Medical Imaging

1
Medical Imaging

• Dr. Hugh Blanton
• ENTC 4390

2
Quantum Mechanics

• Physics of the very very small
• Modification of Newtons laws
• Revolution in physics 1900-1930

3
Plancks Model

• Energy of molecules is quantized En nhf
• n quantum no.
• h 6.63 x 10?34 J?s
• Emit photons in jumping between states
• Not even believed to be real by Planck!

4
X-rays

• How does an x-ray machine work?
• We first accelerate electrons with a high voltage
  (several thousand volts).
• We then allow the high speed electrons to smash
  into a target.
• As the electrons slow down on collision, they can
  emit photons - via
• photoelectric effect or
• Compton scattering.

5

• An electron gun inside the tube shoots high
  energy electrons at a target made of heavy atoms,
  such as tungsten.

6
X-rays

• However, the maximum energy of the electrons
  limits the maximum energy of any photon emitted.
  
• In general glancing collisions will give less
  than the full energy to any photons created.
• This gives rise to the continuous spectrum for
  x-ray production.

7
X-rays

• If an electron knocks out an inner shell
  electron, then the atom will refill that missing
  electron via normal falling of electrons to lower
  levels.
• This provides a characteristic emission of
  photons, and depends on the target material.
• For the inner most shell, we can use a formula
  similar to the Bohr atom formula

8
X-rays

• For the inner most shell, we can use a formula
  similar to the Bohr atom formula
• ?ionization 13.6 eV (Z-1)2
• where the -1 comes from the other inner shell
  electron.

9
X-rays

• If the electrons have this ionization energy,
  then they can knock out this inner electron, and
  we can see the characteristic spectrum for this
  target material.
• For iron, the ionization energy is
• 13.6 eV (26-1)2 1e 8500 volts.

10
X and ? ray penetration

• High energy photons interact with material in
  three ways
• the photoelectric effect (which dominates at low
  energies),
• Compton scattering, and
• pair production (which dominates at high
  energies).

11
X-ray Production Electron Excitation
Ejected electron
12
X-ray Production Photon Excitation
Ejected electron
13
X-ray Production - Line Spectra

• Transition Process for K Line Spectra

E Initial
X-ray emission E X-ray E Initial - E K
Ejected K shell Electron
E K
Vacant state
14
X-ray Line Spectra

• Starting from the K shell the binding energy
  decreases (ie binding energy KgtLgtMgtN).
• Each shell is defined by a set of quantum numbers
  (n,l and m). Selection rules determine the
  values that these quantum numbers may have and
  this in turn determines the shape of the
  electronic orbitals and the number of electrons
  that may occupy each orbital

15
X-ray Line Spectra

• K radiation - occurs when a vacancy is formed in
  the K shell of an atom. All the transitions
  correspond to electrons dropping into the K shell
  (n1) from higher quantum states (n2, 3, ).
• L radiation - occurs when a vacancy is formed in
  the L shell of an atom. X-rays are produced from
  transitions of electrons from n3,4,. to the L
  shell (n2).
• M radiation - occurs when a vacancy is formed in
  the M shell (n3) and arises from electronic
  transitions from n4, 5, down to n3.

16
X-ray Line Spectra
Ka2 Ka1 Kb3 Kb1 Kb2 Kb5
K Series Transitions in X-ray Targets
K
I
L
II
III
Selection Rules for X-ray Transitions change in n
any value change in l 1 change in m -1,
0, 1
I
II
M
III
IV
V
I
N
V
VII
17
X and ? ray penetration

• But whether one photon interacts with one atom is
  a probablistic event.
• I Io e-?x
• where ? depends on the material the x-ray is
  going through.

18
X and ? ray penetration

• ?
• 1 MeV Energy

pair production
total
Compton Scattering
photoelectric effect
19
Measuring Health Effects

• Gamma rays (high energy photons) are very
  penetrating, and so generally spread out their
  ionizations (damage).
• Beta rays (high speed electrons) are less
  penetrating, and so their ionizations are more
  concentrated.
• Alphas (high speed helium nuclei) do not
  penetrate very far since their two positive
  charges interact strongly with the electrons of
  the atoms in the material through which they go.

20
Bremsstrahlung

• When the electrons strike the dense metal target,
  strong Coulomb forces are created between the
  negative electron particles and the strongly
  positive nuclei of the metal.
• This interaction causes the electron to slow down
  (brake), or change directions, very quickly.
  Thus, bremsstrahlung.

21

• Bremsstrahlung is easier to understand using the
  classical idea that radiation is emitted when the
  velocity of the electron shot at the tungsten
  changes.
• The electron slows down after swinging around the
  nucleus of a tungsten atom and loses energy by
  radiating x-rays.

22

• Due to the conservation of energy principle, this
  loss of kinetic energy has to be compensated for
  and is done so by the production of a photon of
  electromagnetic energy.
• We call this photon an X-ray.

23

• X-rays are just like any other kind of
  electromagnetic radiation.
• They can be produced in parcels of energy called
  photons, just like light.

24

• There are two different atomic processes that can
  produce x-ray photons.
• One is called Bremsstrahlung, which is a fancy
  German name meaning "braking radiation."
• The other is called K-shell emission.
• They can both occur in heavy atoms like tungsten.
  

25

• In the quantum picture, a lot of photons of
  different wavelengths are produced, but none of
  the photons has more energy than the electron had
  to begin with.
• After emitting the spectrum of x-ray radiation
  the original electron is slowed down or stopped.

26

• The K-shell is the lowest energy state of an
  atom.
• The incoming electron from the electron gun can
  give a K-shell electron in a tungsten target atom
  enough energy to knock it out of its energy
  state.
• Then, a tungsten electron of higher energy (from
  an outer shell) can fall into the K-shell.
• The energy lost by the falling electron shows up
  in an emitted x-ray photon.
• Meanwhile, higher energy electrons fall into the
  vacated energy state in the outer shell, and so
  on.
• K-shell emission produces higher-intensity x-rays
  than Bremsstrahlung, and the x-ray photon comes
  out at a single wavelength.

27

• The energy lost by the falling electron shows up
  in an emitted x-ray photon.
• Meanwhile, higher energy electrons fall into the
  vacated energy state in the outer shell, and so
  on.
• K-shell emission produces higher-intensity x-rays
  than Bremsstrahlung, and the x-ray photon comes
  out at a single wavelength.

28
Photoelectric Effect

• Shine light on a surface and electrons are
  emitted.

29
Experimental Observations

• No electrons emitted if f lt fc, which depends on
  the type of metal
• Kmax independent of light intensity
• Kmax increases as f increases
• First e? emitted almost instantaneously

30
Einsteins Model

• Light consists of photons

31
Einsteins Model

• Each photon gives its entire energy to a single
  electron

• It loses a fixed energy (the work function)
  escaping the surface.

32
Einsteins Model

• The electron loses some of its energy getting to
  the surface

33
Einsteins Model

• No electrons emitted if f lt fc, which depends on
  the type of metal
• If hf lt ?, no electron will have enough energy to
  escape the surface
• Electrons will share their kinetic energy with
  the metal and warm it up
• fc ?/h

34
Einsteins Model

• Kmax independent of light intensity
• More intensity means more photons
• Each photon still has the same energy
• Therefore, Kmax does not change

35
Einsteins Model

• Kmax increases as f increases
• As f increases, the energy hf of each photon
  increases
• Therefore, each photon gives more energy to each
  electron

36
Einsteins Model

• First electron emitted almost instantaneously
• Any photon can cause an electron to be emitted,
  even the first photon
• There are lots of photons, even in a weak beam.

37
AXAA - 2002

• Production of X-rays

38
Nature of X-rays

• X-rays are electromagnetic radiation that have
  wavelengths in the approximate range 0.1 Å to 50
  Å and corresponding energies in the range 120 to
  0.25 KeV.
• Units of X-ray wavelength is Angstroms (Å )
• 1 Å 10-10m
• Units of X-ray energy are electron volts (eV)

39
Nature of X-rays

• The relationship between energy (E) and
  wavelength (?) is
• E hc ... (1)
• ?
• where
• h Plancks constant 6.626 x 10-34
  joules.sec-1
• c velocity of light in a vacuum 2.998 x 108
  m.sec-1

40
Nature of X-rays

• Substituting for h and c, and expressing E in keV
  (kilo electron volts) and ? in Å equation (1)
  simplifies to
• E 12.396 .. (2)
• ?
• Thus X-rays may be described either in terms of
  their energy or wavelength.

41
X-ray Production

• How are X-rays produced?
• X-rays may be produced when a beam of electrons
  or X-ray photons of sufficient energy interact
  with matter.

42
Electron Excitation

• When electrons impinge on a target a number of
  possible processes can occur
• backscattering from the target. For high atomic
  number elements (eg W) this accounts for
  approximately half the incident electrons.
• collisions with weakly bound valence or
  conduction band electrons. Many of these
  electrons are ejected from the target with
  energies of lt 50eV and are termed secondary
  electrons. Most electrons not backscattered
  undergo this process.

43
X-ray Production Electron Excitation

• Ejection of an inner electron from the target
  atom. In one of two competing processes, the
  resulting excited atom may return to its ground
  state by emitting an X-ray photon. This process
  gives rise to the characteristic line spectrum.
• Inelastic Rutherford scattering, in which the
  electrons experience a rapid loss of energy and
  an X-ray photon is emitted. This process
  generates a continuous spectrum and involves lt 1
  of the incident electrons. The continuous
  spectrum is also referred to as Bremsstrahlung.

44
X-ray Spectra Continuum Electron Excitation
Kb
Ka
l min, Emax
Wavelength --gt
45
X-ray Spectra Continuum Electron Excitation

• Continuous Spectrum characteristics
• short wavelength ?min / high energy Emax limit
  corresponding to V.
• intensity maximum in the region ? 1.5 ? min
• total integrated intensity is proportional to V2
• where V is the voltage across which the
  electrons are accelerated (for XRF/XRD - the tube
  voltage)

46
Line Spectra Electron or Photon Excitation
Kb
Ka
l min, Emax
Wavelength --gt
47
Line Spectra Electron or Photon Excitation

• Characteristic or line spectra are produced when
  incident electrons or X-ray photons have
  sufficient energy to remove electrons from the
  inner shell of an atom. The X-ray photons that
  result when outer electrons fall into the vacancy
  have an energy that is characteristic of a
  particular element.

48
X-ray Production - Line Spectra

• For low atomic number elements only K radiation
  is generated.
• L and M radiation is only generated from higher
  atomic number elements.
• Generally the higher the atomic number the higher
  the energy of the X-ray.
• For a given element EK gt EL gt EM
• The number of possible X-ray emission lines
  increases with increasing atomic number (Z).

49
X-ray Line Spectra

• Ka Radiation La Radiation
• Element Z E(KeV) l(Å) E(KeV) l(Å)
• C 6 0.28 44.7
• Mg 12 1.25 9.89
• Cr 24 5.41 2.29 0.57
  21.60
• Mo 42 17.44 0.71 2.29
  5.41
• Hf 72 55.40 0.22 7.87
  1.57

50
X-ray Line Spectra

• Satellite Lines
• Both the Ka and Kb spectra contain additional
  weak lines known as satellites. They occur in
  the high energy tail of the Ka line and on the
  high and low energy sides of the Kb1,3 line.
• They have intensities of 1 to 5 of the
  principal emission line. Intensity increases with
  decreasing atomic number (Z).

51
X-ray Line Spectra

• Satellite lines arise from doubly ionised atoms
  caused by a single incoming electron or photon.
  When vacancies are created in both the K and one
  of the L sub-shells, all the energy levels are
  shifted and additional splitting of the energy
  levels occurs. Under these conditions six
  possible transitions can occur that are
  equivalent to the Ka1 transition in a singly
  ionised atom.

52
X-ray Intensity

• X-ray intensity is related to the probability
  that the interaction of an incident electron or
  photon with a material will result in the
  emission of an X-ray.

53
The Auger Effect (Electron or Photon Excitation)

• When a vacancy is created in the K or L shell,
  the atom can revert to its ground state in one of
  two ways
• emission of an X-ray photon.
• through a series of radiationless transitions in
  which the excess energy of the exited atom is
  disposed of by releasing an electron from its
  outer shell. The is known as the Auger effect.

54
Fluorescent Yield

• The fluorescent yield represents the probability
  that an ionised atom will emit an X-ray photon
  when a particular shell is ionised.
• The Auger process becomes more dominant as Z
  decreases and hence the fluorescent yield for
  light elements is low.
• The fluorescent yield for the L shell is low.

55
Fluorescent Yield
Element wK wL O 0.003 K 0.118
Cu 0.425 0.006 Mo 0.749 0.039
Sm 0.915 0.180 U 0.960 0.478
56
Relative Intensities of Characteristic Lines

• Calculation of the relative intensities of X-ray
  lines within a given series is a very complex
  task.
• It is virtually impossible to calculate relative
  intensities across series.
• For the K series the line intensities relative to
  the Ka1 line approximate
• Ka2/Ka1 0.5
• Kb1,3/Ka1 0.2
• Kb2,5/Ka1 0.002

57
X-ray Intensity Electron Excitation

• When a high energy electron is incident on a
  target, the probability of ionising atoms by
  knocking out a K shell electron changes with the
  kinetic energy of the incident electron.
• Even though electrons with kinetic energy EK
  (the shell ionisation energy) are capable of
  ionising an atom, very few collisions result in
  any ionisation or X-ray production.
• For most target materials, emitted X-ray
  intensity reaches a peak when the incident
  elections have a kinetic energy of between 3 and
  4 times EK

58
X-ray Tube Intensity
6
X-ray Output
3
2
4
6
Ratio of Electron Energy to Ionisation Energy
59
X-ray Scattering

• When an X-ray beam interacts with matter two
  scattering phenomena can occur
• Rayleigh or Coherent scattering
• Compton or Incoherent scattering
• These scattering processes give rise to spectral
  lines associated with the X-ray source.
• Commonly called Tube lines in the case of XRF.

60
X-ray Scattering - Rayleigh

• Rayleigh scattering occurs when an incident X-ray
  photon interacts with the electrons of an atom
  and is re-emitted without change of energy.
• The Rayleigh scattered tube characteristic lines
  give rise to prominent tube lines in the X-ray
  spectrum of the sample.
• The Rayleigh scattered tube continuum contributes
  to the background.
• Rayleigh scatter intensity increases with
  increasing atomic number of the scattering
  material.

61
X-ray Scattering - Compton

• Compton scattering occurs when an incident X-ray
  photon interacts with the electrons of an atom
  resulting in some loss of energy from the
  incident photon and the ejection of an outer
  shell electron.

Compton Photon E lt Eo
Incident Photon Eo
Mg
Compton Recoil Electron
62
X-ray Scattering - Compton

• The tube characteristic lines give rise to
  Compton tube lines in the X-ray spectrum of the
  sample that occur about 0.024Å longer in
  wavelength than the characteristic lines.
• Compton scatter intensity increases with
• Decreasing atomic number of the scattering
  material.
• Increasing incident X-ray photon energy.
• Rayleigh predominates at low incident X-ray
  energy.
• Compton predominates at high incident X-ray
  energy.

63

• In the same way that x-rays are deflected in the
  target crystal, they are deflected by atoms in
  our body.
• When radiation strikes an atom it has the ability
  to knock electrons out of the orbiting shells.
• Once these atoms are ionized, they seek out other
  atomic particles or ions to make themselves more
  stable.