ct chapter 4: principles of computed tomography. radiography vs. ct both based on differential...
DESCRIPTION
Limitations of Radiography 3D body rendered in 2D Structures superimposed on film Must view structure of interest through underlying / overlying structures Multiple views often required to adequately visualize a structure. Patient X-ray Beam FilmTRANSCRIPT
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CT
Chapter 4:Principles of
Computed Tomography
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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
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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
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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
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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
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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
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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
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Film as a Radiation DetectorAnalog
not quantitativeNot sensitive enough
to distinguish small differences in incident radiation
Applicationsfilm badgestherapy dosimetry
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CT Detectors
electronic / quantitativeextremely sensitive
small radiation input differences reliably & repeatedly measured & discerned
output digitized & sent to computer
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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
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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
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Patient
X-Ray beam
X-Ray detector
Intensitymeasurements
ComputerMemory
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Photon PhateWhat can happen to an x-ray photon
passing through a material (tissue)?
MaterialIncoming X-ray
Photon
???
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Photon Phate #1: NothingPhoton exits unaffected
same energysame direction
MaterialIncoming X-ray
PhotonOutgoing X-ray
Photon
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Photon Phate #2: AbsorptionPhoton disappearsIts energy is absorbed by material
MaterialIncoming X-ray
Photon
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Photon Phate #3: ScatterLower energy photon emerges
energy difference deposited in materialPhoton usually emerges in different direction
MaterialIncoming X-ray
PhotonOutgoing X-ray
Photon
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Photon Beam AttenuationAnything which removes original photon
from beamabsorptionscatter
MaterialIncoming X-ray
Photon
MaterialIncoming X-rayPhoton
Outgoing X-rayPhoton
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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
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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
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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%
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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%
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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%
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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%
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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
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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
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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
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Mono-energetic X-ray Beams
Available from radionuclide sourcesNot used in CT because beam intensity much
lower than that of an x-ray tube
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X-ray Tube BeamHigh intensityProduces poly-energetic beam
#1 #2 #3 #4
1 2 4
Io I
x
I = Ioe-(+++)x
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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
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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
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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
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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
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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
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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
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Common Data-Acquisition Geometries
Tube rotates around patientDetector system
Rotates with x-ray tube (3rd generation)Stationary (4th generation)
360o ring of detectors
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3rd Generation Geometry
Patient
Tube / Collimator
Rotating Detector
Array
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3rd Generation Geometry
Patient
Z-axis orientation perpendicular to page
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4th Generation Geometry
Patient
Tube / Collimator
StationaryDetector
Array
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4th Generation Geometry
Patient
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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
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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.
*
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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
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CT Numbers for Special Stuff
Bone: +1000
Water: 0Air: -1000
t - W)CT # = 1000 X ------------
W
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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
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Display & Display Matrix:Resolution
CT images usually 512 X 512 pixelsDisplay resolution better
often 1024 X 1024can be as high as 2048 X 2048
$$$
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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
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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
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Pixel Values & Gray Shades
CT can discern ~ 4000 gray shadesTypical bit depth: 10 bits = 1024 gray shadesSingle gray shade represents range of pixel
values
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>700
651-700
601-650
551-600
501-550
451-500
401-450
351-400
301-350
<301
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Darks lighterlights lighter
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>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)
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>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
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Darks darker,lights lighter
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>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
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>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
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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
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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”
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X-Ray Production
X-Ray Detection
Computer Systems
Reconstruction
X-Ray Tube
Detectors
A - D Conversion
Display & Format
Printing
Archiving
Generator
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CT AdvantagesExcellent low-contrast resolution
sensitive detectorssmall beam size produces little scatterMuch better than film
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CT AdvantagesAdjustable contrast scale
window / levelOther digital image manipulations
filters bone / soft tissue edge enhancement
Region of interest analysis
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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
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CT Advantages
Muti-sliceScans at much greater speed
ORAllows scanning of same volume with thin
slicesMakes possible additional clinical applications
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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