Radiation Interactions

1. Radiation Interactions Robert Metzger, Ph.D.

2. Interactions with Matter • Charged 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.

3. 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.

4. Charged Particle Tracks • e- follow tortuous paths through matter as the result of multiple Coulombic scattering processes • An α2+, due to it’s higher mass follows a more linear trajectory • Path length = actual distance the particle travels in matter • Range = effective linear penetration depth of the particle in matter • Range ≤ path length c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p.34.

5. Bremsstrahlung • Deceleration of an e- around a nucleus causes it to emit Electromagnetic radiation or bremsstrahlung (G.): ‘breaking radiation’ • Probability of bremsstrahlung emission  Z2 Ratio of e- energy loss due to bremsstrahlung vs. excitation and ionization = KE[MeV]∙Z/820 • Thus, for an 100 keV e- and tungsten (Z=74) ≈ 1% c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p.35.

6. 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.

7. Rayleigh Scattering • Excitation of the total complement of atomic electrons occurs as a result of interaction with the incident photon • No ionization takes place • No loss of E • <5% of interactions at diagnostic energies. c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p. 37.

8. Compton Scattering • Dominant interaction of x-rays with soft tissue in the diagnostic range and beyond (approx. 30 keV - 30MeV) • Occurs between the photon and a “free” e- (outer shell e- considered free when Eg >> binding energy, Eb of the e- ) • Encounter results in ionization of the atom and probabilistic distribution of the incident photon E to that of the scattered photon and the ejected e- • A probabilistic distribution determines the angle of deflection c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p. 38.

9. Compton Scattering • Compton interaction probability is dependent on the total no. of e- in the absorber vol. (e-/cm3 = e-/gm · density) • With the exception of 1H, e-/gm is fairly constant for organic materials (Z/A  0.5), thus the probability of Compton interaction proportional to material density () • Conservation of energy and momentum yield the following equations: • Eo = Esc + Ee- • , where mec2 = 511 keV

10. Compton Scattering • As incident E0 both photon and e- scattered in more forward direction • At a given  fraction of E transferred to the scattered photon decreases with  E0 • For high energy photons most of the energy is transferred to the electron • At diagnostic energies most energy to the scattered photon • Max E to e- at  of 180o; max E scattered photon is 511 keV at  of 90o c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p. 39.

11. Photoelectric Effect • All E transferred to e- (ejected photoelectron) as kinetic energy (Ee) less the binding energy: Ee = E0 – Eb • Empty shell immediately filled with e- from outer orbitals resulting in the emission of characteristic x-rays (E = differences in Eb of orbitals), for example, Iodine: EK = 34 keV, EL = 5 keV, EM = 0.6 keV c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p. 41.

12. Photoelectric Effect • Eb Z2 • Photoe- and cation; characteristic x-rays and/or Auger e- • Probability of photoe- absorption  Z3/E3 (Z = atomic no.) • Explains why contrast  as higher energy x-rays are used in the imaging process • Due to the absorption of the incident x-ray without scatter, maximum subject contrast arises with a photoe- effect interaction • Increased probability of photoe- absorption just above the Eb of the inner shells cause discontinuities in the attenuation profiles (e.g., K-edge)

13. Photoelectric Effect c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 1st ed., p. 26.

14. Photoelectric Effect • Edges become significant factors for higher Z materials as the Eb are in the diagnostic energy range: • Contrast agents – barium (Ba, Z=56) and iodine (I, Z=53) • Rare earth materials used for intensifying screens – lanthanum (La, Z=57) and gadolinium (Gd, Z=64) • Computed radiography (CR) and digital radiography (DR) acquisition – europium (Eu, Z=63) and cesium (Cs, Z=55) • Increased absorption probabilities improve subject contrast and quantum detective efficiency • At photon E << 50 keV, the photoelectric effect plays an important role in imaging soft tissue, amplifying small differences in tissues of slightly different Z, thus improving subject contrast (e.g., in mammography)

15. Pair Production • Conversion of mass to E occurs upon the interaction of a high E photon (> 1.02 MeV; rest mass of e- = 511 keV) in the vicinity of a heavy nucleus • Creates a negatron (β-) - positron (β+) pair • The β+ annihilates with an e- to create two 511 keV photons separated at an  of 180o c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p. 44.

16. Radiation Interactions WHICH ISHIGH kVp CHEST RADIOGRAPH AND WHICH IS LOW kVp CHEST RADIOGRAPH ? A B

17. Compton vs Photoelectric WHICH ISLOW kVp BONE RADIOGRAPHAND WHICH ISHIGH kVp BONE RADIOGRAPH ? A B

18. Linear Attenuation Coef • Cross section is a measure of the probability (‘apparent area’) of interaction: (E) measured in barns (10-24 cm2) • Interaction probability can also be expressed in terms of the thickness of the material – linear attenuation coefficient: (E) [cm-1] = Z [e- /atom] · Navg [atoms/mole] · 1/A [moles/gm] ·  [gm/cm3] · (E) [cm2/e-] • (E)  as E , e.g., for soft tissue • (30 keV) = 0.35 cm-1 and (100 keV) = 0.16 cm-1 • (E) = fractional number of photons removed (attenuated) from the beam by absorption or scattering • Multiply by 100% to get % removed from the beam/cm

19. Attenuation Coefficient • An exponential relationship between the incident radiation intensity (I0) and the transmitted intensity (I) with respect to thickness: • I(E) = I0(E) e-(E)·x • total(E) = PE(E) + CS(E) + RS(E) + PP(E) • At low x-ray E: PE(E) dominates and (E)  Z3/E3 • At high x-ray E: CS(E) dominates and (E)  • Only at very-high E (> 1MeV) does PP(E) contribute • The value of (E) is dependent on the phase state: • water vapor << ice < water

20. Attenuation Coefficient c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p. 46.

21. Mass Attenuation Coef • Mass attenuation coefficient m(E) [cm2/g] – normalization for :m(E) = (E)/Independent of phase state () and represents the fractional number of photons attenuated per gram of material • I(E) = I0(E) e-m(E)··x • Represent “thickness” as g/cm2 - the effective thickness of 1 cm2 of material weighing a specified amount (·x)

22. Half Value Layer • Thickness of material required to reduce the intensity of the incident beam by ½ • ½ = e-(E)·HVL or HVL = 0.693/(E) • Units of HVL expressed in mm Al for a Dx x-ray beam • For a monoenergetic incident photon beam (i.e., that from a synchrotron), the HVL is easily calculated • Remember for any function where dN/dx  N which upon integrating provides an exponential function (e.g., I(E) = I0(E) ∙ e±k·w ), the doubling (or halving) dimension w is given by 69.3%/k% (e.g., 3.5% CD doubles in 20 yr) • For each HVL, I  by ½: 5 HVL  I/I0 = 100%/32 = 3.1%

23. Mean Free Path • Mean free path (avg. path length of x-ray) = 1/ = HVL/0.693 • Beam hardening • The Bremsstrahlung process produces a wide spectrum of energies, resulting in a polyenergetic (polychromatic) x-ray beam • As lower E photons have a greater attenuation coefficient, they are preferentially removed from the beam • Thus the mean energy of the resulting beam is shifted to higher E c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 1st ed., p. 281.

24. Effective Energy • The effective (avg.) E of an x-ray beam is ⅓ to ½ the peak value (kVp) and gives rise to an eff, the (E) that would be measured if the x-ray beam were monoenergetic at the effective E • Homogeneity coefficient = 1st HVL/2nd HVL • A summary description of the x-ray beam polychromaticity • HVL1 < HVL2 < … HVLn; so the homogeneity coefficient < 1 c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p. 45. c.f. Bushberg, et al. The Essential Physics of Medical Imaging, 2nd ed., p. 43.

25. 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

26. 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.