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

Computed Tomography Principles

Ge Wang, Ph.D.Department of Radiology

University of IowaIowa City, Iowa 52242, USA

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

A Little Bit History

Nobel prizesRoentgen (1901): Discovery of X-rays Hounsfield & Cormack (1979): Computed tomography

Computed Tomography Principles

1. Projection measurement

2. Scanning modes

3. Scanner systems

4. Image reconstruction

X-ray Interactions - Photoelectric Effect

Photoelectric effect results in total absorption ofthe X-ray photon and the emission of a bound electron

(From Aracor)

X-ray Interactions - Compton Scatter

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

(From Aracor)

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)

Exponential Attenuation of X-ray

x

No

xio eNN

xio eNN )( 321 Ni

x

X-rays

Attenuatedmore

NoNi

Ni: input intensity of X-rayNo: output intensity of X-ray: linear X-ray attenuation

Ray-Sum of X-ray Attenuation

o

i

kk N

Nx ln

o

i

N

Ndxx ln)(

x

iok

k

eNN

x

NoNi

Ray-sum Line integral

Projection & Sinogram

Sinogramt

Sinogram:All projections

P(t)

f(x,y)

t

y

x

X-rays

Projection:All ray-sums in a direction

Completeness Condition

There exists at least a source on any lineintersecting a cross-section

Computed Tomography Principles

1. Projection measurement

2. Scanning modes

3. Scanner systems

4. Image reconstruction

First Generation

One detectorTranslation-rotationParallel-beam

Second Generation

Multiple detectorsTranslation-rotationSmall fan-beam

Third Generation

Multiple detectorsTranslation-rotationLarge fan-beam

Fourth Generation

Detector ringSource-rotationLarge fan-beam

Third & Fourth Generations

(From Picker)

(From Siemens)

Simultaneous•Source rotation•Table translation•Data acquisition

Spiral/Helical Scanning

Cone-Beam Geometry

X

Z

Y

Scanning modes

• First generationOne detector, translation-rotationParallel-beam

• Second generationMultiple detectors, translation-rotationSmall fan-beam

• Third generationMultiple detectors, rotation-rotationLarge fan-beam

Scanning modes

• Fourth generationDetector ring, source-rotationLarge fan-beam

• Spiral/Helical scanning, cone-beam geometry

Computed Tomography Principles

1. Projection measurement

2. Scanning modes

3. Scanner systems

4. Image reconstruction

Spiral CT Scanner

Gantry

Data acquisitionsystem

Detectors

Storage units:Tapes, disks

Display

Controlconsole

Computer

Parallelprocessor

Table Recording

Source

Network

Filter

Data Acquisition System (DAS)

Source Detector

Pre-Collimator Post-Collimator

Patient

Scattering

Data Acquisition System (DAS)

X-ray Tube

Detectors

CT Gantry(From Siemens)

Filter

Source

Detector

Spiral CT Scanner

• GantryData acquisition system

• Table• Computer

Parallel processors• Control console• Storage units

Tapes, disks• Recording device• Network interfaceX-ray generatorHeat exchanger

(From Elscint)

E-Beam CT Scanner

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

(From Imatron)

Computed Tomography Principles

1. Projection measurement

2. Scanning modes

3. Scanner systems

4. Image reconstruction

Computed Tomography

P(t) f(x,y)P(t)

f(x,y)

t

y

x

X-rays

Computed tomography (CT):Image reconstruction fromprojections

Reconstruction Idea

4

6

3

7

42

31

43

21

Algebraic Reconstruction Technique(ART)

Update a guessbased on

data differences

Guess 1

Guess 0

Guess 2

Error

Error

Fourier Transformation

dudvevuFvuFFyxf

dxdyeyxfyxfFvuF

vyuxj

vyuxj

)(21

)(2

),(),(),(

),(),(),(

FourierTransform

f(x,y) F(u,v)

ImageSpace

FourierSpace

Fourier Slice Theorem

v

u

F(u,v)

P(t)

f(x,y)

t

y

x

X-rays

F[P(t)]

From Projections to Image

y

x

v

u

F-1[F(u,v)]

f(x,y) P(t) F(u,v)

Filtered Backprojection

f(x,y) f(x,y)

P(t) P’(t)

1) Convolve projections with a filter2) Backproject filtered projections

Example: Projection

SinogramIdeal Image

Projection

Projection

Example: Backprojection

Projection

Example: Backprojection

Sinogram Backprojected Image

Example: Filtering

Filtered SinogramSinogram

Example: Filtered Backprojection

Filtered Sinogram Reconstructed Image

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)

http://dolphin.radiology.uiowa.edu/ge (on-line slides & handouts in the Teaching section)