absorption or scattering

Multiply by 100% to get % removed from the beam/cmMultiply by 100% to get % removed from the beam/cm

Attenuation Coefficient An exponential relationship between the incident An exponential relationship between the incident

radiation intensity (Iradiation intensity (I00) and the transmitted intensity (I) ) and the transmitted intensity (I)

with respect to thickness: with respect to thickness: I(E) = II(E) = I00(E) e(E) e--(E)·x(E)·x

totaltotal(E) = (E) = PEPE(E) + (E) + CSCS(E) + (E) + RSRS(E) + (E) + PPPP(E) (E)

At low x-ray E: At low x-ray E: PEPE(E) dominates and (E) dominates and (E) (E) Z Z33/E/E33

At high x-ray E: At high x-ray E: CSCS(E) dominates and (E) dominates and (E) (E)

Only at very-high E (> 1MeV) does Only at very-high E (> 1MeV) does PPPP(E) contribute (E) contribute The value of The value of (E) is dependent on the phase state:(E) is dependent on the phase state: water vaporwater vapor << << iceice < < waterwater

Attenuation Coefficient

c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2ndnd ed., p. 46. ed., p. 46.

Mass Attenuation Coef

Mass attenuation coefficient Mass attenuation coefficient mm(E) [cm(E) [cm22/g] – /g] –

normalization for normalization for :: mm(E) = (E) = (E)/(E)/Independent of Independent of

phase state (phase state () and represents the fractional number ) and represents the fractional number of photons attenuated per gram of material of photons attenuated per gram of material

I(E) = II(E) = I00(E) e(E) e--mm(E)·(E)··x ·x

Represent “thickness” as g/cmRepresent “thickness” as g/cm22 - the effective - the effective thickness of 1 cmthickness of 1 cm22 of material weighing a specified of material weighing a specified amount (amount (·x)·x)

Half Value Layer Thickness of material required to reduce the intensity of Thickness of material required to reduce the intensity of

the incident beam by ½ the incident beam by ½ ½ = e½ = e--(E)·HVL (E)·HVL or or HVL = 0.693/HVL = 0.693/(E) (E) Units of HVL expressed in mm Al for a Dx x-ray beam Units of HVL expressed in mm Al for a Dx x-ray beam For a monoenergetic incident photon beam (i.e., that For a monoenergetic incident photon beam (i.e., that

from a synchrotron), the HVL is easily calculated from a synchrotron), the HVL is easily calculated Remember for any function where dN/dx Remember for any function where dN/dx N which upon N which upon

integrating provides an exponential function (e.g., I(E) = integrating provides an exponential function (e.g., I(E) = II00(E) ∙ e(E) ∙ e±k·w±k·w ), the doubling (or halving) dimension w is ), the doubling (or halving) dimension w is

given by 69.3%/k% (e.g., 3.5% CD doubles in 20 yr) given by 69.3%/k% (e.g., 3.5% CD doubles in 20 yr) For each HVL, I For each HVL, I by ½: 5 HVL by ½: 5 HVL I/I I/I00 = 100%/32 = 3.1% = 100%/32 = 3.1%

Mean Free Path Mean free path (avg. path length of x-ray) = 1/Mean free path (avg. path length of x-ray) = 1/ = HVL/0.693 = HVL/0.693 Beam hardening Beam hardening

The Bremsstrahlung process produces a wide spectrum of energies, resulting The Bremsstrahlung process produces a wide spectrum of energies, resulting in a polyenergetic (polychromatic) x-ray beam in a polyenergetic (polychromatic) x-ray beam

As lower E photons have a greater attenuation coefficient, they are As lower E photons have a greater attenuation coefficient, they are preferentially removed from the beam preferentially removed from the beam

Thus the mean energy of the resulting beam is shifted to higher EThus the mean energy of the resulting beam is shifted to higher E

c.f. Bushberg, et al. The c.f. Bushberg, et al. The Essential Physics of Essential Physics of Medical Imaging, 1Medical Imaging, 1stst ed., p. 281.ed., p. 281.

Effective Energy The effective (avg.) E of an x-ray beam is ⅓ to ½ the peak value The effective (avg.) E of an x-ray beam is ⅓ to ½ the peak value

(kVp)(kVp) and gives rise to an and gives rise to an effeff, the , the (E) that would be measured if (E) that would be measured if

the x-ray beam were monoenergetic at the effective E the x-ray beam were monoenergetic at the effective E Homogeneity coefficient = 1Homogeneity coefficient = 1stst HVL/2 HVL/2ndnd HVL HVL

A summary description of the x-ray beam polychromaticity A summary description of the x-ray beam polychromaticity HVLHVL11 < HVL < HVL22 < … HVL < … HVLnn; so the homogeneity coefficient < 1; so the homogeneity coefficient < 1

c.f. Bushberg, et al. The Essential Physics of c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2Medical Imaging, 2ndnd ed., p. 43. ed., p. 43.

c.f. Bushberg, et al. The Essential Physics of Medical c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2Imaging, 2ndnd ed., p. 45. ed., p. 45.

Shielding

I = BI0 e-x

I is the Intensity in shielded area

I0 is the unattenuated intensity

B is the buildup factor

is the attenuation coefficient

X is the shield thickness

Shielding

The buildup factor is the ratio of scattered photons that scatter back into the beam.Since the photoelectric effect dominates at diagnostic x-ray energies, the buildup factor is 1.0.Therefore lead aprons work well in diagnostic x-ray, but not in Nuclear Medicine (140 keV gammas)Buildup must be considered for PET.