Principle of Computed tomography

嘉義長庚放射科　　廖書柏

Introduction

In 1950 ， Allan M. Cormack develop the theoretical and mathematical methods used to reconstruct CT images.

In 1972 Godfrey N. Hounsfield and colleagues of EMI Central Research Laboratories built the first CAT scan machine, taking Cormack's theoretical calculation into a real application.

For their independent efforts, Cormack and Hounsfield shared the Nobel Prize in medicine and physiology in 1979.

What is CT scanner?

A X-ray device capable of cross-section imaging

-creates images of “slice” through patient

Advantages of CT scanning

Ability of differentiate overlying structure Excellent contrast

-overlying structure don’t decrease contrast

-digital images, so variable window settings

X-ray Source and detectors Source

-rotating anode disk

-small focus spot (down to 0.6 mm)

-polychromatic beam Detectors

-xenon

-solid-state:

NaI(Tl) 、 CsI scintillaton crystals 、 ceramic materials containing rare-earth oxides 、 BGO and CdWO4

xenon

xenon

Pressured xenon gas

ionization

Electrical signal

Solid-state

Ceramic or crystal scintillatior

Photon capture

Photo-diode

Electrical signal

Solid state

Light

Collimators

Pre-patient collimator- control slice thickness Pre-detector collimator-reduce scattered radiation

History of CT

Variations in scanner design based on : X-ray tube and detector movement Detector arrangement Rotating mechanism

First-generation ~1972

single X-ray tube and one detector element

Pencil beam about 5 minutes per slice

from 180 degrees rotation.

Translate-rotate movement

EMI CT1000

Second-generation ~1975

Single X-ray tube and multiple detector elements

Narrow fan beam(~10 。 ) About one minute per slice

Translate-rotate movement

Third-generation ~1975

Single X-ray tube, rotating movement

Multiple detectors in curvilinear design, rotating movement

Fan beam(~30 。 ) Several seconds per slice

Rotate-rotate movement

Fourth-generation ~1976

Single X-ray tube, rotating movement

Fixed ring as many as 8000 detectors inside of gantry

1-s scan time Avoiding ring artifact

problem of 3rd generation scanner

Rotate-stationary movement

Fifth-generation ~1984

four semicircular tungsten target rings spanning 210 degrees about the patient

Multiple detectors of two banks, fixed inside of the gantry

no mechanical movement By using four target rings and two detector banks,

eight slices of the patient may be imaged without moving patient.

EBCT( electron beam CT)

A sub-second scanner, called “Imatron”

Each sweep of a target ring requires 50 ms and 8 ms delay to reset the beam. eight parallel slices (scanned two per sweep) requires approximately 224 milliseconds to complete

Sixth-generation ~1989

Helical /spiral CT was introduced in 1989, based on Generation Three

Single X-ray tube and single-row detector Never-stop and one-direction rotating X-ray tube, detectors Capability to achieve one second image acquisition, or even

sub-second Slip ring replaced with the x-ray tube voltage cables enable

continual tube rotation.

Slip ring technology in 1985

Slip ring allow continuous gantry rotation

Conventional mechanism

Seventh-generation ~1998

Single X-ray tube ,Multiple-row detector, rotating movement

Allow simultaneous acquisition of multiple slice in a single rotation

Half-second rotation(0.5 s) Sub-second scanner

The Basic CT Term

Image matrix Linear attenuation coefficient CT numbers

Image matrix

Every CT slice is subdivided into a matrix of up to 1024X1024 volume element (voxel)

The viewed image is then reconstructed as a corresponding matrix of picture element (pixel)

Each pixel is assigned a numerical value (CT number), which is the average of all the attenuation values contained within the corresponding voxel.

Pixel size=FOV/matrix size

The diameter of image reconstruction is called the field of view (FOV).

Voxel size= pixel size X slice thickness

Linear Attenuation Coefficient (μ)

Basic property of matter Depends on x-ray energy and atomic number (Z) of

materials. Attenuation coefficient reflects the degree to which x-ray

intensity is reduced by a material

I0 x I

I = I0 e-μx

x1 x2 x3I0 I

I = I0 e-(μ1x1+μ2x2)

x1 xn

I = I0 e-Σμixii=1

n

I0 I

                                                                                       

μ(x, y) is the linear attenuation coefficient for the material in the slice

CT numbers

The precise CT number of any given pixel is calculated from the X-ray attenuation coefficient of the tissue contained in the voxel.

CT number ranged from -1000~3095(12 bit)

k

When k=1000, the CT numbers are Hounsfield units

CT numbers normalized in this manner provide a range of several CT numbers for 1% change in attenuation coefficient.

Tissue μ(cm-1)

Bone 0.528

Blood 0.208

Gray matter 0.212

White matter 0.213

CSF 0.207

Water 0.206

Fat 0.185

Air 0.0004

Linear attenuation coefficient of various body tissues for 60 keV x-ray

The hounsfield scale of CT numbers

Image reconstruction

Image reconstruction

The image is reconstructed from projections by a process called Filtered Backprojection .

"Filtered" refers to use digital algorithms called convolution to improve image quality or change certain image quality characteristics, such as detail and noise

"Backprojection" is the actual process used to produce or "reconstruct" the image. 

The filtered backprojection process involves the following steps:

generating a sinogram from a set of N projections filtering the data to compensate for blurring Backprojecting the data

.

Projection and sinogram Ray: the X-ray read by every one detector within a short

time interval. Projection: all rays sum in a direction Sinogram: all projections

P(t)

μ(x,y)

t

y

x

X-rays Sinogramt

P(t) =

Filter a de-blurring function is combined (convolved) with the

projection data to remove most of the blurring before the data are backprojected.

A high-frequency filter reduces noise and makes the image appear “smoother.”

A low-frequency filter enhances edges and makes the image “shaper.”

A low-frequency filter may be referred to as a “high-pass” filter because it suppresses low frequencies and allows high frequencies to pass.

Backprojection Projection data (in Sinogram) 1D-FT filled in k-

space central slice projection theorem 2D-inverse FT CT images

中央切面投影理論中央切面投影理論

(Central Slice Projection Theorem, CSPT)(Central Slice Projection Theorem, CSPT) ：：

If a 1D Fourier Transform is performed on a projection of If a 1D Fourier Transform is performed on a projection of an object of some angle, the result will be identical to one an object of some angle, the result will be identical to one line on 2D Fourier Transform of that object and at that line on 2D Fourier Transform of that object and at that angle.angle.

中央切面投影理論中央切面投影理論

(Central Slice Projection Theorem, CSPT)(Central Slice Projection Theorem, CSPT) ：：

If a 1D Fourier Transform is performed on a projection of If a 1D Fourier Transform is performed on a projection of an object of some angle, the result will be identical to one an object of some angle, the result will be identical to one line on 2D Fourier Transform of that object and at that line on 2D Fourier Transform of that object and at that angle.angle.

Central Slice Projection Central Slice Projection TheoremTheorem

ky

kx

F(kx,ky)

P(t)t

y

xF[P(t)]

μ(x,y)

CSPT can relate the Fourier transform of the projection to one line in the 2D K space formed by the 2D Fourier transform of μ(x,y)

kyy

x

v

u

F-1[F(kx,ky)]

u(x,y) F(kx,ky)

Inverse 2D-FT

kx

object 1D-FT

Inverse 2D-FT

image

Backprojection

Filtered backprojection

Filtered backprojection removes the star-like blurring seen in simple backprojection.

Filtered backprojection

Image display

Image manipulation

Image manipulation belongs to the domain of digital image processing.

Window width and level

The window width covers CT numbers of all the tissue of interest that is displayed as shades of gray, ranging from black to white. Thus width controls the contrast in the displayed image. 

The level control adjust the center of the window and identifies the type of tissue to be imaged.

Reducing window width increases the displayed image contrast among the tissues

WL= 40 WW= 350 WL= -600 WW=1500

Spiral CT technology

Pitch Pitch is defined as the patient couch movement per

rotation divided by the slice thickness. Pitch= couch movement per rotation

beam collimation

Couch movement

Slice thickness

pitch

5 mm/rot

5 mm

5/5=1

10 mm/rot

5 mm

10/5=2

effects of increasing pitch

Faster scan time for a specific volume body.

Dose is reduced because radiation is less concentrated

Image resolution might be reduced

when the pitch is increased, table appears to move faster along the patient's body

Reconstruction interval/increment The RI determines the degree of sectional

overlap to improve image quality. As RI decreases, image quality increases” but

with trade-offs of increase image processing time, data storage requirements, and physician time for image review”

Slice thickness=5 mmRI=2.5 mm overlaping 50%

RI=2 mmoverlaping (5-2)/5=60%

Image quality

Spatial resolution in CT

focal spot size detector dimensions Slice thickness Pixel size Pitch artifact

Pixel size= FOV/matrix size

Image Artifact in CT

Image Artifact

Artifacts are any discrepancy between the CT numbers represented in the image and the expected CT numbers

Common artifacts

Beam hardening Partial volume effect bad detector(3th scanner) Metal Patient motion

Beam hardening effect Linear attenuation coefficients vary with photon energy. After passing through a given thickness of tissue , lower-energy

x-rays are attenuated to a greater extent than high-energy x-rays are.

artifacts such as a reduced attenuation toward the center of tissue (cupping) and streaks that connect tissues with strong attenuation.

polychromatic spectrums

Cupping Artifact

Means for suppressing beam hardening effect

pre-filtering X-rays avoiding high X-ray absorbing regions if

possible applying appropriate algorithms

Partial volume effect Partial volume artifacts are the result of a variety of

different tissue types being contained within a single voxel Measured attenuation coefficient are averaged by all

components use thinner slice to reduce

bad detector(3th scanner)

Each detector views a separate ring of an anatomy.

any single detector or a bank of detectors malfunctions will produce ring artifact

Metal artifact

Metal materials can cause the streaking artifacts due to block parts of projection data

ex: Dental fillings

Prosthetic devices

Surgical clip Remove the metal material as possible to reduce the

artifact

Patient motion

Voluntary and involuntary motion can cause streaking artifacts in the reconstructed image.

Reduce motion:

-Shorter scan time

-Immobilization and

positioning aid

Effect of reducing projections

96 24 12

the number of views (projections)

Effect of reducing rays

200 50 25

The numbers of the data point (rays) per projection

Thanks for your attention~