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:

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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

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E = h × f [eV ]

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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

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f =c

λ

1

sec

⎡ ⎣ ⎢

⎤ ⎦ ⎥

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c = 3⋅108 m

sec

⎡ ⎣ ⎢

⎤ ⎦ ⎥

Speed of lightin vacuum

Wavelength [m]

Frequency [Hz]

Energy [ev]

EM radiation

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E =hc

λ eV[ ]

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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]

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E = h ⋅ f

eV ⋅sec[ ] sec−1[ ]

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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

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E =hc

λ eV[ ]

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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)

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E =hc

λ eV[ ]

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E = h ⋅ f

eV ⋅sec[ ] sec−1[ ]

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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

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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