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Image Reconstruction and Inverse Treatment Planning – Sharpening the Edge – Thomas Bortfeld

Image Reconstruction and Inverse Treatment Planning – Sharpening the Edge – Thomas Bortfeld. CT Image Reconstruction Inverse Treatment Planning. Syllabus. 2/13 Advances in imaging for therapy (Chen) 2/20 Treatment with protons and heavier particles; tour of proton facility (Kooy)

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Image Reconstruction and Inverse Treatment Planning – Sharpening the Edge – Thomas Bortfeld

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  1. Image Reconstruction andInverse Treatment Planning– Sharpening the Edge – Thomas Bortfeld CT Image Reconstruction Inverse Treatment Planning

  2. Syllabus 2/13 Advances in imaging for therapy (Chen) 2/20 Treatment with protons and heavier particles; tour of proton facility (Kooy) 2/27 Treatment delivery techniques with photons, electrons; tour of photon clinic (Biggs, Folkert) 3/6 Intensity-modulated radiation therapy (IMRT, IMPT) (Seco, Trofimov) 3/13 Dose calculation (Monte Carlo + otherwise) (Paganetti, Kooy) 3/20 Treatment planning (photons, IMRT, protons) (Doppke + NN)

  3. Syllabus 3/27 Inverse treatment planning and optimization (Bortfeld) 4/3 Optimization with motion and uncertainties (Trofimov, Unkelbach) 4/10 Mathematics of multi-objective optimization and robust optimization (Craft, Chan) 4/17 Dose painting (Grosu) 4/24 Image-guided radiation therapy (Sharp) 5/1 Special treatment techniques for moving targets (Engelsman)

  4. Planigraphy, Tomosynthesis“Verwischungstomographie” x-ray source x-ray tube focus slice object film film Ziedses des Plantes (Netherlands), 1932

  5. Computerized Tomography Greek: • tomos = section, slice • graphia = to write, to draw tomograph = slice drawer

  6. Nobel prize 1979Drs. Hounsfield and Cormack Sir Godfrey N. Hounsfield(Electrical Engineer) EMI Allan M. Cormack (Physicist) South Africa, Boston

  7. First CT scanner prototype Hounsfield apparatus

  8. CT “generations” 1st generation 2nd generation translation-rotation scanners

  9. CT “generations” 3rd generation(fan detector) 4th generation(ring detector) Rotation-only scanners

  10. Imatron: Electron beam CT (EBT)

  11. Imatron: Electron beam CT (EBT)

  12. Helical (“spiral”) CT Trajectory of the continuously rotating X-ray tube Start of spiral scan Table motion

  13. From transmission to projection A.M. Cormack

  14. Projection

  15. p f ? f Sinogram p Sinogram, “Radon” transform, Â(Johann Radon, Vienna, 1917) Object

  16. Backprojection

  17. Backprojection Shepp&Logan phantom “Reconstruction” by backprojection

  18. Backprojection

  19. Backprojection Projections of point object from three directions Back-projection onto reconstruction plane

  20. Backprojection Object Image f(r) 1/r f(r) Profile through object Profile through image Terry Peters (Robarts Institute)

  21. Backprojection This is a convolution (f *h) of f(r) with the point spread function (PSF) h=1/|r|

  22. What is Convolution?

  23. Convolution theorem • Periodic sine-like functions are the Eigenfunctions of the convolution operation. • This means, convolution changes the amplitude of a sine wave but nothing else. • Hence, convolution is completely described by the transfer function or frequency response (Fourier transform of the PSF), which determines how much amplitude is transmitted for different frequencies

  24. Convolution theorem

  25. r-filtered layergram reconstruction • Backproject measured projections, and integrate over f • Fourier transform in 2D • Multiply with distance from the origin, |r|, in the frequency space • Inverse Fourier transform

  26. Central slice theorem

  27. Filtered backprojection

  28. Transform back to get filter in spatial domain: Deconvolution (filtering) in the spatial domain Ramp filter in the frequency domain: sampling interval

  29. Deconvolution (filtering) in the spatial domain Sample at discrete points p = nDp: sampling interval Filter of Ramachandran and Lakshminarayanan (Ram-Lak)

  30. Ram-Lak filter negative components

  31. Shepp&Logan filter

  32. Backprojecting filtered projections Terry Peters (Robarts Institute)

  33. Filtered backprojection Filtered backprojection Shepp&Logan phantom “Reconstruction” by backprojection

  34. Filtered Backprojection Simple backprojection Filtered backprojection

  35. Reconstruction from fan projections k+l = 7: parallel k: counter of source positions l: counter of projection lines

  36. Summary CT image reconstruction • In CT we measure projections, i.e., line integrals • The set of projection lines from all directions is called Radon transform or sinogram • Backprojection leads back into image space but introduces severe 1/r blurring

  37. Summary CT image reconstruction, cont’d • Image can be de-blurred with deconvolution techniques • Deconvolution can be done in projection space using the central slice theorem • A common filter function is the Ram-Lak filter • Filters have negative components (“eraser”) to remove blurring

  38. Image Reconstruction andInverse Treatment Planning– Sharpening the Edge – Thomas Bortfeld CT Image Reconstruction Inverse Treatment Planning

  39. Brahme, Roos, Lax 1982 Source Phantom Target OAR Dose

  40. The idea of IMRT "Classical" Conformation Intensity Modulation Treated Volume Treated Volume Target Volume Target Volume Tumor Tumor OAR OAR Collimator

  41. “Inverse” treatment planning "Conventional" Planning Inverse Planning Treated Volume Target Volume Treated Volume Target Volume OAR OAR Collimator

  42. Computer Tomography Conformal Radiotherapy Projection Intensity Modulation Target Radiation Source Detectors Radiation Source

  43. Image Reconstruction (Filtered Backprojection) Conformal Radiotherapy (Filtered Projection) Density Distribution of the Tissue Set of Prescribed 2D Dose Distributions x-ray Projection (CT-Scanner) Projection (Computer) 1D Filtering of the Projections 1D Filtering of the Projections Backprojection IMRT with Filtered Projections Set of 2D Slice Images Dose Distribution

  44. G. Birkhoff: On drawings composed of uniform straight lines Journ. de Math., tome XIX, - Fasc. 3, 1940.

  45. Negative Intensities After filtering: Intensity - x

  46. Consider the inverse problem as an optimization problem. Define the objectives of the treatment and let the computer determine the parameters giving optimal results. The inverse problem has no solution!

  47. Optimization basics Mathematical optimization: Minimization of objective functions Objective FunctionF(x) = Si (di - pi)2, di = f(x1,.., xn) F(x) = NTCP × (1-TCP) Constraints di < dtolxi > 0 DVH constraints NTCP < 5% Parameters x = (x1, . . ., xn) (e.g., intensity values) actual dose prescribed dose

  48. “Decision variables” • Intensity profiles • Beam weights, segment weights • Beam angles (gantry angle, table angle) • Number of beams • Energy (especially in charged particle therapy) • Type of radiation (photons, electrons, ...)

  49. The “standard model” of inverse planning minimize beam intensities dose values all the physics is here : dose contribution of pencil beam j to voxel i

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