Why CT ? CT scanner physics Mikael Jensen Radiation Research Department Risø National Laboratory Early CT scanner geometry Implementation of CT Single slice Single projection Single direction Very long scan time! Original system devised by Hounsfield in late 1960ties Algebraic reconstruction Io Io Io µ1 µ2 I21 Io µ3 µ4 I22 I11 I12 proj_demo 1 Algebraic reconstruction(2) Back projection I11 = I 0 ⋅ exp(− µ1 ⋅ dx) ⋅ exp(− µ3 ⋅ dx ) I12 = I 0 ⋅ exp(− µ 4 ⋅ dx) ⋅ exp(− µ 2 ⋅ dx) I 21 = I 0 ⋅ exp(− µ1 ⋅ dx) ⋅ exp(− µ 2 ⋅ dx ) I 22 = I 0 ⋅ exp(− µ 3 ⋅ dx) ⋅ exp(− µ 4 ⋅ dx ) ⎧ I0 ⎫ −1 ⎪ln( I )dx = µ1 + µ3 ⎪ 11 ⎪ ⎪ ⎪ I0 ⎪ −1 ⎪ln( I )dx = µ 4 + µ 2 ⎪ ⎪ ⎪ 12 ⎨ ⎬4 equations,4 unknown ⎪ln( I 0 )dx −1 = µ + µ ⎪ 1 2 ⎪ I 21 ⎪ ⎪ ⎪ ⎪ln( I 0 )dx −1 = µ + µ ⎪ 3 4 ⎪⎩ I 22 ⎪⎭ 1 2 5 3 7 3 4 5 3 2 1 2 3 4 5 6 7 1 For all projections, the measured values are added to all contributing pixels Filtered back projection ct_demo 2 Hounsfield unit Table 1: Typical H.U. Values Windowing 3 4 Slip Rings 5 Electron Beam CT Examples from the abdomen Combination of multiple slices – 3D reconstruction and segmentation 6 Segmentation 7 CT- fusion with other modalities (PET/CT) 8

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