Interactions of radiation and matter

Question 1

What three interactions does an x-ray beam have with a patient, and what effect do these interactions cause?

Answer 1

• X-ray transmitted, forms image.
• absorbed (photoelectric effect), dose to patient.
• Scatter (Compton and some elastic), dose to staff.

Question 2

What are the units of particle fluence and energy fluence?

Answer 2

• Particle fluence: m^-2s^-1 .

- Energy fluence: Jm^-2s^-1.

Question 3

What is the equation for energy fluence?

Answer 3

• Energy fluence = sum (particle fluence * energy) .

- e.g. for 50cm^-2s^-1 at 50Kev and 50cm^-2s^-1 at 100KeV: energy fluence is 5050 + 50100 = 7500KeVcm^-2s^-1 .

Question 4

What is the attenuation equation for number of transmitted photons N passing through a material of thickness x?

Answer 4

N=N0e(-μx).

Question 5

What is the half value layer?

Answer 5

-The thickness of material which reduces the incident intensity to half. i.e. (N/N0) = 0.5.

Question 6

Why do real beams not follow a true exponential curve when attenuated?

Answer 6

• Spectrum of energies.
• Low energies preferentially attenuated (photoelectric ~ 1/E^3).
• Also scatter from irradiated volume.

Question 7

Draw the characteristic spectrum for a diagnostic x-ray beam at 100KVp with filtration.

Answer 7

• Bremsstrahlung curve starting at around 20KeV.
• Characteristic lines from K shell transitions (Photoelectric).
• Max photon energy 100KeV

Question 8

How does the width of an x-ray beam affect the attenuation?

Answer 8

• Narrow beam - less scatter reaches detector, greater attenuation.
• Broad beam - More scattered radiation hits detector, less attenuation.

Question 9

How does the energy of an x-ray beam affect it’s attenuation?

Answer 9

• Increase in E leads to a decrease in μ or increase in HVL.

- So higher E x-rays are more penetrating.

Question 10

How does the linear attenuation coefficient μ change with density?

Answer 10

-μ increases with increasing density since there are more molecules per unit volume.

Question 11

Define the mass attenuation coefficient and its units

Answer 11

-μ/ρ [cm^2g^-1] .

Question 12

What is the difference between attenuation and absorption?

Answer 12

• Attenuation: removal of radiation from the beam.

- Absorption: Taking up of energy from the beam by irradiated material.

Question 13

Define the absorbed dose and state what needs to be specified when using absorbed dose.

Answer 13

• D = ΔE/Δm, the energy ΔE absorbed in mass Δm in units of Gy (JKg^-1).
• Need to specify the material in which energy is absorbed.

Question 14

What is air KERMA and what are its units?

Answer 14

• Kinetic Energy Released per unit Mass (in air).
• Energy transferred from the x-ray beam (photons) to the electrons at the specified point.
• Units Gy.

Question 15

Why is air KERMA not necessarily equal to absorbed dose in air?

Answer 15

• Energy removed from the beam is not necessarily equal to the energy absorbed in the mass.
• Some secondary electron energy may be re-radiated as Bremsstrahlung radiation and escape.
• Point of removal of energy not necessarily equal to point of energy deposition because of finite x-ray range.

Question 16

Give two reasons why air KERMA may be approximated as dose to air for the diagnostic x-ray energy range.

Answer 16

• Negligible Bremsstrahlung.

- Electron ranges very short.

Question 17

Define Exposure and give the units.

Answer 17

• X=ΔQ/ΔM [CKg^-1].
• The ability of the radiation to produce ionization in air.
• The absolute value of the total charge (ΔQ) of the ions of one sign produced in air when all the electrons liberated by the photons per unit mass of air are completely stopped.
• Δm is the mass of air in volume Δv.

Question 18

How do you convert from absorbed dose in air to absorbed dose in another medium?

Answer 18

• D(m)/D(a) = μ/ρ/μ/ρ.
• Depends on the mass attenuation coefficient.
• known for variety of substances at specific photon energy spectra.

Question 19

Describe the photoelectric effect.

Answer 19

• X-ray photon ejects inner k-shell electron.
• Transfers all energy to electron.
• Electron energy = photon energy - binding energy.
• Vacancy filled by outer shell electron.
• characteristic photon emitted.
• characteristic photon absorbed in soft tissue (low z).

Question 20

What is the alternative to characteristic x-ray emission from the photoelectric effect?

Answer 20

• Outer electron emitted.

- Auger electron.

Question 21

What is the fluorescent yield for the photoelectric effect and what does this tell us?

Answer 21

• ωk = no of k x-ray photons emitted/no of k shell vacancies.
• proportion of characteristic photons and Auger electrons.
• ωk=1 no Auger electrons.
• ωk=0 all Auger electrons.

Question 22

How does the probability of the photoelectric effect vary with Z and E?

Answer 22

• ~ Z^3.

- ~1/E^3.

Question 23

Describe Compton scattering.

Answer 23

• Inelastic scattering of photon off “free” electron.
• Scattered photon has reduced energy.
• recoil electron.
• change in energy depends on initial photon energy and angle of scatter.

Question 24

What is the change in wavelength of a Compton scattered photon?

Answer 24

-Δλ=(h/mc)*(1-cosθ).

Question 25

What is the change in photon energy when it undergoes Compton scattering?

Answer 25

• ΔE=E0(α(1-cosθ))/(1+α(1-cosθ)).

- α =E0/0.511 in MeV .

Question 26

What is the relationship of probability of Compton scatter with photon energy and Z?

Answer 26

• In diagnostic range, approximately constant with energy.
• At higher energies, decreases slowly with increasing energy by ~ 1/E (for E > 100KeV).
• independent of Z

Question 27

State 2 negatives associated with Compton scattering during patient examinations.

Answer 27

• Scattered radiation is hazardous to staff.

- Scattered radiation reduces images contrast.

Question 28

How do you calculate backscatter factor and what are typical values?

Answer 28

• Backscatter factor = dose at P with scatter/dose at P without scatter
• typically 1.2-1.3

Question 29

Describe elastic scattering and give percentage of elastically scattered photons.

Answer 29

-Whole atom absorbs recoil.
-Resonance: “bound” electrons vibrate at frequency of photons.
-Electrons re-radiate energy at the same frequency (and energy) of photon.
Scattering in forward direction.
-<10% of total interaction - little practical importance.

Question 30

What is the relationship between the probability of elastic scattering and Z and E?

Answer 30

• ~Z^2

- ~1/E^2

Question 31

Describe how the k-edge is used in imaging with x-rays.

Answer 31

• Match energy peak of spectrum to K-edge of detector material - maximize absorption in detector.
• Fewer photons for given optical density, lower dose to patient.
• Also for contrast agent - e.g. iodine (k-edge 33KeV), barium (K-edge 37KeV).
• Have K-edges due to photoelectric effect.
• Match energy of peak of x-ray spectrum (~1/3 KVp) with the K-edge of the contrast media.
• Maximizes absorption in contrast media - maximizes contrast.

Question 32

Describe pair production.

Answer 32

• Need a photon with E > 1.022MeV.
• When high E photon passed near a nucleus, can produce e- e+ pair.
• e- and e+ then lose energy by interaction with other electrons.
• e+ annihilates with a free electron releasing back to back 0.511MeV photons.

Question 33

What is the relationship between the probability of pair production and E and Z.

Answer 33

• ~E-1.022MeV.

- ~Z.

Question 34

Write an equation for the mass attenuation coefficient of a mixture.

Answer 34

• (μ/ρ)={W1(μ/ρ)1}+{W2(μ/ρ)2}+{W3*(μ/ρ)3}+….

- W1 = fraction of weight of element 1 etc.

Question 35

For elastic scatter, Compton scatter, the photoelectric effect and pair production state whether there is absorption and/or attenuation.

Answer 35

• Elastic: no absorption, there is attenuation.
• Compton scatter: Partial absorption (greater proportion of removed energy absorbed at higher energies), there is attenuation.
• Photoelectric: Partial absorption (characteristic radiation. But total absorption to a good approximation in soft tissue), there is attenuation.
• Pair production: Partial absorption (0.511 Mev annihilation photons can escape), there is attenuation.

Question 36

Describe the different neutrons and give their energies and mechanisms by which they lose energy.

Answer 36

• Fast neutrons: >0.1MeV. Elastic and inelastic scatter.
• Thermal neutrons: 0.025eV (room temp.). Captured by nuclei.
• Intermediate neutrons.

Question 37

What material is suitable to shield against neutrons?

Answer 37

-Low atomic number material e.g. boron.

Question 38

In which medical equipment can neutron capture occur causing the production of radioactive material?

Answer 38

-Heads of high energy linacs.