x-ray computed tomography: principle and recent advancements · x-ray computed tomography:...

Jiang Hsieh SPIE MI 2003 Course Note 1

X-ray Computed Tomography: Principle and Recent Advancements

X-ray Computed Tomography:Principle and Recent Advancements

Jiang Hsieh, Ph.D.

GE Medical Systems, Milwaukee, WI



Principle and Recent Advancements in X-ray Computed Tomography

• Basics of Computed Tomography• Image Artifacts and Corrections• Recent Advancement in CT Technology• Recent Advancement in CT Applications



The First Attempt• In 1921, Bocage conducted the first experiment of tomography.

x-ray source

focal plane

film

A

B

A1 B1

x-ray source

focal planeA

B

A1+A2B1 B2



Computed Tomography• In 1967, Godfrey N. Housfield at the Central Research Laboratories

of EMI conducted a CT experiment.



First Clinical Scanner• The first clinical scanner was installed in Atkinson-Morley

Hospital in September 1971.

photo courtesy of Mr. N. Keat at the ImPACT group



The Modern CT Scanner• In the last 30+ years, CT technology has undergone tremendous

development.



Utility of CT• Application of CT is not limited to humans.



Acquisition Speedup

• Scan time/slice for consecutive volume coverage has reduced by a factor of 15,000 over the last 30+ years.

• This is a reduction of factor 1.36/year. Data acquisition speed doubles every 2.2 years!

0.01

0.1

1

10

100

1000

1970

1975

1980

1985

1990

1995

2000

2005

year

scan time per slice (s)



detector

x-ray tube1st translation

91st

tran

slat

ion

1oin

crem

ent

x-ray tube

detector

detector

x-ray tube1st translation

16th

tran

slat

ion

6oin

crem

ent

detector

x-ray tube

1ST

GEN

ERAT

ION

2ND

GEN

ERAT

ION

3RD

GEN

ERAT

ION

4TH

GEN

ERAT

ION



Electron Beam Scanner• Electron Beam scanner was built between 1980 and 1984 for

cardiac applications.

electron gun

section of vacuum drift tube and magnetic focus and deflection coils

electron beam

x-ray fan beam

scan field

detector



Sampling Geometries• The sampling geometry of CT scanners can be described the

following three configurations.• We will limit our discussion to the parallel sampling geometry.

detector

source

detector

source

detector

source

parallel beam fan beam cone beam



X-ray Generation• X-ray photons are produced when a substance is bombarded by high-

speed electrons.

0

0.01

0.02

0.03

0.04

0 20 40 60 80 100 120 140

x-ray energy (keV)

norm

aliz

ed o

utpu

thigh-speed electron

Bremsstra-hlung M L K

high-speed electron

ejected K electron

K characteristic radiation

bremsstrahlung



X-ray Tube• Early vintage of x-ray tube is built with glass envelope and the newer

designs employ metal frames.

target

rotor assembly

cathode



X-ray Detector• Most CT scanners employ either Xenon gas detectors or solid-state

detectors.

XeXe

XeXe+

Xe+

x-ray photon x-ray photon

Xe

e−

e−

Xe

XeXe+

e−

+ +−

x-ray photons

light photons

photodiodes

reflective material

scintillating material

Xenon Solid-state



CT Data Measurement• Under ideal conditions, x-ray intensity observes exponential decay

law.

Iox

oeII ∆−= µ

∆x

Io

xxxo neeeII ∆−∆−∆− ⋅⋅⋅= µµµ 21

µ2 µ3 µ4 µn

( ) xo neI ∆⋅+⋅⋅++−= µµµ 21

∫=

−= dxx

IIPo

)(ln µ

µ1

∫→ − dxxoeI )(µ



Ideal Projections• The measured data are not line integrals of attenuation coefficients.

– beam hardening– scattered radiation– detector and data acquisition non-linearity– off-focal radiation– patient motion– others

• The measured data has to be calibrated prior to the tomographic reconstruction to obtain artifact-free images.



Trajectory of a Point• For parallel geometry, the loci of a point (r,φ) in the rotating

coordinate system is

( )βφ −⋅= cos' rx

object

projection

x

yx’

φφ ββ

ββ

x’x’sinogram



Sinogram• A plot of projection over 2πview angle forms a sinogram.

object cross-section sinogram



Image Reconstruction• Image reconstruction can be treated as a pure algebraic problem by

solving a set of simultaneous equations.

1 2

3 4

3

7

µµµµ1111 µµµµ2222


=+=+=+=+

5473

41

31

43

21

µµµµµµµµ

====

4321

4

3

2

1

µµµµ4 equations

4 unknowns

54



Image Reconstruction• Independence conditions have to be satisfied for valid solution.

1 2

3 4

3

7

4 6



=+=+=+=+

6473

42

31

43

21

µµµµµµµµ

4 equations3 independent Infinite numberInfinite number

of possible solutionsof possible solutions



),( yxf dydxeyxfvuF vyuxi∫ ∫∞

∞−

∞

∞−

+−= )(2),(),( π

Image Reconstruction• In most commercial CT scanners, reconstruction algorithm is

based on the Fourier Slice Theorem (central slice theorem).• The theorem is based on the one-to-one correspondence between

a two dimensional function and its Fourier transform.

FT

IFT



2D FFT

),( yxf dydxeyxfvuF vyuxi∫ ∫∞

∞−

∞

∞−

+−= )(2),(),( π

∫∞

∞−= dyyxfxp ),()( ∫ ∫

∞

∞−

∞

∞−

−= dxdyeyxfuP uxi π2),()( ∫ ∫∞

∞−

∞

∞−

−= dxdyeyxfuP uxi π2),()(

0

3000

6000

1 2550

900

1800

1 255

FFT

=v=0PROJECTION

0

900

1800

1 255



Implementation Issues• Due to sampling pattern, direct implementation of the Fourier slice

theorem is difficult.

Cartesian gridCartesian grid

sample locationsample location



Filtered Backprojection• For parallel geometry, a projection sample can be

uniquely specified by the projection angle, θ, and the distance, t.

θθ

xx

yy

tt



Filtered Backprojection

• The filtered backprojection formula can be derived as follows. Any image function, f(x,y) can be recovered from its Fourier transform, F(u,v), by the inverse Fourier transform:

dudvevuFyxf vyuxj∫ ∫∞∞−

∞∞−

+= )(2),(),( π



Filtered Backprojection• Express the equation in a polar coordinate system (w,q) and

make use of the symmetry, F(ω,θ+π)=F(-ω, θ):

∫ ∫∞∞−= π πω θωωθω0

2),(),( ddeFyxf tj

Make use of the Fourier slice theorem:

∫ ∫∞∞−= π πω

θ θωω02)(),( ddeuPyxf tj



Implementation• The filter kernel as specified does not exist.

∫∞∞−= ωω πω detk tj2)(

The filter needs to be band-limited:

∫−= WW

tj detk ωω πω2)(

K(K(ωω))

ωω--ww ww



Filtered Backprojection• Filtered backprojection uses weighting function to approximate

ideal condition.

weighting function

ideal frequency dataideal frequency datafrom one projectionfrom one projection

actual frequency dataactual frequency datafrom one projectionfrom one projection

weighting functionweighting functionfor approximationfor approximation



Filter Characteristics• The filter emphasizes high frequency contents of the projection

over the low frequency contents. It acts as an edge enhancement.

0

200

400

600

800

1000

1200

0 200 400 600 800

channels

inte

nsity

-60

-40

-20

0

20

0 200 400 600 800channels

inte

nsity



Filtering

Original SinogramOriginal Sinogram Filtered SinogramFiltered SinogramObjectObject

• Let us consider an example of reconstructing a phantom object oftwo rods.

Jiang Hsieh SPIE MI 2003 Course Note


Backprojection• Backprojection is performed by painting the intensity of the entire

ray path with the filtered sample.

filtered projection



Backprojection

0o-30o 0o-60o 0o-90o

0o-120o 0o-150o 0o-180o



Filtered Backprojection

prepre--processed dataprocessed data

filter the datafilter the data

backprojectionbackprojection

convolve the data withconvolve the data withthe ramp filter to achievethe ramp filter to achieve“de“de--blurring”blurring”

sum up the contributionsum up the contributionof the filtered projectionof the filtered projectionover all view angle, for over all view angle, for pixel in the image.pixel in the image.

• The filtered backprojection process can be described by the following flow chart.



Equiangular Fan Beam Reconstruction• When detector cells with identical size is arranged along an arc

concentric to the x-ray focus, equiangular sampling is formed.• Each ray in a fan beam can be specified by β and γ.

fan beam geometryfan beam geometry

xx

yy

ββββββββγγγγγγγγ

• Reconstruction formula can be derived by specifying each sample in (γ, β) coordinate with a (t, θ) coordinate.



Equiangular Fan Beam Reconstruction

• The projection is first multiplied by the cosine of the detector angle.

• In the backprojection process, the filtered sample is scaled by the distance to the source.

∫ ∫−− −=

π γ

γγγγγβγβ

2

0

2 cos)'(),(),(m

m

dDhpdLyxf



Fan Beam Reconstruction• Alternatively, the fan beam data can be converted to a set of

parallel samples. Parallel reconstruction algorithms can be used for image formation.

detector angle, γ

proj

ectio

n an

gle,

β

β=ββ=ββ=ββ=β0000−−−−γγγγparallel samples



Definition of CT Number

• One of the key advantages of CT over conventional x-ray is its low-contrast differentiability (a fraction of a percent).

• Attenuation coefficient of soft-tissue is similar to that of water.• CT images are typically represented by a remapped scale of the

linear attenuation coefficients of the object, called CT number.

1000_ ×−=water

waterNumberCTµ

µµ



Display Window Width and Level

• Most display devices has either 8-bit of dynamic range (256 gray levels).

• The reconstructed images are typically 16-bit (well over 30,000 distinct values).

• Display window width and level is used to map a small range of the intensities to the display device.

WLWW

originalCT number

remapped intensity

−1000

>3000

0

256



Display Window Width and Level• For the same reconstructed image, its appearance varies

significantly over the selection of display window and level.

WW=2700 HU WW=100 HU, WL=20 HU



Image Reformation

• With the introduction of helical and multi-slice CT, there is an explosion on the number of images available for each exam.

• Advanced image display techniques provide opportunities to reduce the amount of information and provides better visualization of the data.

• These display techniques include MPR, shaded surface display, MIP, and volume rendering.



MPR• Multi-planar reformation produces coronal, sagittal, or oblique

plane images from a stack of axial images.

left

right

anterior

posteriorsuperior

coronal plane axial

plane

sagittalplane

stac

k of

CT

imag

es



MPRcoronal plane

left

right

coronal plane



MPRcurved plane

left

right

superior

curved plane

• MPR planes does not need to be flat. This feature is useful for vascular or bone structure display.



Maximum Intensity Projection (MIP)

• The projection intensity equals the maximum pixel intensity along the ray path.

mathematical rays

hypothetical screen

3D volume data

observer



Maximum Intensity Projection (MIP)

• MIP offers improved contrast and visibility for vascular structures.



Volume Rendering

mathematical rays

hypothetical screen

3D volume data

observer

pixel intensity (HU)op

acity

0

1

• The projection intensity equals weighted sum of pixel intensities based on opacity function.



Volume Rendering

• Volume rendering provides improved visualization of structural relationship.



Shaded Surface Display

mathematical rays

hypothetical screen

3D volume data

• The projection intensity equals the reflected light intensity off the object surface.

observer

light source



Shaded Surface Display

• Shaded surface display provides geometric information about the surface of the object.



Key Performance Parameters

• There are many important performance parameters for x-ray computed tomography.

• The most important parameters are:– CT number accuracy– Spatial resolution– Low contrast detect-ability– Temporal resolution– Noise– Dose



CT Number Accuracy• By definition, CT number of water is zero and air is -1000.• In addition, the CT number has to be homogeneous over the

entire FOV.



Spatial Resolution• The MTF was originally defined as the Fourier transform of the

PSF of the system.• Two dimensional Fourier transform is performed on the

reconstructed thin wire and the magnitude of the function represent the MTF.

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

frequency (LP/cm)

MTF



Impact of Reconstruction Kernel• By modifying the cutoff frequency and the window function of the

reconstruction kernel, spatial resolution of the image can be changed.

Standard Bone



Why z-resolution is important?

• In many clinical practice today, radiologists are viewing images in 3D instead of 2D.

• Images are reformatted, volume rendered, or MIP.

• Iso-tropic spatial resolution is crucial.

• Multi-slice CT allow clinicians not to be forced to trade off SSP vs. coverage.



16x0.625mmusing conjugate

sampling

16x0.75mmusing rowsampling

16x1.25mmusing conjugate

sampling

Spatial Resolution in ZAAPM resolution insert was scanned so that resolution pattern is along z. Reformatted image is used to examine the spatial resolution in z

0.4

mm

0.5

mm

0.6

mm

0.75

mm

1.0

mm

1.25

mm

1.5

mm

1.75

mm z



Low-Contrast Resolution

• Visibility of an object depends on the size of the object and its contrast to background.

disc size

cont

rast

to b

ackg

roun

d



Low-Contrast Resolution

• Visibility of an object also depends on the noise level of the image.

noise level

cont

rast

to b

ackg

roun

d



Measurement of Dose

• For the step-and-shoot mode, all radiation dose is confined to a thin section, T.

• X-ray dose is also delivered to regions outside the primary beam due to beam divergence, scattered radiation, and beam penumbra.

0

0.2

0.4

0.6

0.8

1

-7.5 -5 -2.5 0 2.5 5 7.5

distance (cm)

rela

tive

dose

T



Measurement of Dose

• To account for the contribution of the tails with multiple scans, multiple-scan-averaged-dose (MSAD) is defined:

0

0.4

0.8

1.2

1.6

-7.5 -5 -2.5 0 2.5 5 7.5

distance (cm)

rela

tive

dose

T

MSAD

∫−=2/

2/, )(1 I

IIN dzzD

IMSAD



Factors That Impact Dose• Scan Mode

– full scan– half scan

• Beam Quality– Flat filter (Al, Cu, etc.)– Bowtie filter

• Scan Technique– X-ray tube current and voltage– Scan time– Beam umbra to penumbra ratio– Tube current modulation



Image Artifacts

• Image artifacts can be defined as any discrepancy between the reconstructed value and the true attenuation.

• We limit our discussion to the ones that are clinically significant.

• In a typical CT, nearly 106 independent measurements are used to form an image. Therefore, CT is more sensitive to artifacts.



Artifact Appearance-streaking artifact

• When a few channels in a few projections deviates significantly from the true signal, streaking artifact appears.

filtered filtered projectionprojection

reconstructedreconstructedimageimage

error signalerror signal



Artifact Appearance-ring artifact

• When a single channel deviates from true signal for an extended projection angle, a ring artifact is formed.

reconstructed imagereconstructed image

backprojecting ofbackprojecting ofan error channelan error channel



Artifact Appearance-shading artifact

• When a group of adjacent signals deviate gradually from true signal for several projections, shading artifacts are formed.

reconstructed imagereconstructed image

error channelserror channels



Outline• SYSTEM LEVEL ARTIFACT

– aliasing, partial volume, scatter, noise streaks• X-RAY TUBE INDUCED ARTIFACT

– off-focal radiation, tube arcing, rotor wobble• DETECTOR RELATED ARTIFACT

– offset/nonlinearity/radiation damage, primary speed afterglow

• PATIENT INDUCED ARTIFACT– motion, beam hardening, metal, truncated

projection



Aliasing Artifact• Shannon theory states that the sampling rate needs to be twice the

highest frequency contents in the signal.

distance frequency−δ δ −1/δ 1/δ

Fouriertransform



Aliasing Artifact• For a third generation CT scanner, this condition could not be

easily met. Aliasing artifacts will result.

x-ray tube

detector reconstructed image of a wirereconstructed image of a wire



4th Generation Scanner• To overcome aliasing artifact, the concept of 4th generation

scanner was developed.

detector

x-ray tube



Detector Quarter Offset• Sampling density can be increased by detector quarter offset.

1/4 detector1/4 detector

angle=angle=ββ angle=angle=ββ

angle=angle=β+πβ+π



Detector Quarter Offset• The same concept can be applied to fan beam.

iso-center

1/4 detector

detector

180o rotation

originaloriginal quarter offsetquarter offset



Focal Spot Wobble(flying focal spot)

• Double sampling can be obtained by deflecting x-ray focal spot.

detector

x-ray focal spot

detector

x-ray focal spot



Image Quality Comparison• Computer simulation was performed to compare the image

performance.

originaloriginal quarter offsetquarter offset focal spot wobblefocal spot wobble



View Aliasing• Similar to projection aliasing, the view sampling has to satisfy

conditions to ensure aliasing-free image.

sampling pattern of isosampling pattern of iso--rayray

For parallel beam:For parallel beam:

MRN νπ2min =

For fan beam:For fan beam:

−

=

2sin1

4min ψ

νπ MRN

maximum resolvablemaximum resolvablespatial frequencyspatial frequency

maximummaximumfan anglefan angle



View Aliasing Artifact• View aliasing can be observed when view number is reduced.

984 views984 views 704 views704 views



Partial Volume• When the object scanned is smaller than the slice thickness,

partial volume can result.• Partial volume error is in general projection angle dependent.

iso-center

x-ray sourcedetector

partially intruded object

x-ray beam at angle βx-ray beam at angle β+π

z



Partial Volume• The most effective method of combating partial volume artifact is

to use thin slices.

7mm aperture7mm aperture 1mm aperture1mm aperture



Scatter

• A significant portion of the x-ray photon exiting from the object is scattered photon.

• Scattered photons generally deviate from their original path.

• Post patient collimator can be used effectively to reject the scatter.

• A small portion of the scattered radiation can reach the detector.

primary photons

object

scattered photons

collimator

scintillator photo-diode

input x-rayphotons



Impact of Scatter• Scattered radiation creates a low

frequency bias to the true projection signal.

• The low frequency bias produces shading artifact.

originaloriginal

with scatterwith scatter

inte

nsity

inte

nsity

distancedistance

true projectiontrue projection

scatter scatter signalsignal



Photon Starvation

• At low signal level, the noise in the projection is no longer dominated by the x-ray photon.

• Convolution filtering operation will further amplify the noise and streak artifacts will result.

example of a patient scanexample of a patient scan



Artifact Reduction• Correction algorithm can be derived that adaptively filters out the

noise for the channels with low photon counts.

original imageoriginal image adaptively filtered imageadaptively filtered image



X-ray Tube

Cathode

Focal spotFocal track (region of off-Focal radiation

Target (anode)



Off-focal Radiation-compensation

• Off-focal radiation can be minimized by placing a collimator near the x-ray focal spot.

x-ray

collimator

x-ray fromfocal spot

Detectedoff-focal radiation

off-focalx-ray

focal spot



Off-focal Radiation-algorithmic correction

• Off-focal radiation effect can also be corrected by algorithmic correction.

image without correctionimage without correction image with correctionimage with correction



Tube Rotor Wobble• X-ray tube target rotates at as high as 10,000 RPM.• In conjunction with high temperature, significant wear and tear

occurs to the tube assembly.

with rotor wobblewith rotor wobble without rotor wobblewithout rotor wobble



Primary Speed and Afterglow

• The output signal of most solid state detector does not reach zero right after the termination of x-rays.

• The primary speed (fastest decay) is mainly determined by the nature of the activator.

• The afterglow (slower decay) is related in general to the impurities (traps) in the material.

• The detector primary speed and afterglow can be improved by doping the detector with rare-earth materials.



Impact of Slow Decay• potential loss of spatial resolution• possible production of image artifact.

1.0s scan 0.5s scan



Experimental Result

• No loss of resolution or image artifact can be observed:

1.0s scan 0.5s scan



MTF Measurement• Quantitative analysis on spatial resolution

0.5s4.0s

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

frequency (LP/cm)

MTF

4.0s 0.5s 50% MTF (LP/cm) 8.06 8.40 10% MTF (LP/cm) 11.38 11.45

0.5s

4.0s



Noise Comparison• Standard deviation measured on water phantom:

0

5

10

15

20

25

20 30 40 50 60 70 80 90 100

distance to iso (mm)

stan

dard

dev

iatio

n

0.5s 4.0s



Impact of Afterglow• Non-uniform afterglow can cause rings and shading in the image.• Afterglow can also be corrected with software.

originaloriginal with correctionwith correction



Patient Motion• Patient motion causes inconsistency in the projection data set.• Patient motion can cause steaks and shading artifacts.

example of a patient scanexample of a patient scan

motion artifactmotion artifact



Patient Motion Correction• The most inconsistency occurs between the start and end of a scan.• Patient motion effect can be reduced by suppressing the

contribution of the projections in the worst regions.

start of the scan

end of scan

NN∆∆tt

∆∆tt

detector channel

proj

ectio

n vi

ew

00

22ππ

regionsof mostmotion



Patient Motion Correction• By weighting the projections prior to the reconstruction, patient

motion artifacts can be significantly reduced.• The weighting function needs to be continuous and differentiable.

without correction with correction



Beam Hardening• The attenuation characteristics, µ(E), are dependent on the input x-

ray energy. For all commercially available CT scanners, the x-ray generated by x-ray tube, T(E), is poly-energetic.

I T E e dEs E ds= − ∫∫ ( ) ( , )µ

• The measured projection does not represent the line integral of µ.

energy, E

x-ra

y flu

x, T

(E)

energy, E

µ(E)



Water Beam Hardening• If not properly compensated for, cupping artifact will result.

path length

-- lnln(I

/I(I/I oo))

ideal

actual

no correction



Water Beam Hardening• Water beam hardening can be corrected with polynomial

expansion of the projections.

path length

-- lnln(I

/I(I/I oo))

ideal

actual

no correction with correction

corrected

∑=

=N

n

nn pp

1

' α



Bone Beam Hardening• The attenuation characteristics of bone is significantly different

from that of soft tissue.

path length

-- lnln(I

/I(I/I oo))

water

bone

WATER BH CORRECTED



Bone Beam Hardening• Software correction schemes can be used to reduce the bone

induced artifacts.

threshold forwardprojection

sinogramof bones

polynomial mapping

errorprojection

filtered back-projection

errorimage

scale/subtraction



Bone Beam Hardening• Software correction schemes can be used to reduce the bone

induced artifacts.

ORIGINALORIGINAL CORRECTEDCORRECTED



Note

• CT is inherently prone to image artifacts.• Artifacts can be the results of malfunction of any

component in the system, data acquisition protocols, inherent physics limitations, or the scanned object.

• We discussed only the causes and corrections of artifacts that are in the public domain.



Helical Scanning• In helical scanning, the patient is translated at a constant speed

while the gantry rotates.• Helical pitch:

dqh =

qq

distance gantry travel in one rotationdistance gantry travel in one rotation

collimator aperturecollimator aperture



Helical Scanning

• Advantage– Larger volume coverage due to zero inter-scan delay.– Reconstruction at arbitrary locations due to uniform sampling

pattern in z.• Better 3D image quality• Improved contrast due to object centering

– Improved tube utilization– Slice thickness modifiable with reconstruction algorithm



Clinical Examples



Helical Scanning

• Disadvantage– Inherent projection inconsistency



Helical Scanning• The helical data collection is inherently inconsistent. If proper

correction is not rendered, image artifact will result.

reconstructed helical scan without correctionreconstructed helical scan without correction



Helical Reconstruction

• The plane of reconstruction is typically at the mid-point between the start and end planes.

• Interpolation is performed to estimate a set of projections at the plane of reconstruction.

data sampling helixdata sampling helix

end of data set planeend of data set plane

plane of reconstructionplane of reconstruction

start of data set planestart of data set plane



Helical Reconstruction-360o interpolation

• Samples at the plane of reconstruction is estimated using two projections that are 360o apart.

)2,()1(),(),(' πβγβγβγ +−+= pwwpp

data sampling helix

p(γ,β) p(γ,β+2π)p’(γ,β)

xq

qxqw −=

wherewhere




• In fan beam, each ray path is sampled by two conjugate samples that are related by:

−+=−=

γπββγγ

2''

For helical scan, these two samples are taken at different z location because of the table motion.



ppkk((γ,βγ,β))

ppnn((--γ,β+πγ,β+π−−2γ2γ))

plane of reconstructionplane of reconstruction

zz--axisaxis


• Linear interpolation is used to estimate the projection samples at the plane of reconstruction.

• Because the samples are taken at different view angles, the weights are γ and β dependent.

)2,()1(),( γπβγβγ −+−−+ pwwp



Interpolation Verses Weighting

• The backprojection process is essentially a summation operation.

• The interpolation first weights the samples and sums up the weighted samples.

• If we weight the samples prior to the filtering operation, the summation process will be performed automatically by the backprojection process.



Artifact Suppression• Helical reconstruction algorithm effectively suppresses helical artifacts.

withoutwithouthelicalhelicalcorrectioncorrection

with with helicalhelicalcorrectioncorrection



Algorithm Comparision-slice sensitivity profile

• Because 180o based interpolation interpolate two points that are located closer than the 360o based interpolation, 180o based has a better slice sensitivity profile.

• 360o interpolation uses 4πprojection data and has better noise property.

180 degree interpolation180 degree interpolation 360 degree interpolation360 degree interpolation



Helical Reconstruction-projection weighting

• Interpolation can be performed by weighting the projections prior to the filtered backprojection. The backprojection step sums up contribution from different views.

prepre--processed dataprocessed data

multiply data by weightsmultiply data by weights

filter the datafilter the data

backprojectionbackprojection



Artifact Property• In single slice CT, image artifacts increase monotonically with the helical

pitch.

p=0p=0 p=1p=1

p=1.5p=1.5 p=2p=2



• 3D graphics techniques often enhances the artifacts that are notvisible in 2D images.

3D image (helical scan, 5mm collimator at 1mm spacing)

3D image (axial scan, rotating start angle, 5mm collimator at 1mm spacing)

Surface Rendering Artifact



3D SSD image (threshold=10%) with new reconstruction

• The artifact can be reduced by modifying the weighting function in the reconstruction process.

3D SSD image original (threshold=10%)

Artifact Suppression



• The noise ratio is a function of the starting angle of the scan as well as the spatial location.

0.8

1.61.6

0.8

HI HE

Noise In-homogeneity



• Dark and bright bands will result in MIP or volume rendered images if not properly corrected.

48” POLY PHANTOM

PATIENT

MIP Artifacts



• Based on the noise analysis, adaptive filtering schemes can be derived to combat the artifact.

Artifact Reduction

ORIGINALORIGINAL FILTEREDFILTERED

ORIGINALORIGINAL FILTEREDFILTERED



Multi-slice CT• Multi-slice CT contains multiple

detector rows.• For each gantry rotation, multiple

slices of projections are acquired.• Similar to the single slice

configuration, the scan can be taken in either the step-and-shoot mode or helical mode.

• Unlike the single slice, the slice thickness is defined by detector aperture.

xx--ray sourceray source

detectordetector



Advantages of Multi-slice Helical

• Large coverage and faster scan speed

• Better contrast utilization• Less patient motion

artifacts• Near-isotropic spatial

resolution

8-slice data acquisition



Advantages of Multi-slice Helical

• Large coverage and faster scan speed

• Better contrast utilization• Less patient motion

artifacts• Isotropic spatial

resolution



Detector Configuration

4x1.25mm 4x1mm

4x2.5mm

4x3.75mm

4x5mm

4x2.5mm

4x5mm

matrix array adaptive array



Detector Configuration

16x0.625mm

16x1.25mm

mixed array • To provide sub-mm slice thickness, the center 8 detector cells are further sub-divided into two cells.

• Similar to the 4 or 8 slice configuration, neighboring cells can be grouped to form a single cell.



Multi-slice Helical

• When acquiring data in a helical mode, the N (4 or higher) detector rows form N interweaving helixes.

• Because multiple detector rows are used in the data acquisition,the acquisition speed is typically higher.

• Similar to the single slice helical, the projection data are inherently inconsistent.



Major Challenges

• Two major challenges of multi-slice helical reconstruction are helical interpolation and cone beam.

• Cone beam challenge is due to the fact that the projections collected from multi-detector rows are not parallel to each other.

• For all multi-slice scanner on the market, the cone angle is about 1o.

z

single-slice multi-slice



• Helical reconstruction requires interpolation of the acquired projections to a consistent set of projections.

• Either row-to-row or conjugate interpolation can be used.

11 22 33 44

11 22 33 44

11 22 33 44

proj

ectio

n an

gle

plane of reconstruction

detector location in z

11 22 33 44

11 22 33 44

Reconstruction Algorithm Impact



• Projection samples from conjugate samples are used to interpolate projections at the plane of reconstruction.

• In general, row-to-row interpolation produces roughly 30% thicker FWHM than the conjugate interpolation.

11 22 33 44

11 22 33 44

proj

ectio

n an

gle plane of reconstruction

detector location in z

ββ

β+πβ+π

Reconstruction Algorithm Impact



Cone Beam Artifact

z

multi-slice

centerslice

edgeslice



Cone Beam Algorithm (1)

• FDK-based algorithm is one of the popular cone beam reconstruction algorithms.

• FDK-based algorithm uses projection weighting combined with 3D backprojection that follows the actual cone beam sampling geometry.

z

multi-slice



Example

FDK-basedsimple

• FDK algorithm can be combined with different weighting functionsto optimize its performance in different performance parameters.



• For high pitch multi-slice helical scan, the interpolated sample and the plane of reconstruction overlaps only at the iso-center.

• To overcome the discrepancy, tilted planes are defined as the plane of reconstruction.


helical path

z

tilted plane

conventional POR

interpolatedsample

plane of reconstruction



Example• When the SAME weighting function is used, reconstructions with

the tilted plane produces better image quality than the conventional reconstruction plane with 2D backprojection.

conventional plane tilted plane




• In helical mode, each ray path is sampled multiple times by different detector rows.

• Samples from different detector rows can be treated differently.

• The final result is the convolution of several weighting functions.

z

multi-slice



Exampleacquired with 16x0.625mm at 26:1 helical pitch and reconstructed with Standard kernel

ww=400, wl=-50



Single vs. Quad

axialaxialaxialaxial

singlesingle1.5:1 pitch1.5:1 pitch

singlesingle2:1 pitch2:1 pitch

quadquad3:1 pitch3:1 pitch

quadquad6:1 pitch6:1 pitch



• Slice thickness can be selected by modifying the reconstruction process.

• By low-pass filtering in the z-direction, the slice sensitivity profile can be broadened to any desired shape and thickness.

• From an image artifact point of view, images generated with the thinner slice aperture is better.

Slice Thickness Change with Algorithms

FilteringFiltering zz



• Z filtering can be applied in either the projection domain or the image domain.

• In general, z-smoothing provides artifact suppression capability.

Example

16x0.625mm detector aperture at 1.75:1 helical pitch

FWHM=0.625mm FWHM=2.5mm



• It is always better to scan with thin slice and reconstruct to thicker slice than scan with thicker slice from artifact point of view.

Thick Scan vs. Thick Reconstruction

2.5mm reconstructed from 8x2.5mmat 1.675:1 helical pitch

2.5mm reconstructed from 16x0.625mmat 1.75:1 helical pitch



Recent Advancement in CT Applications

• Cardiac • Fluoroscopy• Perfusion• Screening



Cardiac CT• Two key factors contribute to the recent advancement

of cardiac application:– faster scan speed (0.5s or faster)– introduction of multi-slice CT

• Two type of cardiac application:– calcification screening– coronary artery imaging

• One of the key performance parameters for cardiac CT is the reduction or elimination of motion artifacts.



Single-Cycle Gated Cardiac Scans• Projection data used in the reconstruction is selected based on the

EKG signal to minimize motion artifacts.

-350

-300

-250

-200

-150

-100

-50

0 0.5 1 1.5 2 2.5 3 3.5 4

time (sec)

mag

nitu

de

acquisition interval forimage No. 1






cycle 2

Selection of Helical Pitch• Improper selection of helical pitch results in either overlapped

coverage or gaps in the coverage.

detector location (z)

time

overlapped region

coverage


time


time

gap

detector row 1, 2, 3, 4detector row 1, 2, 3, 4 detector row 1, 2, 3, 4

cycle 1

cycle 3



Half Scan Reconstruction• For relatively slow heart rate, single sector reconstruction

produces satisfactory results.



Selection of Helical Pitch• Volume rendering technique is also used for image display.



Image Artifacts-Motion• Cardiac motion artifacts can result due to non-optimal gating.



Image Artifacts-High Density Objects• Metal or high-density objects, such as pacemaker leads, can

produce severe image artifacts.



Image Artifacts-Phase Mis-registration• Inconsistency in the gating can produce artifacts in reformatted

images.



Multi-cycle Gated Cardiac Scans• Projection data used in the reconstruction is selected based on the

EKG signal to minimize motion artifacts.

-350

-300

-250

-200

-150

-100

-50

0 0.5 1 1.5 2 2.5 3 3.5 4

time (sec)

mag

nitu

de

acquisition interval for one image

total acquisition interval for one image



Performance Comparison

single-cycle gating four-cycle gating

• Motion artifacts can be further reduced by utilization of multi-cycle gating.



CT Fluoroscopy Device

table-sidemonitor

hand-heldcontrol

floatabletable



Volumetric Display• With the introduction of multi-slice scanner, volumetric display

of fluoroscopy images become feasible.



Image Reconstruction

• CT fluoroscopy requires images to be reconstructed and display in “real time” to provide timely feedback to the operator.

• State-of-the-art reconstruction with conventional algorithm takes 0.5s/image.

• Specialized reconstruction algorithms have to be utilized to obtain significantly improvement in reconstruction speed.



Rapid Image Reconstruction• One of the key performance parameters is the image reconstruction

speed.

Sr, n

Su, n+1 Su, n+2 Su, n+3 Su, n+4 Su, n+5 Su, n+6

Sd, n+8

Sr, n Sd, n+1 Sr, n+8 Sd, n+9

Su, n+7

−−−− ++++image n

image n+1



Rapid Image Reconstruction• An example of a weighting function:

+≤≤

−+−

−+

<≤

<≤

−

=

0

3

0

02

0

0

0

0

3

0

2

0

22,2223

2,1

0,23

)(

βπβπβ

ββπβ

ββππββ

ββββ

ββ

βw

• The production of image In+1 from image In is described:

9,8,1,,1 ++++ ++−−= ndnrndnrnn SSSSII

Sr,n and Sd,n is the sub-images produced by the ascending anddescending weighting functions.



CT Perfusion• Blood flow provide oxygen and nutrients to the brain.• Basic brain functions are interrupted at different blood flow levels.

arterial inletvenous outlet

vascular structure

CBV

CBF

MTT



Perfusion• Human brains has intricate self-regulating system.• Measurement of cerebral blood flow (CBF) alone is inadequate to

assess the viability of brain tissue.• Cerebral blood volume is the total volume of blood in the large

conductance vessels, arteries, arterioles, capillaries, venules, and sinuses.

• Mean transit time (MTT) is defined as the average time for the blood to travel from the arterial inlet to the venous outlet.

MTTCBFCBV ×=• The algorithms to measure CBV, CBF, and MTT can be

classified into two classes: direct-measurement based and de-convolution based.



massconcentration

Q(t)

Direct Measurement Methods

• These methods are based on Fick principle.

• Based on the conservation of contrast medium, the rate of accumulation of contrast medium in an organ is the difference between the influx rate and the efflux rate of the contrast.

flow x arterial concentration

F Ca(t)

flow x venous concentration

F Cv(t)



Fick Principle (direct-measurement based)• For an arterial contrast medium of concentration Ca(t) and CBF of

F, the rate of contrast influx into a volume is Ca(t)F.• Due to the conservation of contrast medium, the rate of contrast

accumulation, q(t), is the derivative of the total amount of contrast in the volume, Q(t):

[ ])()()()( tCtCFdt

tdQtq va −==

−= ∫ ∫

t t

va dttCdttCFtQ0 0

)()()(

Ca(t) and Q(t) are the time density curve (TDC) measured atartery and the entire volume.



Fick Principle (direct-measurement based)• If we ignore the venous outflow (Cv(t)=0), the blood flow can be

approximated by:

)()(tCtQF

a=

• To reduce the underestimation of blood flow due to the no venousflow assumption, we need to either reduce total contrast volume or increase injection rate.

• Reduction of contrast volume leads to poor signal-to-noise ratio of the time-density curve.

• Increase injection rate raises patient safety concerns.



De-convolution Method• De-convolution methods treat the organ perfusion as a linear

system.

h(t)

δδδδ(t): contrast mediumof unit volume injected

over extremely short time

system impulse response (residual function)

h(t)*g(t)

g(t): contrast mediuminjected clinically system response



Impulse Residual Function• The residual function, h(t), represents the tissue TDC to an

arterial bolus of contrast of unity volume over an extremely short period of time.

h(t)

t0

1

∆∆∆∆h

t, t+∆∆∆∆t

fraction of the contrast with transit time, t

• The area under the impulse residual function represents the mean-transit time:

∫=1

0tdhMTT



Linear System Approach• Impulse residual function cannot be measured directly in clinical

practice.• Based on the linear system theory, we have:

)()()()()( tgtCthFtCtQ aa ⊗=⊗=

• Q(t) and Ca(t) are the measured TDC of the volume and artery.• g(t) can be solved by de-convolution. F is the height of the

plateau of g(t). • Area under g(t) represents CBV (product of MTT and CBF).



Example of Brain Perfusion



Example of Body Perfusion



Screening

• With the recent technology development, examination of the whole body by CT can be completed in a single breath-hold. CT can be a useful tool for screening applications.

• The key to the screening application is the reduction of x-ray dose encountered in a CT exam.

• Because of the large amount of images involved, computed assistant detection (CAD) becomes a necessity.



Impact of Reconstruction Kernel• The shape and size of the lung nodule can vary significantly with

the selection of different reconstruction kernel.

Standard Bone Lung



Impact of Reconstruction Kernel

• All images were acquired with axial mode at 0.63mm at 0.63mm spacing and reconstructed with 20cm FOV.

141.79axial 0.63mm/0.63mm

Bone

137.95axial 0.63mm/0.63mm

Lung

160.54axial 0.63mm/0.63mm

Standard

Volume (mm3)AcquisitionKernel



Impact of Data Acquisition• The size and shape of the nodule also vary significantly with the

selection of data acquisition.• Different slice thickness and data acquisition modes were used.

All reconstructed with Standard algorithm at 20cm FOV.

193.994x2.5HS/0.63mmhelical173.714x1.25HS/0.63mmhelical173.045mm/5mmaxial178.802.5mm/2.5mmaxial166.311.25mm/1.25mmaxial160.540.63mm/0.63mmaxial

volume (mm3)thickness/spacingmode



Impact of Data Acquisition

axial 0.63mm at0.63mm spacing




helical 4x1.25mm HS0.63mm spacing

helical 4x2.50mm HS0.63mm spacing



Future TechnologyVolumetric CT (VCT)

• Advantages of VCT include the improved temporal resolution and multi-modes operation.



Future TechnologySuper-high Spatial Resolution

• Current CT scanners are capable of providing spatial resolution of 20-30LP/cm with 1mm detector size.

• Using new detector technology, the detector cell size can be reduced to 50µm to 200µm.



VCT for Dental Application

VCT 140µµµµm Resolution

Clinical CT Today



Resolution Challenges in Animal ImagingResolution Challenges in Animal Imaging

Mouse Volume CT Image

Size does matter ...Size does matter ...

VCT Provides resolution required for small animal imaging



Summary

• We outline the principles and key performance parameters of x-ray computed tomography.

• We present causes and corrections of various image artifacts. New artifacts are likely to be produced with the introduction of new technologies.



Summary

• X-ray computed tomography is experiencing tremendous technology advancement in recent years.

• These technology advancements have inspired more advanced clinical applications.

• The advancement of x-ray CT is only the beginning. The technology and applications of CT will likely be significantly different than what we see today.



REFERENCES

• J. Hsieh, Computed Tomography: principles, design, artifacts, and recent advances, SPIE Press, 2002.

• Categorical Courses in Diagnostic Radiology Physics: CT and US Cross-sectional Imaging, ed. L. W. Goldman and J. B. Fowlkes, RSNA, Oakbrook, IL, 2000.

• A. Kak and M. Slaney, Principles of Computed Tomographic Imaging, IEEE Press, 1988.

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