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Computed Tomography Principles Ge Wang, Ph.D. Department of Radiology University of Iowa Iowa City, Iowa 52242, USA

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Learning Objectives CT terms Data acquisition Basic elements of CT scanner Scanning modes Image reconstruction Spiral/helical CT Image resolution and artifacts Interaction among imaging parameters Quality assurance Radiation exposure

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A Little Bit History Nobel prizes Roentgen (1901): Discovery of X-rays Hounsfield & Cormack (1979): Computed tomography

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Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction

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X-ray Interactions - Photoelectric Effect Photoelectric effect results in total absorption of the X-ray photon and the emission of a bound electron (From Aracor)

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X-ray Interactions - Compton Scatter Compton Scatter results in a free electron & a scattered (less energetic) photon (From Aracor)

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Source - Rotating anode disk - Small focal spot down to 0.6 mm - Polychromatic beam Detectors - Xenon (50-60%) - Scintillation (>90%) Source and Detectors (From Siemens)

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Exponential Attenuation of X-ray x NoNo NiNi x X-rays Attenuated more NoNo NiNi N i : input intensity of X-ray N o : output intensity of X-ray : linear X-ray attenuation

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Ray-Sum of X-ray Attenuation x NoNo NiNi Ray-sum Line integral

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Projection & Sinogram Sinogram t Sinogram: All projections P( t) f(x,y) t y x X-rays Projection: All ray-sums in a direction

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Completeness Condition There exists at least a source on any line intersecting a cross-section

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Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction

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First Generation One detector Translation-rotation Parallel-beam

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Second Generation Multiple detectors Translation-rotation Small fan-beam

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Third Generation Multiple detectors Translation-rotation Large fan-beam

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Fourth Generation Detector ring Source-rotation Large fan-beam

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Third & Fourth Generations (From Picker) (From Siemens)

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Simultaneous Source rotation Table translation Data acquisition Spiral/Helical Scanning

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Cone-Beam Geometry

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Scanning modes First generation One detector, translation-rotation Parallel-beam Second generation Multiple detectors, translation-rotation Small fan-beam Third generation Multiple detectors, rotation-rotation Large fan-beam

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Scanning modes Fourth generation Detector ring, source-rotation Large fan-beam Spiral/Helical scanning, cone-beam geometry

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Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction

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Spiral CT Scanner Gantry Data acquisition system Detectors Storage units: Tapes, disks Display Control console Computer Parallel processor Table Recording Source Network

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Filter Data Acquisition System (DAS) Source Detector Pre-CollimatorPost-Collimator Patient Scattering

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Data Acquisition System (DAS) X-ray Tube Detectors CT Gantry (From Siemens) Filter Source Detector

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Spiral CT Scanner Gantry Data acquisition system Table Computer Parallel processors Control console Storage units Tapes, disks Recording device Network interface X-ray generator Heat exchanger (From Elscint)

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E-Beam CT Scanner Speed: 50, 100 ms Thickness: 1.5, 3, 6, 10 mm ECG trigger cardiac images (From Imatron)

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Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction

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Computed Tomography P( t) f(x,y) P( t) f(x,y) t y x X-rays Computed tomography (CT): Image reconstruction from projections

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Reconstruction Idea

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Algebraic Reconstruction Technique (ART) Update a guess based on data differences Guess 1 Guess 0 Guess 2 Error

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Fourier Transformation Fourier Transform f(x,y) F(u,v) Image Space Fourier Space

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Fourier Slice Theorem v u F(u,v) P( t) f(x,y) t y x X-rays F[P( t)]

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From Projections to Image y x v u F -1 [F(u,v)] f(x,y) P( t) F(u,v)

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Filtered Backprojection f(x,y) P( t) 1) Convolve projections with a filter 2) Backproject filtered projections

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Example: Projection Sinogram Ideal Image Projection

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Example: Backprojection Projection

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Example: Backprojection SinogramBackprojected Image

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Example: Filtering Filtered SinogramSinogram

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Example: Filtered Backprojection Filtered Sinogram Reconstructed Image

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References T. S. Curry III, J. E. Dowdey, R. C. Murry Jr. Christensens physics of diagnostic Radiology (4th edition), Lea & Febiger (for residents) G. Wang, M. W. Vannier: Computerized tomography. Encyclopedia of Electrical and Electronics Engineering, edited by Webster JG, to be published by John Wiley & Sons (for engineers) (on-line slides & handouts in the Teaching section)

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