Download Computed Tomography (CT)

Computed Tomography
Computed Tomography (CT):
Physics and Technology
Hounsfield’s CT Scanner
Projection radiography
Detector
I0
γ source
JH
JH Siewerdsen
Siewerdsen PhD
PhD
Dept.
Dept. of
of Medical
Medical Biophysics,
Biophysics, University
University of
of Toronto
Toronto
Ontario
Ontario Cancer
Cancer Institute,
Institute, Princess
Princess Margaret
Margaret Hospital
Hospital
[email protected]
Clinical Applications
M
M O’Malley
O’Malley MD
MD
Dept.
Dept. of
of Medical
Medical Imaging,
Imaging, University
University of
of Toronto
Toronto
Dept.
Dept. of
of Medical
Medical Imaging,
Imaging, University
University Health
Health Network
Network // Mt.
Mt. Sinai
Sinai Hospital
Hospital
martin.o’[email protected]
Ontario Cancer Institute
Princess Margaret Hospital
University Health Network
Medical Biophysics
Medical Imaging
IBBME
Overview
Circa 1895
Sir Godfrey Hounsfield
Nobel Prize, 1979
Turntable I
d and linear track
I = Io e-0∫µ(x,y)dy
9-day acquisition
2.5-hr recon
P = ln(Io/I) = ∫µ(x,y)dy
First Generation CT
• Computed Tomography (CT)
- Basic principles of CT
Natural history of scanner technologies (“generations”)
Scan and Rotate:
Linear scan of source and detector
- CT reconstruction
Fourier slice theorem
Filtered backprojection
Other techniques
- Image quality / artifacts
Physical factors
Performance metrics
- Radiation dose
Magnitude and risk (in context)
- Applications
Diagnostic imaging… IG interventions… Radiation therapy
Line integral measured
at each position: P(x)
Rotate source-detector ∆θ
Repeat linear scan…
Projection data: P(x;θ)
P(x)
x xx xxx x x
CT “Generations”
1st Generation (1970)
2nd Generation (1972)
Fourier Slice Theorem
The Fourier Transform of a projection of an object at a given angle
yields a slice of the Fourier Transform of the object
at the corresponding angle in the Fourier domain.
y
v
FT
u
x
Pencil Beam
Translation / Rotation
Fan Beam
Translation / Rotation
F(u,v)
f(x,y)
WA Kalender, Computed Tomography, 2nd Edition (2005)
CT “Generations”
3rd Generation (1976)
CT Image Reconstruction
Fourier Slice Theorem
4th Generation (1978)
p(ξ,θ)
F [p(ξ,θ)]
y
θ
Fan Beam
Continuous Rotation
Fan Beam
Continuous Tube Rotation
Stationary Detector
v
ξ
x
θ
F(u,v)
f(x,y)
X-rays
u
CT Image Reconstruction
F -1[F(u,v)]
y
Sinogram p(x,θ)
“Sinogram”
v
x
Sinogram:
Line integral projection: p(x)
u
p(x;θ)
p(x) = ln(Io/I) = ∫µ(x,y)dy
θ
measured at each angle (θ)
Projection data (sinogram): p(x;θ)
f(x,y)
p(ξ,θ)
F(u,v)
Backprojection
P(x;θ)
x
CT Image Reconstruction
Filtered Back-Projection
Simple Backprojection:
Trace projection data P(x;θ)
through the reconstruction matrix
from the detector (x) to the source
Projection p(θ,ξ)
Simple backprojection yields
radial density (1/r)
Therefore, a point-object is
reconstructed as (1/r)
Solution: “Filter” the projection data
by a “ramp filter” |r|
X-ray source
Object
Sinogram
Filtered
Sinogram
CT Image Reconstruction
Filtered Backprojection: Implementation
Ba
c
kPr
oj
ec
t
Loop over all views (all θ)
Filtered Back-Projection
Object Space
Projection at angle θ
p(ξ,θ)
Filtered Projection
g(ξ,θ)
Backproject g(ξ,θ).
Add to image µ(x,y)
µ(x,y)
Filtered Sinogram
CT Image Reconstruction
Helical CT
Filtered Back-Projection
Slip ring gantry
Continuous gantry rotation
Continuous couch translation
Pitch <1 :
Overlap
Higher z-resolution
Higher patient dose
k-P
Bac
ct
roje
Reconstructed
Image
Object Space
Pitch =
Table increment / rotation (mm)
Beam collimation width (mm)
Filtered Sinogram
WA Kalender, Computed Tomography, 2nd Edition (2005)
Pitch >1:
Non-overlap
Lower z-resolution
Lower patient dose
Recent Advances: Dual-Source CT
From “Fan” to “Cone”
Two complete x-ray and data acquisition systems on one gantry.
330 ms rotation time
(effective 83 ms scan time)
Siemens Medical Solutions – Somatom Definition
Recent Advances: Multi-Detector CT
Recent Advances: Multi-Detector CT
• Multiple slices acquired in
each revolution
• Higher speed
• Reduced slice thickness
(Improved axial resolution)
4x
1.25 mm
4x
4x
2.5 mm 3.75 mm
4x
5.0 mm
GE Light Speed multi-row CT detector
Fast (whole-body) scans
at high resolution (thin slices)
Dynamic (4D) imaging
Recent Advances: Cone-Beam CT
Fully 3-D Volumetric CT
CT Detectors
Gas (Xenon)
Conventional CT:
Fan-Beam
1-D Detector Rows
Slice Reconstruction
Multiple Rotations
Cone-Beam CT:
Cone-Beam Collimation
Large-Area Detector
3-D Volume Images
Single Rotation
Cone-Beam CT
Projection data (2D)
200 – 2000 projections
over 180o – 360o
Conventional (old)
Single-slice CT only
Scintillator / Semiconductor
State of the art
Well-suited to MDCT
K. Kanal, University of Wisconsin
Single-Slice CT vs Multi-Detector CT
Volume reconstruction
~1 mm spatial resolution
+ soft tissue visibility
K. Kanal, University of Wisconsin
Contrast
Cone-Beam Filtered Backprojection
Why CCT >> Crad?
2D
Interpolation
Filter
Weight
CT
Radiograph
Geometry
Reconstruction
Volume
19 22 40 17 30 21 25 63 25 20
282
Contrast =
Repeat ×
20 19 25 19 22 18 24 25 25 40
I1 – I2
(I1 + I2)/2
CCT =
# of voxels
# of projections
CT Image Reconstructions
237
63–25
=86%
(63+25)/2
Crad =
282–237
=17%
(282+237)/2
CT Number (Pixel Value)
The CT image pixel values have units of
the attenuation coefficient, µ (cm-1 or mm-1)
GB
Commonly converted to a convenient scale: Hounsfield Units (HU)
Pancreas
HU’ = 1000
µ’ - µwater
µwater
(+1000)
(sometimes)
Fat (-100)
AO
Liver (+85)
Liver
Polyeth (-60)
Water (0)
Spleen
Brain (8)
Spine
1975
2000
Breast (-50)
Hounsfield Units (HU)
Reconstruction Filter
Noise
(3.8 ± 4.2)
2
σ vox
=
(5.6 ± 2.4)
(-1.3 ± 6.2)
“Smooth”
“Sharp”
Reduced Spatial Resolution
Lower Noise
Improved SNR
Improved Soft-Tissue Visibility
Improved Spatial Resolution
Higher Noise
Reduced SNR
Reduced Soft-Tissue Visibility
Noise:
Standard deviation in voxel
values in an otherwise
uniform region of interest
(4.6 ± 3.2)
(4.4 ± 4.2)
k E K xy
Do η a 3xy a z
Bandwidth Integral
fc
2
K xy ∝ ∫ df Twin2 Tinterp
0
(Fourier domain integral over the
low-pass ‘smoothing’ filters)
www.impactscan.org
Artifacts
Spatial Resolution
Factors affecting spatial resolution:
Focal spot size
Detector pixel size
Slice thickness
Pitch
Number of projections
Reconstruction filter (kernel)
Field of view
Patient motion
Metrics of spatial resolution:
Minimum resolvable line-pair
Minimum resolvable
Point-spread function (psf)
line-pair group
Modulation transfer function (MTF)
Rings
Shading
Streaks
Metal
Lag
Truncation
Motion
“Cone-Beam”
Radiation Dose
Dosimetrics
Measure
Common Units
SI Units
Activity
Exposure
Absorbed Dose
Effective Dose
Ci
R
rad
rem
Bq
C/kg
Gy
Sv
(disintegrations / sec)
(ionization in air)
Surface dose > Central dose
Head: (Dsurf / Dcenter ) ~1
Body: (Dsurf / Dcenter) ~2
Electrometer (mGy / C)
(1 Gy = 1 J/kg = 1 Rad)
(1 Sv = 100 rem)
CTDIw combines:
Peripheral dose: CTDIperiph
Central dose: CTDIcenter
Some forms of radiation more efficient than others at transferring energy to the cell.
To level the playing field, multiply dose (Gy) by a quality factor (Q).
Q compares biological damage to that associated with the same dose of X rays
(photons). The resulting unit is the Sv (seivert). Thus, Sv = Gy x Q.
Ion Chamber
CTDIw =
(2/3 CTDIperiph +
+1/3 CTDIcenter)
1 Sv is the amount of (any type of) radiation which would cause the same amount of
biological damage as would result from 1 Gy of X rays.
center
periphery
16 or 32 cm Diameter
Acrylic Cylinder
Bushberg, The Essential Physics of Medical Imaging, 2nd Ed.
CT Dose Measurement (CTDI)
Dose estimate from a single scan:
CT Dose Index (CTDI)
CTDI =
fX
L
T
f = exposure-to-dose factor (mGy/R)
X = exposure (R)
L = length of ion chamber (100 mm)
T = slice thickness (mm)
Factors Affecting Radiation Dose
kVp
Dose
α~(kVp)2
mAs
Dose α mAs
Standard (Cylindrical) Phantoms:
Head (16 cm diameter acrylic)
Body (32 cm diameter acrylic)
Kanal, University of Wisconsin
Kanal, University of Wisconsin
Typical Skin Dose:
Head ~ 20 mGy
Body ~ 40 mGy
(induction of erythema: ~2 Gy)
Computed Tomography
Effective Dose
• Key to numerous areas of medical imaging
- Screening
Region
Factor
Head
Neck
Chest
Abdomen
Pelvis
0.0023
0.0054
0.017
0.015
0.019
30 mGy x 30 cm = 900 mGy.cm
20 mGy x 50 cm = 1000 mGy.cm
Effective
Dose
(mSv)
2
8
10-20
10-20
(mSv/mGy.cm)
E.g., low-dose CT screening of early-stage lung cancer
- Diagnosis
E.g., almost everything…
- Staging and prognosis
E.g., PET-CT
- Treatment planning
E.g., Dose calculation in radiation therapy
- Image guidance
E.g., CT-guided biopsy, interventions, surgery, and RT
- Response assessment
E.g., Tumor regression; perfusion changes
- Pre-clinical imaging
E.g., Micro-CT of mice (drug development, etc.)
Effective Dose
Radiography
Skull
Chest (PA)
Abdomen
Pelvis
Ba swallow
Ba enema
CT
Exam
Head
Chest
Abdomen
Pelvis
Effective Equivalent
Dose (mSv)
# CXR
0.07
0.02
1.0
0.7
1.5
7
3.5
1
50
35
75
350
2
8
10-20
10-20
100
400
500
500
Computed Tomography
Approx. Period
Backround
Radiation
3 days
6 months
4 months
3.6 yrs
4.5 yrs
4.5 yrs
(typical background
= 3 mSv / yr)
• Remaining Challenges
- Reduced imaging dose
E.g., pediatrics… mA modulation… Low-dose protocols
- Imaging speed
Cardiac imaging… 4D… CT-fluoroscopy
- Image quality
E.g., Improved SNR… Artifact management
• Ongoing Developments
- Multi-detector CT (“The Slice Wars”)
Single-slice → 8 → 16 → 64 → 256 slice → Volume CT
- Alternative source configurations (“The Source Wars)
Dual-source… Multiple-source… → No moving parts
- CT imaging functionality and applications