1. BME 560 Medical Imaging: X-ray, CT, and Nuclear Methods
Radiation Physics Part 2

2. Today EM Radiation interactions with matter
Rayleigh scatter
Photoelectric effect
Compton scatter
Pair production
Attenuation of EM Radiation

3. X-ray interactions with matter
Possible outcomes for an x-ray or gamma ray when traveling through matter are:
No effect (a)
(it travels along the original path with original energy)
Absorption (b)
(it is absorbed in the matter)
Scatter (c)
(It changes its direction of travel and/or energy)
(a)
(b)
(c)
Imaging detector

4. EM Radiation Four possible interactions with matter
Rayleigh scatter
Photoelectric effect
Compton scatter
Pair production
Each has its own physical properties

5. huincident = huscattered ; lincident = lscattered
Rayleigh Scattering
Elastic (coherent, classical) scattering -
scatter with direction change but no energy loss.
huincident = huscattered ; lincident = lscattered
Characteristics
an interaction of the x-ray with the entire atom via a refractory mechanism (wavelength ~ atomic radius)
occurs for longer wavelengths (low x-ray energies in the mammography range keV)
reduces imaging quality in x-ray imaging.
E(keV)
P(%)
~30
<12
>70
<5
P: probability

6. Compton scattering
It is also referred as inelastic or non-classical scattering
an interaction of incident x-ray with outer shell electrons;
almost atomic (proton) number (Z) independent;
proportional to re;
weakly energy dependent until energy is high (1MeV);
a disturbance to x-ray image quality.

7. Compton Scatter Equation
Planck’s constant
Scatter angle
Electron rest mass
wavelengths

8. Compton Scattering energy and angular dependence
hu0
husc
Ee- q f
Energy and momentum conservation q

9. f = 00 & q = 1800 Compton scattering
(Max energy transfer to electron)
hu0
husc
Ee- q f

10. q = 900 Compton scattering
hu0
husc
Ee- q f

11. Compton scatter angular distribution
hu0
husc
Ee- q f
The lower the incident x-ray energy, the more isotropic (angular distribution) the (compton) scattered x-ray is.
(Isotropic - each point of compton interaction becomes an x-ray source - bad for imaging)

12. Photoelectric Effect (PE)
An total absorption event (not a scatter): all or none;
An interaction of incident x-ray with inner shell electron;
Highly dependent on atomic (proton) number (Z) - Z3;
Highly energy dependent - E-3;

13. Photoelectric effect
Incident electron deposits all of its energy into a shell electron
Must overcome electron binding energy
The shell electron (photoelectron) escapes
Ionization event
Energetic electron interacts with tissue (short range)
The photon must start with energy greater than the electron binding energy.

14. Photoelectric Effect “K-edges”
Photoelectric attenuation as a function of energy is discontinuous at the shell binding energies.
We make use of this property in several ways.
From Sprawls, The Physical Basis of Medical Imaging

15. Photoelectric effect energy and Z dependence
High Z dependence (Z3) of PE is the basic reason why diagnostic x-ray is suited to medical imaging:
PE completely removes the incident x-ray (no scatter or partial absorption)
PE differentiates different atomic compositions in tissue (bone and fat);
PE is behind the use of high Z image contrast materials;
PE decreases drastically (E-3) with increasing x-ray energy
(not good for imaging but good for therapy)

16. X-ray imaging contrast
ZBa=56; r =3.5g/cm3 Zwater, effective=7.25; r =1g/cm3
(ZBa/Zwater)3=512

17. Pair Production
occurs under strong electric field of nucleus (=>Z dependent);
only occurs if the incident x-ray energy is > 1.022MeV (enough to create the rest masses of an e- and a e+);
completely removes the incident x-ray (no scatter or partial absorption)
increases with increasing x-ray energy
generates an electron and a positron

18. Positron annihilation
2nd part of fig 3-12, redbook
Positron annihilation gamma rays are ~1800 apart;
each gamma ray has 511keV;
principle of PET scanner (a measure of PET agent distribution in patient).

19. EM Radiation Interactions
Rayleigh scatter: only significant at low energies
Compton scatter: dominates at imaging energies
Photoelectric effect: significant at imaging energies
Pair production: cannot occur at imaging energies

20. Total linear attenuation coefficient
Soft Tissue

21. X-ray attenuation incident N Absorbed & scattered n N-n Dx transmitted
Linear attenuation coefficient m (cm-1):
m= 0.10 cm-1 ==> 10% per cm.

22. Total attenuation coefficients of water and lead
Characteristic x-ray peak (K-shell)
Table of interaction vs. x-ray energy (Khan?)

23. Relative importance of each x-ray interaction in water

24. m/r (cm2/g) = m (cm-1) /r (g/cm3) Nx = N0 e- (m/r) r x
Mass attenuation coefficient (m/r) linear attenuation coefficient (m) normalized to the density (r) of the irradiated material. Therefore it is independent of density.
m/r (cm2/g) = m (cm-1) /r (g/cm3)
Nx = N0 e- (m/r) r x

25. Exercise xap xat Given:
CT x-ray energy is120kVp. The patient thickness is 20 cm and 25 cm in the AP and lateral direction, respectively. If the x-rays attenuate 20% per cm of tissue, what is the x-ray intensity difference as measured by the detector in the AP and lateral positions?
xap
patient
xat
Solution: m = 0.20 cm-1
X-ray detector

26. Half Value Layer (HVL) 100 50 = 100/2 (a) (b) (c)
HVL or m is a function of BOTH the
x-ray (E) and the matter (Z, r).
T1/2 is a function of radionucleus only.
50 = 100/2

27. Narrow-beam and broad-beam HVL
which HVL is larger, broad-beam or narrow-beam?

28. Beam Hardening: HVL (x)
Polyenergetic x-ray beam
Beam Hardening: HVL (x)
Beam hardening - mean energy of a poly energetic x-ray beam increases as it travels through the irradiated material.
Reason - lower energy x-rays have larger m than higher energy x-rays and thus attenuate quicker.
HVL(x1) < HVL (x2) when x1 < x2 (for polyenergetic x-ray beams)

29. Review of interactions
Particles (electrons) EM
Collisional
Ionization, heat
Radiative
X-rays (characteristic, Bremsstrahlung)
Rayleigh scatter
Change direction, no energy loss
Compton scatter
Change direction, energy loss
Photoelectric
Absorption, photoelectron released
Pair production
Absorption, electron-positron pair released