8/15/2011
A medical imaging system
is a machine that transforms
people into numbers.
Turning People into Numbers:
A Quantitative Perspective
on Medical Image Acquisition
Jeff Siewerdsen, Ph.D.
Department of Biomedical Engineering
Johns Hopkins University
M. Kessler
Johns Hopkins University
Schools of Medicine and Engineering
This is not a pipe. It is…
28%
Warming Up…
27%
22%
24%
1. whatever you
want it to be.
2. in French, so
I don’t know.
3. an image of a
pipe.
4. Too nice
outside to be in this dark room
discussing existentialism.
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8/15/2011
Overview
This is not a pipe. It is…
• How do we get the numbers?
fC
- Image acquisition and reconstruction
- MR, CT, PET, US, and radiography
1. whatever you
want it to be.
2. in French, so
I don’t know. fy 0
3. an image of
a pipe.
-fC
4. Too nice
-fC
dark room 0
outside to be in this
fx
discussing existentialism.
• How good are the numbers?
- Image quality
- Accuracy, noise, spatial resolution, …
• A few ways the numbers are important:
fC
Imaging Configurations:
X-Ray Projection Radiography
Imaging Configurations
Source
Object
Detector
Processor
Display
- Detection, localization, and segmentation
- Interpreting the numbers
- Registration
- Aligning the numbers
- Transformation
- Turning one set of numbers in to another
Observer
Source
Object
Detector
?
• Source-Obj-Det configurations vary among modalities
 Physical arrangement of source-object-detector
 Physical nature of the source (x-rays, sound, radionuclide, B-field)
 Type of detector [convert EM or Mech energy to a signal (typically e-)]
• Proc-Disp-Obs configurations are comparatively similar
Reconstruction, enhancement, display
Segmentation, registration
Interpretation (human or computer-assisted)
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Imaging Configurations:
X-Ray Computed Tomography (CT)
Source
Object
Imaging Configurations:
X-Ray Computed Tomography (CT)
Detector
Detector
Object
Source
Imaging Configurations:
Positron Emission Tomography (PET)
Imaging Configurations:
Ultrasound Imaging
Source
Detector
Detector
Object
Object
Source
Source-Detector
Transducer
Source
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8/15/2011
Imaging Configurations:
Magnetic Resonance (MR) Imaging
Source
Object
Imaging Configurations:
Magnetic Resonance (MR) Imaging
Detector
Detector
Gz
Object
Gy
B
Gx
Source
Multi-Modality Imaging
Morphology
Function
SPECT
CT
MR
Implications for Imaging in IGI
Geometry




Patient access
Field of view
Portability
Compatibility
Time
PET
 Speed of acquisition
 Speed of reconstruction
Oops!
Cost
US
Optical
 Relative to other aspects of Tx
 “Comparative effectiveness”
Radiation Dose
 For IGI (e.g., IG surgery and IGRT), should minimize dose
and demonstrate a benefit to therapeutic outcome
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8/15/2011
How to Get the Numbers (Signal)
For Example: Photon Detectors
Incident X-ray
Photomultiplier
Tube
(PMT)
Getting the Numbers
X-ray Converter
(Scintillator)
Secondary Quanta
(photons or e-)
X-ray Image
Intensifier
(XRII)
Coupling
Conversion
Readout
Amplification
Flat-panel
Detector
(FPD)
Digitization
Computed Tomography
Computed Tomography
Incident X-ray
Hounsfield’s CT Scanner
Detector
g source
X-ray Converter
(Scintillator)
Hounsfield’s
CT Scanner
Projection
radiography
Detector
g source
I0
Secondary Quanta
(photons or e-)
Coupling
Conversion
Turntable
and linear track
9-day acquisition
Amplification
2.5-hr recon
Sir Godfrey Hounsfield
Nobel Prize, 1979
Turntable
and linear track
Readout
9-day acquisition
2.5-hr recon
Circa 1895
Digitization
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How to Reconstruct the Numbers?
p(x)
The Sinogram:
Line integral projection p(x)
… measured at each angle q
 p(x;q) “Sinogram”
How to Reconstruct the Numbers?
The Filtered Sinogram:
Convolve with RampKernel(x)
p(x)*RampKernel(x)
Equivalent to Fourier product
P(f)|f|
p(x;q)
p(x;q)
p(x;q)*RampKernel(x)
p(x;q)
q
q
x
x
How to Reconstruct the Numbers?
Backprojection
Repeat 
X-ray source
Evolution and Proliferation of CT

# of voxels
# of projections
c. 1975
c. 2011
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What are the Numbers: Voxel Value
The CT voxel has units of
the attenuation coefficient, m (cm-1 or mm-1)
Commonly converted to a convenient scale: Hounsfield Units (HU)
HU’ = 1000
m’ - mwater
mwater
Contrast
A “large-area transfer characteristic”
Defined:
 As an absolute difference in mean pixel values:
For example:
C = |0.18 cm-1 – 0.20 cm-1|
= 0.02 cm-2
or
C = |-100 HU – 0 HU|
= 100 HU
Fat (-100)
Liver (+85)
Polyeth (-60)
ROI #1
ROI #2
 As a relative difference in mean pixel values:
Water (0)
For example:
C = |0.18 cm-1 – 0.20 cm-1|
0.19 cm-1
~ 10%
Brain (8)
Breast (-50)
Hounsfield Units (HU)
Contrast is higher in CT
than x-ray projections, because:
19%
20%
23%
18%
19%
1.
2.
3.
4.
5.
CT uses a higher dose.
CT uses contrast agents.
CT uses lower-energy x-rays.
CT has lower noise.
Because:
Contrast is higher in CT
than x-ray projections, because:
1.
2.
3.
4.
5.
CT uses a higher dose.
CT uses contrast agents.
CT uses lower-energy x-rays.
CT has lower noise.
Because:
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Contrast
Why CCT >> Crad?
CT
Radiograph
More Numbers (MRI)
19 22 40 17 30 21 25 63 25 20
282
Contrast =
I1 – I2
(I1 + I2)/2
237
20 19 25 19 22 18 24 25 25 40
CCT =
63–25
=86%
(63+25)/2
Crad =
282–237
=17%
(282+237)/2
MR Image Acquisition
MR Image Acquisition
LBNL 0.5 T MRI (circa 1988)
T1
Magnetic Resonance (MR) Images:
 Tissue Contrast
 Physiology / Function
 Metabolites
 Acquisition in Arbitrary Planes
Acquisition by means of various
MR Pulse Sequences:
Magnetic Dipoles
T2
DWI
Nuclei (e.g., protons)
behave like magnetic
dipoles
(Magnetic Moment)
Gd
Alignment and Precession
Flair
In the absence of an
external magnetic field,
the orientation of the
dipoles is random.
In the presence of an
external magnetic field the
dipoles align with direction
of the applied B0 field.
In the same manner
that a spinning top
precesses around a
gravitational field,
the dipoles precess
around the external
B0 field
w = g B0
Larmor Frequency
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MR Image Acquisition
Net Longitudinal
Magnetization
Transverse
Magnetization
Mo=Mz
MR Image Acquisition
Measure the increase in
Longitudinal Magnetization (Mz)
Spin Flip +
Phase Coherence
… and the decrease in
Transverse Magnetization (Mxy)
Mx
y
Bo
0.63
Mxy
Mz
Apply RF pulse (B1 field)
at Larmor frequency
in transverse plane
Flip Angle
a = gB1t
MR Image Signal and Contrast
0.37
1
2
3
1
T1 Spin-Lattice
Relaxation Time
2
3
T2 Spin-Spin
Relaxation Time
Contrast Weighting
T1 Contrast
Spin-Lattice
T2 Contrast
Spin-Spin
T2 (ms)
Transverse Magnetization
T1 (sec)
Longitudinal Magnetization
Intrinsic Tissue Properties  Tissue Contrast
DMo
Time
Water
Long T1
Long T2
Dark T1 signal
Bright T2 signal
Fat
Short T1
Long T2
Bright T1 signal
Gray T2 signal
Gd Contrast
DMxy
Reduces T1
Reduces T2
Enhanced T1 sig
Reduced T2 sig
Time
T1 Weighting
T2 Weighting
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A short T1 signal (bright)
could imply:
20%
1.
2.
19% 3.
22% 4.
24% 5.
16%
A short T1 signal (bright)
could imply:
Small molecules with strong spin-spin interaction
Large molecules with weak spin-spin interaction
Strong spin-lattice interaction
Weak spin-lattice interaction
Time is up
T1
1.
Small molecules with strong spin-spin interaction
2.
Large molecules with weak spin-spin interaction
3.
Strong spin-lattice interaction
4.
Weak spin-lattice interaction
5.
Time is up
T2
T1
T2
Fundamentals of MRI
William G. Bradley, MD PhD FACR
Image Quality:
Beyond Contrast
How Good
are the Numbers?
(Image Quality)
Artifact-Limited
Spatial Resolution-Limited
Contrast-to-Noise Limited
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Spatial Resolution
blur
1 mm
“128”
“256”
“512”
Reconstruction Filter
“Smooth”
“Sharp”
Reduced Spatial Resolution
Lower Noise
Improved CNR
Improved Soft-Tissue Visibility
Improved Spatial Resolution
Higher Noise
Reduced CNR
Reduced Soft-Tissue Visibility
Voxel “Image
Size
Size”
0.2 mm “1024”
0.2
sampling
FWHM (mm)
Axial image of steel wire
Voxel Size (mm)
0.8
0.6
0.4
“1024”
Image Size
Voxel size: 0.12 mm voxels
Full-width at half-max: ~0.42 mm
Hanning reconstruction filter
0.4 mm
“512”
0.8 mm
“256”
www.impactscan.org
Spatial Resolution
Modulation Transfer Function (MTF)
Metrics of spatial resolution:
Minimum resolvable line-pair
Point-spread function (psf)
Modulation transfer function (MTF)
127 mm Wire in H2O
1.0
J
J
JJ
J
J
J
Steel Wire
Signal (mm-1)
J
J
0.8
J
J
J
J
J
0.6
J
J
System MTF
J
J
J
0.4
J
J
J
J
J
J
J
J
Measured
0.2
J
J
JJ
JJ
J
JJ
JJ
JJ
JJ
JJJ
0.0
0.0
0.5
1.0
1.5
-1
JJJ
JJJJJJ
2.0
Spatial Frequency (mm )
Minimum resolvable
line-pair group
MTF  f x , f y   FT LSF  x, y 
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Image Noise
Noise / Resolution Tradeoff
• CT image noise depends on
– Dose Do
– Detector efficiency
– Voxel size
Axial axy
Slice thickness az
– Reconstruction filter
fc
2
Kxy   df Trecon
0

k E 1 K xy
3
Do h a xy
az
Smooth
2 
1
1
1


3
Do
az
a xy
Sharp
h
Reconstruction Filter
Barrett, Gordon, and Hershel (1976)
Image Quality: Implications for IGI
Localization / Targeting
 Soft-tissue visibility
 Spatial resolution
 Geometric accuracy
The main image quality advantage
of CT over radiography is:
22%
21%
Segmentation
 For example: intensity-based thresholding
 Contrast-to-noise ratio
 Artifacts (shading and streaks)
19%
20%
18%
1.
2.
3.
4.
5.
Spatial resolution
Contrast resolution
Temporal resolution
Speed
Reimbursement
Registration
 Pixel value / contrast
 Intensity- or Non-intensity-based
 Consistent image information
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The main image quality advantage
of CT over radiography is:
1.
2.
3.
4.
5.
Spatial resolution
Contrast resolution
Temporal resolution
Speed
Reimbursement
Dr. Tork complains that he cannot see the
trabecular bone details in a CT image.
A reasonable course of action is to:
18%
20%
23%
21%
18%
1.
2.
3.
4.
5.
Acquire a radiograph.
Administer contrast agent.
Re-scan at higher mAs.
Re-reconstruct with a different filter.
Display on a bigger monitor.
Reference:
The Essential Physics of Medical Imaging
Bushberg et al.
Dr. Tork complains that he cannot see the
trabecular bone details in a CT image.
A reasonable course of action is to:
1.
2.
3.
4.
5.
Acquire a radiograph.
Administer contrast agent.
Re-scan at higher mAs.
Re-reconstruct with a different filter.
Display on a bigger monitor.
How the Numbers
are Useful
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Image Registration
Image Registration
Planning CT
Parametric
(rigid, affine,
splines,…)
Transform
Model
Soft-Tissue
and Bone
Online CBCT
m
f
# Pixels
# Pixels
Optimizer
Gradient descent
Regularization / filtering
Air
0
Air
0.2
0
Voxel Value (cm -1)
Non-Parametric
(linear elastic,
viscoelastic,
Demons,
finite element)
Soft-Tissue
and Bone
0.2
1.0
Voxel Value (cm -1)
TRUE
Metric
Image-Based
(SSD, CC, MI, …)
Demons
Force
Geometry Based
(Points, lines, contours surfaces, …)
Clarity™ in Simulation
Hip Replacement
CT
Clarity
Pixel Values: Implications for IGI
CT with Clarity contour
Image 0
Image Registration
Image 1
Proj
 Intensity-based registration
 For example:
- Mean-square difference
- Demons algorithm
 Non-intensity based registration
 For example:
- Mutual information (MI)
- Finite element models (FEM)
CT
PET
US
MR
Images courtesy of Marc Kessler (University of Michigan)
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MIMECS Flowchart
2. Find sparse
linear combination
of patches in the
M1 atlas image
that equals the
source patch
Transforming
the Numbers
1. Consider any
patch in the M1
source image
Atlas Images
M1
3. Find patches in
the M2 atlas in the
same position as
those in the M1 atlas
M2
M1
M2
Source
Image
Synthetic
Image
4. Combine these
patches using the
same weights that
were computed in
step 2
Jerry Prince (Johns Hopkins University)
For Example: T1  T2 and FLAIR
Conclusions
Images are numbers
True Images
Magnitude, correlation, variance, …
T2
FLAIR
Atlas
Synthetic
T1
MIMECS
Source T1
Synthetic T2
Synthetic FLAIR
Imaging systems differ:
In their contrast mechanism:
CT: attenuation coefficient
MR: relaxation times
PET: activity
Ultrasound: impedance, reflectivity
Radiography: line integrals
Applicability to IGI:
Cost, geometry, logistics
Speed, resolution, radiation dose
The numbers are important
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THANK
YOU
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Detection, localization, segmentation
Registration
Transformation
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