CT

Chapter 4:Principles of

Computed Tomography

Radiography vs. CTBoth based on differential

attenuation of x-rays passing through body

Radiography“Shadowgraph” using x-ray light

sourceCT

Cross-sectional imageImage computed from pencil

beam intensity measurements through only slice of interest

Limitations of Radiography

3D body rendered in 2DStructures superimposed

on filmMust view structure of

interest through underlying / overlying structures

Multiple views often required to adequately visualize a structure.

Patient

X-rayBeam

Film

Limitations of Radiography

Optical density dictated by total attenuation encountered by beam

Thin highly-attenuating objects appear to be same density as thicker low-attenuating object.

Patient

X-rayBeam

Film

Thin denseobject

Thick lessdense object

Early Solution: Conventional Tomography

Tube and film moveRotate around fulcrum

Image produced on filmObjects above or below

fulcrum plane change position on film & thus blur

Limitations of Conventional Tomography

Overlying / underlying structures blurred, not removed

5-10% subject contrast difference required for objects to appear differentmany anatomic systems do not have this

subject contrast

CT AdvantagesView anatomy without looking

through underlying / overlying structuresimproves contrast

Uses tightly collimated beamminimizes scattered radiationimproves contrast

Demonstrates very small contrast differences reliable & repeatedly

CT X-rayBeam

Conventional X-ray Beam

Film as a Radiation DetectorAnalog

not quantitativeNot sensitive enough

to distinguish small differences in incident radiation

Applicationsfilm badgestherapy dosimetry

CT Detectors

electronic / quantitativeextremely sensitive

small radiation input differences reliably & repeatedly measured & discerned

output digitized & sent to computer

Data AquisitionSlice by slice

One slice at a timeVolume acquisition

data for an entire volume collectedpatient moves in axial direction during scantube traces spiral-helical path through

patient

ScanningX-ray tube rotates around patient

detectors also rotate for 3rd generation CT

Detectors measure radiation transmitted through patient for various pencil beam projectionsRelative transmissions calculated

Fraction of beam exiting patient

Patient

X-Ray beams

Patient

X-Ray beam

X-Ray detector

Intensitymeasurements

ComputerMemory

Photon PhateWhat can happen to an x-ray photon

passing through a material (tissue)?

MaterialIncoming X-ray

Photon

???

Photon Phate #1: NothingPhoton exits unaffected

same energysame direction

MaterialIncoming X-ray

PhotonOutgoing X-ray

Photon

Photon Phate #2: AbsorptionPhoton disappearsIts energy is absorbed by material

MaterialIncoming X-ray

Photon

Photon Phate #3: ScatterLower energy photon emerges

energy difference deposited in materialPhoton usually emerges in different direction

MaterialIncoming X-ray

PhotonOutgoing X-ray

Photon

Photon Beam AttenuationAnything which removes original photon

from beamabsorptionscatter

MaterialIncoming X-ray

Photon

MaterialIncoming X-rayPhoton

Outgoing X-rayPhoton

Example Beam Attenuation(Mono-energy source)

Each cm of material reduces beam intensity 20%exiting beam intensity 80% of incident for 1 cm

absorber

1cm 1cm 1cm 1cm

100 100 * .8 =80

80 * .8 =64

64 * .8 =51

51 * .8 =41

I = Ioe-x

I = Exiting beam intensityIo = Incident beam intensitye = constant (2.718…) = linear attenuation coefficient

•property of•absorber material•beam energy

x = absorber thickness

MaterialIo

I

x

For photons which are neither absorbed nor scattered

Example Beam AttenuationUsing equation to calculate beam intensity for

various absorber thicknesses ( = .223)

1cm100 80

I = Ioe-x

100*e-(0.223)(1) = 80-20%

Example Beam AttenuationUsing equation to calculate beam intensity for

various absorber thicknesses ( = .223)

1cm 1cm100 80 64

I = Ioe-x

100*e-(0.223)(2) = 64

-20% -20%

Example Beam AttenuationUsing equation to calculate beam intensity for

various absorber thicknesses ( = .223)

1cm 1cm 1cm100 80 64 51

I = Ioe-x

100*e-(0.223)(3) = 51

-20% -20% -20%

Example Beam AttenuationUsing equation to calculate beam intensity for

various absorber thicknesses ( = .223)

1cm 1cm 1cm 1cm100 80 64 51 41

I = Ioe-x

100*e-(0.223)(4) = 41

-20% -20% -20% -20%

More Realistic CT Example Beam Attenuation for non-uniform Material4 different materials4 different attenuation coefficients

#1 #2 #3 #4

1 2 4

Io I

x

I = Ioe-(+++)x

Effect of Beam Energy on AttenuationLow energy photons more easily absorbedHigh energy photons more penetratingAll materials attenuate a larger fraction of

low than high energy photons

Material100 80

Higher-energymono-energeticbeam

30Material

Lower-energymono-energeticbeam

100

Mono vs. Poly-energetic X-ray BeamEquations below assume Mono-energetic x-

ray beam

#1 #2 #3 #4

1 2 4

Io I

x

I = Ioe-(+++)xI = Ioe-x

Mono-energetic X-ray Beams

Available from radionuclide sourcesNot used in CT because beam intensity much

lower than that of an x-ray tube

X-ray Tube BeamHigh intensityProduces poly-energetic beam

#1 #2 #3 #4

1 2 4

Io I

x

I = Ioe-(+++)x

Beam Hardening ComplicationAttenuation coefficients n depend on beam

energy!!!Beam energy incident on each block unknownFour ’s, each for a different & unknown energy

1 2 4

1cm 1cm 1cm 1cm

I = Ioe-(+++)x

Beam Hardening ComplicationBeam quality changes as it travels through absorber

greater fraction of low-energy photons removed from beamAverage beam energy increases

1cm 1cm 1cm 1cm

Fewer PhotonsBut higher avg

kV than A

Fewer PhotonsBut higher avg

kV than B

A B

Fewer PhotonsBut higher avg

kV than C

C D

Fewer PhotonsBut higher avg

kV than D

E

Your Job: Stop People at the GateSet up multiple gates, one behind the

otherCatch as many as you can at first gateCatch as many as you can who got

through gate #1 at gate #2Monitor average weight of crowd getting

through each gate

ReconstructionScanner measures “I” for thousands of pencil beam projectionsComputer calculates tens of thousands of attenuation coefficients

one for each pixelComputer must correct for beam hardening

effect of increase in average beam energy from one side of projection to other

I = Ioe-(++++)x

Data Acquisition GeometriesAll CT generations obtain same set of

multi-line transmission measurements in many directions

Generational differencesProtocol for obtaining line transmissions

geometry / location of tube / detector motion

# of line transmissions obtained simultaneously speed

Why is CT done with High kV’s?

Less dependence of attenuation coefficient on photon energyAttenuation coefficient changes less at higher

kV’sReduce contrast of bone relative to soft tissueProduce high radiation flux at detector

Common Data-Acquisition Geometries

Tube rotates around patientDetector system

Rotates with x-ray tube (3rd generation)Stationary (4th generation)

360o ring of detectors

3rd Generation Geometry

Patient

Tube / Collimator

Rotating Detector

Array

3rd Generation Geometry

Patient

Z-axis orientation perpendicular to page

4th Generation Geometry

Patient

Tube / Collimator

StationaryDetector

Array

4th Generation Geometry

Patient

One of these equations for every projection line

IA = Ioe-(++++)x

Projection #A

IC = Ioe-(C+C+C+C+)x

Projection #C

Projection #B

IB = Ioe-(++++)x

IA = Ioe-(++++)x

IB = Ioe-(++++)x

IC = Ioe-(C+C+C+C+)x

Projection #A

Projection #B

Projection #C

IA, IB, IC, ...What We Measure:

A1, A2, A3, ...

Reconstruction Calculates:

B1, B2, B3, ...C1, C2, C3, ...

Etc.

*

CT Number

Calculated from reconstructed pixel attenuation coefficient

t - W)CT # = 1000 X ------------

W

Where:ut = linear attenuation coefficient for tissue in pixeluW = linear attenuation coefficient for water

CT Numbers for Special Stuff

Bone: +1000

Water: 0Air: -1000

t - W)CT # = 1000 X ------------

W

Display & WindowingGray shade assigned to each pixel value (CT

#)Windowing

Assignment of display brightness to pixel valuesdoes not disturb original pixel values in memoryOperator controllable

window level

47

93

Display & Display Matrix:Resolution

CT images usually 512 X 512 pixelsDisplay resolution better

often 1024 X 1024can be as high as 2048 X 2048

$$$

Display & Display Matrix:Contrast

CT #range -1000 to 3000

Monitor can display far fewer gray shadesEye can discern few gray shadesPurpose of Window & Leveling

display only portion of CT # values Emphasize only those CT #’s display of CT #’s above & below window all black OR

all white

Pixel Values & Gray Shades

# of valid pixel values depends on bit depth1 bit: 2 values2 bits: 4 values3 bits: 8 values8 bits: 256 values10 bits: 1024 valuesn bits: 2n values

Pixel Values & Gray Shades

CT can discern ~ 4000 gray shadesTypical bit depth: 10 bits = 1024 gray shadesSingle gray shade represents range of pixel

values

>700

651-700

601-650

551-600

501-550

451-500

401-450

351-400

301-350

<301

Darks lighterlights lighter

>700

651-700

601-650

551-600

501-550

451-500

401-450

351-400

301-350

<301

>200

151-200

101-150

51-100

1-50

(-49)-0

(-99)-(-50)

(-149)-(-100)

(-199)-(-150)

<(-199)

>700

651-700

601-650

551-600

501-550

451-500

401-450

351-400

301-350

<301

>200

151-200

101-150

51-100

1-50

(-49)-0

(-99)-(-50)

(-149)-(-100)

(-199)-(-150)

<(-199)

3000

-1000

0

1000

2000

Window: 400Level: 500

Window: 400Level: 0

Darks darker,lights lighter

>700

651-700

601-650

551-600

501-550

451-500

401-450

351-400

301-350

<301

>900

801-900

701-800

601-700

501-600

401-500

301-400

201-300

101-200

<101

>700

651-700

601-650

551-600

501-550

451-500

401-450

351-400

301-350

<301

3000

-1000

0

1000

2000

>900

801-900

701-800

601-700

501-600

401-500

301-400

201-300

101-200

<101

Window: 800Level: 500

Window: 400Level: 500

Pixels & VoxelsPixel is 2D component of an image

Voxel is 3D cube of anatomy

CT reconstruction calculates attenuation coefficients of Voxels

CT displays CT numbers of Pixels as gray shades

Pixel & Voxel SizeVoxel depth

same as slice thicknessPixel dimension

field of view / matrix size

FOV =12 inches

256 pixels

12 inchesPixel size = ------------

256 pixels

Pixel size = .047”

X-Ray Production

X-Ray Detection

Computer Systems

Reconstruction

X-Ray Tube

Detectors

A - D Conversion

Display & Format

Printing

Archiving

Generator

CT AdvantagesExcellent low-contrast resolution

sensitive detectorssmall beam size produces little scatterMuch better than film

CT AdvantagesAdjustable contrast scale

window / levelOther digital image manipulations

filters bone / soft tissue edge enhancement

Region of interest analysis

CT Advantages

Spiralvolume data acquisition in single breath hold

no delay between slicesimproved 3D imagingimproved multi-planar image reformatting

Special applicationsbone mineral contentradiation treatment planningCT angiography

CT Advantages

Muti-sliceScans at much greater speed

ORAllows scanning of same volume with thin

slicesMakes possible additional clinical applications

CT DisadvantagesPoorer spatial resolution than filmHigher dose to in-slice tissuePhysical set-up can limit to axial / near-

axial slicesArtifacts at abrupt transitions

bone / soft tissue interfacesmetallic objects