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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**

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

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**X-ray Interactions - Compton Scatter**

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

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

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**Exponential Attenuation of X-ray**

Ni No m Ni: input intensity of X-ray No: output intensity of X-ray m: linear X-ray attenuation x Ni No x Attenuated more X-rays

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**Ray-Sum of X-ray Attenuation**

Ni No k x Ray-sum Line integral

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**Projection & Sinogram y P(t) t p x f(x,y) t X-rays Sinogram**

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

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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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**Spiral/Helical Scanning**

Simultaneous Source rotation Table translation Data acquisition

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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 Network Gantry Source Computer Parallel processor**

Display Control console Table Recording Detectors Data acquisition system Storage units: Tapes, disks

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**Data Acquisition System (DAS)**

Pre-Collimator Post-Collimator Scattering Source Detector Filter Patient

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**Data Acquisition System (DAS)**

X-ray Tube Source Filter Detectors CT Gantry (From Siemens) 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 y Computed tomography (CT): Image reconstruction from projections t P(t) P(t) f(x,y) x f(x,y) X-rays

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Reconstruction Idea =4 2=3 3=2 4=1

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**Algebraic Reconstruction Technique (ART)**

3 2 4 1 6 -2 Update a guess based on data differences Guess 1 Guess 0 Guess 2 Error

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**Fourier Transformation**

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

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

X-rays v F[P(t)] u F(u,v)

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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) P’(t) 1) Convolve projections with a filter 2) Backproject filtered projections

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Example: Projection Projection Projection Sinogram Ideal Image

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**Example: Backprojection**

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**Example: Backprojection**

Sinogram Backprojected Image

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Example: Filtering Sinogram Filtered Sinogram

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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. Christensen’s 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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