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Biomedical Imaging I

Biomedical Imaging I. Class 1 – X-Ray Imaging I: Background and Physics 9/14/05. Background. Introduction. Aim of medical imaging: Creating images of internal structures (and functions) in a living (human) organism Preferably non (or minimally) destructive / noninvasive

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Biomedical Imaging I

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  1. Biomedical Imaging I Class 1 – X-Ray Imaging I: Background and Physics 9/14/05

  2. Background

  3. Introduction • Aim of medical imaging: • Creating images of internal structures (and functions) in a living (human) organism • Preferably non (or minimally) destructive / noninvasive • Diagnostic implications • Achieved by using the capability of various forms of energy to penetrate and interact with matter. • Historic starting point: W. K. Röntgen’s discovery of the X rays experimenting with a cathode ray tube and fluorescent screen/photographic film (1895, 1901 first Nobel award in physics).

  4. Discovery of x-rays Wilhelm Konrad Röntgen (1845-1923) (photographed in 1896) Physical Institute, University of Würzburg, Germany. X-ray history on the web: http://www.xray.hmc.psu.edu/rci/centennial.html

  5. Discovery of x-rays Wilhelm Konrad Röntgen (1845-1923) (photographed in 1896) Cover of Original Publication: "A New Kind of Rays"

  6. First x-ray images The famous radiograph made by Roentgen on 22 December 1895, and sent to physicist Franz Exner in Vienna. This is traditionally known as "the first X-ray picture" and "the radiograph of Mrs. Roentgen's hand. " Radiograph of the hand of Albert von Kolliker, made at the conclusion of Roentgen's lecture and demonstration at the Würzburg Physical-Medical Society on 23 January 1896.

  7. Early x-ray setup

  8. X-rays in clinical use Dr. Edwin Frost (1866-1935) is credited with making the first diagnostic radiograph in the U.S. at Dartmouth on 3 February 1896.

  9. X-rays in clinical use E. Haschek and 0. Lindenthal produce first contrast-enhanced radiograph of veins in hand (Vienna, January 1896).

  10. X-ray dangers Mihran Kassabian (1870-1910) meticulously noted and photographed his hands during progressive necroses and serial amputations.

  11. X-ray publications In May of 1897, Heber Robarts, M.D., of St. Louis, launched the American X-ray Journal.

  12. X-ray imaging background, foundations: (History) X-rays Atomic structure Important x-ray-matter interactions X-ray instrumentation / applications: Generation of x-ray Detection of x-ray Specific applications X-ray imaging principle

  13. Physical foundations

  14. Emission E = hn = E2 - E1 Excitation - - Absorption - Relaxation E = hn = E3 - E2 + n = 1 n = 2 n = 3 Atom and electronic transitions • Electrons (-) are organized in shells around nucleus (+) • Higher shell (greater shell radius) = higher electronic energy • Electronic transitions between shells require or release energy

  15. Valence electron K-shell (n=1, strongly bound) - - L-shell (n=2) - 22 Na - + - M-shell (n=3, weakly bound) + + + 11 - - + + ... + + + - - - - Complex Atoms • Number of protons Z: Atomic number (determines element) • Number of neutrons N: Neutron number • Number of protons + neutrons Am = Z + N: Mass number

  16. Continuum Zero N M L K E Energy scheme • Binding energy (BE): energy binding electron to atom • Ionization energy IK,L,…= - BE: amount of energy needed to remove electron from atom • BE counted in negative units of electron volts (eV) • At infinity, BE= 0. • Binding energy for 53I: -33.2 keV (K), -4.3 keV (L), -0.6 keV (M) • BE for valence electrons: ~ -10 eV (H: -13.6 eV)

  17. A hn n Wave vs. particle interpretation • X-ray as electromagnetic wave: • Frequency n = 1/T [s-1 = Hz] • Wavelength l [m] • Propagation at speed of light c = l n  inverse relationship of l and n • X-ray as particle (photon): • Stream of weightless, neutral particles moving at speed of light • Each photon carries energy: • Radiation intensity I [W/cm2]: • Ep=hn= hc/l

  18. Electromagnetic spectrum

  19. X-rays characteristics • EM radiation at wavelengths 0.1 – 100 keV (10 – 0.01 nm) • Diagnostic Range ~1-100 keV • Ionization energy for valence electrons < ~10 eV  X-rays is ionizing radiation (harmful)

  20. - 1V + Energy units • SI unit: 1 Joule [J] = 1 Nm = 1 kg m2 s-2 • Electron volt [eV]: The potential energy of one elementary charge gained/lost (e = 1.610-19 C) when crossing a potential difference of 1V:1 eV = 1.610-19 C 1 V = 1.610-19 [A s V] = 1.610-19 J • 100 keV = 105 1.610-19 J = 1.610-14 J = 16 fJ (… per photon)

  21. X-Ray Interaction with Matter

  22. Interaction Processes • Absorption: photon is destroyed and its entire energy is transferred to the target • Scattering: photon is deflected and might or might not transfer portion of its energy to the target (inelastic & elastic scattering, respectively) • Each interaction removes photon from beam path, thereby decreasing the beam intensity detector target beam path

  23. X-Rays in a Homogeneous Target Target I0 I I - dI Id 0 l x dx Consider the relative change in intensity dI across small distance dx: dI is proportional to: – I dx m = st rn:linear attenuation coefficient

  24. Exponential Law of Absorption • Integration over entire target length: • The exponential law of absorption:

  25. Linear attenuation coefficient • Linear attenuation coefficient m [cm-1] depends on photon energy and material  absorption spectra • Half value layer HVL = the thickness after which intensity is reduced to half of the initial value: • Mass-attenuation coefficient m /r [cm2/g]  independent of physical state of material

  26. Physical interaction processes • Relevant interaction processes and their individual coefficients: • Photoelectric absorption • Compton scattering •  linear absorption coefficient is the sum of individual absorption and scattering coefficients m = mpe + mcs • Coefficients m = mpe + mcs are proportional to the interaction probabilities (also: “cross-section” [t and s, respectively]) of each process. • Questions: • What are the mechanisms for the different interaction processes? • What do they depend on?

  27. Ke Ep = hn - - - - - - - - K M L - - - Continuum 0 IN IM IL IK E Photoelectric absorption • The photon knocks an electron out of one of the inner shells of a target atom. The electron is excited into the continuum; the photon is destroyed in the process. • Possible for a given shell only if photon energy Ep exceeds ionizing energy for the shell: • Kinetic energy of electron Keaccording to energy conservation: Ep IK, L, M,... Ke= Ep-IK, L, M,...

  28. Photoelectric absorption depends on: Z – The atomic number of the element E – The radiation (photon) energy Photoelectric absorption • Photoelectric absorption process is most likely – i.e. the cross section t is largest – for Ep 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

  29. y y E'p Ep  x x F Ee Compton scattering • The x-ray photon interacts with one of the weakly bound electrons of the atom. This electron can be considered free because Ex-ray 1-100 keV >> Ee,b few eV. • Inelastic scattering process:

  30. Compton cross-section s • Compton scattering cross-section decreases with photon energy • Compton scattering cross-section increases withelectron density re[electrons/cm3] • Weak dependence (increase) on Z  Compton scattering depends on: E – The radiation (photon) energy re – The electron density

  31. Compton scattering angular distribution • Likelihood of a photon to be scattered into a certain direction depends on photon energy Ep: • Low Ep high “backscatter” probability (~180) • High Ep high “forward scatter” probability (peaked distribution,~ 0) incidentphotons 0 180

  32. Cross section examples I s PE: Photoelectric absorptionsS: Compton scattersPR: Pair production (for E > 2MeV, not relevant for medical imaging)

  33. m /r[cm2/g] Z = 6 Z = 53 Z = 82 Cross section examples II Not discussed in detail in lecture: sr: Raleigh scatterptr: Triplett productionmtr: mass energy transfer coeff.ttr: photoelectric energy transfer coeff.men: mass energy absorption coeff. Legend: t: Photoelectric absorptions: Compton scatterp: Pair production

  34. Attenuation coefficient dependencies r Z3/4 Legend:t-6: photoelectric cross-sect. @ Z = 6(C)t-64: photoelectric cross-sect. @ Z = 64 (Gd)s-6: Compton cross-sect. @ Z = 6(C)s-64: Compton cross-sect. @ Z = 64 (Gd) t-20: photoelectric cross-sect. @ 20 keVt-60: photoelectric cross-sect. @ 60 keVs-20: Compton cross-sect. @ 20 keVs-60: Compton cross-sect. @ 60 keV

  35. Contribution of interactions Z (tissue) < 10 E (diagnostic x-ray) < 10…100 keV

  36. I x X-ray contrast • Soft tissue components: Z< 10 • Bone: 20Ca • Air filled spaces

  37. X-ray contrast examples

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