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  • Raylman et al.: “An estimated 25% of women receiving mammograms have radiographically dense breasts, which make lesion detection difficult or impossible because the tumors are virtually indistinguishable from dense normal breast tissue. This number is certain to rise in light of the recent recommendation by the National Cancer Institute that women over the age of 40 and at average risk for breast cancer start regular mammographic screening; considering dense breasts are most common in women under the age of 50.”
  • This image should be used to explain the principle of filtered back projection. Note that the image contains an animation.
  • Additional Material

    1. 1. Supplementary Material Emission Computed Tomography Thanks to those that post interesting material on the internet. This supplement is a collection from several.
    2. 2. Emission Tomography f(x,y,z)f(x,y,z) ProjectionsProjections ReconstructionReconstruction f(x,y,z)f(x,y,z) SlicesSlices projection projection
    3. 3. SPECT Single Photon Emission Computed Tomography collimator only one gamma photon is detected per decay NaI(Tl) crystal Rotating scintillator camera
    4. 4. detector detector PET Positron Emission Tomography  What do we want to detect in PET? – 2 photons of 511 keV in coincidence, coming in a straight line from the same annihilation e- e+ γ γ unstable nucleus emits positron positron annihilates with electron two 511 photons are emitted simultaneously in opposite directions TRUE coincidence
    5. 5. Types of Coincidence  True coincidence is the simultaneous detection of the two emissions resulting from a single decay event.  Scatter coincidence is when one or both photons from a single event are scattered and both are detected.  Random coincidence is the simultaneous detection of emission from more than one decay event. Coincidences: True Scatter Random
    6. 6. PET radiation detection  PET scanner – Typical configuration:  whole-body (patient port ∅~60 cm; axial FOV~15 cm)  scintillator crystals coupled to photomultiplier tubes (PMTs)  cylindrical geometry  ~24-32 rings of detector crystals  hundreds of crystals/ring  several millions of Lines Of Response (LORs) (only a few are shown) True True Other configurations for special-purpose applications: - brain imaging - animal PET - mammography, other PET CT
    7. 7. PET/CT CT PET CT+PET General Electric Medical Systems
    8. 8. PET data acquisition  Organization of data – True counts in LORs are accumulated – In some cases, groups of nearby LORs are grouped into one average LOR (“mashing”) – LORs are organized into projections etc…
    9. 9. PET data acquisition  2D and 3D acquisition modes septa 2D mode (= with septa) 3D mode (= no septa) In the 3D mode there are no septa: photons from a larger number of incident angles are accepted, increasing the sensitivity. Note that despite the name, the 2D mode provides three-dimensional reconstructed images (a collection of transaxial, sagittal and transaxial slices), just like the 3D mode!
    10. 10. PET data acquisition  2D mode vs. 3D mode 2D mode (= with septa) 3D mode (= no septa) True detected True not detected (septa block photons)
    11. 11. PET data acquisition  Organization of data – In 3D, there are extra LORs relative to 2D 3D mode same planes as 2D oblique planes ... ... + +
    12. 12. PET evolution: spatial resolution Human brain Animal PET ~1998 Monkey brain Image credits: CTI PET Systems Image credits: Crump Institute, UCLA
    13. 13. J. Fessler, 2002 “Part of the goal is to bring order to this alphabet soup.”
    14. 14. PET image reconstruction Projection Object P(φ 2 ,r) ∫= ),( ),(),( rline dlyxfrP φ φ Radon Transform φ1 φ2 P(φ1 ,r) f(x,y) r r
    15. 15. PET image reconstruction Sinogram r φ Projection angle Projection bin Object
    16. 16. PET image reconstruction SinogramObject r φ
    17. 17. PET image reconstruction SinogramObject r φ
    18. 18. PET image reconstruction SinogramObject r φ
    19. 19. PET image reconstruction SinogramObject r φ
    20. 20. PET image reconstruction r φ SinogramObject
    21. 21. Sinogram  Other representations can be used instead of the sinogram (linogram, planogram) SPECT: 360º (1 photon) PET: 180º (2 opposite photons)
    22. 22. PET image reconstruction  2D Reconstruction – Each parallel slice is reconstructed independently (a 2D sinogram originates a 2D slice) – Slices are stacked to form a 3D volume f(x,y,z) 2D reconstruction Plane 5 Slice 5 etc etc 2D reconstruction Plane 4 Slice 4 2D reconstruction Plane 3 Slice 3 2D reconstruction Plane 2 Slice 2 2D reconstruction Plane 1 Slice 1 2D Reconstruction2D Reconstruction
    23. 23. PET image reconstruction  Projection and Backprojection Projection Backprojection 2D Reconstruction2D Reconstruction
    24. 24. 4 projections 16 projections 128 projections Backprojection Filtered Backprojection Object PET image reconstruction2D Reconstruction2D Reconstruction
    25. 25. Noise In PET Images  Noise in PET images is dominated by the counting statistics of the coincidence events detected.  Noise can be reduced at the cost of image resolution by using an apodizing window on ramp filter in image reconstruction (FBP algorithm). 105 106 107 counts Unapodized ramp filter Hanning window, 4mm Hanning window, 8mm
    26. 26. Scattered coincidences component Attenuation Random coincidences component Detector efficiency effects True coincidences component PET image reconstruction  Data corrections are necessary – the measured projections are not the same as the projections assumed during image reconstruction Object (uniform cylinder) projection measured projection assumed integral of the activity along the line or tube of response
    27. 27. Analytical methods  Advantages – Fast – Simple – Predictable, linear behaviour  Disadvantages – Not very flexible – Image formation process is not modelled ⇒ image properties are sub-optimal (noise, resolution)
    28. 28. Iterative methods  Advantages – Can accurately model the image formation process (use with non-standard geometries, e.g. not all angles measured, gaps) – Allow use of constraints and a priori information (non- negativity, boundaries) – Corrections can be included in the reconstruction process (attenuation, scatter, etc)  Disadvantages – Slow – Less predictive behaviour (noise? convergence?)
    29. 29. PET Image reconstruction  Iterative methods CurrentCurrent estimateestimate MeasuredMeasured projectionprojection CompareCompare (e.g.(e.g. –– oror // )) ErrorError projectionprojection projectionprojection EstimatedEstimated projectionprojection image spaceimage space projection spaceprojection space backprojectionbackprojection ErrorError imageimage UpdateUpdate Iteration 1
    30. 30. PET Image reconstruction  Iterative methods CurrentCurrent estimateestimate MeasuredMeasured projectionprojection CompareCompare (e.g.(e.g. -- oror // )) ErrorError projectionprojection projectionprojection EstimatedEstimated projectionprojection image spaceimage space projection spaceprojection space backprojectionbackprojection ErrorError imageimage UpdateUpdate EstimatedEstimated projectionprojection EstimatedEstimated projectionprojection Iteration 2
    31. 31. PET Image reconstruction  Iterative methods CurrentCurrent estimateestimate MeasuredMeasured projectionprojection CompareCompare (e.g.(e.g. -- oror // )) ErrorError projectionprojection projectionprojection image spaceimage space projection spaceprojection space backprojectionbackprojection ErrorError imageimage UpdateUpdate EstimatedEstimated projectionprojection EstimatedEstimated projectionprojection EstimatedEstimated projectionprojection EstimatedEstimated projectionprojection Iteration N
    32. 32. Algorithm comparison  600 000 counts (including scatter) original 3DRP Hanning 3D OSEM + filt. 6 subsets 5 iter. Gauss .5cm FORE + OSEM 6 subsets 2 iter. 3D OSEM 6 subsets 2 iter. Image credits: Kris Thielemans MRC CU, London (now IRSL – www.irsl.org)
    33. 33. Reconstruction of a slice from projections example = myocardial perfusion, left ventricle, long axis courtesy of Dr. K. Kouris
    34. 34. Iterative reconstruction methods conventional iterative algebraic methods algebraic reconstruction technique (ART) simultaneous iterative reconstruction technique (SIRT) iterative least-squares technique (ILST) iterative statistical reconstruction methods (with and without using a priori information) gradient and conjugate gradient (CG) algorithms maximum likelihood expectation maximization (MLEM) ordered-subsets expectation maximization (OSEM) maximum a posteriori (MAP) algorithms
    35. 35. algorithm (a recipe) (1) make the first arbitrary estimate of the slice (homogeneous image), (2) project the estimated slice into projections analogous to those measured by the camera (important: in this step, physical corrections can be introduced - for attenuation, scatter, and depth-dependent collimator resolution), (3) compare the projections of the estimate with measured projections (subtract or divide the corresponding projections in order to obtain correction factors - in the form of differences or quotients), (4) stop or continue: if the correction factors are approaching zero, if they do not change in subsequent iterations, or if the maximum number of iterations was achieved, then finish; otherwise (5) apply corrections to the estimate (add the differences to individual pixels or multiply pixel values by correction quotients) - thus make the new estimate of the slice, (6) go to step (2).
    36. 36. Iterative reconstruction - multiplicative corrections
    37. 37. Iterative reconstruction - differences between individual iterations
    38. 38. Iterative reconstruction - multiplicative corrections
    39. 39. Filtered back-projection  very fast  direct inversion of the projection formula  corrections for scatter, non-uniform attenuation and other physical factors are difficult  it needs a lot of filtering - trade-off between blurring and noise  quantitative imaging difficult
    40. 40. Iterative reconstruction  discreteness of data included in the model  it is easy to model and handle projection noise, especially when the counts are low  it is easy to model the imaging physics such as geometry, non-uniform attenuation, scatter, etc.  quantitative imaging possible  amplification of noise  long calculation time
    41. 41. References: Groch MW, Erwin WD. SPECT in the year 2000: basic principles. J Nucl Med Techol 2000; 28:233-244, http://www.snm.org. Groch MW, Erwin WD. Single-photon emission computed tomography in the year 2001: instrumentation and quality control. J Nucl Med Technol 2001; 20:9-15, http://www.snm.org. Bruyant PP. Analytic and iterative reconstruction algorithms in SPECT. J Nucl Med 2002; 43:1343-1358, http://www.snm.org. Zeng GL. Image reconstruction - a tutorial. Computerized Med Imaging and Graphics 2001; 25(2):97-103, http://www.elsevier.com/locate/compmedimag. Vandenberghe S et al. Iterative reconstruction algorithms in nuclear medicine. Computerized Med Imaging and Graphics 2001; 25(2):105-111, http://www.elsevier.com/locate/compmedimag.
    42. 42. References: Patterson HE, Hutton BF (eds.). Distance Assisted Training Programme for Nuclear Medicine Technologists. IAEA, Vienna, 2003, http://www.iaea.org. Busemann-Sokole E. IAEA Quality Control Atlas for Scintillation Camera Systems. IAEA, Vienna, 2003, ISBN 92-0-101303-5, http://www.iaea.org/worldatom/books, http://www.iaea.org/Publications. Steves AM. Review of nuclear medicine technology. Society of Nuclear Medicine Inc., Reston, 1996, ISBN 0-032004-45-8, http://www.snm.org. Steves AM. Preparation for examinations in nuclear medicine technology. Society of Nuclear Medicine Inc., Reston, 1997, ISBN 0-932004-49-0, http://www.snm.org. Graham LS (ed.). Nuclear medicine self study program II: Instrumentation. Society of Nuclear Medicine Inc., Reston, 1996, ISBN 0-932004-44-X, http://www.snm.org. Saha GB. Physics and radiobiology of nuclear medicine. Springer- Verlag, New York, 1993, ISBN 3-540-94036-7.

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