Transcript You Already Know Some Electronics!

CT
Chapter 4:
Principles of
Computed
Tomography
Radiography vs. CT
 Both based on differential attenuation
of x-rays passing through body
 Radiography
 “Shadowgraph” using x-ray light source
 CT
 Cross-sectional image
 Image computed from pencil beam
intensity measurements through only
slice of interest
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.
X-ray
Beam
Patient
Film
Limitations of Radiography
 Optical density dictated by
total attenuation
encountered by beam
Thin dense
object
 Thin highly-attenuating
objects appear to be same
density as thicker lowattenuating object.
X-ray
Beam
Patient
Thick less
dense object
Film
Early Solution: Conventional Tomography
 Tube and film move
 Rotate around fulcrum
 Image produced on film
 Objects 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 different
 many anatomic systems do not have this subject
contrast
CT Advantages
 View anatomy without looking through
underlying / overlying structures
 improves contrast
Conventional
X-ray Beam
 Uses tightly collimated beam
 minimizes scattered radiation
 improves contrast
 Demonstrates very small contrast
differences reliable & repeatedly
CT X-ray
Beam
Film as a Radiation Detector
 Analog
 not quantitative
 Not sensitive enough to
distinguish small
differences in incident
radiation
 Applications
 film badges
 therapy dosimetry
CT Detectors
 electronic / quantitative
 extremely sensitive
 small radiation input
differences reliably &
repeatedly measured &
discerned
 output digitized & sent to
computer
Data Aquisition
 Slice by slice
 One slice at a time
 Volume acquisition
 data for an entire volume collected
 patient moves in axial direction during scan
 tube traces spiral-helical path through patient
Scanning
 X-ray tube rotates around patient
 detectors also rotate for 3rd
generation CT
 Detectors measure radiation
Patient
transmitted through patient for
various pencil beam projections
 Relative transmissions calculated

Fraction of beam exiting patient
X-Ray beams
Scanning
Patient
X-Ray beam
X-Ray detector
Intensity
measurements
Computer
Memory
Photon Phate
 What can happen to an x-ray photon passing
through a material (tissue)?
Incoming X-ray
Photon
Material
???
Photon Phate #1: Nothing
 Photon exits unaffected
 same energy
 same direction
Incoming X-ray
Photon
Material
Outgoing X-ray
Photon
Photon Phate #2: Absorption
 Photon disappears
 Its energy is absorbed by material
Incoming X-ray
Photon
Material
Photon Phate #3: Scatter
 Lower energy photon emerges
 energy difference deposited in material
 Photon usually emerges in different direction
Incoming X-ray
Photon
Material
Outgoing X-ray
Photon
Photon Beam Attenuation
 Anything which removes original photon from
beam
 absorption
 scatter
Incoming X-ray
Photon
Incoming X-ray
Photon
Material
Material
Outgoing X-ray
Photon
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
100
1cm
100 * .8 =
80
1cm
80 * .8 =
64
1cm
64 * .8 =
51
51 * .8 =
41
Attenuation Equation for
Mono-energetic Photon Beams
I = Io
-mx
e
I = Exiting beam intensity
Io = Incident beam intensity
e = constant (2.718…)
m = linear attenuation coefficient
•property of
•absorber material
•beam energy
x = absorber thickness
For photons
which are neither
absorbed nor
scattered
Material
Io
x
I
Example Beam Attenuation
 Using equation to calculate beam intensity for various
absorber thicknesses (m = .223)
I = Ioe-mx
100
1cm
80
-20%
100*e-(0.223)(1) = 80
Example Beam Attenuation
 Using equation to calculate beam intensity for various
absorber thicknesses (m = .223)
I = Ioe-mx
100
1cm
-20%
80
1cm
64
-20%
100*e-(0.223)(2) = 64
Example Beam Attenuation
 Using equation to calculate beam intensity for various
absorber thicknesses (m = .223)
I = Ioe-mx
100
1cm
-20%
80
1cm
-20%
64
1cm
-20%
100*e-(0.223)(3) = 51
51
Example Beam Attenuation
 Using equation to calculate beam intensity for various
absorber thicknesses (m = .223)
I = Ioe-mx
100
1cm
-20%
80
1cm
-20%
64
1cm
51
-20%
100*e-(0.223)(4) = 41
1cm
41
-20%
More Realistic CT Example Beam
Attenuation for non-uniform Material
 4 different materials
 4 different attenuation coefficients
x
#1 #2 #3 #4
Io
I
m1 m2 m3 m4
I = Io
-(m
+m
+m
+m
)x
1
2
3
4
e
Effect of Beam Energy on
Attenuation
 Low energy photons more easily absorbed
 High energy photons more penetrating
 All materials attenuate a larger fraction of low than
high energy photons
Material
100
Higher-energy
mono-energetic
beam
80
100
Material
Lower-energy
mono-energetic
beam
30
Mono vs. Poly-energetic X-ray Beam
 Equations below assume Mono-energetic x-ray beam
x
#1 #2 #3 #4
Io
I
m1 m2 m3 m4
I = Io
-mx
e
I = Io
-(m
+m
+m
+m
)x
1
2
3
4
e
Mono-energetic X-ray Beams
 Available from radionuclide sources
 Not used in CT because beam intensity much lower
than that of an x-ray tube
X-ray Tube Beam
 High intensity
 Produces poly-energetic beam
x
#1 #2 #3 #4
Io
I
m1 m2 m3 m4
I = Io
-(m
+m
+m
+m
)x
1
2
3
4
e
Beam Hardening Complication
 Attenuation coefficients mn depend on beam energy!!!
 Beam energy incident on each block unknown
 Four m’s, each for a different & unknown energy
1cm
1cm
1cm
1cm
m1
m2
m3
m4
I = Io
-(m
+m
+m
+m
)x
1
2
3
4
e
Beam Hardening Complication
 Beam quality changes as it travels through absorber
 greater fraction of low-energy photons removed from beam
 Average beam energy increases
A
1cm
B
Fewer Photons
But higher avg
kV than A
1cm
C
1cm
Fewer Photons
But higher avg
kV than B
D
1cm
Fewer Photons
But higher avg
kV than C
E
Fewer Photons
But higher avg
kV than D
Your Job: Stop People at the Gate
 Set up multiple gates, one behind the other
 Catch as many as you can at first gate
 Catch as many as you can who got through gate #1
at gate #2
 Monitor average weight of crowd getting through
each gate
Reconstruction
 Scanner measures “I” for thousands of pencil beam
projections
 Computer calculates tens of thousands of attenuation
coefficients
 one for each pixel
 Computer must correct for beam hardening
 effect of increase in average beam energy from one side of projection to
other
I = Io
-(m
+m
+m
+m
+...)x
1
2
3
4
e
Data Acquisition Geometries
 All CT generations obtain same set of multi-
line transmission measurements in many
directions
 Generational differences
 Protocol 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
energy
 Attenuation coefficient changes less at higher kV’s
 Reduce contrast of bone relative to soft tissue
 Produce high radiation flux at detector
Common Data-Acquisition
Geometries
 Tube rotates around patient
 Detector system
 Rotates with x-ray tube (3rd generation)
 Stationary (4th generation)

360o ring of detectors
3rd Generation Geometry
Tube /
Collimator
Patient
Rotating
Detector
Array
3rd Generation Geometry
Z-axis orientation
perpendicular to page
Patient
4th Generation Geometry
Tube /
Collimator
Patient
Stationary
Detector
Array
4th Generation Geometry
Patient
Image Reconstruction
Projection #A
One of these equations for
every projection line
IA = Ioe-(mA1+mA2+mA3+mA4 +...)x
Projection #B
IB = Ioe-(mB1+mB2+mB3+mB4 +...)x
Projection #C
IC = Ioe-(mC1+mC2+mC3+mC4 +...)x
Image Reconstruction
*
Projection #A
What We Measure:
IA, IB, IC, ...
IA = Ioe-(mA1+mA2+mA3+mA4 +...)x
Projection #B
IB = Ioe-(mB1+mB2+mB3+mB4 +...)x
Projection #C
IC = Ioe-(mC1+mC2+mC3+mC4 +...)x
Reconstruction
Calculates:
mA1, mA2, mA3, ...
mB1, mB2, mB3, ...
mC1, mC2, mC3, ...
Etc.
CT Number
Calculated from reconstructed pixel attenuation
coefficient
(mt - mW)
CT # = 1000 X -----------mW
Where:
ut = linear attenuation coefficient for tissue in pixel
uW = linear attenuation coefficient for water
CT Numbers for Special Stuff
 Bone: +1000
 Water: 0
 Air: -1000
(mt - mW)
CT # = 1000 X -----------mW
Display & Windowing
 Gray shade assigned to each pixel value (CT #)
 Windowing
47
93
 Assignment of display brightness to pixel values
 does not disturb original pixel values in memory
 Operator controllable


window
level
Display & Display Matrix:
Resolution
 CT images usually 512 X 512 pixels
 Display resolution better
 often 1024 X 1024
 can be as high as 2048 X 2048

$$$
Display & Display Matrix:
Contrast
 CT #range
 -1000 to 3000
 Monitor can display far fewer gray shades
 Eye can discern few gray shades
 Purpose 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 depth
 1 bit: 2 values
 2 bits: 4 values
 3 bits: 8 values
 8 bits: 256 values
 10 bits: 1024 values
 n bits: 2n values
Pixel Values & Gray Shades
 CT can discern ~ 4000 gray shades
 Typical bit depth: 10 bits = 1024 gray shades
 Single gray shade represents range of pixel values
Silly CT # Display Example:
10 Gray Shades
>700
651-700
601-650
551-600
501-550
451-500
401-450
351-400
301-350
<301
CT # Level Change
Darks lighter
lights lighter
CT # Level Change
>700
>200
651-700
151-200
601-650
101-150
551-600
51-100
501-550
1-50
451-500
(-49)-0
401-450
(-99)-(-50)
351-400
(-149)-(-100)
301-350
(-199)-(-150)
<301
<(-199)
Window: 400
Level: 500
CT # Level Change
3000
Window: 400
Level: 0
>700
>200
651-700
151-200
601-650
2000
101-150
551-600
51-100
501-550
1-50
1000
451-500
(-49)-0
401-450
(-99)-(-50)
351-400
0
(-149)-(-100)
301-350
(-199)-(-150)
<301
<(-199)
-1000
CT # Window Change
Darks darker,
lights lighter
CT # Window Change
>700
>900
651-700
801-900
601-650
701-800
551-600
601-700
501-550
501-600
451-500
401-500
401-450
301-400
351-400
201-300
301-350
101-200
<301
<101
CT # Window Change
Window: 400
Level: 500
3000
Window: 800
Level: 500
>700
>900
651-700
801-900
601-650
2000
701-800
551-600
601-700
501-550
501-600
1000
451-500
401-500
401-450
301-400
351-400
0
201-300
301-350
101-200
<301
<101
-1000
Pixels & Voxels
 Pixel 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 Size
 Voxel depth
 same as slice thickness
 Pixel dimension
 field of view / matrix size
256 pixels
FOV =
12 inches
12 inches
Pixel size = -----------256 pixels
Pixel size = .047”
CT Systems
X-Ray Production
X-Ray Tube
Generator
Detectors
X-Ray Detection
A - D Conversion
Reconstruction
Display & Format
Computer Systems
Printing
Archiving
CT Advantages
 Excellent low-contrast resolution
 sensitive detectors
 small beam size produces little scatter
 Much better than film
CT Advantages
 Adjustable contrast scale
 window / level
 Other digital image manipulations
 filters


bone / soft tissue
edge enhancement
 Region of interest analysis
CT Advantages
 Spiral
 volume data acquisition in single breath hold

no delay between slices
 improved 3D imaging
 improved multi-planar image reformatting
 Special applications
 bone mineral content
 radiation treatment planning
 CT angiography
CT Advantages
 Muti-slice
 Scans at much greater speed
OR
 Allows scanning of same volume with thin slices
 Makes possible additional clinical applications
CT Disadvantages
 Poorer spatial resolution than film
 Higher dose to in-slice tissue
 Physical set-up can limit to axial / near-axial slices
 Artifacts at abrupt transitions
 bone / soft tissue interfaces
 metallic objects