1 / 63

Medical Imaging

Medical Imaging. Dr. Hugh Blanton ENTC 4390. Quantum Mechanics. Physics of the very very small Modification of Newton’s laws Revolution in physics 1900-1930. Planck’s Model. Energy of molecules is quantized E n = nhf n = quantum no. h = 6.63 x 10  34 J s

devon
Download Presentation

Medical Imaging

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Medical Imaging Dr. Hugh Blanton ENTC 4390

  2. Quantum Mechanics • Physics of the very very small • Modification of Newton’s laws • Revolution in physics 1900-1930 Dr. Blanton - ENTC 4307 - X-Ray 2

  3. Planck’s 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! Dr. Blanton - ENTC 4307 - X-Ray 3

  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. Dr. Blanton - ENTC 4307 - X-Ray 4

  5. An electron gun inside the tube shoots high energy electrons at a target made of heavy atoms, such as tungsten. Dr. Blanton - ENTC 4307 - X-Ray 5

  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. Dr. Blanton - ENTC 4307 - X-Ray 6

  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: Dr. Blanton - ENTC 4307 - X-Ray 7

  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. Dr. Blanton - ENTC 4307 - X-Ray 8

  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. • Foriron, the ionization energy is: 13.6 eV * (26-1)2 = 1e * 8500 volts. Dr. Blanton - ENTC 4307 - X-Ray 9

  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). Dr. Blanton - ENTC 4307 - X-Ray 10

  11. X-ray Production – Electron Excitation Ejected electron Dr. Blanton - ENTC 4307 - X-Ray 11

  12. X-ray Production – Photon Excitation Ejected electron Dr. Blanton - ENTC 4307 - X-Ray 12

  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 Dr. Blanton - ENTC 4307 - X-Ray 13

  14. X-ray Line Spectra • Starting from the K shell the binding energy decreases (ie binding energy K>L>M>N). • 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 Dr. Blanton - ENTC 4307 - X-Ray 14

  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 (n=1) from higher quantum states (n=2, 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 n=3,4,…. to the L shell (n=2). • M radiation - occurs when a vacancy is formed in the M shell (n=3) and arises from electronic transitions from n=4, 5, … down to n=3. Dr. Blanton - ENTC 4307 - X-Ray 15

  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 Dr. Blanton - ENTC 4307 - X-Ray 16

  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. Dr. Blanton - ENTC 4307 - X-Ray 17

  18. X and  ray penetration  1 MeV Energy pair production total Compton Scattering photoelectric effect Dr. Blanton - ENTC 4307 - X-Ray 18

  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. Dr. Blanton - ENTC 4307 - X-Ray 19

  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. Dr. Blanton - ENTC 4307 - X-Ray 20

  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. Dr. Blanton - ENTC 4307 - X-Ray 21

  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. Dr. Blanton - ENTC 4307 - X-Ray 22

  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. Dr. Blanton - ENTC 4307 - X-Ray 23

  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. Dr. Blanton - ENTC 4307 - X-Ray 24

  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. Dr. Blanton - ENTC 4307 - X-Ray 25

  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. Dr. Blanton - ENTC 4307 - X-Ray 26

  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. Dr. Blanton - ENTC 4307 - X-Ray 27

  28. Photoelectric Effect • Shine light on a surface and electrons are emitted. Dr. Blanton - ENTC 4307 - X-Ray 28

  29. Experimental Observations • No electrons emitted if f < fc, which depends on the type of metal • Kmax independent of light intensity • Kmax increases as f increases • First e emitted almost instantaneously Dr. Blanton - ENTC 4307 - X-Ray 29

  30. Einstein’s Model • Light consists of photons Dr. Blanton - ENTC 4307 - X-Ray 30

  31. e e Einstein’s Model • Each photon gives its entire energy to a single electron • It loses a fixed energy (the work function) escaping the surface. Dr. Blanton - ENTC 4307 - X-Ray 31

  32. e e e Einstein’s Model The electron loses some of its energy getting to the surface Dr. Blanton - ENTC 4307 - X-Ray 32

  33. Einstein’s Model • No electrons emitted if f < fc, which depends on the type of metal • If hf < , 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 Dr. Blanton - ENTC 4307 - X-Ray 33

  34. Einstein’s Model • Kmax independent of light intensity • More intensity means more photons • Each photon still has the same energy • Therefore, Kmax does not change Dr. Blanton - ENTC 4307 - X-Ray 34

  35. Einstein’s 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 Dr. Blanton - ENTC 4307 - X-Ray 35

  36. Einstein’s 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. Dr. Blanton - ENTC 4307 - X-Ray 36

  37. AXAA - 2002 Production of X-rays Dr. Blanton - ENTC 4307 - X-Ray 37

  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) Dr. Blanton - ENTC 4307 - X-Ray 38

  39. Nature of X-rays • The relationship between energy (E) and wavelength () is: E = hc ………...……… (1)  where: h = Planck’s constant = 6.626 x 10-34 joules.sec-1 c = velocity of light in a vacuum = 2.998 x 108 m.sec-1 Dr. Blanton - ENTC 4307 - X-Ray 39

  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. Dr. Blanton - ENTC 4307 - X-Ray 40

  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. Dr. Blanton - ENTC 4307 - X-Ray 41

  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 < 50eV and are termed secondary electrons. Most electrons not backscattered undergo this process. Dr. Blanton - ENTC 4307 - X-Ray 42

  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 < 1% of the incident electrons. The continuous spectrum is also referred to as Bremsstrahlung. Dr. Blanton - ENTC 4307 - X-Ray 43

  44. X-ray Spectra Continuum – Electron Excitation Kb Ka l min, Emax Wavelength --> Dr. Blanton - ENTC 4307 - X-Ray 44

  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 tubevoltage) Dr. Blanton - ENTC 4307 - X-Ray 45

  46. Line Spectra – Electron or Photon Excitation Kb Ka l min, Emax Wavelength --> Dr. Blanton - ENTC 4307 - X-Ray 46

  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. Dr. Blanton - ENTC 4307 - X-Ray 47

  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 > EL > EM • The number of possible X-ray emission lines increases with increasing atomic number (Z). Dr. Blanton - ENTC 4307 - X-Ray 48

  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 Dr. Blanton - ENTC 4307 - X-Ray 49

  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”). Dr. Blanton - ENTC 4307 - X-Ray 50

More Related