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Medical Imaging
Radiation I
Naked to the Bone: Medical Imaging in the Twentieth Century (Paperback)by Bettyann Kevles
E=mc2: A Biography of the World’s Most Famous Equation by David Bodanis
More suggested reading:
Energy that travels through space and matter
We are interested in electromagnetic radiation: X-ray waves Visible waves Radio waves Gamma-rays (...)
Radiation is:
€
φ x, t( ) = φo cos ωt − kx( )
Monochromatic radiation, electric and magnetic field
can be represented as:
This is the solution of the one dimensional wave equation
€
∂2φ
∂ 2x=
1
c 2
∂ 2φ
∂ 2t
Electromagnetic wave
The electromagnetic wave:
ADD steve EM wave
f = 1 / T
Period
Wavelength
The electromagnetic wave:
red=300nmblue=900nm
The electromagnetic wave:
Wavelength [m]
Frequency [Hz]
Energy [ev]
EM radiation
€
E = h × f [eV ]
€
h = 4.1333e -15
eV ⋅sec[ ]
Plank's constant
Electron volt [eV]: is the kinetic energy gained when a single electron is accelerated between two plates that differ in potential by 1V. Before leaving the negatively charged plate, the electron has potential energy of 1eV.
Energy eV
+-
---
+++
1eV=1.6x10-19 J1Joule [J]=1kg m2 s-2
Wavelength [m]
Frequency [Hz]
Energy [eV]
EM radiation
€
f =c
λ
1
sec
⎡ ⎣ ⎢
⎤ ⎦ ⎥
€
c = 3⋅108 m
sec
⎡ ⎣ ⎢
⎤ ⎦ ⎥
Speed of lightin vacuum
Wavelength [m]
Frequency [Hz]
Energy [ev]
EM radiation
€
E =hc
λ eV[ ]
€
h = 4.1333e -15 eV ⋅sec[ ]
c = 3⋅108 m
sec
⎡ ⎣ ⎢
⎤ ⎦ ⎥
Why is knowing the wavelength important?
EM spectrum
Wavelength[m]
Wavelength and size of an object!
Is object large or small compared to the wavelength?
0 0.5 1 1.5 2 2.5 3x 1022
10-15
10-10
10-5
100
105
1010
frequency [Hz]
wavelength [nm]Energy [keV]
€
E = h ⋅ f
eV ⋅sec[ ] sec−1[ ]
€
h = 4.1333e -15
eV ⋅sec[ ]
Frequency,Energy, Wavelength are related
E
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1000010-10
10-5
100
105
1010
1015
1020
1025
wavelength [m]
frequency [Hz]Energy [keV]
Frequency,Energy, Wavelength are related
E
f
€
E =hc
λ eV[ ]
€
f =c
λ
1
sec
⎡ ⎣ ⎢
⎤ ⎦ ⎥
The photon The smallest amount of EM radiation
possible, fundamental particle Has no rest mass Move at speed of light c, (c/n in media) Travel in straight line (bends at interfaces)
€
E =hc
λ eV[ ]
€
E = h ⋅ f
eV ⋅sec[ ] sec−1[ ]
€
f =c
λ
1
sec
⎡ ⎣ ⎢
⎤ ⎦ ⎥
The atom
2e-8e-
18e-
K L M N O P
32e-
50e-72e-
Bohr model
Electron
Nucleus
Orbitals
98e-
Binding Energy (BE) Energy binding electron to atom A photon will need an energy > than
binding energy to remove an electron from a atom
Nomenclature - binding energies are negative (eV)
Ionization Energy = - BE, energy necessary to remove 1 electron from the atom.
Binding Energy
Stronger bound (KeV)
Less strong bound
Weak bound (eV)
Valence electrons, # of electrons in outer orbital, determines chemicalproperties of atom
The atom
2e-8e-
18e-
K L M
Z-Atomic Number, # of protonsN-Neutron number, # of neutronsMass Number, Am = Z + N
Na22
11
Atomic Mass, actual mass ofthe atom
Protons
Neutrons
Oxygen-16Atomic Mass -> 15.9949 amuMass Number ->16
Excitation
AbsorptionE = E3-E2
Photon
Electrons want tobe as close as possibleto the nucleus
BREAK !!
Relaxation Emission E = E2-E1
Photon
Vacancy
-Visible-IR-X-Ray
DEPENDS ONATOMIC NUMBERI.E BE
emission shorter or longer ??
Radiation II Ch. 3 of, The essential physics of
medical imaging, Bushberg et al. We focus on X-rays and Gamma-rays
production and interaction with matter
X-Rays (-Rays) interactions
Scattering and Absorption Absorption - All energy of incident
photon is absorbed by a material, the photon is destroyed
Scattering - Photon path is altered by a “scattering event”, loss of energy can occur (inelastic scattering) or not (elastic scattering)
Transmission - No interaction
Absorption
Photon detector
Scattering
Photon detector
Transmission
Photon detector
X-rays, -rays interactions
Rayleigh scattering (coherent) Compton Scattering Photoelectric effect Pair production
Rayleigh scattering Photon excites the ALL ATOM Low energy X-rays (15-30 keV) Photon energy makes all electrons
oscillate in phase A photon is emitted in a different
direction NON IONIZING It’s noise in X-ray imaging 12% of photons <30 keV 5% of photons >70 keV
Rayleigh scattering
Incident photon
Scattered photon
What is important to note here
Rayleigh scattering Polarized radiation
Isotropic radiation
Compton scattering Inelastic scattering Dominates X-Rays scattering from
26keV to 30MeV in soft tissue Photon interact with valence electrons Electron is ejected from shell
generating an ion Compton scattering is noise in X-Rays
imaging Safety hazard!
Compton scattering
Incident photon
Compton scattering
Incident photon
Compton electron
Scattered photon
sc
Esc=Eo-Ee-
Esc
Ee-
Eo
€
E sc =Eo
1+Eo
511keV(1− cos(θ))
Compton scattering
Higher Eo generate more forward scattering photons (smaller )
=mec2=511keV
Compton scattering
Forwardscattering
Backscattering
Photoelectric effect All incident photon energy is absorbed Often interaction between photon and
electrons in K shell An electron in the K shell is ejected Ee-=Eo-Eb
Lower binding energy electron fills the empty orbital - electron cascade
Emitted energy can be Auger or X-Rays
Photoelectric effect
Incident photon
Photoelectric effect
Incident photon
Photoelectric effect
Incident photon
Photoelectric effect
Incident photon
X-rays
Photoelectric effect
Incident photon
Auger Electron
Photoelectric effect
Incident photon
Auger Electron
Photoelectric effect
Incident photon
Auger Electron
X-rays
Photoelectric absorption
€
τ ∝ Z 3
Eo3
Photoelectric cross section
likelihood of p.e. absorption to occur
Atomic Number
Photon energy
Photoelectric effectPhotoelectric absorption process is most likely for
Eo IK, L, M,... (resonance)
Photoelectric absorption cross section decreases strongly with photon energy ( Ep
-3) as photon energy increases relative to IK, L, M,...
Photoelectric absorption cross section increases strongly with Z (~ Z3) because I Z
Photoelectric absorption in K shell usually dominates
Photoelectric effect
Absorption edge
33.3keV is 6 times most likely to have photoelectric interaction than 33.1keV in iodine atom
40 60 80 x103
K edge
Pair production & photodisintegration Require high energy photons >1MeV Interaction with nuclei Pair production photon is absorbed by
nucleus the energy is converted into an electron and positronElectron (511keV) positron (511keV)Pair production threshold 1.02MeV
Photodisintegration, photon absorbed by nucleus, nucleons are ejected by nucleus
/ [
cm2 /
g]
Z = 6 Z = 53 Z = 82
Legend:τ: Photoelectric absorption: Compton scatter: Pair productionr: Raleigh scatter
X-Rays generation
White radiation, Bremsstrahlung
X-Ray
Coulombic interaction
-Inelastic interaction with nuclei-Loss of kinetic energy-Xray (E) = lost kinetic E
-High kinetic energy-Forward radiation
-Emission Z2
(Atomic number)# of protons
(Brake)
electron
White radiation, Bremsstrahlung
X-Ray
a
-Smaller a produce larger X-ray-Broad range of wavelengths