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

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

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

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

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 - 15 - 30keV) reduces imaging quality in x-ray imaging. E(keV) P(%) ~30 <12 >70 <5 P: probability

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.

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

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

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

q = 900 Compton scattering hu0 husc Ee- q f

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)

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;

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.

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

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)

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

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

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).

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

Total linear attenuation coefficient Soft Tissue

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.

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

Relative importance of each x-ray interaction in water

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

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

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

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

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)

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