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```Medical Imaging


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


Energy that travels through space
and matter
We are interested in electromagnetic





X-ray waves
Visible waves
Gamma-rays
(...)
Electromagnetic wave
Monochromatic radiation, electric and magnetic field
can be represented as:
 x,t   o cost  kx
This is the solution of the one dimensional wave
equation

 2 1  2
 2 2
2
 x c  t
The electromagnetic wave:
The electromagnetic wave:
Period
f=1/T
Wavelength
The electromagnetic wave:
red=300nm
blue=900nm

Wavelength [m]

Frequency [Hz]
E  h  f [eV]

Energy [ev]

h  4.1333e -15
eV  sec
Plank' s constant
Energy eV

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.
-
-
+
+
+
+
1eV=1.6x10-19 J
1Joule [J]=1kg m2 s-2


Wavelength [m]
c  1 
f   
 sec 
Frequency [Hz]


Energy [eV]
 m 
c  310  
sec 
8
Speed of light
in vacuum



Wavelength [m]
Frequency [Hz]
Energy [ev]

E
hc

eV 
h  4.1333e -15 eV  sec
 m 
c  310  
sec 
8
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?
Frequency,Energy,
Wavelength are related
10
10
wavelength [nm]
Energy [keV]
105
10
E
0
E  h f

10
-5
10
-10
10-15
0
1
eV

sec
sec

 
h  4.1333e -15
0.5
1
1.5
frequency [Hz]
2
2.5
3
x 10

22
eV  sec
Frequency,Energy,
Wavelength are related
10
25
frequency [Hz]
Energy [keV]
10
20
10
15
10
10
10
5
10
0
10
-5
f
10-10
0
E
1000
2000
3000
4000
5000
6000
wavelength [m]
7000
E

8000
9000

10000
hc

eV 
c  1 
f   
 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

eV 
E  h f
eV  sec sec1

c  1 
f   
 sec 
The atom
50e-
72e-
98e-
32e-
Electron
2e-
8e-
18e-
K L
M
N
O
P
Orbitals
Nucleus
Bohr model
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 chemical
properties of atom
The atom
2e-
8e-
Z-Atomic Number, # of protons
N-Neutron number, # of neutrons
Mass Number, Am = Z + N
18e-
22
K L
M
Na
11
Atomic Mass, actual mass of
the atom
Protons
Neutrons
Oxygen-16
Atomic Mass -> 15.9949 amu
Mass Number ->16
Excitation
Photon
Absorption
E = E3-E2
Electrons want to
be as close as
possible
to the nucleus
BREAK !!
Relaxation
Emission
E = E2-E1
Photon
-Visible
-IR
-X-Ray
Vacancy
emission shorter or
longer ??
DEPENDS ON
ATOMIC NUMBER
I.E BE


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 (g-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, g-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
Scattered photon

Incident photon
What is
important to
note here
Rayleigh scattering

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
Compton
electron
Ee-
Esc=Eo-EeIncident photon
Eo
1
1<2
Eo>Esc
q
2
Scattered photon
Esc
Compton scattering
E sc 
Eo
Eo
1
(1 cos(q ))
511keV
a=mec2=511keV
Higher Eo generate more forward scattering photons (smaller q)
Compton scattering
Back
scattering
Forward
scattering
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
Emitted energy can be Auger or X-Rays
Photoelectric effect
Incident photon

Photoelectric effect
Incident photon

Photoelectric effect
2
Incident photon

Photoelectric effect
3
Incident photon

X-rays
<2 <3
Auger Electron
Photoelectric effect
2
Incident photon

Auger Electron
Photoelectric effect
2
Incident photon

Auger Electron
Photoelectric effect
2
X-rays
Incident photon

Photoelectric absorption
Atomic Number
3
Z
 3
Eo
Photoelectric
cross section
likelihood of p.e.
absorption to
occur

Photon energy
Photoelectric effect
Photoelectric 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
K edge
40
60
80
x103
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 positron
Electron (511keV) positron (511keV)
Pair production threshold 1.02MeV
Photodisintegration, photon absorbed
by nucleus, nucleons are ejected by
nucleus
m/r [cm2/g]
Z=6
Legend:
: Photoelectric absorption
s: Compton scatter
p: Pair production
sr: Raleigh scatter
Z = 53
Z = 82
X-Rays generation
(Brake)
-Inelastic interaction with nuclei
-Loss of kinetic energy
-Xray (E) = lost kinetic E
electron
Coulombic interaction
X-Ray
-High kinetic energy