Chap. 15 Radiation Imaging

Transcription

1 Chap. 15 Radiation Imaging

2 15.1 INTRODUCTION Modern Medical Imaging Devices Incorporating fundamental concepts in physical science and innovations in computer technology Nobel prize (physics) : 1895 Wilhelm Conrad Roentgen Nobel prize (physiology & medicine): 1979 Allan Macleod Cormack, Gogfrey Newbold Hounsfield Two types of Ionizing Radiations introduced into the body, thereby making the patient the source of radiation emissions externally produced radiation, which passes through the patient and is detected by radiation-sensitive devices behind the patient

3 15.2 EMISSION IMAGING SYSTEMS Nuclear medicine Emission scanning for the purpose of helping physicians for proper diagnosis 3 Components ; Radioactive tracers(or radiopharmaceuticals) Instrumentation devices Relationship relationship between the activity of the radioactive tracer and specific physiological processes

4 15.2 EMISSION IMAGING SYSTEMS Basic Concepts

5 15.2 EMISSION IMAGING SYSTEMS Basic Concepts X-ray : Roentgen 1895 Fluorescence, Phosphorescence : Henri Becquerel 1896 Radioactivity in uranium, radium 1898 : Marie Curie, Pierre Curie Atomic Model : Dalton, J.J Thompson, Ernest Rutherford 1911, Niels Bohr 1913

6 15.2 EMISSION IMAGING SYSTEMS Basic Concepts Three types of Radiation : Curies Radiation Characteristics Alpha particles, which are positively charged and identical to the nucleus of the helium atom Beta particles, which are negatively charged electrons; Gamma rays, which are pure electromagnetic radiation with zero mass and charge.

7 15.2 EMISSION IMAGING SYSTEMS Elementary Particles Atomic mass unit(amu) = arbitrary value of 12 assigned to carbon 12 Figure 15.1 Planetary view of atomic structures. The primary mass is the nucleus, which contains protons and neutrons. The nucleus, which has a net positive charge, is surrounded by smaller orbiting electrons. In stable atoms, the net charge of electrons in orbit is equal and opposite to that of the nucleus. The atom illustrated is helium.

8 15.2 EMISSION IMAGING SYSTEMS Elementary Particles isotope(from the Greek, meaning same place ) atoms whose nuclei have the same number of protons [same atomic number (Z)] and at the same time may have a different number of neutrons [ different atomic mass (A)] Three types of hydrogen : hydrogen( 1 H), deuterium( 2 H), and tritium( 3 H) nuclide : a particular combination of neutrons and protons (nucleon). isotopes are nuclides that have the same atomic number

9 15.2 EMISSION IMAGING SYSTEMS Elementary Particles Radioactive isotope All elements with an atomic number (Z) greater than 83, and/or atomic mass (A) greater than 209 are radioactive they decay spontaneously into other elements this decay causes the emission of active particles Unstable nuclide = radionuclide

10 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Quantum mechanical principles by Wolfgang Pauli 1925: 4 quantum numbers, no two electrons in an atom can have the same set of quantum numbers n is the principal quantum number (integer and scalar quantity); l is the angular momentum quantum number (integral values 0 ~ n-1, vector quantity); m1 is the magnetic quantum number (integral values ranging from -1 to 1); ms is the spin magnetic quantum number (+1/2 and -1/2).

11 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Transition of electron binding energy Emission of photon : characteristic X-ray Another orbital electron : Auger electron Fluorescent yield : probability for the yield of characteristic x-ray Arrangement of nucleus state Ground state : most stable state Metastable state : unstable state with relatively long lifetime before transforming into another state Excited state : so unstable that it has only a transient existence before transforming into another state

12 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Binding energy of nucleons Represented by E=mc 2 Example Problem 15.1 : the energy released by 1 amu

13 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Radionuclide eventually comes to a stable condition with the emission of ionizing radiation after a specific probability of life expectancy Two classifications : natural and artificial modes or phases of transformation : divided into six different categories: (1) (alpha) decay/emission, (2) - (negatron) decay, (3) + (positron) decay, (4) electron capture(ec), (5) isomeric transition (IT), and (6) fission

14 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Alpha() decay reducing Z by 2 and A by 4 (helium atom) Example Problem 15.2 & 15.3 radium radon

15 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Beta decay atomic number (Z) is increased by 1 Neutrino () the emitted electrons have kinetic energies less than this predicted value a third particle must be present 0 electric charge, resting mass smaller than the electron Weakly interaction with matter, difficult to detect

16 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Beta decay De-excitation : a second decay after major radioactive decay The photons emitted in such a de-excitation process are called gamma rays Most of the radionuclides undergoing - decay also emit rays, almost simultaneously Excited state

17 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Positron(+) decay: produces a different element by decreasing Z by 1, with A being the same a particle is produced that is identical to the electron except that is has a positive charge of +e also associated with -ray emission often annihilated as a result of a collision with an electron within one nanosecond to produce a pair of photons of 0.511MeV that move in opposite directions minimum transition energy of 1.022MeV is required for any positron decay.

18 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Electron Capture or K Capture An orbital electron, usually from the inner shell (K shell), may be captured by the nucleus (as if a proton captured an electron and converted itself to a neutron). produces a different element by decreasing Z by 1, with A being the same (similar to + decay). also causes a vacancy in the inner shell, which leads to the emission of a characteristic x-ray or Auger electron.

19 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Isomeric Transition and Internal Conversion Radionuclides at a metastable state emit only rays. The element remains the same with no change in A (isomeric transition) denoted by Am. ( 99 mtc decays to 99 Tc) there is a definite probability that instead of a photon coming out, the instead of a photon coming out, energy may be transferred to an inner orbital electron. (internal conversion)

20 15.2 EMISSION IMAGING SYSTEMS Atomic Structure and Emissions Nuclear Fission heavy nuclide may break up into two nuclides may happen spontaneously, but is more likely with the capture of a neutron The uranium fission products mostly range between atomic numbers 42 and 56. medically useful radionuclides are produced as fission products, such as Xenon 133, which may be extracted by appropriate radiochemical procedures.

21 15.2 EMISSION IMAGING SYSTEMS Radioactive Decay Radioactive decay the rate of the decay process remains constant this decay process is a random event. every atom in a radioactive element has the same probability of disintegrating The unit of activity is curie (Ci) SI unit of activity becquerel (Bq)

22 15.2 EMISSION IMAGING SYSTEMS Radioactive Decay Radioactive decay a number of atoms (N) of a radionuclide present at a time t, is the transformation constant. Transformation rate = -dn/dt (decay/decrease) - Figure 15.2 The rate of decay of the radioactive material is exponential. The natural logarithm (see insert) of this decay process is therefore a straight line.

23 15.2 EMISSION IMAGING SYSTEMS Measurement of Radiation: Units All radioactive substances decay and in the process emit various types of radiation (alpha, beta, and/or gamma) during decay process. Activity measurement techniques: (1) counting the number of disintegrations that occur per second in a radioactive material : the curie (Ci) (2) noting how effective this radiation is in producing atoms (ions) possessing a net positive or negative charge : the roentgen (R) (3) measuring the energy absorbed by matter from the radiation penetrating it : the radiation-absorbed dose (rad) while the curie defines a source, the roentgen and rad define the effect of the source on an object. (4) others the rem (roentgen equivalent man) specifies the biological effect of radiation. the gray (Gy) : radiation dose to tissue

24 15.2 EMISSION IMAGING SYSTEMS Measurement of Radiation: Units TABLE 15.2 Commonly Used Radionuclides in Nuclear Medicine

25 15.3 INSTRUMENTATION AND IMAGING DEVICES Techniques for radiation measurement: Photography : the blackening of film when it is exposed to a specific type of radiation such as x- rays Ionization: The passage of radiation through a volume of gas produces ion pairs. most effective in measuring alpha radiation and least effective in measuring gamma radiation. Luminescence : the fluorescent effect produced by ionizing radiation is the basis of the scintillation detector

26 15.3 INSTRUMENTATION AND IMAGING DEVICES Scintillation Detectors Figure 15.3 Basic scintillation detection system.

27 15.3 INSTRUMENTATION AND IMAGING DEVICES Scintillation Detectors Visible Light Photon 0 V 100 V 300 V 500 V 700 V Glass Tube Current Pulse 200 V 600 V Photocathode Dynode Anode Schematic of a photomultiplier tube coupled to a scintillator

28 15.3 INSTRUMENTATION AND IMAGING DEVICES The Gamma Camera Figure 15.4 Basic elements of a gamma curve.

29 15.3 INSTRUMENTATION AND IMAGING DEVICES The Gamma Camera Figure 15.5 (a) Multihole collimator used in conjunction with scintillation detector. Event x is represented at only one location in the crystal, whereas event y has multiple sites associated with its occurrence. (b) The pinhole collimator allows magnification and is used for viewing small organs at short range.

30 15.3 INSTRUMENTATION AND IMAGING DEVICES Positron Imaging Imaging Principles : The positrons emitted through transformation of a radionuclide can travel only a short distance in a tissue (a few millimeters), and then are annihilated. A pair of 511-keV photons that travel at 180 to one another is created. A pair of scintillation detectors can sense positron emission by measuring the two photons in coincidence. cyclotron-produced short-lived radiopharmaceuticals (mainly carbon 11, nitrogen 13, and fluorine 18) to provide structural as well as metabolic information.

31 15.3 INSTRUMENTATION AND IMAGING DEVICES Positron Imaging Schematic view of a detector block and ring of a PET scanner Schema of a PET acquisition process

32 15.4 RADIOGRAPHIC IMAGING SYSTEMS Basic Concepts X-ray Imaging System : externally produced radiation that passes through the patient and is detected by radiation-sensitive devices behind the patient. Diagnostic medical x-ray systems utilize externally generated x-rays with energies of kev. differential attenuation of x-rays to produce an image contrast (that is, the ability to differentiate between body parts such as fat and muscle). X-ray tube (cathode ray tube) collimator patient x-ray film, an image intensifier, or a set of x-ray detectors.

33 Attenuation di n Idx di / dx I I e 0 n I x n : atoms per unit volume of the material I : X-ray intensity at x I 0 : incident X-ray intensity :linear attenuation coefficient[np/cm or cm -1 ] Half-value layer : the propagation length required to the intensity of the original beam by ½ HVL = 0.693/ mass attenuation coefficient is independent of its physical state (ex, water, ice, water vapor), [cm 2 /g] MAC= /, where is mass density of the material

34 Attenuation Coefficient attenuation decreases as photon energy increases (X-ray as smaller particle) abrupt increase in attenuation at binding energy level of orbital electron (photoelectric effect) coh pho com s a coh pho com Z E 2 1 ZE 3 3 E e 1 Z : atomic number : density e : electron dencity

35 Linear Attenuation Coefficient N 0 N N = N 0 e -x x N N x x -(1+ 2) x N = N e 0

36 Attenuation Coefficient Calculation N 0 N 0 N N 1 N N 2 -(1+ 2) N 1 = N e 0 -(3+ 4) N 2 = N e 0 -(1+ 3) N 3 = N e 0 -(2+ 4) N 4 = N e 0 N 3 N 4 C 1 C 2 C 3 C 4 = C 1 = - C 2 = - C 3 = - C 4 = Ln N 1 / N 0 = 1+ 2 Ln N 2 / N 0 = 3+ 4 Ln N 3 / N 0 = 1+ 4 Ln N 4 / N 0 = 2+ 4

37 15.4 RADIOGRAPHIC IMAGING SYSTEMS Basic Concepts Figure 15.7 Sketch of a cross-sectional image available using computerized tomography. Each image is divided into discrete three-dimensional sections of tissue referred to as voxels (or volume elements). On the computer monitor, the slice is viewed in two dimensions as pixels, or picture elements, in this case mm. Figure 15.8 Sketch of a manner in which the absorption coefficient values for each picture element are obtained.

38 15.4 RADIOGRAPHIC IMAGING SYSTEMS Basic Concepts Linear attenuation coefficient : relative value to that of water K is arbitrary integer, usually 500 or 1000 CT Number = p K w w Figure 15.9 Hounsfield scale for absorption coefficients.

39 Figure 15.6 Overview of the three x-ray techniques used to obtain medical images (a) A conventional x-ray picture is made by having the x-rays diverge from a source, pass through the body, and then fall on a sheet of photographic film. (b) A tomogram is made by having the x-ray source move in one direction during the exposure and the film in the other direction. In the projected image, only one plane in the body remains stationary with respect to the moving film. In the picture, all other planes in the body are blurred. (c) In computerized tomography, a reconstruction from projections is made by mounting the x-ray source and an x- ray detector on a yoke and moving them past the body. The yoke is also rotated through a series of angles around the body. Data recorded by the detector are processed by a special computer algorithm or program. The computer generates a picture on a cathode-ray screen.

40 Computerized Tomography 1917: J. Radon, Mathematical basis 1963: A. Cormack(Tuffs Univ.), Popularizing the idea 1972: G.N. Hounsfield(EMI), built practical scanner Allan M. Cormack USA Tufts University Medford, MA, USA Sir Godfrey N. Hounsfield, UK Central Research Laboratories, EMI, London, UK The Nobel Prize in Physiology or Medicine 1979 "for the development of computer assisted tomography"

41 Reconstruction Problem What is the problem?? from projected data only How to reconstruct? Need COMPUTER!

42 Reconstruction Problem Is the problem mathematically solvable? (1) Iterative method (2) Fourier transform method (3) Back projection method C w 1,1 w 1,2 w 1, w C 2,1 w 2,2 w 2, C 3 3. =. c 1,c 2,c, 3,.c C w 65536,,1 w 65536,,

43 Algebraic Reconstruction Technique (ART) cross section f g N j q1 q i1 ij fij N f q ij Where q=indicator for the iteration #. f ij (calculated element) N elements per line g j (measured projection)

44 Iterative ray-by-ray reconstruction Object Next Iteration st Iteration

45 Radon Transform Radon transform operator performs the line integral of the 2-D image data along y The function p (x ) is the 1-D projection of f(x,y) at an angle Properties The projections are periodic in with a period of 2 and symmetric; therefore, p (x ) = p (-x ) The Radon transform leads to the projection or central slice theorem through a 1-D or 2-D Fourier Transform. The Radon transform domain data provide a sinogram.

46 Radon Transform (Cont.) y y Object f(x,y) y Projection x 0 x p x f x y dy ( ') (, ) ' x' x x =x 1 x 1 p ( x ') R[ f ( x, y)] f ( x, y) ( x cos y sin x ') dxdy f ( x 'cos y 'sin, x 'sin y 'cos ) dy ' where x' cos sin x y' sin cos y or x cos sin x' y sin cos y'

47 Projection Theorem Relationship between the 2-D Fourier transform of the object function f(x,y) and 1-D Fourier transform of its Radon transform or the projection data p (x ). P ( ) [ p ( x ')] 1 p ( x ')exp( i x ') dx ' f ( x 'cos y 'sin, x 'sin y 'cos )exp( ix ') dx' dy ' f ( x, y)exp[ i ( x cos y sin )] dxdy F( cos, sin ) F(, ) F(, ) x y

48 Fourier Reconstruction (FR) A 1-D Fourier transform of the projection data p (x ) at a given view angle is the same as the radial data passing through the origin at a given angle in the 2-D Fourier transform domain data.

49 Fourier Transform Method f(x,y) inverse 2-D transform construct 2-D Spectrum F(, ) p (x ) 1-D transform P ()

50 15.4 RADIOGRAPHIC IMAGING SYSTEMS CT Technology Data Handling Systems Figure Illustration of a projection via the centralsectioning theorem. Figure Sketch of the results obtained with simple backprojection algorithm.

51 15.4 RADIOGRAPHIC IMAGING SYSTEMS Basic Concepts the process of backpropagation.

52 Reconstruction by Back Projection

53 Artifact in Back Projection

54 Back Projection If the back projection function of a projection function, p (x ) in the y direction is given by g (x,y ), which involves the smearing of p (x ) along the y axis, we have; in polar coordinates, g ( x ', y ') p ( x ') g ( r, ) p [ r cos( )] for all y, where x r cos, y r sin x ' x cos y sin r cos( ), y ' xsin y cos r sin( )

55 Back Projection(Cont.) Following back projection of n projection functions, the discretely summed image s(r,) can be represented by; n n 1 1 s( r, ) g ( x ', y ') p [ r cos( i)] i n i i1 n i1 Approximate the summation by an integral, 1 1 s( r, ) g( x ', y ') d p[ r cos( )] d 0 0

56 Back Projection Filtering point response of the summed back projection, f ( x, y) ( x) ( y), p ( x ') ( x ') ( y ') dy ' ( x ') 1 s( r, ) h( r, ) d ( x ') ( y ') dy ' ( x ') d [ r cos( )] d 0 0 r If the back projection process is considered a linear system process, it can easily be seen that for an object with an attenuation coefficient distribution (x,y ), the summed back projection function s(x,y ) is related to the point response h(x,y ) by; s( x ', y ') ( x ', y ') h( x ', y ') S(, ) (, ) (, ) B(, ) RS(, ) 1 1 [ ] ( 2 2 ) 1/ 2 R r :Operation, S multiplied by R, represents a spatial filtering

57 Inverse Radon Transform Inverse 2-D Fourier Transform f x y 1 (, ) [ F(, )] 2 x y F(, ) exp[ i( x y )] d d f ( r, ) x y x y x y f ( r, ) F (, ) exp[ i ( x cos y sin )] J dd where 0 x y x y cos sin ',, tan [ ] x y cos, sin, x y J x x y y cos sin sin cos x

58 Inverse Radon Transform The estimated image function f(x,y) can be obtained simply by the inverse Fourier transform: f ( r, ) P ( )exp[ i ( x cos y sin )] dd 0 (using Slice Theorem; P ( ) F(, )) Back projection of the filtered projection data p ( x ') d, where p ( x ') P ( )exp( i x ') d [ P ( )] [ ] p ( x ') where asterisk denotes the 1-D convolution operator

59 Filtered Back Projection projection f(x,y) 1D Fourier transform P () filtering p (x ) P () f(x,y) back projection 1D inverse Fourier transform p (x )

60 Algorithms F.T. B.P.F. F.B.P. proj f(x,y) p (x ) 1D FT P () F(,) f(x,y) scan proj f(x,y) p (x ) back proj g (x,y ) scan Inv. filter (**1/r) -1 ( 1/R) -1 f(x,y) proj f(x,y) p (x ) filter ( ) p (x ) back proj g (x,y ) f(x,y) scan Radon Inverse Radon

61 Figure Four generations of scanning gantry designs. With modern slip ring technology, third- or fourth-generation geometry allows spiral volumetric scanning using slice widths from 1 to 10 mm and pixel matrixes to Typically, a 50-cm volume can be imaged with a single breath hold RADIOGRAPHIC IMAGING SYSTEMS CT Technology Scanning gantry

62 Figure Illustration of an ultrafast CT scanner. In this device, magnetic coils focus and steer the electron beam through the evacuated drift tube where they strike the target rings. The presence of four target rings and multiple x-ray collimators allows four unique x-ray beams to pass through the patient. These beams are then interrupted by two contiguous detector arrays and form eight unique image slices (courtesy of Imatrol) RADIOGRAPHIC IMAGING SYSTEMS CT Technology X-ray Tubes and Detectors