Computed Tomography Principles

1
Computed Tomography Principles
Ge Wang, Ph.D.Department of RadiologyUniversity
of IowaIowa City, Iowa 52242, USA
2
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

3
A Little Bit History
Nobel prizesRoentgen (1901) Discovery of X-rays
Hounsfield Cormack (1979) Computed tomography
4
Computed Tomography Principles
1. Projection measurement 2. Scanning modes 3.
Scanner systems 4. Image reconstruction
5
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
6
X-ray Interactions - Compton Scatter
(From Aracor)
Compton Scatter results in a free electron a
scattered (less energetic) photon
7
Source and Detectors
Source - Rotating anode disk - Small focal
spot down to 0.6 mm - Polychromatic
beamDetectors - Xenon (50-60) -
Scintillation (gt90)
(From Siemens)
8
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
Attenuatedmore
X-rays
9
Ray-Sum of X-ray Attenuation
Ni
No
?k
?x
Ray-sum
Line integral
10
Projection Sinogram
SinogramAll projections
ProjectionAll ray-sums in a direction
?
y
P(??t)
t
p
?
x
f(x,y)
t
X-rays
Sinogram
11
Completeness Condition
There exists at least a source on any
line intersecting a cross-section
12
Computed Tomography Principles
1. Projection measurement 2. Scanning modes 3.
Scanner systems 4. Image reconstruction
13
First Generation
One detector Translation-rotation Parallel-beam
14
Second Generation
Multiple detectors Translation-rotation Small
fan-beam
15
Third Generation
Multiple detectors Translation-rotation Large
fan-beam
16
Fourth Generation
Detector ring Source-rotation Large fan-beam
17
Third Fourth Generations
18
Spiral/Helical Scanning

• Simultaneous
• Source rotation
• Table translation
• Data acquisition

19
Cone-Beam Geometry
20
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

21
Scanning modes

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

22
Computed Tomography Principles
1. Projection measurement 2. Scanning modes 3.
Scanner systems 4. Image reconstruction
23
Spiral CT Scanner
Network
Gantry
Source
Display Control console
Computer Parallel processor
Table
Recording
Detectors
Data acquisition system
Storage units Tapes, disks
24
Data Acquisition System (DAS)
Pre-Collimator
Post-Collimator
Scattering
Source
Detector
Filter
Patient
25
Data Acquisition System (DAS)
X-ray Tube
Source
Filter
Detectors
CT Gantry(From Siemens)
Detector
26
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)
27
E-Beam CT Scanner

• Speed 50, 100 ms
• Thickness 1.5, 3, 6, 10 mm
• ECG trigger cardiac images

(From Imatron)
28
Computed Tomography Principles
1. Projection measurement 2. Scanning modes 3.
Scanner systems 4. Image reconstruction
29
Computed Tomography
y
Computed tomography (CT)Image reconstruction
fromprojections
t
P(??t)
f(x,y)
P(??t)
?
x
f(x,y)
X-rays
30
Reconstruction Idea
??4
?23
?32
?41
31
Algebraic Reconstruction Technique(ART)
32
Fourier Transformation
f(x,y)
F(u,v)
Fourier Transform
Image Space
Fourier Space
33
Fourier Slice Theorem
v
FP(??t)
u
?
F(u,v)
34
From Projections to Image
35
Filtered Backprojection
36
Example Projection
Projection
Projection
Sinogram
Ideal Image
37
Example Backprojection
Projection
38
Example Backprojection
Sinogram
Backprojected Image
39
Example Filtering
Filtered Sinogram
Sinogram
40
Example Filtered Backprojection
Filtered Sinogram
Reconstructed Image
41
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) http//dolphin.radiology.uiowa.edu/ge
(on-line slides handouts in the Teaching
section)